%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO630-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.18s 0.51s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO630-1 : TPTP v9.0.0. Released v7.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:22:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.51 % SZS status Unsatisfiable
% 0.18/0.51 % SZS output start Proof
% 0.18/0.51 tff(tptp_fun__LE__type, type, (
% 0.18/0.51 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.18/0.51 tff(s_type, type, (
% 0.18/0.51 s: $i > $i)).
% 0.18/0.51 tff(tptp_fun__0__type, type, (
% 0.18/0.51 tptp_fun__0_: $i)).
% 0.18/0.51 tff(f_type, type, (
% 0.18/0.51 f: $i > $i)).
% 0.18/0.51 tff(g_type, type, (
% 0.18/0.51 g: $i > $i)).
% 0.18/0.51 tff(elem_0_type, type, (
% 0.18/0.51 elem_0: $i)).
% 0.18/0.51 tff(tptp_fun__E__type, type, (
% 0.18/0.51 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.18/0.51 tff(iLEQ_type, type, (
% 0.18/0.51 iLEQ: ( $i * $i ) > $o)).
% 0.18/0.51 tff(1,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.51 tff(2,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))), introduced(assumption)).
% 0.18/0.51 tff(3,assumption,(~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))), introduced(assumption)).
% 0.18/0.51 tff(4,plain,
% 0.18/0.51 (^[A_11: $i] : refl(iLEQ(A_11, A_11) <=> iLEQ(A_11, A_11))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(5,plain,
% 0.18/0.51 (![A_11: $i] : iLEQ(A_11, A_11) <=> ![A_11: $i] : iLEQ(A_11, A_11)),
% 0.18/0.51 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.51 tff(6,plain,
% 0.18/0.51 (![A_11: $i] : iLEQ(A_11, A_11) <=> ![A_11: $i] : iLEQ(A_11, A_11)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(7,axiom,(![A_11: $i] : iLEQ(A_11, A_11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2_29')).
% 0.18/0.51 tff(8,plain,
% 0.18/0.51 (![A_11: $i] : iLEQ(A_11, A_11)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.51 tff(9,plain,(
% 0.18/0.51 ![A_11: $i] : iLEQ(A_11, A_11)),
% 0.18/0.51 inference(skolemize,[status(sab)],[8])).
% 0.18/0.51 tff(10,plain,
% 0.18/0.51 (![A_11: $i] : iLEQ(A_11, A_11)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.51 tff(11,plain,
% 0.18/0.51 ((~![A_11: $i] : iLEQ(A_11, A_11)) | iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(12,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 0.18/0.51 tff(13,plain,(iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(14,plain,
% 0.18/0.51 (^[A_15: $i] : refl((~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> (~tptp_fun__LE_(f(g(A_15)), |'0'|)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(15,plain,
% 0.18/0.51 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.51 tff(16,plain,
% 0.18/0.51 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(17,axiom,(![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_23_14')).
% 0.18/0.51 tff(18,plain,
% 0.18/0.51 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.51 tff(19,plain,(
% 0.18/0.51 ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.18/0.51 inference(skolemize,[status(sab)],[18])).
% 0.18/0.51 tff(20,plain,
% 0.18/0.51 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.51 tff(21,plain,
% 0.18/0.51 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(22,plain,
% 0.18/0.51 (~tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.51 tff(23,plain,
% 0.18/0.51 (^[B_8: $i, A_13: $i] : refl((tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(24,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.51 tff(25,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(26,plain,
% 0.18/0.51 (^[B_8: $i, A_13: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) <=> ((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) <=> (((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_8))))), rewrite((((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_8))) <=> (tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) <=> (tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))))), (((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) | tptp_fun__LE_(f(B_8), |'0'|)) <=> ((tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) | tptp_fun__LE_(f(B_8), |'0'|)))), rewrite(((tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|)))) | tptp_fun__LE_(f(B_8), |'0'|)) <=> (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))), (((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) | tptp_fun__LE_(f(B_8), |'0'|)) <=> (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(27,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : ((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) | tptp_fun__LE_(f(B_8), |'0'|)) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.51 tff(28,axiom,(![B_8: $i, A_13: $i] : ((((~tptp_fun__LE_(f(A_13), s(|'0'|))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(|'0'|, f(B_8))) | tptp_fun__LE_(f(B_8), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1_06')).
% 0.18/0.51 tff(29,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.51 tff(30,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.18/0.51 tff(31,plain,(
% 0.18/0.51 ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[30])).
% 0.18/0.51 tff(32,plain,
% 0.18/0.51 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.51 tff(33,plain,
% 0.18/0.51 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(34,plain,
% 0.18/0.51 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(35,plain,
% 0.18/0.51 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'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(|'0'|)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.51 tff(36,plain,
% 0.18/0.51 (tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[35, 32, 22, 13])).
% 0.18/0.51 tff(37,plain,
% 0.18/0.51 (tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[36, 2])).
% 0.18/0.51 tff(38,plain,
% 0.18/0.51 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(39,plain,
% 0.18/0.51 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[38, 20])).
% 0.18/0.51 tff(40,plain,
% 0.18/0.51 (^[A_2: $i] : refl(iLEQ(A_2, g(A_2)) <=> iLEQ(A_2, g(A_2)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(41,plain,
% 0.18/0.51 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.51 tff(42,plain,
% 0.18/0.51 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(43,axiom,(![A_2: $i] : iLEQ(A_2, g(A_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_13_02')).
% 0.18/0.51 tff(44,plain,
% 0.18/0.51 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.51 tff(45,plain,(
% 0.18/0.51 ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.18/0.51 inference(skolemize,[status(sab)],[44])).
% 0.18/0.51 tff(46,plain,
% 0.18/0.51 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.51 tff(47,plain,
% 0.18/0.51 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(48,plain,
% 0.18/0.51 (iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.18/0.51 tff(49,plain,
% 0.18/0.51 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(50,plain,
% 0.18/0.51 ((tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(elem!0)))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(51,plain,
% 0.18/0.51 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(elem!0)))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[50])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(elem!0)))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[51, 49])).
% 0.18/0.51 tff(53,plain,
% 0.18/0.51 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(elem!0)))), s(|'0'|))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.51 tff(55,plain,
% 0.18/0.51 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[54, 32, 48])).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[55, 39])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 (tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[56, 2])).
% 0.18/0.51 tff(58,plain,
% 0.18/0.51 (^[A_14: $i] : refl((~tptp_fun__E_(f(A_14), f(g(A_14)))) <=> (~tptp_fun__E_(f(A_14), f(g(A_14)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(59,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(61,axiom,(![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_24_31')).
% 0.18/0.51 tff(62,plain,
% 0.18/0.51 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.51 tff(63,plain,(
% 0.18/0.51 ![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[62])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 ((~![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)))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (~tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (^[A_15: $i] : refl((tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15)))) <=> (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 (![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15)))) <=> ![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 (![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15)))) <=> ![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (^[A_15: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15))))) | tptp_fun__E_(f(A_15), f(g(A_15)))) <=> (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (![A_15: $i] : (((~tptp_fun__E_(|'0'|, f(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15))))) | tptp_fun__E_(f(A_15), f(g(A_15)))) <=> ![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.51 tff(72,axiom,(![A_15: $i] : (((~tptp_fun__E_(|'0'|, f(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15))))) | tptp_fun__E_(f(A_15), f(g(A_15))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_29_24')).
% 0.18/0.51 tff(73,plain,
% 0.18/0.51 (![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.51 tff(74,plain,
% 0.18/0.51 (![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.18/0.51 tff(75,plain,(
% 0.18/0.51 ![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[74])).
% 0.18/0.51 tff(76,plain,
% 0.18/0.51 (![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.18/0.51 tff(77,plain,
% 0.18/0.51 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'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_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(78,plain,
% 0.18/0.51 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(79,plain,
% 0.18/0.51 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[78])).
% 0.18/0.51 tff(80,plain,
% 0.18/0.51 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[79, 77])).
% 0.18/0.51 tff(81,plain,
% 0.18/0.51 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(82,plain,
% 0.18/0.51 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.51 tff(83,plain,
% 0.18/0.51 ((~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[82, 76, 66])).
% 0.18/0.51 tff(84,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[83, 57, 37])).
% 0.18/0.51 tff(85,plain,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(86,plain,
% 0.18/0.51 (^[B_6: $i, A_10: $i] : refl(((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(87,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.51 tff(88,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(89,plain,
% 0.18/0.51 (^[B_6: $i, A_10: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) <=> ((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))), ((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) <=> (((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(B_6))))), rewrite((((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(B_6))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))), ((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))))), (((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) | tptp_fun__LE_(f(B_6), s(|'0'|))) <=> (((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) | tptp_fun__LE_(f(B_6), s(|'0'|))))), rewrite((((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|))))) | tptp_fun__LE_(f(B_6), s(|'0'|))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))), (((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) | tptp_fun__LE_(f(B_6), s(|'0'|))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(90,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) | tptp_fun__LE_(f(B_6), s(|'0'|))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.51 tff(91,axiom,(![B_6: $i, A_10: $i] : ((((~tptp_fun__LE_(f(A_10), s(s(|'0'|)))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(|'0'|), f(B_6))) | tptp_fun__LE_(f(B_6), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_17_32')).
% 0.18/0.51 tff(92,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.51 tff(93,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.18/0.51 tff(94,plain,(
% 0.18/0.51 ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[93])).
% 0.18/0.51 tff(95,plain,
% 0.18/0.51 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.18/0.51 tff(96,plain,
% 0.18/0.51 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(97,plain,
% 0.18/0.51 (((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(98,plain,
% 0.18/0.51 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[97])).
% 0.18/0.51 tff(99,plain,
% 0.18/0.51 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[98, 96])).
% 0.18/0.51 tff(100,plain,
% 0.18/0.51 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(101,plain,
% 0.18/0.52 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(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(|'0'|))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.52 tff(102,plain,
% 0.18/0.52 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[101, 95, 13])).
% 0.18/0.52 tff(103,plain,
% 0.18/0.52 (tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[102, 85])).
% 0.18/0.52 tff(104,plain,
% 0.18/0.52 (tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[103, 1])).
% 0.18/0.52 tff(105,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), introduced(assumption)).
% 0.18/0.52 tff(106,assumption,(~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))), introduced(assumption)).
% 0.18/0.52 tff(107,plain,
% 0.18/0.52 ((~![A_11: $i] : iLEQ(A_11, A_11)) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(108,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[107, 10, 106])).
% 0.18/0.52 tff(109,plain,(iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(110,plain,
% 0.18/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(111,plain,
% 0.18/0.52 ((tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(|'0'|)))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(112,plain,
% 0.18/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[111])).
% 0.18/0.52 tff(113,plain,
% 0.18/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[112, 110])).
% 0.18/0.52 tff(114,plain,
% 0.18/0.52 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'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(|'0'|))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(115,plain,
% 0.18/0.52 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.52 tff(116,plain,
% 0.18/0.52 (tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[115, 32, 39, 109])).
% 0.18/0.52 tff(117,plain,
% 0.18/0.52 (tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[116, 105])).
% 0.18/0.52 tff(118,plain,
% 0.18/0.52 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(119,plain,
% 0.18/0.52 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[118, 20])).
% 0.18/0.52 tff(120,plain,
% 0.18/0.52 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(121,plain,
% 0.18/0.52 (iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[120, 46])).
% 0.18/0.52 tff(122,plain,
% 0.18/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(123,plain,
% 0.18/0.52 ((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(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(124,plain,
% 0.18/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0)))))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[123])).
% 0.35/0.52 tff(125,plain,
% 0.35/0.52 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.35/0.52 inference(transitivity,[status(thm)],[124, 122])).
% 0.35/0.52 tff(126,plain,
% 0.35/0.52 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(127,plain,
% 0.35/0.52 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(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(elem!0)))), g(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.35/0.52 tff(128,plain,
% 0.35/0.52 ((~tptp_fun__LE_(f(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)))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[127, 32, 121])).
% 0.35/0.52 tff(129,plain,
% 0.35/0.52 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[128, 105, 119])).
% 0.35/0.52 tff(130,plain,
% 0.35/0.52 ((~![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))))))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(131,plain,
% 0.35/0.52 (~tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[130, 64])).
% 0.35/0.52 tff(132,plain,
% 0.35/0.52 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'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_(|'0'|, f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'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_(|'0'|, f(g(g(g(g(g(elem!0)))))))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(133,plain,
% 0.35/0.52 ((tptp_fun__E_(f(g(g(g(g(elem!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(elem!0)))))))) <=> ((~tptp_fun__E_(|'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_(|'0'|, f(g(g(g(g(g(elem!0)))))))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(134,plain,
% 0.35/0.52 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(g(elem!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(elem!0))))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'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_(|'0'|, f(g(g(g(g(g(elem!0))))))))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[133])).
% 0.35/0.52 tff(135,plain,
% 0.35/0.52 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(g(elem!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(elem!0))))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'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_(|'0'|, f(g(g(g(g(g(elem!0)))))))))),
% 0.35/0.52 inference(transitivity,[status(thm)],[134, 132])).
% 0.35/0.52 tff(136,plain,
% 0.35/0.52 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(g(g(elem!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(elem!0))))))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(137,plain,
% 0.35/0.52 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.35/0.52 tff(138,plain,
% 0.35/0.52 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[137, 76, 131])).
% 0.35/0.52 tff(139,plain,
% 0.35/0.52 ($false),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[138, 129, 117])).
% 0.35/0.52 tff(140,plain,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.52 tff(141,plain,
% 0.35/0.52 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(142,plain,
% 0.35/0.52 (((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))))) <=> ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(143,plain,
% 0.35/0.52 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[142])).
% 0.35/0.52 tff(144,plain,
% 0.35/0.52 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))))),
% 0.35/0.52 inference(transitivity,[status(thm)],[143, 141])).
% 0.35/0.52 tff(145,plain,
% 0.35/0.52 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(146,plain,
% 0.35/0.52 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.35/0.52 tff(147,plain,
% 0.35/0.52 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[146, 95, 48])).
% 0.35/0.52 tff(148,plain,
% 0.35/0.52 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[147, 140])).
% 0.35/0.52 tff(149,plain,
% 0.35/0.52 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[148, 1])).
% 0.35/0.52 tff(150,plain,
% 0.35/0.52 (^[A_14: $i] : refl((tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14)))) <=> (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14)))))),
% 0.35/0.52 inference(bind,[status(th)],[])).
% 0.35/0.52 tff(151,plain,
% 0.35/0.52 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14)))) <=> ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.52 inference(quant_intro,[status(thm)],[150])).
% 0.35/0.52 tff(152,plain,
% 0.35/0.52 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14)))) <=> ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(153,plain,
% 0.35/0.52 (^[A_14: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_14))) | (~tptp_fun__E_(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(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14)))))),
% 0.35/0.52 inference(bind,[status(th)],[])).
% 0.35/0.52 tff(154,plain,
% 0.35/0.52 (![A_14: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_14))) | (~tptp_fun__E_(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(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.52 inference(quant_intro,[status(thm)],[153])).
% 0.35/0.52 tff(155,axiom,(![A_14: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14))))) | tptp_fun__E_(f(A_14), f(g(A_14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_30_13')).
% 0.35/0.52 tff(156,plain,
% 0.35/0.52 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.35/0.52 tff(157,plain,
% 0.35/0.52 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.35/0.52 tff(158,plain,(
% 0.35/0.52 ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.53 inference(skolemize,[status(sab)],[157])).
% 0.35/0.53 tff(159,plain,
% 0.35/0.53 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.35/0.53 tff(160,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(161,plain,
% 0.35/0.53 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(162,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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))))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[161])).
% 0.35/0.53 tff(163,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[162, 160])).
% 0.35/0.53 tff(164,plain,
% 0.35/0.53 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(165,plain,
% 0.35/0.53 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.35/0.53 tff(166,plain,
% 0.35/0.53 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[165, 159, 66])).
% 0.35/0.53 tff(167,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[166, 149, 104])).
% 0.35/0.53 tff(168,plain,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(169,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))), introduced(assumption)).
% 0.35/0.53 tff(170,plain,
% 0.35/0.53 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(171,plain,
% 0.35/0.53 (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[170, 20])).
% 0.35/0.53 tff(172,assumption,(~iLEQ(g(g(elem!0)), g(g(elem!0)))), introduced(assumption)).
% 0.35/0.53 tff(173,plain,
% 0.35/0.53 ((~![A_11: $i] : iLEQ(A_11, A_11)) | iLEQ(g(g(elem!0)), g(g(elem!0)))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(174,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[173, 10, 172])).
% 0.35/0.53 tff(175,plain,(iLEQ(g(g(elem!0)), g(g(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(176,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(177,plain,
% 0.35/0.53 ((tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))) <=> ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(178,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[177])).
% 0.35/0.53 tff(179,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[178, 176])).
% 0.35/0.53 tff(180,plain,
% 0.35/0.53 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(181,plain,
% 0.35/0.53 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.35/0.53 tff(182,plain,
% 0.35/0.53 (tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[181, 32, 175])).
% 0.35/0.53 tff(183,plain,
% 0.35/0.53 (tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[182, 171])).
% 0.35/0.53 tff(184,plain,
% 0.35/0.53 (tptp_fun__E_(|'0'|, f(g(g(elem!0))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[183, 169])).
% 0.35/0.53 tff(185,plain,
% 0.35/0.53 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(186,plain,
% 0.35/0.53 (iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[185, 46])).
% 0.35/0.53 tff(187,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(188,plain,
% 0.35/0.53 ((tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(189,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[188])).
% 0.35/0.53 tff(190,plain,
% 0.35/0.53 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[189, 187])).
% 0.35/0.53 tff(191,plain,
% 0.35/0.53 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(192,plain,
% 0.35/0.53 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.35/0.53 tff(193,plain,
% 0.35/0.53 ((~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[192, 32, 186])).
% 0.35/0.53 tff(194,plain,
% 0.35/0.53 ((~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[193, 22])).
% 0.35/0.53 tff(195,plain,
% 0.35/0.53 (tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[194, 169])).
% 0.35/0.53 tff(196,plain,
% 0.35/0.53 ((~![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))))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(197,plain,
% 0.35/0.53 (~tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[196, 64])).
% 0.35/0.53 tff(198,plain,
% 0.35/0.53 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(199,plain,
% 0.35/0.53 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(200,plain,
% 0.35/0.53 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | ((~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[199])).
% 0.35/0.53 tff(201,plain,
% 0.35/0.53 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[200, 198])).
% 0.35/0.53 tff(202,plain,
% 0.35/0.53 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0)))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(203,plain,
% 0.35/0.53 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.35/0.53 tff(204,plain,
% 0.35/0.53 ((~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[203, 76, 197])).
% 0.35/0.53 tff(205,plain,
% 0.35/0.53 ($false),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[204, 195, 184])).
% 0.35/0.53 tff(206,plain,(~tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.53 tff(207,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))), introduced(assumption)).
% 0.35/0.53 tff(208,plain,
% 0.35/0.53 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(209,plain,
% 0.35/0.53 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(210,plain,
% 0.35/0.53 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.35/0.53 tff(211,plain,
% 0.35/0.53 (tptp_fun__LE_(f(g(g(elem!0))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[210, 95, 175])).
% 0.35/0.53 tff(212,plain,
% 0.35/0.53 (tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[211, 207, 206])).
% 0.35/0.53 tff(213,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))), introduced(assumption)).
% 0.35/0.53 tff(214,plain,
% 0.35/0.53 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(215,plain,
% 0.35/0.53 (((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(216,plain,
% 0.35/0.53 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[215])).
% 0.35/0.53 tff(217,plain,
% 0.35/0.53 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[216, 214])).
% 0.35/0.53 tff(218,plain,
% 0.35/0.53 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(219,plain,
% 0.35/0.53 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.35/0.53 tff(220,plain,
% 0.35/0.53 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[219, 95, 186])).
% 0.35/0.53 tff(221,plain,
% 0.35/0.53 (tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[220, 207, 213])).
% 0.35/0.53 tff(222,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(223,plain,
% 0.35/0.53 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(224,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[223])).
% 0.35/0.53 tff(225,plain,
% 0.35/0.53 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[224, 222])).
% 0.35/0.53 tff(226,plain,
% 0.35/0.53 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(227,plain,
% 0.35/0.53 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.36/0.54 tff(228,plain,
% 0.36/0.54 ((~tptp_fun__E_(s(|'0'|), f(g(g(elem!0))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(elem!0))))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[227, 159, 197])).
% 0.36/0.54 tff(229,plain,
% 0.36/0.54 ($false),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[228, 221, 212])).
% 0.36/0.54 tff(230,plain,((~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.54 tff(231,plain,
% 0.36/0.54 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[230, 85])).
% 0.36/0.54 tff(232,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))), introduced(assumption)).
% 0.36/0.54 tff(233,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.36/0.54 tff(234,plain,
% 0.36/0.54 (^[A_7: $i, B_4: $i] : refl((tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))))),
% 0.36/0.54 inference(bind,[status(th)],[])).
% 0.36/0.54 tff(235,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) <=> ![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(quant_intro,[status(thm)],[234])).
% 0.36/0.54 tff(236,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) <=> ![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(237,plain,
% 0.36/0.54 (^[A_7: $i, B_4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) <=> ((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))), ((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) <=> (((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))))), rewrite((((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))), ((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))))), (((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(|'0'|)))) <=> ((tptp_fun__E_(s(s(|'0'|)), f(B_4)) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) | tptp_fun__LE_(f(B_4), s(s(|'0'|)))))), rewrite(((tptp_fun__E_(s(s(|'0'|)), f(B_4)) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|)))))) | tptp_fun__LE_(f(B_4), s(s(|'0'|)))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))), (((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(|'0'|)))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))))),
% 0.36/0.54 inference(bind,[status(th)],[])).
% 0.36/0.54 tff(238,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : ((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(|'0'|)))) <=> ![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(quant_intro,[status(thm)],[237])).
% 0.36/0.54 tff(239,axiom,(![A_7: $i, B_4: $i] : ((((~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(|'0'|)), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_16_15')).
% 0.36/0.54 tff(240,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.36/0.54 tff(241,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.36/0.54 tff(242,plain,(
% 0.36/0.54 ![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(skolemize,[status(sab)],[241])).
% 0.36/0.54 tff(243,plain,
% 0.36/0.54 (![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[242, 235])).
% 0.36/0.54 tff(244,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(245,plain,
% 0.36/0.54 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(246,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[245])).
% 0.36/0.54 tff(247,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.36/0.54 inference(transitivity,[status(thm)],[246, 244])).
% 0.36/0.54 tff(248,plain,
% 0.36/0.54 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(249,plain,
% 0.36/0.54 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.36/0.54 tff(250,plain,
% 0.36/0.54 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[249, 243, 186])).
% 0.36/0.54 tff(251,plain,
% 0.36/0.54 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[250, 233, 232])).
% 0.36/0.54 tff(252,assumption,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|)))), introduced(assumption)).
% 0.36/0.54 tff(253,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(254,plain,
% 0.36/0.54 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))) <=> ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(255,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[254])).
% 0.36/0.54 tff(256,plain,
% 0.36/0.54 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(transitivity,[status(thm)],[255, 253])).
% 0.36/0.54 tff(257,plain,
% 0.36/0.54 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(258,plain,
% 0.36/0.54 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.36/0.54 tff(259,plain,
% 0.36/0.54 (tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[258, 243, 175])).
% 0.36/0.54 tff(260,plain,
% 0.36/0.54 (tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[259, 233, 252])).
% 0.36/0.54 tff(261,plain,
% 0.36/0.54 (^[A_11: $i] : refl((tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11)))) <=> (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11)))))),
% 0.36/0.54 inference(bind,[status(th)],[])).
% 0.36/0.54 tff(262,plain,
% 0.36/0.54 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11)))) <=> ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(quant_intro,[status(thm)],[261])).
% 0.36/0.54 tff(263,plain,
% 0.36/0.54 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11)))) <=> ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(264,plain,
% 0.36/0.54 (^[A_11: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_11))) | (~tptp_fun__E_(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(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11)))))),
% 0.36/0.54 inference(bind,[status(th)],[])).
% 0.36/0.54 tff(265,plain,
% 0.36/0.54 (![A_11: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_11))) | (~tptp_fun__E_(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(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(quant_intro,[status(thm)],[264])).
% 0.36/0.54 tff(266,axiom,(![A_11: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_11))) | (~tptp_fun__E_(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_27_12')).
% 0.36/0.54 tff(267,plain,
% 0.36/0.54 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.36/0.54 tff(268,plain,
% 0.36/0.54 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.36/0.54 tff(269,plain,(
% 0.36/0.54 ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(skolemize,[status(sab)],[268])).
% 0.36/0.54 tff(270,plain,
% 0.36/0.54 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.36/0.54 tff(271,plain,
% 0.36/0.54 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | ((~tptp_fun__E_(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(|'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(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(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(|'0'|)), f(g(g(g(elem!0)))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(272,plain,
% 0.36/0.54 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(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(|'0'|)), f(g(g(g(elem!0)))))))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(273,plain,
% 0.36/0.54 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | ((~tptp_fun__E_(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(|'0'|)), f(g(g(g(elem!0))))))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[272])).
% 0.36/0.54 tff(274,plain,
% 0.36/0.54 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(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(|'0'|)), f(g(g(g(elem!0)))))))),
% 0.36/0.54 inference(transitivity,[status(thm)],[273, 271])).
% 0.36/0.54 tff(275,plain,
% 0.36/0.54 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(276,plain,
% 0.36/0.54 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.36/0.54 tff(277,plain,
% 0.36/0.54 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[276, 270, 197])).
% 0.36/0.54 tff(278,plain,
% 0.36/0.54 ($false),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[277, 260, 251])).
% 0.36/0.54 tff(279,plain,((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.54 tff(280,plain,
% 0.36/0.54 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[279, 231])).
% 0.36/0.54 tff(281,plain,
% 0.36/0.54 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[280, 168])).
% 0.36/0.54 tff(282,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), introduced(assumption)).
% 0.36/0.54 tff(283,plain,
% 0.36/0.54 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(284,plain,
% 0.36/0.54 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[283, 20])).
% 0.36/0.54 tff(285,plain,
% 0.36/0.54 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(286,plain,
% 0.36/0.55 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[285, 46])).
% 0.36/0.55 tff(287,plain,
% 0.36/0.55 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(288,plain,
% 0.36/0.55 ((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)))))))) | (~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(|'0'|)))) <=> ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(289,plain,
% 0.36/0.55 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'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)))))))) | (~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(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|)))))),
% 0.36/0.55 inference(monotonicity,[status(thm)],[288])).
% 0.36/0.55 tff(290,plain,
% 0.36/0.55 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'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)))))))) | (~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(|'0'|))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|))))),
% 0.36/0.55 inference(transitivity,[status(thm)],[289, 287])).
% 0.36/0.55 tff(291,plain,
% 0.36/0.55 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'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)))))))) | (~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(|'0'|))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(292,plain,
% 0.36/0.55 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!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'|)))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.36/0.55 tff(293,plain,
% 0.36/0.55 (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'|)))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[292, 32, 286])).
% 0.36/0.55 tff(294,plain,
% 0.36/0.55 (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'|)))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[293, 284])).
% 0.36/0.55 tff(295,plain,
% 0.36/0.55 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[294, 282])).
% 0.36/0.55 tff(296,plain,
% 0.36/0.55 (^[A_14: $i] : refl(iLEQ(A_14, A_14) <=> iLEQ(A_14, A_14))),
% 0.36/0.55 inference(bind,[status(th)],[])).
% 0.36/0.55 tff(297,plain,
% 0.36/0.55 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.36/0.55 inference(quant_intro,[status(thm)],[296])).
% 0.36/0.55 tff(298,plain,
% 0.36/0.55 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(299,axiom,(![A_14: $i] : iLEQ(A_14, A_14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18_04')).
% 0.36/0.55 tff(300,plain,
% 0.36/0.55 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.36/0.55 tff(301,plain,(
% 0.36/0.55 ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.36/0.55 inference(skolemize,[status(sab)],[300])).
% 0.36/0.55 tff(302,plain,
% 0.36/0.55 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.36/0.55 tff(303,plain,
% 0.36/0.55 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(304,plain,
% 0.36/0.55 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.36/0.55 tff(305,plain,
% 0.36/0.55 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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'|))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(306,plain,
% 0.36/0.55 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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'|))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(307,plain,
% 0.36/0.55 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), |'0'|) | tptp_fun__E_(|'0'|, f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), 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'|)))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.36/0.55 tff(308,plain,
% 0.36/0.55 (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'|)))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[307, 32, 119, 304])).
% 0.36/0.55 tff(309,plain,
% 0.36/0.55 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[308, 282])).
% 0.36/0.55 tff(310,plain,
% 0.36/0.55 ((~![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)))))))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(311,plain,
% 0.36/0.55 (~tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[310, 64])).
% 0.36/0.55 tff(312,plain,
% 0.36/0.55 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (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(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | 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(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(313,plain,
% 0.36/0.55 ((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_(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(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(314,plain,
% 0.36/0.55 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (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_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (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(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))))),
% 0.36/0.55 inference(monotonicity,[status(thm)],[313])).
% 0.36/0.55 tff(315,plain,
% 0.36/0.55 (((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (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_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | 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(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))),
% 0.36/0.55 inference(transitivity,[status(thm)],[314, 312])).
% 0.36/0.55 tff(316,plain,
% 0.36/0.55 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (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)))))))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(317,plain,
% 0.36/0.55 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.36/0.55 tff(318,plain,
% 0.36/0.55 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[317, 76, 311])).
% 0.36/0.55 tff(319,plain,
% 0.36/0.55 ($false),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[318, 309, 295])).
% 0.36/0.55 tff(320,plain,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.55 tff(321,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), introduced(assumption)).
% 0.36/0.55 tff(322,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))), introduced(assumption)).
% 0.36/0.55 tff(323,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(324,plain,
% 0.36/0.55 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(325,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(monotonicity,[status(thm)],[324])).
% 0.36/0.55 tff(326,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(transitivity,[status(thm)],[325, 323])).
% 0.36/0.55 tff(327,plain,
% 0.36/0.55 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(328,plain,
% 0.36/0.55 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.36/0.55 tff(329,plain,
% 0.36/0.55 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[328, 95])).
% 0.36/0.55 tff(330,plain,
% 0.36/0.55 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[329, 109])).
% 0.36/0.55 tff(331,plain,
% 0.36/0.55 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[330, 322, 321])).
% 0.36/0.55 tff(332,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), introduced(assumption)).
% 0.36/0.55 tff(333,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(334,plain,
% 0.36/0.55 (((~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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(335,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0)))))))))),
% 0.36/0.55 inference(monotonicity,[status(thm)],[334])).
% 0.36/0.55 tff(336,plain,
% 0.36/0.55 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(transitivity,[status(thm)],[335, 333])).
% 0.36/0.55 tff(337,plain,
% 0.36/0.55 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), 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(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(338,plain,
% 0.36/0.55 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.36/0.55 tff(339,plain,
% 0.36/0.55 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'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)))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[338, 95, 121])).
% 0.36/0.55 tff(340,plain,
% 0.36/0.55 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[339, 322, 332])).
% 0.36/0.55 tff(341,plain,
% 0.36/0.55 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(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(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(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(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(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(342,plain,
% 0.36/0.55 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(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(elem!0)))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(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(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(rewrite,[status(thm)],[])).
% 0.36/0.55 tff(343,plain,
% 0.36/0.55 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(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(|'0'|), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(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(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | ((~tptp_fun__E_(s(|'0'|), f(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(elem!0))))), f(g(g(g(g(g(elem!0)))))))))),
% 0.36/0.55 inference(monotonicity,[status(thm)],[342])).
% 0.36/0.55 tff(344,plain,
% 0.36/0.55 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(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(|'0'|), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(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(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(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(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(transitivity,[status(thm)],[343, 341])).
% 0.36/0.55 tff(345,plain,
% 0.36/0.55 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(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(|'0'|), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(quant_inst,[status(thm)],[])).
% 0.36/0.55 tff(346,plain,
% 0.36/0.55 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(|'0'|), f(g(A_14)))) | (~tptp_fun__E_(s(|'0'|), f(A_14))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 0.36/0.55 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.36/0.55 tff(347,plain,
% 0.36/0.55 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[346, 159, 131])).
% 0.36/0.55 tff(348,plain,
% 0.36/0.55 ($false),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[347, 340, 331])).
% 0.36/0.55 tff(349,plain,((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.55 tff(350,plain,
% 0.36/0.55 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[349, 140])).
% 0.36/0.55 tff(351,plain,
% 0.36/0.55 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))),
% 0.36/0.55 inference(unit_resolution,[status(thm)],[350, 320])).
% 0.36/0.55 tff(352,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.36/0.55 tff(353,plain,
% 0.36/0.55 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(354,plain,
% 0.36/0.56 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(355,plain,
% 0.36/0.56 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 0.36/0.56 inference(monotonicity,[status(thm)],[354])).
% 0.36/0.56 tff(356,plain,
% 0.36/0.56 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.56 inference(transitivity,[status(thm)],[355, 353])).
% 0.36/0.56 tff(357,plain,
% 0.36/0.56 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))))))),
% 0.36/0.56 inference(quant_inst,[status(thm)],[])).
% 0.36/0.56 tff(358,plain,
% 0.36/0.56 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.36/0.56 tff(359,plain,
% 0.36/0.56 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[358, 243])).
% 0.36/0.56 tff(360,plain,
% 0.36/0.56 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[359, 13])).
% 0.36/0.56 tff(361,plain,
% 0.36/0.56 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[360, 352, 232])).
% 0.36/0.56 tff(362,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))), introduced(assumption)).
% 0.36/0.56 tff(363,plain,
% 0.36/0.56 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(364,plain,
% 0.36/0.56 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(365,plain,
% 0.36/0.56 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))))),
% 0.36/0.56 inference(monotonicity,[status(thm)],[364])).
% 0.36/0.56 tff(366,plain,
% 0.36/0.56 (((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))) <=> ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.36/0.56 inference(transitivity,[status(thm)],[365, 363])).
% 0.36/0.56 tff(367,plain,
% 0.36/0.56 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))),
% 0.36/0.56 inference(quant_inst,[status(thm)],[])).
% 0.36/0.56 tff(368,plain,
% 0.36/0.56 ((~![A_7: $i, B_4: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(|'0'|))) | (~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), 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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.36/0.56 tff(369,plain,
% 0.36/0.56 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[368, 243, 48])).
% 0.36/0.56 tff(370,plain,
% 0.36/0.56 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[369, 352, 362])).
% 0.36/0.56 tff(371,plain,
% 0.36/0.56 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(372,plain,
% 0.36/0.56 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(373,plain,
% 0.36/0.56 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(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(|'0'|)), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(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(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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))))))))),
% 0.36/0.56 inference(monotonicity,[status(thm)],[372])).
% 0.36/0.56 tff(374,plain,
% 0.36/0.56 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(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(|'0'|)), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(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(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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)))))))),
% 0.36/0.56 inference(transitivity,[status(thm)],[373, 371])).
% 0.36/0.56 tff(375,plain,
% 0.36/0.56 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(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(|'0'|)), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))))),
% 0.36/0.56 inference(quant_inst,[status(thm)],[])).
% 0.36/0.56 tff(376,plain,
% 0.36/0.56 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.36/0.56 tff(377,plain,
% 0.36/0.56 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[376, 270, 66])).
% 0.36/0.56 tff(378,plain,
% 0.36/0.56 ($false),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[377, 370, 361])).
% 0.36/0.56 tff(379,plain,((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.56 tff(380,plain,
% 0.36/0.56 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))),
% 0.36/0.56 inference(unit_resolution,[status(thm)],[379, 168, 351])).
% 0.36/0.56 tff(381,assumption,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.36/0.56 tff(382,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.36/0.56 tff(383,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.36/0.56 tff(384,plain,
% 0.36/0.56 (^[A_4: $i, B_2: $i] : refl((tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))))),
% 0.36/0.56 inference(bind,[status(th)],[])).
% 0.36/0.56 tff(385,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) <=> ![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(quant_intro,[status(thm)],[384])).
% 0.36/0.56 tff(386,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) <=> ![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(387,plain,
% 0.36/0.56 (^[A_4: $i, B_2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_4), 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(|'0'|)))))))), ((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) <=> (((~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))))), rewrite((((~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))), ((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))))), (((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|))))) <=> ((tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|))))))), rewrite(((tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))))),
% 0.36/0.56 inference(bind,[status(th)],[])).
% 0.36/0.56 tff(388,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : ((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|))))) <=> ![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(quant_intro,[status(thm)],[387])).
% 0.36/0.56 tff(389,axiom,(![A_4: $i, B_2: $i] : ((((~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_26_17')).
% 0.36/0.56 tff(390,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.36/0.56 tff(391,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[390, 386])).
% 0.36/0.56 tff(392,plain,(
% 0.36/0.56 ![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(skolemize,[status(sab)],[391])).
% 0.36/0.56 tff(393,plain,
% 0.36/0.56 (![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))),
% 0.36/0.56 inference(modus_ponens,[status(thm)],[392, 385])).
% 0.36/0.56 tff(394,plain,
% 0.36/0.56 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(395,plain,
% 0.36/0.56 ((tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.36/0.56 inference(rewrite,[status(thm)],[])).
% 0.36/0.56 tff(396,plain,
% 0.36/0.56 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.36/0.56 inference(monotonicity,[status(thm)],[395])).
% 0.36/0.56 tff(397,plain,
% 0.36/0.56 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.36/0.56 inference(transitivity,[status(thm)],[396, 394])).
% 0.36/0.56 tff(398,plain,
% 0.36/0.56 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(399,plain,
% 0.36/0.57 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), 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(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.36/0.57 tff(400,plain,
% 0.36/0.57 ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[399, 393])).
% 0.36/0.57 tff(401,plain,
% 0.36/0.57 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[400, 175])).
% 0.36/0.57 tff(402,plain,
% 0.36/0.57 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[401, 383, 381])).
% 0.36/0.57 tff(403,plain,
% 0.36/0.57 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(404,plain,
% 0.36/0.57 ((tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(405,plain,
% 0.36/0.57 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))),
% 0.36/0.57 inference(monotonicity,[status(thm)],[404])).
% 0.36/0.57 tff(406,plain,
% 0.36/0.57 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.36/0.57 inference(transitivity,[status(thm)],[405, 403])).
% 0.36/0.57 tff(407,plain,
% 0.36/0.57 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(408,plain,
% 0.36/0.57 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.36/0.57 tff(409,plain,
% 0.36/0.57 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[408, 393, 186])).
% 0.36/0.57 tff(410,plain,
% 0.36/0.57 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[409, 383, 382])).
% 0.36/0.57 tff(411,plain,
% 0.36/0.57 (^[A_8: $i] : refl((tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8)))) <=> (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8)))))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(412,plain,
% 0.36/0.57 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[411])).
% 0.36/0.57 tff(413,plain,
% 0.36/0.57 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(414,plain,
% 0.36/0.57 (^[A_8: $i] : rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8)))))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(415,plain,
% 0.36/0.57 (![A_8: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[414])).
% 0.36/0.57 tff(416,axiom,(![A_8: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))) | (~tptp_fun__E_(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_21_11')).
% 0.36/0.57 tff(417,plain,
% 0.36/0.57 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.36/0.57 tff(418,plain,
% 0.36/0.57 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[417, 413])).
% 0.36/0.57 tff(419,plain,(
% 0.36/0.57 ![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(skolemize,[status(sab)],[418])).
% 0.36/0.57 tff(420,plain,
% 0.36/0.57 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[419, 412])).
% 0.36/0.57 tff(421,plain,
% 0.36/0.57 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(422,plain,
% 0.36/0.57 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(423,plain,
% 0.36/0.57 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(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(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))))),
% 0.36/0.57 inference(monotonicity,[status(thm)],[422])).
% 0.36/0.57 tff(424,plain,
% 0.36/0.57 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(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(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 0.36/0.57 inference(transitivity,[status(thm)],[423, 421])).
% 0.36/0.57 tff(425,plain,
% 0.36/0.57 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(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(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(426,plain,
% 0.36/0.57 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.36/0.57 tff(427,plain,
% 0.36/0.57 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[426, 420, 197])).
% 0.36/0.57 tff(428,plain,
% 0.36/0.57 ($false),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[427, 410, 402])).
% 0.36/0.57 tff(429,plain,((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.57 tff(430,plain,
% 0.36/0.57 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[429, 382, 381])).
% 0.36/0.57 tff(431,assumption,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.36/0.57 tff(432,assumption,(~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))), introduced(assumption)).
% 0.36/0.57 tff(433,plain,
% 0.36/0.57 (^[A_8: $i] : refl(iLEQ(A_8, g(A_8)) <=> iLEQ(A_8, g(A_8)))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(434,plain,
% 0.36/0.57 (![A_8: $i] : iLEQ(A_8, g(A_8)) <=> ![A_8: $i] : iLEQ(A_8, g(A_8))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[433])).
% 0.36/0.57 tff(435,plain,
% 0.36/0.57 (![A_8: $i] : iLEQ(A_8, g(A_8)) <=> ![A_8: $i] : iLEQ(A_8, g(A_8))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(436,axiom,(![A_8: $i] : iLEQ(A_8, g(A_8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_22_25')).
% 0.36/0.57 tff(437,plain,
% 0.36/0.57 (![A_8: $i] : iLEQ(A_8, g(A_8))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.36/0.57 tff(438,plain,(
% 0.36/0.57 ![A_8: $i] : iLEQ(A_8, g(A_8))),
% 0.36/0.57 inference(skolemize,[status(sab)],[437])).
% 0.36/0.57 tff(439,plain,
% 0.36/0.57 (![A_8: $i] : iLEQ(A_8, g(A_8))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.36/0.57 tff(440,plain,
% 0.36/0.57 ((~![A_8: $i] : iLEQ(A_8, g(A_8))) | iLEQ(g(elem!0), g(g(elem!0)))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(441,plain,
% 0.36/0.57 (iLEQ(g(elem!0), g(g(elem!0)))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[440, 439])).
% 0.36/0.57 tff(442,plain,
% 0.36/0.57 (^[A_1: $i, B_0: $i] : refl(((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(443,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) <=> ![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[442])).
% 0.36/0.57 tff(444,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) <=> ![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(445,plain,
% 0.36/0.57 (^[A_1: $i, B_0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_1), 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(|'0'|))))))))), ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) <=> (((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(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(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) <=> ((~iLEQ(A_1, B_0)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) <=> ((~iLEQ(A_1, B_0)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|)))))) <=> (((~iLEQ(A_1, B_0)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|)))))))), rewrite((((~iLEQ(A_1, B_0)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|)))))) <=> ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))), (((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|)))))) <=> ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(446,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|)))))) <=> ![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[445])).
% 0.36/0.57 tff(447,axiom,(![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7_16')).
% 0.36/0.57 tff(448,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.36/0.57 tff(449,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[448, 444])).
% 0.36/0.57 tff(450,plain,(
% 0.36/0.57 ![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(skolemize,[status(sab)],[449])).
% 0.36/0.57 tff(451,plain,
% 0.36/0.57 (![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[450, 443])).
% 0.36/0.57 tff(452,plain,
% 0.36/0.57 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(453,plain,
% 0.36/0.57 (((~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(454,plain,
% 0.36/0.57 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.57 inference(monotonicity,[status(thm)],[453])).
% 0.36/0.57 tff(455,plain,
% 0.36/0.57 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|))))))),
% 0.36/0.57 inference(transitivity,[status(thm)],[454, 452])).
% 0.36/0.57 tff(456,plain,
% 0.36/0.57 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(457,plain,
% 0.36/0.57 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(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(|'0'|)))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.36/0.57 tff(458,plain,
% 0.36/0.57 ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[457, 451, 441])).
% 0.36/0.57 tff(459,plain,
% 0.36/0.57 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.36/0.57 inference(unit_resolution,[status(thm)],[458, 432, 431])).
% 0.36/0.57 tff(460,plain,
% 0.36/0.57 (^[A: $i] : refl((tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.57 inference(bind,[status(th)],[])).
% 0.36/0.57 tff(461,plain,
% 0.36/0.57 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) <=> ![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(quant_intro,[status(thm)],[460])).
% 0.36/0.57 tff(462,plain,
% 0.36/0.57 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) <=> ![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(463,axiom,(![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8_01')).
% 0.36/0.57 tff(464,plain,
% 0.36/0.57 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.36/0.57 tff(465,plain,(
% 0.36/0.57 ![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(skolemize,[status(sab)],[464])).
% 0.36/0.57 tff(466,plain,
% 0.36/0.57 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(modus_ponens,[status(thm)],[465, 461])).
% 0.36/0.57 tff(467,plain,
% 0.36/0.57 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(rewrite,[status(thm)],[])).
% 0.36/0.57 tff(468,plain,
% 0.36/0.57 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.57 inference(quant_inst,[status(thm)],[])).
% 0.36/0.57 tff(469,plain,
% 0.36/0.57 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.36/0.58 tff(470,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[469, 466])).
% 0.36/0.58 tff(471,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[470, 459])).
% 0.36/0.58 tff(472,plain,
% 0.36/0.58 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(473,plain,
% 0.36/0.58 (((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(474,plain,
% 0.36/0.58 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))))),
% 0.36/0.58 inference(monotonicity,[status(thm)],[473])).
% 0.36/0.58 tff(475,plain,
% 0.36/0.58 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.58 inference(transitivity,[status(thm)],[474, 472])).
% 0.36/0.58 tff(476,plain,
% 0.36/0.58 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(477,plain,
% 0.36/0.58 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.36/0.58 tff(478,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[477, 451, 175])).
% 0.36/0.58 tff(479,plain,
% 0.36/0.58 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[478, 432, 431])).
% 0.36/0.58 tff(480,plain,
% 0.36/0.58 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(481,plain,
% 0.36/0.58 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(482,plain,
% 0.36/0.58 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.36/0.58 tff(483,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[482, 466])).
% 0.36/0.58 tff(484,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[483, 479])).
% 0.36/0.58 tff(485,plain,
% 0.36/0.58 ((~![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)))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(486,plain,
% 0.36/0.58 (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[485, 64])).
% 0.36/0.58 tff(487,plain,
% 0.36/0.58 (^[A_2: $i] : refl((tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2)))))),
% 0.36/0.58 inference(bind,[status(th)],[])).
% 0.36/0.58 tff(488,plain,
% 0.36/0.58 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(quant_intro,[status(thm)],[487])).
% 0.36/0.58 tff(489,plain,
% 0.36/0.58 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(490,plain,
% 0.36/0.58 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2)))))),
% 0.36/0.58 inference(bind,[status(th)],[])).
% 0.36/0.58 tff(491,plain,
% 0.36/0.58 (![A_2: $i] : (((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(quant_intro,[status(thm)],[490])).
% 0.36/0.58 tff(492,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))) | (~tptp_fun__E_(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_3_10')).
% 0.36/0.58 tff(493,plain,
% 0.36/0.58 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.36/0.58 tff(494,plain,
% 0.36/0.58 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[493, 489])).
% 0.36/0.58 tff(495,plain,(
% 0.36/0.58 ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(skolemize,[status(sab)],[494])).
% 0.36/0.58 tff(496,plain,
% 0.36/0.58 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[495, 488])).
% 0.36/0.58 tff(497,plain,
% 0.36/0.58 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | ((~tptp_fun__E_(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(|'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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(498,plain,
% 0.36/0.58 ((tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0))))) <=> ((~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(499,plain,
% 0.36/0.58 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | ((~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0)))))))),
% 0.36/0.58 inference(monotonicity,[status(thm)],[498])).
% 0.36/0.58 tff(500,plain,
% 0.36/0.58 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(transitivity,[status(thm)],[499, 497])).
% 0.36/0.58 tff(501,plain,
% 0.36/0.58 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(502,plain,
% 0.36/0.58 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.36/0.58 tff(503,plain,
% 0.36/0.58 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[502, 496, 486])).
% 0.36/0.58 tff(504,plain,
% 0.36/0.58 ($false),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[503, 484, 471])).
% 0.36/0.58 tff(505,plain,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.58 tff(506,plain,
% 0.36/0.58 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[505, 430])).
% 0.36/0.58 tff(507,plain,
% 0.36/0.58 (^[A_5: $i] : refl((tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5)))))),
% 0.36/0.58 inference(bind,[status(th)],[])).
% 0.36/0.58 tff(508,plain,
% 0.36/0.58 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(quant_intro,[status(thm)],[507])).
% 0.36/0.58 tff(509,plain,
% 0.36/0.58 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(510,plain,
% 0.36/0.58 (^[A_5: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5)))))),
% 0.36/0.58 inference(bind,[status(th)],[])).
% 0.36/0.58 tff(511,plain,
% 0.36/0.58 (![A_5: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(quant_intro,[status(thm)],[510])).
% 0.36/0.58 tff(512,axiom,(![A_5: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))) | (~tptp_fun__E_(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_12_30')).
% 0.36/0.58 tff(513,plain,
% 0.36/0.58 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.36/0.58 tff(514,plain,
% 0.36/0.58 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[513, 509])).
% 0.36/0.58 tff(515,plain,(
% 0.36/0.58 ![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(skolemize,[status(sab)],[514])).
% 0.36/0.58 tff(516,plain,
% 0.36/0.58 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[515, 508])).
% 0.36/0.58 tff(517,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | ((~tptp_fun__E_(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(|'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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(518,plain,
% 0.36/0.58 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(519,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | ((~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0))))))))),
% 0.36/0.58 inference(monotonicity,[status(thm)],[518])).
% 0.36/0.58 tff(520,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))))),
% 0.36/0.58 inference(transitivity,[status(thm)],[519, 517])).
% 0.36/0.58 tff(521,plain,
% 0.36/0.58 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(522,plain,
% 0.36/0.58 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(g(elem!0))))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.36/0.58 tff(523,plain,
% 0.36/0.58 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[522, 516, 197])).
% 0.36/0.58 tff(524,plain,
% 0.36/0.58 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[523, 506])).
% 0.36/0.58 tff(525,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | ((~tptp_fun__E_(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(|'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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(526,plain,
% 0.36/0.58 ((tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))))) <=> ((~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(527,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | ((~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0)))))))),
% 0.36/0.58 inference(monotonicity,[status(thm)],[526])).
% 0.36/0.58 tff(528,plain,
% 0.36/0.58 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))))),
% 0.36/0.58 inference(transitivity,[status(thm)],[527, 525])).
% 0.36/0.58 tff(529,plain,
% 0.36/0.58 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0)))))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(530,plain,
% 0.36/0.58 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0)))))),
% 0.36/0.58 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.36/0.58 tff(531,plain,
% 0.36/0.58 ((~tptp_fun__E_(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(|'0'|)))), f(g(g(elem!0)))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[530, 516])).
% 0.36/0.58 tff(532,plain,
% 0.36/0.58 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[531, 486])).
% 0.36/0.58 tff(533,plain,
% 0.36/0.58 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0)))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[532, 506])).
% 0.36/0.58 tff(534,assumption,(~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.36/0.58 tff(535,assumption,(~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0)))), introduced(assumption)).
% 0.36/0.58 tff(536,plain,
% 0.36/0.58 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(elem!0, g(elem!0))),
% 0.36/0.58 inference(quant_inst,[status(thm)],[])).
% 0.36/0.58 tff(537,plain,
% 0.36/0.58 (iLEQ(elem!0, g(elem!0))),
% 0.36/0.58 inference(unit_resolution,[status(thm)],[536, 46])).
% 0.36/0.58 tff(538,plain,
% 0.36/0.58 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.58 inference(rewrite,[status(thm)],[])).
% 0.36/0.58 tff(539,plain,
% 0.36/0.58 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(540,plain,
% 0.36/0.59 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.36/0.59 tff(541,plain,
% 0.36/0.59 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[540, 451, 537])).
% 0.36/0.59 tff(542,plain,
% 0.36/0.59 (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[541, 535, 534])).
% 0.36/0.59 tff(543,plain,
% 0.36/0.59 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|)))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(544,plain,
% 0.36/0.59 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(545,plain,
% 0.36/0.59 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.36/0.59 tff(546,plain,
% 0.36/0.59 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[545, 466])).
% 0.36/0.59 tff(547,plain,
% 0.36/0.59 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[546, 542])).
% 0.36/0.59 tff(548,assumption,(~iLEQ(g(elem!0), g(elem!0))), introduced(assumption)).
% 0.36/0.59 tff(549,plain,
% 0.36/0.59 ((~![A_11: $i] : iLEQ(A_11, A_11)) | iLEQ(g(elem!0), g(elem!0))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(550,plain,
% 0.36/0.59 ($false),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[549, 10, 548])).
% 0.36/0.59 tff(551,plain,(iLEQ(g(elem!0), g(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.59 tff(552,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(553,plain,
% 0.36/0.59 (((~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(554,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))))),
% 0.36/0.59 inference(monotonicity,[status(thm)],[553])).
% 0.36/0.59 tff(555,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.59 inference(transitivity,[status(thm)],[554, 552])).
% 0.36/0.59 tff(556,plain,
% 0.36/0.59 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(557,plain,
% 0.36/0.59 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.36/0.59 tff(558,plain,
% 0.36/0.59 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[557, 451])).
% 0.36/0.59 tff(559,plain,
% 0.36/0.59 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[558, 551])).
% 0.36/0.59 tff(560,plain,
% 0.36/0.59 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[559, 535, 534])).
% 0.36/0.59 tff(561,plain,
% 0.36/0.59 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[470, 560])).
% 0.36/0.59 tff(562,plain,
% 0.36/0.59 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(elem!0), f(g(elem!0))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(563,plain,
% 0.36/0.59 (~tptp_fun__E_(f(elem!0), f(g(elem!0)))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[562, 64])).
% 0.36/0.59 tff(564,plain,
% 0.36/0.59 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(565,plain,
% 0.36/0.59 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(566,plain,
% 0.36/0.59 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.36/0.59 tff(567,plain,
% 0.36/0.59 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[566, 496, 563])).
% 0.36/0.59 tff(568,plain,
% 0.36/0.59 ($false),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[567, 561, 547])).
% 0.36/0.59 tff(569,plain,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.59 tff(570,plain,
% 0.36/0.59 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[569, 533])).
% 0.36/0.59 tff(571,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(572,plain,
% 0.36/0.59 ((tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(573,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0))))))),
% 0.36/0.59 inference(monotonicity,[status(thm)],[572])).
% 0.36/0.59 tff(574,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.36/0.59 inference(transitivity,[status(thm)],[573, 571])).
% 0.36/0.59 tff(575,plain,
% 0.36/0.59 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(576,plain,
% 0.36/0.59 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))) | (~iLEQ(g(elem!0), g(g(elem!0))))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.36/0.59 tff(577,plain,
% 0.36/0.59 ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[576, 393, 441])).
% 0.36/0.59 tff(578,plain,
% 0.36/0.59 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[577, 570, 381])).
% 0.36/0.59 tff(579,plain,
% 0.36/0.59 (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[427, 578])).
% 0.36/0.59 tff(580,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(581,plain,
% 0.36/0.59 ((tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(582,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 0.36/0.59 inference(monotonicity,[status(thm)],[581])).
% 0.36/0.59 tff(583,plain,
% 0.36/0.59 (((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.36/0.59 inference(transitivity,[status(thm)],[582, 580])).
% 0.36/0.59 tff(584,plain,
% 0.36/0.59 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))),
% 0.36/0.59 inference(quant_inst,[status(thm)],[])).
% 0.36/0.59 tff(585,plain,
% 0.36/0.59 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 0.36/0.59 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.36/0.59 tff(586,plain,
% 0.36/0.59 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[585, 393, 13])).
% 0.36/0.59 tff(587,plain,
% 0.36/0.59 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))),
% 0.36/0.59 inference(unit_resolution,[status(thm)],[586, 579, 382])).
% 0.36/0.59 tff(588,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(589,plain,
% 0.36/0.59 (((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))))),
% 0.36/0.59 inference(rewrite,[status(thm)],[])).
% 0.36/0.59 tff(590,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))))),
% 0.36/0.59 inference(monotonicity,[status(thm)],[589])).
% 0.36/0.59 tff(591,plain,
% 0.36/0.59 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))))),
% 0.36/0.60 inference(transitivity,[status(thm)],[590, 588])).
% 0.36/0.60 tff(592,plain,
% 0.36/0.60 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.36/0.60 inference(quant_inst,[status(thm)],[])).
% 0.36/0.60 tff(593,plain,
% 0.36/0.60 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), 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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.36/0.60 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.36/0.60 tff(594,plain,
% 0.36/0.60 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[593, 451, 186])).
% 0.36/0.60 tff(595,plain,
% 0.36/0.60 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[594, 587, 524])).
% 0.36/0.60 tff(596,plain,
% 0.36/0.60 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[483, 595])).
% 0.36/0.60 tff(597,plain,
% 0.36/0.60 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.60 inference(rewrite,[status(thm)],[])).
% 0.36/0.60 tff(598,plain,
% 0.36/0.60 (((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))) <=> (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.60 inference(rewrite,[status(thm)],[])).
% 0.36/0.60 tff(599,plain,
% 0.36/0.60 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))))),
% 0.36/0.60 inference(monotonicity,[status(thm)],[598])).
% 0.36/0.60 tff(600,plain,
% 0.36/0.60 (((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))) <=> ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.60 inference(transitivity,[status(thm)],[599, 597])).
% 0.36/0.60 tff(601,plain,
% 0.36/0.60 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), 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(|'0'|))))) | tptp_fun__E_(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(|'0'|))))))))),
% 0.36/0.60 inference(quant_inst,[status(thm)],[])).
% 0.36/0.60 tff(602,plain,
% 0.36/0.60 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.60 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.36/0.60 tff(603,plain,
% 0.36/0.60 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[602, 451])).
% 0.36/0.60 tff(604,plain,
% 0.36/0.60 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[603, 13])).
% 0.36/0.60 tff(605,plain,
% 0.36/0.60 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[604, 587, 524])).
% 0.36/0.60 tff(606,plain,
% 0.36/0.60 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.60 inference(rewrite,[status(thm)],[])).
% 0.36/0.60 tff(607,plain,
% 0.36/0.60 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(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(|'0'|)))))))),
% 0.36/0.60 inference(quant_inst,[status(thm)],[])).
% 0.36/0.60 tff(608,plain,
% 0.36/0.60 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(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(|'0'|))))))),
% 0.36/0.60 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.36/0.60 tff(609,plain,
% 0.36/0.60 (tptp_fun__E_(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(|'0'|))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[608, 466])).
% 0.36/0.60 tff(610,plain,
% 0.36/0.60 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[609, 605])).
% 0.36/0.60 tff(611,plain,
% 0.36/0.60 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | ((~tptp_fun__E_(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(|'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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))))),
% 0.36/0.60 inference(rewrite,[status(thm)],[])).
% 0.36/0.60 tff(612,plain,
% 0.36/0.60 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))))),
% 0.36/0.60 inference(rewrite,[status(thm)],[])).
% 0.36/0.60 tff(613,plain,
% 0.36/0.60 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | ((~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0))))))))),
% 0.36/0.60 inference(monotonicity,[status(thm)],[612])).
% 0.36/0.60 tff(614,plain,
% 0.36/0.60 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))))),
% 0.36/0.60 inference(transitivity,[status(thm)],[613, 611])).
% 0.36/0.60 tff(615,plain,
% 0.36/0.60 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(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(|'0'|))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))))),
% 0.36/0.60 inference(quant_inst,[status(thm)],[])).
% 0.36/0.60 tff(616,plain,
% 0.36/0.60 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0))))))),
% 0.36/0.60 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.36/0.60 tff(617,plain,
% 0.36/0.60 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0))))))),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[616, 496, 197])).
% 0.36/0.60 tff(618,plain,
% 0.36/0.60 ($false),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[617, 610, 596])).
% 0.36/0.60 tff(619,plain,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.60 tff(620,plain,
% 0.36/0.60 ($false),
% 0.36/0.60 inference(unit_resolution,[status(thm)],[619, 380, 281])).
% 0.36/0.60 % SZS output end Proof
% 0.36/0.60 % E exiting
%------------------------------------------------------------------------------