TSTP Solution File: SYO629-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO629-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Fri Sep 30 01:41:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO629-1 : TPTP v8.1.0. Released v7.1.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.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 : Mon Sep 5 15:55:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun__E__type, type, (
% 0.19/0.39 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.19/0.39 tff(f_type, type, (
% 0.19/0.39 f: $i > $i)).
% 0.19/0.39 tff(elem_0_type, type, (
% 0.19/0.39 elem_0: $i)).
% 0.19/0.39 tff(tptp_fun__0__type, type, (
% 0.19/0.39 tptp_fun__0_: $i)).
% 0.19/0.39 tff(tptp_fun__LE__type, type, (
% 0.19/0.39 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.19/0.39 tff(s_type, type, (
% 0.19/0.39 s: $i > $i)).
% 0.19/0.39 tff(g_type, type, (
% 0.19/0.39 g: $i > $i)).
% 0.19/0.39 tff(iLEQ_type, type, (
% 0.19/0.39 iLEQ: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(tptp_fun__LE_(f(g(elem!0)), s(|'0'|))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[A_3: $i] : refl(iLEQ(A_3, A_3) <=> iLEQ(A_3, A_3))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, A_3) <=> ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, A_3) <=> ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![A_3: $i] : iLEQ(A_3, A_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_0_02')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, A_3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![A_3: $i] : iLEQ(A_3, A_3)),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, A_3)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~![A_3: $i] : iLEQ(A_3, A_3)) | iLEQ(g(elem!0), g(elem!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (iLEQ(g(elem!0), g(elem!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[A_3: $i] : refl((~tptp_fun__LE_(f(g(A_3)), |'0'|)) <=> (~tptp_fun__LE_(f(g(A_3)), |'0'|)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,axiom,(![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2_08')).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,(
% 0.19/0.39 ![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))),
% 0.19/0.39 inference(skolemize,[status(sab)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))) | (~tptp_fun__LE_(f(g(elem!0)), |'0'|))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~tptp_fun__LE_(f(g(elem!0)), |'0'|)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (^[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'|)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (^[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'|))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.39 tff(25,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')).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.39 tff(28,plain,(
% 0.19/0.39 ![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'|))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![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'|))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (((~![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(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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![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(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)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![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(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))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![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(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'|))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~![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(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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (tptp_fun__E_(|'0'|, f(g(elem!0))) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 29, 19, 10])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![A_3: $i] : (~tptp_fun__LE_(f(g(A_3)), |'0'|))) | (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~tptp_fun__LE_(f(g(g(elem!0))), |'0'|)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 17])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (^[A_3: $i] : refl(iLEQ(A_3, g(A_3)) <=> iLEQ(A_3, g(A_3)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, g(A_3)) <=> ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, g(A_3)) <=> ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,axiom,(![A_3: $i] : iLEQ(A_3, g(A_3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3_09')).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.39 tff(45,plain,(
% 0.19/0.39 ![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.19/0.39 inference(skolemize,[status(sab)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![A_3: $i] : iLEQ(A_3, g(A_3))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![A_3: $i] : iLEQ(A_3, g(A_3))) | iLEQ(g(elem!0), g(g(elem!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (iLEQ(g(elem!0), g(g(elem!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~![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(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(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(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((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(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (((~![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(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(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (((~![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(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(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![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(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'|))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![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(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (tptp_fun__LE_(f(g(g(elem!0))), |'0'|) | (~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(elem!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 29, 48])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (tptp_fun__E_(|'0'|, f(g(g(elem!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 1, 39])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (^[A_2: $i] : refl((~tptp_fun__E_(f(A_2), f(g(A_2)))) <=> (~tptp_fun__E_(f(A_2), f(g(A_2)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(60,axiom,(![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4_11')).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,(
% 0.19/0.40 ![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~![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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.40 tff(71,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')).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.40 tff(74,plain,(
% 0.19/0.40 ![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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~![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_(|'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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~![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(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)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~![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(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))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~![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(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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(g(g(elem!0)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 75, 65])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 56, 37])).
% 0.19/0.40 tff(84,plain,(~tptp_fun__LE_(f(g(elem!0)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (^[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'|))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![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'|)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![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'|)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,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')).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,(
% 0.19/0.40 ![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![A: $i] : (tptp_fun__E_(s(|'0'|), f(A)) | tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (((~![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'|)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((~![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'|)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~![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'|))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (tptp_fun__E_(s(|'0'|), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(|'0'|))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (tptp_fun__E_(s(|'0'|), f(g(elem!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[95, 84])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![A_2: $i] : (~tptp_fun__E_(f(A_2), f(g(A_2))))) | (~tptp_fun__E_(f(elem!0), f(g(elem!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (~tptp_fun__E_(f(elem!0), f(g(elem!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[97, 63])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (![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)))) <=> ![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![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)))) <=> ![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.41 tff(104,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')).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.41 tff(107,plain,(
% 0.19/0.41 ![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))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~![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(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~tptp_fun__E_(s(|'0'|), f(g(elem!0)))) | (~tptp_fun__E_(s(|'0'|), f(elem!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 108, 98])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (~tptp_fun__E_(s(|'0'|), f(elem!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 96])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (((~![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'|)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 ((~![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'|)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![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'|))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (tptp_fun__E_(s(|'0'|), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(|'0'|))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[116, 91])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (tptp_fun__LE_(f(elem!0), s(|'0'|))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 113])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (^[A_3: $i] : refl((~tptp_fun__LE_(f(A_3), |'0'|)) <=> (~tptp_fun__LE_(f(A_3), |'0'|)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|)) <=> ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,axiom,(![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7_05')).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.41 tff(124,plain,(
% 0.19/0.41 ![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.19/0.41 inference(skolemize,[status(sab)],[123])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![A_3: $i] : (~tptp_fun__LE_(f(A_3), |'0'|))) | (~tptp_fun__LE_(f(elem!0), |'0'|))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (~tptp_fun__LE_(f(elem!0), |'0'|)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ((~![A_3: $i] : iLEQ(A_3, A_3)) | iLEQ(elem!0, elem!0)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (iLEQ(elem!0, elem!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[128, 8])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (((~![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(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'|))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~![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(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ((~![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(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~iLEQ(elem!0, elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (tptp_fun__LE_(f(elem!0), |'0'|) | tptp_fun__E_(|'0'|, f(elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 29, 129])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (tptp_fun__E_(|'0'|, f(elem!0)) | (~tptp_fun__LE_(f(elem!0), s(|'0'|)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[133, 127])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (tptp_fun__E_(|'0'|, f(elem!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[134, 118])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~![A_3: $i] : iLEQ(A_3, g(A_3))) | iLEQ(elem!0, g(elem!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (iLEQ(elem!0, g(elem!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[136, 46])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (((~![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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 ((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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (((~![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(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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (((~![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(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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~![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(elem!0, g(elem!0))) | (~tptp_fun__LE_(f(elem!0), s(|'0'|))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 ((~![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(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 ((~tptp_fun__LE_(f(elem!0), s(|'0'|))) | tptp_fun__LE_(f(g(elem!0)), |'0'|) | tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 29, 137])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((~tptp_fun__LE_(f(elem!0), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[144, 19])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (tptp_fun__E_(|'0'|, f(g(elem!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[145, 118])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (((~![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(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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 ((~![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(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 ((~![A_3: $i] : (tptp_fun__E_(f(A_3), f(g(A_3))) | (~tptp_fun__E_(|'0'|, f(g(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 ((~tptp_fun__E_(|'0'|, f(g(elem!0)))) | (~tptp_fun__E_(|'0'|, f(elem!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[149, 75, 98])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[150, 146, 135])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------