%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO629-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO629-1 : TPTP v9.0.0. Released v7.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:21:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(tptp_fun__E__type, type, (
% 0.12/0.39 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.12/0.39 tff(f_type, type, (
% 0.12/0.39 f: $i > $i)).
% 0.12/0.39 tff(g_type, type, (
% 0.12/0.39 g: $i > $i)).
% 0.12/0.39 tff(elem_0_type, type, (
% 0.12/0.39 elem_0: $i)).
% 0.12/0.39 tff(tptp_fun__0__type, type, (
% 0.12/0.39 tptp_fun__0_: $i)).
% 0.12/0.39 tff(iLEQ_type, type, (
% 0.12/0.39 iLEQ: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun__LE__type, type, (
% 0.12/0.39 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.12/0.39 tff(s_type, type, (
% 0.12/0.39 s: $i > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[A_2: $i] : refl(iLEQ(A_2, g(A_2)) <=> iLEQ(A_2, g(A_2)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![A_2: $i] : iLEQ(A_2, g(A_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5_10')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(elem!0), g(g(elem!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (iLEQ(g(elem!0), g(g(elem!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (^[A_3: $i] : refl((~tptp_fun__LE_(f(A_3), |'0'|)) <=> (~tptp_fun__LE_(f(A_3), |'0'|)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,axiom,(![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7_05')).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,(
% 0.12/0.39 ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.12/0.39 inference(skolemize,[status(sab)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,assumption,(~tptp_fun__E_(|'0'|, f(g(g(elem!0))))), introduced(assumption)).
% 0.12/0.39 tff(20,assumption,(tptp_fun__LE_(f(elem!0), s(|'0'|))), introduced(assumption)).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))) | (~tptp_fun__LE_(f(elem!0), |'0'|))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (~tptp_fun__LE_(f(elem!0), |'0'|)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[A_3: $i] : refl(iLEQ(A_3, A_3) <=> iLEQ(A_3, A_3))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A_3: $i] : iLEQ(A_3, A_3) <=> ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A_3: $i] : iLEQ(A_3, A_3) <=> ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,axiom,(![A_3: $i] : iLEQ(A_3, A_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_0_02')).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![A_3: $i] : iLEQ(A_3, A_3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.39 tff(28,plain,(
% 0.12/0.39 ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.12/0.39 inference(skolemize,[status(sab)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![A_3: $i] : iLEQ(A_3, A_3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![A_3: $i] : iLEQ(A_3, A_3)) | iLEQ(elem!0, elem!0)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (iLEQ(elem!0, elem!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (^[A_1: $i, B_0: $i] : refl((tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) <=> ![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) <=> ![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (^[A_1: $i, B_0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) <=> ((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) <=> (((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_0))))), rewrite((((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_0))) <=> (tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) <=> (tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))))), (((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) | tptp_fun__LE_(f(B_0), |'0'|)) <=> ((tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) | tptp_fun__LE_(f(B_0), |'0'|)))), rewrite(((tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|)))) | tptp_fun__LE_(f(B_0), |'0'|)) <=> (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))), (((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) | tptp_fun__LE_(f(B_0), |'0'|)) <=> (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) | tptp_fun__LE_(f(B_0), |'0'|)) <=> ![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.39 tff(37,axiom,(![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(|'0'|))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(|'0'|, f(B_0))) | tptp_fun__LE_(f(B_0), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10_06')).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.39 tff(40,plain,(
% 0.12/0.39 ![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (tptp_fun__E_(|'0'|, f(elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[44, 41, 31, 22])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (tptp_fun__E_(|'0'|, f(elem!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[45, 20])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))) | (~tptp_fun__LE_(f(g(elem!0)), |'0'|))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (~tptp_fun__LE_(f(g(elem!0)), |'0'|)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 16])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[A_3: $i] : refl(iLEQ(A_3, g(A_3)) <=> iLEQ(A_3, g(A_3)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![A_3: $i] : iLEQ(A_3, g(A_3)) <=> ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![A_3: $i] : iLEQ(A_3, g(A_3)) <=> ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,axiom,(![A_3: $i] : iLEQ(A_3, g(A_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3_09')).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,(
% 0.12/0.40 ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.12/0.40 inference(skolemize,[status(sab)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 ((~![A_3: $i] : iLEQ(A_3, g(A_3))) | iLEQ(elem!0, g(elem!0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (iLEQ(elem!0, g(elem!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))) <=> (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))) | (~iLEQ(elem!0, g(elem!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[63, 41, 57, 48])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[64, 20])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (^[A_3: $i] : refl((~tptp_fun__E_(f(A_3), f(g(A_3)))) <=> (~tptp_fun__E_(f(A_3), f(g(A_3)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3)))) <=> ![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3)))) <=> ![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,axiom,(![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8_01')).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,(
% 0.20/0.40 ![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~![A_3: $i] : (~tptp_fun__E_(f(A_3), f(g(A_3))))) | (~tptp_fun__E_(f(elem!0), f(g(elem!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (~tptp_fun__E_(f(elem!0), f(g(elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (^[A_3: $i] : refl((tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (^[A_3: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3))))) | tptp_fun__E_(f(A_3), f(g(A_3)))) <=> (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3))))) | tptp_fun__E_(f(A_3), f(g(A_3)))) <=> ![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.40 tff(80,axiom,(![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3))))) | tptp_fun__E_(f(A_3), f(g(A_3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11_03')).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.40 tff(83,plain,(
% 0.20/0.40 ![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[82])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0))))) <=> ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[88, 65, 46])).
% 0.20/0.40 tff(90,plain,(~tptp_fun__LE_(f(elem!0), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (^[A: $i] : refl((tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|))) <=> ![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|))) <=> ![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(94,axiom,(![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6_04')).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.40 tff(96,plain,(
% 0.20/0.40 ![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[95])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|)))) <=> ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (tptp_fun__E_(s(|'0'|), f(elem!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[101, 90])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (^[A_2: $i] : refl((tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(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(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 (![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(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(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.40 tff(108,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2))))) | tptp_fun__E_(f(A_2), f(g(A_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1_07')).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.40 tff(111,plain,(
% 0.20/0.40 ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[110])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0)))) <=> (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(|'0'|), f(g(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~tptp_fun__E_(s(|'0'|), f(elem!0))) | (~tptp_fun__E_(s(|'0'|), f(g(elem!0))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[118, 112, 74])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (~tptp_fun__E_(s(|'0'|), f(g(elem!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 102])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))) <=> ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((~![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 97])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (tptp_fun__LE_(f(g(elem!0)), s(|'0'|))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[124, 120])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(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'|))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(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'|))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 ((tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(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'|))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(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'|)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(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'|))),
% 0.20/0.41 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), |'0'|)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[131, 41, 125, 19, 18, 9])).
% 0.20/0.41 tff(133,plain,(tptp_fun__E_(|'0'|, f(g(g(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(134,assumption,(~iLEQ(g(elem!0), g(elem!0))), introduced(assumption)).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 ((~![A_3: $i] : iLEQ(A_3, A_3)) | iLEQ(g(elem!0), g(elem!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[135, 29, 134])).
% 0.20/0.41 tff(137,plain,(iLEQ(g(elem!0), g(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 ((tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))) <=> (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | (tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__LE_(f(B_0), |'0'|) | tptp_fun__E_(|'0'|, f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(|'0'|))))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | (~iLEQ(g(elem!0), g(elem!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[143, 41, 125, 48])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[144, 137])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 (((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))) <=> ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 ((tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0))))) <=> ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))))) <=> ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))))) <=> ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[148, 146])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[151, 84, 145])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[152, 133])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 (^[A_2: $i] : refl((~tptp_fun__E_(f(A_2), f(g(A_2)))) <=> (~tptp_fun__E_(f(A_2), f(g(A_2)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2)))) <=> ![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2)))) <=> ![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(157,axiom,(![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4_11')).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.42 tff(159,plain,(
% 0.20/0.42 ![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[158])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 ((~![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))) | (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[161, 160, 153])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------