TSTP Solution File: SYO630-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO630-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 0.52s 0.60s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO630-1 : TPTP v8.1.0. Released v7.1.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 15:38:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.52/0.60 % SZS status Unsatisfiable
% 0.52/0.60 % SZS output start Proof
% 0.52/0.60 tff(tptp_fun__E__type, type, (
% 0.52/0.60 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.52/0.60 tff(f_type, type, (
% 0.52/0.60 f: $i > $i)).
% 0.52/0.60 tff(g_type, type, (
% 0.52/0.60 g: $i > $i)).
% 0.52/0.60 tff(elem_0_type, type, (
% 0.52/0.60 elem_0: $i)).
% 0.52/0.60 tff(s_type, type, (
% 0.52/0.60 s: $i > $i)).
% 0.52/0.60 tff(tptp_fun__0__type, type, (
% 0.52/0.60 tptp_fun__0_: $i)).
% 0.52/0.60 tff(tptp_fun__LE__type, type, (
% 0.52/0.60 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.52/0.60 tff(iLEQ_type, type, (
% 0.52/0.60 iLEQ: ( $i * $i ) > $o)).
% 0.52/0.60 tff(1,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), introduced(assumption)).
% 0.52/0.60 tff(2,plain,
% 0.52/0.60 (^[A_15: $i] : refl((~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> (~tptp_fun__LE_(f(g(A_15)), |'0'|)))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(3,plain,
% 0.52/0.60 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.52/0.60 inference(quant_intro,[status(thm)],[2])).
% 0.52/0.60 tff(4,plain,
% 0.52/0.60 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|)) <=> ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(5,axiom,(![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_23_14')).
% 0.52/0.60 tff(6,plain,
% 0.52/0.60 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.52/0.60 tff(7,plain,(
% 0.52/0.60 ![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.52/0.60 inference(skolemize,[status(sab)],[6])).
% 0.52/0.60 tff(8,plain,
% 0.52/0.60 (![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.52/0.60 tff(9,plain,
% 0.52/0.60 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(10,plain,
% 0.52/0.60 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|)),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.52/0.60 tff(11,plain,
% 0.52/0.60 (^[A_2: $i] : refl(iLEQ(A_2, g(A_2)) <=> iLEQ(A_2, g(A_2)))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(12,plain,
% 0.52/0.60 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.52/0.60 inference(quant_intro,[status(thm)],[11])).
% 0.52/0.60 tff(13,plain,
% 0.52/0.60 (![A_2: $i] : iLEQ(A_2, g(A_2)) <=> ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(14,axiom,(![A_2: $i] : iLEQ(A_2, g(A_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_13_02')).
% 0.52/0.60 tff(15,plain,
% 0.52/0.60 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.52/0.60 tff(16,plain,(
% 0.52/0.60 ![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.52/0.60 inference(skolemize,[status(sab)],[15])).
% 0.52/0.60 tff(17,plain,
% 0.52/0.60 (![A_2: $i] : iLEQ(A_2, g(A_2))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.52/0.60 tff(18,plain,
% 0.52/0.60 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(19,plain,
% 0.52/0.60 (iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.52/0.60 tff(20,plain,
% 0.52/0.60 (^[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'|)))))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(21,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(quant_intro,[status(thm)],[20])).
% 0.52/0.60 tff(22,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(23,plain,
% 0.52/0.60 (^[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'|))))))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(24,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(quant_intro,[status(thm)],[23])).
% 0.52/0.60 tff(25,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')).
% 0.52/0.60 tff(26,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.52/0.60 tff(27,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.52/0.60 tff(28,plain,(
% 0.52/0.60 ![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'|))))),
% 0.52/0.60 inference(skolemize,[status(sab)],[27])).
% 0.52/0.60 tff(29,plain,
% 0.52/0.60 (![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'|))))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.52/0.60 tff(30,plain,
% 0.52/0.60 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(31,plain,
% 0.52/0.60 ((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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(32,plain,
% 0.52/0.60 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|)))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[31])).
% 0.52/0.60 tff(33,plain,
% 0.52/0.60 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.60 inference(transitivity,[status(thm)],[32, 30])).
% 0.52/0.60 tff(34,plain,
% 0.52/0.60 ((~![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'|))))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(35,plain,
% 0.52/0.60 ((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|)))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.52/0.60 tff(36,plain,
% 0.52/0.60 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[35, 29, 19])).
% 0.52/0.60 tff(37,plain,
% 0.52/0.60 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[36, 10])).
% 0.52/0.60 tff(38,plain,
% 0.52/0.60 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.52/0.60 tff(39,plain,
% 0.52/0.60 (^[A_14: $i] : refl(iLEQ(A_14, A_14) <=> iLEQ(A_14, A_14))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(40,plain,
% 0.52/0.60 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.52/0.60 inference(quant_intro,[status(thm)],[39])).
% 0.52/0.60 tff(41,plain,
% 0.52/0.60 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(42,axiom,(![A_14: $i] : iLEQ(A_14, A_14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18_04')).
% 0.52/0.60 tff(43,plain,
% 0.52/0.60 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.52/0.60 tff(44,plain,(
% 0.52/0.60 ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.52/0.60 inference(skolemize,[status(sab)],[43])).
% 0.52/0.60 tff(45,plain,
% 0.52/0.60 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.52/0.60 tff(46,plain,
% 0.52/0.60 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(47,plain,
% 0.52/0.60 (iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.52/0.60 tff(48,plain,
% 0.52/0.60 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(49,plain,
% 0.52/0.61 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), |'0'|)),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[48, 8])).
% 0.52/0.61 tff(50,plain,
% 0.52/0.61 (((~![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(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)))))))) <=> ((~![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(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)))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(51,plain,
% 0.52/0.61 ((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))))), 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)))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(52,plain,
% 0.52/0.61 (((~![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))))), 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))))))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[51])).
% 0.52/0.61 tff(53,plain,
% 0.52/0.61 (((~![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))))), 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)))))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[52, 50])).
% 0.52/0.61 tff(54,plain,
% 0.52/0.61 ((~![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'|))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(55,plain,
% 0.52/0.61 ((~![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(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))))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.52/0.61 tff(56,plain,
% 0.52/0.61 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[55, 29, 49, 47])).
% 0.52/0.61 tff(57,plain,
% 0.52/0.61 (tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[56, 1])).
% 0.52/0.61 tff(58,plain,
% 0.52/0.61 (^[A_14: $i] : refl((~tptp_fun__E_(f(A_14), f(g(A_14)))) <=> (~tptp_fun__E_(f(A_14), f(g(A_14)))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(59,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[58])).
% 0.52/0.61 tff(60,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 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')).
% 0.52/0.61 tff(62,plain,
% 0.52/0.61 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.52/0.61 tff(63,plain,(
% 0.52/0.61 ![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.52/0.61 inference(skolemize,[status(sab)],[62])).
% 0.52/0.61 tff(64,plain,
% 0.52/0.61 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.52/0.61 tff(65,plain,
% 0.52/0.61 ((~![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))))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(66,plain,
% 0.52/0.61 (~tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.52/0.61 tff(67,plain,
% 0.52/0.61 (^[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)))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(68,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[67])).
% 0.52/0.61 tff(69,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(70,plain,
% 0.52/0.61 (^[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)))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(71,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[70])).
% 0.52/0.61 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')).
% 0.52/0.61 tff(73,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.52/0.61 tff(74,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.52/0.61 tff(75,plain,(
% 0.52/0.61 ![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))))),
% 0.52/0.61 inference(skolemize,[status(sab)],[74])).
% 0.52/0.61 tff(76,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.52/0.61 tff(77,plain,
% 0.52/0.61 (((~![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)))))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(78,plain,
% 0.52/0.61 ((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)))))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(79,plain,
% 0.52/0.61 (((~![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))))))))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[78])).
% 0.52/0.61 tff(80,plain,
% 0.52/0.61 (((~![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)))))))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[79, 77])).
% 0.52/0.61 tff(81,plain,
% 0.52/0.61 ((~![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))))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(82,plain,
% 0.52/0.61 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.52/0.61 tff(83,plain,
% 0.52/0.61 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[82, 76, 66])).
% 0.52/0.61 tff(84,plain,
% 0.52/0.61 ($false),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[83, 57, 38])).
% 0.52/0.61 tff(85,plain,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.61 tff(86,plain,
% 0.52/0.61 ((~![A_15: $i] : (~tptp_fun__LE_(f(g(A_15)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(87,plain,
% 0.52/0.61 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|)),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[86, 8])).
% 0.52/0.61 tff(88,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), introduced(assumption)).
% 0.52/0.61 tff(89,plain,
% 0.52/0.61 ((~![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)))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(90,plain,
% 0.52/0.61 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[89, 17])).
% 0.52/0.61 tff(91,plain,
% 0.52/0.61 (((~![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__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(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'|))))) | 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(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(92,plain,
% 0.52/0.61 ((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'|)))) <=> (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(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(93,plain,
% 0.52/0.61 (((~![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'|))))) | (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(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[92])).
% 0.52/0.61 tff(94,plain,
% 0.52/0.61 (((~![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'|))))) | 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(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[93, 91])).
% 0.52/0.61 tff(95,plain,
% 0.52/0.61 ((~![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'|))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(96,plain,
% 0.52/0.61 ((~![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__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(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.52/0.61 tff(97,plain,
% 0.52/0.61 (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'|)))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[96, 29, 90])).
% 0.52/0.61 tff(98,plain,
% 0.52/0.61 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[97, 88, 87])).
% 0.52/0.61 tff(99,plain,
% 0.52/0.61 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(100,plain,
% 0.52/0.61 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[99, 45])).
% 0.52/0.61 tff(101,plain,
% 0.52/0.61 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(102,plain,
% 0.52/0.61 ((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'|)))) <=> (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(103,plain,
% 0.52/0.61 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|)))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[102])).
% 0.52/0.61 tff(104,plain,
% 0.52/0.61 (((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[103, 101])).
% 0.52/0.61 tff(105,plain,
% 0.52/0.61 ((~![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'|))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(106,plain,
% 0.52/0.61 ((~![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__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'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'|)))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.52/0.61 tff(107,plain,
% 0.52/0.61 (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'|)))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[106, 29, 10, 100])).
% 0.52/0.61 tff(108,plain,
% 0.52/0.61 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[107, 88])).
% 0.52/0.61 tff(109,plain,
% 0.52/0.61 ((~![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)))))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(110,plain,
% 0.52/0.61 (~tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[109, 64])).
% 0.52/0.61 tff(111,plain,
% 0.52/0.61 (((~![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))))))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(112,plain,
% 0.52/0.61 ((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))))))))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(113,plain,
% 0.52/0.61 (((~![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)))))))))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[112])).
% 0.52/0.61 tff(114,plain,
% 0.52/0.61 (((~![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))))))))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[113, 111])).
% 0.52/0.61 tff(115,plain,
% 0.52/0.61 ((~![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)))))))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(116,plain,
% 0.52/0.61 ((~![A_15: $i] : (tptp_fun__E_(f(A_15), f(g(A_15))) | (~tptp_fun__E_(|'0'|, f(g(A_15)))) | (~tptp_fun__E_(|'0'|, f(A_15))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.52/0.61 tff(117,plain,
% 0.52/0.61 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[116, 76, 110])).
% 0.52/0.61 tff(118,plain,
% 0.52/0.61 ($false),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[117, 108, 98])).
% 0.52/0.61 tff(119,plain,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.61 tff(120,assumption,(~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 0.52/0.61 tff(121,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.52/0.62 tff(122,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), introduced(assumption)).
% 0.52/0.62 tff(123,plain,
% 0.52/0.62 (^[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'|))))))),
% 0.52/0.62 inference(bind,[status(th)],[])).
% 0.52/0.62 tff(124,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(quant_intro,[status(thm)],[123])).
% 0.52/0.62 tff(125,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(126,plain,
% 0.52/0.62 (^[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'|)))))))),
% 0.52/0.62 inference(bind,[status(th)],[])).
% 0.52/0.62 tff(127,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(quant_intro,[status(thm)],[126])).
% 0.52/0.62 tff(128,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')).
% 0.52/0.62 tff(129,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.52/0.62 tff(130,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.52/0.62 tff(131,plain,(
% 0.52/0.62 ![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'|)))))),
% 0.52/0.62 inference(skolemize,[status(sab)],[130])).
% 0.52/0.62 tff(132,plain,
% 0.52/0.62 (![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'|)))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.52/0.62 tff(133,plain,
% 0.52/0.62 (((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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'|)))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(134,plain,
% 0.52/0.62 (((~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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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'|)))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(135,plain,
% 0.52/0.62 (((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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'|))))))),
% 0.52/0.62 inference(monotonicity,[status(thm)],[134])).
% 0.52/0.62 tff(136,plain,
% 0.52/0.62 (((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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'|)))))),
% 0.52/0.62 inference(transitivity,[status(thm)],[135, 133])).
% 0.52/0.62 tff(137,plain,
% 0.52/0.62 ((~![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'|)))))),
% 0.52/0.62 inference(quant_inst,[status(thm)],[])).
% 0.52/0.62 tff(138,plain,
% 0.52/0.62 ((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!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'|))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.52/0.62 tff(139,plain,
% 0.52/0.62 (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'|))))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[138, 132, 19])).
% 0.52/0.62 tff(140,plain,
% 0.52/0.62 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[139, 122, 120])).
% 0.52/0.62 tff(141,plain,
% 0.52/0.62 (^[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'|)))))))),
% 0.52/0.62 inference(bind,[status(th)],[])).
% 0.52/0.62 tff(142,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(quant_intro,[status(thm)],[141])).
% 0.52/0.62 tff(143,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(144,plain,
% 0.52/0.62 (^[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'|))))))))),
% 0.52/0.62 inference(bind,[status(th)],[])).
% 0.52/0.62 tff(145,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(quant_intro,[status(thm)],[144])).
% 0.52/0.62 tff(146,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')).
% 0.52/0.62 tff(147,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.52/0.62 tff(148,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.52/0.62 tff(149,plain,(
% 0.52/0.62 ![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'|))))))),
% 0.52/0.62 inference(skolemize,[status(sab)],[148])).
% 0.52/0.62 tff(150,plain,
% 0.52/0.62 (![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'|))))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.52/0.62 tff(151,plain,
% 0.52/0.62 (((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(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(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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(152,plain,
% 0.52/0.62 ((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.52/0.62 inference(quant_inst,[status(thm)],[])).
% 0.52/0.62 tff(153,plain,
% 0.52/0.62 ((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.52/0.62 tff(154,plain,
% 0.52/0.62 (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'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[153, 150, 47])).
% 0.52/0.62 tff(155,plain,
% 0.52/0.62 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[154, 140, 121])).
% 0.52/0.62 tff(156,plain,
% 0.52/0.62 (((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(157,plain,
% 0.52/0.62 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(158,plain,
% 0.52/0.62 (((~![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(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))))),
% 0.52/0.62 inference(monotonicity,[status(thm)],[157])).
% 0.52/0.62 tff(159,plain,
% 0.52/0.62 (((~![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(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 0.52/0.62 inference(transitivity,[status(thm)],[158, 156])).
% 0.52/0.62 tff(160,plain,
% 0.52/0.62 ((~![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(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 0.52/0.62 inference(quant_inst,[status(thm)],[])).
% 0.52/0.62 tff(161,plain,
% 0.52/0.62 ((~![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(g(elem!0)))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.52/0.62 tff(162,plain,
% 0.52/0.62 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[161, 132, 100])).
% 0.52/0.62 tff(163,plain,
% 0.52/0.62 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[162, 122, 120])).
% 0.52/0.62 tff(164,plain,
% 0.52/0.62 (((~![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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(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'|))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(165,plain,
% 0.52/0.62 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(166,plain,
% 0.58/0.63 (((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[165])).
% 0.58/0.63 tff(167,plain,
% 0.58/0.63 (((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.58/0.63 inference(transitivity,[status(thm)],[166, 164])).
% 0.58/0.63 tff(168,plain,
% 0.58/0.63 ((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(169,plain,
% 0.58/0.63 ((~![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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.58/0.63 tff(170,plain,
% 0.58/0.63 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[169, 150, 19])).
% 0.58/0.63 tff(171,plain,
% 0.58/0.63 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[170, 163, 121])).
% 0.58/0.63 tff(172,plain,
% 0.58/0.63 (^[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)))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(173,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[172])).
% 0.58/0.63 tff(174,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(175,plain,
% 0.58/0.63 (^[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)))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(176,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[175])).
% 0.58/0.63 tff(177,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')).
% 0.58/0.63 tff(178,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.58/0.63 tff(179,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.58/0.63 tff(180,plain,(
% 0.58/0.63 ![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))))),
% 0.58/0.63 inference(skolemize,[status(sab)],[179])).
% 0.58/0.63 tff(181,plain,
% 0.58/0.63 (![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))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.58/0.63 tff(182,plain,
% 0.58/0.63 (((~![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(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(183,plain,
% 0.58/0.63 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(184,plain,
% 0.58/0.63 (((~![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(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(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(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[183])).
% 0.58/0.63 tff(185,plain,
% 0.58/0.63 (((~![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(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(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(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))),
% 0.58/0.63 inference(transitivity,[status(thm)],[184, 182])).
% 0.58/0.63 tff(186,plain,
% 0.58/0.63 ((~![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(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(187,plain,
% 0.58/0.63 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.58/0.63 tff(188,plain,
% 0.58/0.63 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[187, 181, 66])).
% 0.58/0.63 tff(189,plain,
% 0.58/0.63 ($false),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[188, 171, 155])).
% 0.58/0.63 tff(190,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.63 tff(191,plain,
% 0.58/0.63 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[190, 120, 119])).
% 0.58/0.63 tff(192,plain,
% 0.58/0.63 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[162, 120, 119])).
% 0.58/0.63 tff(193,plain,
% 0.58/0.63 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[139, 120, 119])).
% 0.58/0.63 tff(194,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.58/0.63 tff(195,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.58/0.63 tff(196,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.58/0.63 tff(197,plain,
% 0.58/0.63 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(198,plain,
% 0.58/0.63 (iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[197, 17])).
% 0.58/0.63 tff(199,plain,
% 0.58/0.63 (^[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'|))))))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(200,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[199])).
% 0.58/0.63 tff(201,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(202,plain,
% 0.58/0.63 (^[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'|)))))))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(203,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[202])).
% 0.58/0.63 tff(204,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')).
% 0.58/0.63 tff(205,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.58/0.63 tff(206,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.58/0.63 tff(207,plain,(
% 0.58/0.63 ![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'|)))))))),
% 0.58/0.63 inference(skolemize,[status(sab)],[206])).
% 0.58/0.63 tff(208,plain,
% 0.58/0.63 (![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'|)))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.58/0.63 tff(209,plain,
% 0.58/0.63 (((~![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(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!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__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(210,plain,
% 0.58/0.63 ((tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(211,plain,
% 0.58/0.63 (((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'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__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))))),
% 0.58/0.63 inference(monotonicity,[status(thm)],[210])).
% 0.58/0.63 tff(212,plain,
% 0.58/0.63 (((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'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__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))),
% 0.58/0.63 inference(transitivity,[status(thm)],[211, 209])).
% 0.58/0.63 tff(213,plain,
% 0.58/0.63 ((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(214,plain,
% 0.58/0.63 ((~![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(g(g(elem!0))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.58/0.63 tff(215,plain,
% 0.58/0.63 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|))))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[214, 208, 198])).
% 0.58/0.63 tff(216,plain,
% 0.58/0.63 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[215, 196, 195])).
% 0.58/0.63 tff(217,plain,
% 0.58/0.63 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))),
% 0.58/0.63 inference(quant_inst,[status(thm)],[])).
% 0.58/0.63 tff(218,plain,
% 0.58/0.63 (iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))),
% 0.58/0.63 inference(unit_resolution,[status(thm)],[217, 45])).
% 0.58/0.63 tff(219,plain,
% 0.58/0.63 (((~![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))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(220,plain,
% 0.58/0.64 ((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))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(221,plain,
% 0.58/0.64 (((~![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)))))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[220])).
% 0.58/0.64 tff(222,plain,
% 0.58/0.64 (((~![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))))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[221, 219])).
% 0.58/0.64 tff(223,plain,
% 0.58/0.64 ((~![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'|)))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(224,plain,
% 0.58/0.64 ((~![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)))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.58/0.64 tff(225,plain,
% 0.58/0.64 (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'|))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[224, 208, 218])).
% 0.58/0.64 tff(226,plain,
% 0.58/0.64 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[225, 196, 194])).
% 0.58/0.64 tff(227,plain,
% 0.58/0.64 ((~![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)))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(228,plain,
% 0.58/0.64 (~tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[227, 64])).
% 0.58/0.64 tff(229,plain,
% 0.58/0.64 (^[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)))))),
% 0.58/0.64 inference(bind,[status(th)],[])).
% 0.58/0.64 tff(230,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(quant_intro,[status(thm)],[229])).
% 0.58/0.64 tff(231,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(232,plain,
% 0.58/0.64 (^[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)))))),
% 0.58/0.64 inference(bind,[status(th)],[])).
% 0.58/0.64 tff(233,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(quant_intro,[status(thm)],[232])).
% 0.58/0.64 tff(234,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')).
% 0.58/0.64 tff(235,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.58/0.64 tff(236,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.58/0.64 tff(237,plain,(
% 0.58/0.64 ![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))))),
% 0.58/0.64 inference(skolemize,[status(sab)],[236])).
% 0.58/0.64 tff(238,plain,
% 0.58/0.64 (![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))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.58/0.64 tff(239,plain,
% 0.58/0.64 (((~![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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))) <=> ((~![A_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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(240,plain,
% 0.58/0.64 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(241,plain,
% 0.58/0.64 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))))),
% 0.58/0.64 inference(monotonicity,[status(thm)],[240])).
% 0.58/0.64 tff(242,plain,
% 0.58/0.64 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.58/0.64 inference(transitivity,[status(thm)],[241, 239])).
% 0.58/0.64 tff(243,plain,
% 0.58/0.64 ((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(244,plain,
% 0.58/0.64 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.58/0.64 tff(245,plain,
% 0.58/0.64 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[244, 238, 228])).
% 0.58/0.64 tff(246,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[245, 226, 216])).
% 0.58/0.64 tff(247,plain,((~tptp_fun__LE_(f(g(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(g(g(elem!0))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(248,plain,
% 0.58/0.64 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[247, 194, 195])).
% 0.58/0.64 tff(249,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.58/0.64 tff(250,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.58/0.64 tff(251,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.58/0.64 tff(252,plain,
% 0.58/0.64 (^[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'|)))))))))),
% 0.58/0.64 inference(bind,[status(th)],[])).
% 0.58/0.64 tff(253,plain,
% 0.58/0.64 (![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'|))))))))),
% 0.58/0.64 inference(quant_intro,[status(thm)],[252])).
% 0.58/0.64 tff(254,plain,
% 0.58/0.64 (![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'|))))))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(255,plain,
% 0.58/0.65 (^[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'|))))))))))),
% 0.58/0.65 inference(bind,[status(th)],[])).
% 0.58/0.65 tff(256,plain,
% 0.58/0.65 (![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'|))))))))),
% 0.58/0.65 inference(quant_intro,[status(thm)],[255])).
% 0.58/0.65 tff(257,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')).
% 0.58/0.65 tff(258,plain,
% 0.58/0.65 (![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'|))))))))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.58/0.65 tff(259,plain,
% 0.58/0.65 (![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'|))))))))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.58/0.65 tff(260,plain,(
% 0.58/0.65 ![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'|))))))))),
% 0.58/0.65 inference(skolemize,[status(sab)],[259])).
% 0.58/0.65 tff(261,plain,
% 0.58/0.65 (![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'|))))))))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.58/0.65 tff(262,plain,
% 0.58/0.65 (((~![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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), 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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(263,plain,
% 0.61/0.65 (((~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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(264,plain,
% 0.61/0.65 (((~![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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[263])).
% 0.61/0.65 tff(265,plain,
% 0.61/0.65 (((~![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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 0.61/0.65 inference(transitivity,[status(thm)],[264, 262])).
% 0.61/0.65 tff(266,plain,
% 0.61/0.65 ((~![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'|))))))))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(267,plain,
% 0.61/0.65 ((~![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__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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.61/0.65 tff(268,plain,
% 0.61/0.65 (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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[267, 261, 218])).
% 0.61/0.65 tff(269,plain,
% 0.61/0.65 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[268, 251, 249])).
% 0.61/0.65 tff(270,plain,
% 0.61/0.65 (((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(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'|))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(271,plain,
% 0.61/0.65 (((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(272,plain,
% 0.61/0.65 (((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'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(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[271])).
% 0.61/0.65 tff(273,plain,
% 0.61/0.65 (((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'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(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.65 inference(transitivity,[status(thm)],[272, 270])).
% 0.61/0.65 tff(274,plain,
% 0.61/0.65 ((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(275,plain,
% 0.61/0.65 ((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.61/0.65 tff(276,plain,
% 0.61/0.65 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[275, 261, 198])).
% 0.61/0.65 tff(277,plain,
% 0.61/0.65 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[276, 251, 250])).
% 0.61/0.65 tff(278,plain,
% 0.61/0.65 (^[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)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(279,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[278])).
% 0.61/0.65 tff(280,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(281,plain,
% 0.61/0.65 (^[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)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(282,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[281])).
% 0.61/0.65 tff(283,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')).
% 0.61/0.65 tff(284,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.61/0.65 tff(285,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.61/0.65 tff(286,plain,(
% 0.61/0.65 ![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))))),
% 0.61/0.65 inference(skolemize,[status(sab)],[285])).
% 0.61/0.65 tff(287,plain,
% 0.61/0.65 (![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))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[286, 279])).
% 0.61/0.65 tff(288,plain,
% 0.61/0.65 (((~![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(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'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(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(289,plain,
% 0.61/0.65 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(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(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(290,plain,
% 0.61/0.66 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(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(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[289])).
% 0.61/0.66 tff(291,plain,
% 0.61/0.66 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(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(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[290, 288])).
% 0.61/0.66 tff(292,plain,
% 0.61/0.66 ((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(293,plain,
% 0.61/0.66 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.61/0.66 tff(294,plain,
% 0.61/0.66 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[293, 287, 228])).
% 0.61/0.66 tff(295,plain,
% 0.61/0.66 ($false),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[294, 277, 269])).
% 0.61/0.66 tff(296,plain,((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.66 tff(297,plain,
% 0.61/0.66 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[296, 250, 249])).
% 0.61/0.66 tff(298,plain,
% 0.61/0.66 (^[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'|))))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(299,plain,
% 0.61/0.66 (![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'|)))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[298])).
% 0.61/0.66 tff(300,plain,
% 0.61/0.66 (![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'|)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(301,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')).
% 0.61/0.66 tff(302,plain,
% 0.61/0.66 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.61/0.66 tff(303,plain,(
% 0.61/0.66 ![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(skolemize,[status(sab)],[302])).
% 0.61/0.66 tff(304,plain,
% 0.61/0.66 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.61/0.66 tff(305,plain,
% 0.61/0.66 (((~![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'|)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(306,plain,
% 0.61/0.66 ((~![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'|)))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(307,plain,
% 0.61/0.66 ((~![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'|))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.61/0.66 tff(308,plain,
% 0.61/0.66 (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'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[307, 304])).
% 0.61/0.66 tff(309,plain,
% 0.61/0.66 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[308, 297])).
% 0.61/0.66 tff(310,plain,
% 0.61/0.66 ((~![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))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(311,plain,
% 0.61/0.66 (~tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[310, 64])).
% 0.61/0.66 tff(312,plain,
% 0.61/0.66 (^[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)))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(313,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[312])).
% 0.61/0.66 tff(314,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(315,plain,
% 0.61/0.66 (^[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)))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(316,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[315])).
% 0.61/0.66 tff(317,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')).
% 0.61/0.66 tff(318,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.61/0.66 tff(319,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.61/0.66 tff(320,plain,(
% 0.61/0.66 ![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))))),
% 0.61/0.66 inference(skolemize,[status(sab)],[319])).
% 0.61/0.66 tff(321,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.61/0.66 tff(322,plain,
% 0.61/0.66 (((~![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)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(323,plain,
% 0.61/0.66 ((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)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(324,plain,
% 0.61/0.66 (((~![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))))))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[323])).
% 0.61/0.66 tff(325,plain,
% 0.61/0.66 (((~![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)))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[324, 322])).
% 0.61/0.66 tff(326,plain,
% 0.61/0.66 ((~![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))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(327,plain,
% 0.61/0.66 ((~![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))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.61/0.66 tff(328,plain,
% 0.61/0.66 ((~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))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[327, 321, 311])).
% 0.61/0.66 tff(329,plain,
% 0.61/0.66 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[328, 309])).
% 0.61/0.66 tff(330,plain,
% 0.61/0.66 (((~![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'|)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(331,plain,
% 0.61/0.66 ((~![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'|)))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(332,plain,
% 0.61/0.66 ((~![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'|))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.61/0.66 tff(333,plain,
% 0.61/0.66 (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'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[332, 304])).
% 0.61/0.66 tff(334,plain,
% 0.61/0.66 (tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[333, 329])).
% 0.61/0.66 tff(335,plain,
% 0.61/0.66 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(336,plain,
% 0.61/0.66 (iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[335, 17])).
% 0.61/0.66 tff(337,plain,
% 0.61/0.66 (((~![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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), 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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(338,plain,
% 0.61/0.66 (((~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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(339,plain,
% 0.61/0.66 (((~![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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[338])).
% 0.61/0.66 tff(340,plain,
% 0.61/0.66 (((~![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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[339, 337])).
% 0.61/0.66 tff(341,plain,
% 0.61/0.66 ((~![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'|))))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(342,plain,
% 0.61/0.66 ((~![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__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(|'0'|))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.61/0.66 tff(343,plain,
% 0.61/0.66 (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(|'0'|))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[342, 261, 336])).
% 0.61/0.66 tff(344,plain,
% 0.61/0.66 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[343, 334, 249])).
% 0.61/0.66 tff(345,plain,
% 0.61/0.66 (((~![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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(346,plain,
% 0.61/0.66 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(347,plain,
% 0.61/0.66 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[346])).
% 0.61/0.66 tff(348,plain,
% 0.61/0.66 (((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[347, 345])).
% 0.61/0.66 tff(349,plain,
% 0.61/0.66 ((~![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(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(350,plain,
% 0.61/0.66 ((~![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(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.61/0.66 tff(351,plain,
% 0.61/0.66 ((~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(g(g(elem!0)))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[350, 321, 228])).
% 0.61/0.66 tff(352,plain,
% 0.61/0.66 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[351, 309])).
% 0.61/0.66 tff(353,plain,
% 0.61/0.66 (((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(354,plain,
% 0.61/0.66 ((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(355,plain,
% 0.61/0.66 ((~![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(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.61/0.66 tff(356,plain,
% 0.61/0.66 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[355, 304])).
% 0.61/0.66 tff(357,plain,
% 0.61/0.66 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[356, 352])).
% 0.61/0.66 tff(358,plain,
% 0.61/0.66 (((~![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(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'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(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(359,plain,
% 0.61/0.67 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(360,plain,
% 0.61/0.67 (((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'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(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[359])).
% 0.61/0.67 tff(361,plain,
% 0.61/0.67 (((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'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(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.67 inference(transitivity,[status(thm)],[360, 358])).
% 0.61/0.67 tff(362,plain,
% 0.61/0.67 ((~![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(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(363,plain,
% 0.61/0.67 ((~![A_1: $i, B_0: $i] : ((~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.61/0.67 tff(364,plain,
% 0.61/0.67 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[363, 261, 47])).
% 0.61/0.67 tff(365,plain,
% 0.61/0.67 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[364, 357, 250])).
% 0.61/0.67 tff(366,plain,
% 0.61/0.67 ($false),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[294, 365, 344])).
% 0.61/0.67 tff(367,plain,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.67 tff(368,plain,
% 0.61/0.67 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[367, 248])).
% 0.61/0.67 tff(369,plain,
% 0.61/0.67 (((~![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(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'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(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(370,plain,
% 0.61/0.67 ((tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(371,plain,
% 0.61/0.67 (((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(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__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[370])).
% 0.61/0.67 tff(372,plain,
% 0.61/0.67 (((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(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__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(transitivity,[status(thm)],[371, 369])).
% 0.61/0.67 tff(373,plain,
% 0.61/0.67 ((~![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(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(374,plain,
% 0.61/0.67 ((~![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(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.61/0.67 tff(375,plain,
% 0.61/0.67 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[374, 208, 47])).
% 0.61/0.67 tff(376,plain,
% 0.61/0.67 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[375, 368, 195])).
% 0.61/0.67 tff(377,plain,
% 0.61/0.67 (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[245, 376])).
% 0.61/0.67 tff(378,plain,
% 0.61/0.67 (((~![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'|)))))) | 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'|)))) | (~iLEQ(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__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'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(379,plain,
% 0.61/0.67 ((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'|)))))) | 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'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(380,plain,
% 0.61/0.67 (((~![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'|)))))) | 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'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[379])).
% 0.61/0.67 tff(381,plain,
% 0.61/0.67 (((~![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'|)))))) | 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'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 0.61/0.67 inference(transitivity,[status(thm)],[380, 378])).
% 0.61/0.67 tff(382,plain,
% 0.61/0.67 ((~![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'|)))))))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(383,plain,
% 0.61/0.67 ((~![A_4: $i, B_2: $i] : (tptp_fun__E_(s(s(s(|'0'|))), f(B_2)) | (~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(A_4), s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.61/0.67 tff(384,plain,
% 0.61/0.67 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[383, 208, 336])).
% 0.61/0.67 tff(385,plain,
% 0.61/0.67 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[384, 377, 194])).
% 0.61/0.67 tff(386,assumption,(~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))), introduced(assumption)).
% 0.61/0.67 tff(387,plain,
% 0.61/0.67 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[343, 386, 249])).
% 0.61/0.67 tff(388,plain,
% 0.61/0.67 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[333, 387])).
% 0.61/0.67 tff(389,plain,
% 0.61/0.67 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[268, 386, 249])).
% 0.61/0.67 tff(390,plain,
% 0.61/0.67 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[308, 389])).
% 0.61/0.67 tff(391,plain,
% 0.61/0.67 ($false),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[328, 390, 388])).
% 0.61/0.67 tff(392,plain,(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(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.67 tff(393,plain,
% 0.61/0.67 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[392, 248])).
% 0.61/0.67 tff(394,plain,
% 0.61/0.67 (((~![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)))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(395,plain,
% 0.61/0.67 ((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)))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(396,plain,
% 0.61/0.67 (((~![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))))))))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[395])).
% 0.61/0.67 tff(397,plain,
% 0.61/0.67 (((~![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)))))))),
% 0.61/0.67 inference(transitivity,[status(thm)],[396, 394])).
% 0.61/0.67 tff(398,plain,
% 0.61/0.67 ((~![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))))))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(399,plain,
% 0.61/0.67 ((~![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))))))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.61/0.67 tff(400,plain,
% 0.61/0.67 ((~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))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[399, 287, 311])).
% 0.61/0.67 tff(401,plain,
% 0.61/0.67 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[400, 393])).
% 0.61/0.67 tff(402,plain,
% 0.61/0.67 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(g(elem!0), g(g(elem!0)))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(403,plain,
% 0.61/0.67 (iLEQ(g(elem!0), g(g(elem!0)))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[402, 17])).
% 0.61/0.67 tff(404,plain,
% 0.61/0.67 (((~![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'|))))))))) | (~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'|))))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(405,plain,
% 0.61/0.67 ((~![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'|))))))))),
% 0.61/0.67 inference(quant_inst,[status(thm)],[])).
% 0.61/0.67 tff(406,plain,
% 0.61/0.67 ((~![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'|)))))))),
% 0.61/0.67 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.61/0.67 tff(407,plain,
% 0.61/0.67 (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'|)))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[406, 261, 403])).
% 0.61/0.67 tff(408,plain,
% 0.61/0.67 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.61/0.67 inference(unit_resolution,[status(thm)],[407, 401, 385])).
% 0.61/0.67 tff(409,plain,
% 0.61/0.67 (((~![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'|)))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(410,plain,
% 0.61/0.68 ((~![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'|)))))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(411,plain,
% 0.61/0.68 ((~![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'|))))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.61/0.68 tff(412,plain,
% 0.61/0.68 (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'|))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[411, 304])).
% 0.61/0.68 tff(413,plain,
% 0.61/0.68 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[412, 408])).
% 0.61/0.68 tff(414,plain,
% 0.61/0.68 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(elem!0)), g(g(elem!0)))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(415,plain,
% 0.61/0.68 (iLEQ(g(g(elem!0)), g(g(elem!0)))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[414, 45])).
% 0.61/0.68 tff(416,plain,
% 0.61/0.68 (((~![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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(417,plain,
% 0.61/0.68 (((~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'|)))))))) <=> (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)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(418,plain,
% 0.61/0.68 (((~![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'|))))))))) | (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)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[417])).
% 0.61/0.68 tff(419,plain,
% 0.61/0.68 (((~![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'|))))))))) | 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)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[418, 416])).
% 0.61/0.68 tff(420,plain,
% 0.61/0.68 ((~![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'|))))))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(421,plain,
% 0.61/0.68 ((~![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(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.61/0.68 tff(422,plain,
% 0.61/0.68 (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'|)))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[421, 261, 415])).
% 0.61/0.68 tff(423,plain,
% 0.61/0.68 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[422, 401, 385])).
% 0.61/0.68 tff(424,plain,
% 0.61/0.68 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[333, 423])).
% 0.61/0.68 tff(425,plain,
% 0.61/0.68 ((~![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)))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(426,plain,
% 0.61/0.68 (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[425, 64])).
% 0.61/0.68 tff(427,plain,
% 0.61/0.68 (((~![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))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(428,plain,
% 0.61/0.68 ((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))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(429,plain,
% 0.61/0.68 (((~![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)))))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[428])).
% 0.61/0.68 tff(430,plain,
% 0.61/0.68 (((~![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))))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[429, 427])).
% 0.61/0.68 tff(431,plain,
% 0.61/0.68 ((~![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)))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(432,plain,
% 0.61/0.68 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.61/0.68 tff(433,plain,
% 0.61/0.68 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0)))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[432, 321, 426])).
% 0.61/0.68 tff(434,plain,
% 0.61/0.68 ($false),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[433, 424, 413])).
% 0.61/0.68 tff(435,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(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.68 tff(436,plain,
% 0.61/0.68 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[435, 191])).
% 0.61/0.68 tff(437,plain,
% 0.61/0.68 (((~![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(g(elem!0))), g(g(g(g(elem!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'|))) | (~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'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(438,plain,
% 0.61/0.68 ((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'|)))))) <=> ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(439,plain,
% 0.61/0.68 (((~![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'|))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[438])).
% 0.61/0.68 tff(440,plain,
% 0.61/0.68 (((~![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'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[439, 437])).
% 0.61/0.68 tff(441,plain,
% 0.61/0.68 ((~![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'|))))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(442,plain,
% 0.61/0.68 ((~![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(g(elem!0))), g(g(g(g(elem!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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.61/0.68 tff(443,plain,
% 0.61/0.68 (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'|))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|)))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[442, 150, 198])).
% 0.61/0.68 tff(444,plain,
% 0.61/0.68 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[443, 436, 193])).
% 0.61/0.68 tff(445,plain,
% 0.61/0.68 (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[188, 444])).
% 0.61/0.68 tff(446,plain,
% 0.61/0.68 (((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(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'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(447,plain,
% 0.61/0.68 ((tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))) <=> ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(448,plain,
% 0.61/0.68 (((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[447])).
% 0.61/0.68 tff(449,plain,
% 0.61/0.68 (((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[448, 446])).
% 0.61/0.68 tff(450,plain,
% 0.61/0.68 ((~![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(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 0.61/0.68 inference(quant_inst,[status(thm)],[])).
% 0.61/0.68 tff(451,plain,
% 0.61/0.68 ((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.61/0.68 tff(452,plain,
% 0.61/0.68 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[451, 150, 100])).
% 0.61/0.68 tff(453,plain,
% 0.61/0.68 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[452, 445, 192])).
% 0.61/0.68 tff(454,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.61/0.68 tff(455,plain,
% 0.61/0.68 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))),
% 0.61/0.68 inference(unit_resolution,[status(thm)],[375, 454, 195])).
% 0.61/0.68 tff(456,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.61/0.68 tff(457,plain,
% 0.61/0.68 (((~![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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(458,plain,
% 0.61/0.68 ((tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(459,plain,
% 0.61/0.68 (((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(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'|)))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[458])).
% 0.61/0.69 tff(460,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(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'|)))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(transitivity,[status(thm)],[459, 457])).
% 0.61/0.69 tff(461,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(462,plain,
% 0.61/0.69 ((~![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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.61/0.69 tff(463,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[462, 208, 19])).
% 0.61/0.69 tff(464,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[463, 454, 456])).
% 0.61/0.69 tff(465,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(466,plain,
% 0.61/0.69 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(467,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))))))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[466])).
% 0.61/0.69 tff(468,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.69 inference(transitivity,[status(thm)],[467, 465])).
% 0.61/0.69 tff(469,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(470,plain,
% 0.61/0.69 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.61/0.69 tff(471,plain,
% 0.61/0.69 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[470, 238, 66])).
% 0.61/0.69 tff(472,plain,
% 0.61/0.69 ($false),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[471, 464, 455])).
% 0.61/0.69 tff(473,plain,((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.69 tff(474,plain,
% 0.61/0.69 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(|'0'|)))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[473, 453, 191])).
% 0.61/0.69 tff(475,plain,
% 0.61/0.69 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[367, 474])).
% 0.61/0.69 tff(476,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(elem!0))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[215, 475, 191])).
% 0.61/0.69 tff(477,plain,
% 0.61/0.69 (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[471, 476])).
% 0.61/0.69 tff(478,plain,
% 0.61/0.69 (((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))) <=> ((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(479,plain,
% 0.61/0.69 ((tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))) <=> ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(480,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(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'|)))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[479])).
% 0.61/0.69 tff(481,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(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'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(transitivity,[status(thm)],[480, 478])).
% 0.61/0.69 tff(482,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(483,plain,
% 0.61/0.69 ((~![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(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.61/0.69 tff(484,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[483, 208, 100])).
% 0.61/0.69 tff(485,plain,
% 0.61/0.69 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[484, 477, 453])).
% 0.61/0.69 tff(486,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.61/0.69 tff(487,assumption,(~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 0.61/0.69 tff(488,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_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(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(489,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(490,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.61/0.69 tff(491,plain,
% 0.61/0.69 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[490, 261, 100])).
% 0.61/0.69 tff(492,plain,
% 0.61/0.69 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[491, 487, 486])).
% 0.61/0.69 tff(493,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(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(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(494,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(495,plain,
% 0.61/0.69 ((~![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(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.61/0.69 tff(496,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[495, 304])).
% 0.61/0.69 tff(497,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[496, 492])).
% 0.61/0.69 tff(498,plain,
% 0.61/0.69 (((~![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(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(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(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(499,plain,
% 0.61/0.69 ((~![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(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(500,plain,
% 0.61/0.69 ((~![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(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.61/0.69 tff(501,plain,
% 0.61/0.69 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|)))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[500, 261, 19])).
% 0.61/0.69 tff(502,plain,
% 0.61/0.69 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[501, 487, 486])).
% 0.61/0.69 tff(503,plain,
% 0.61/0.69 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[356, 502])).
% 0.61/0.69 tff(504,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(505,plain,
% 0.61/0.69 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(506,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))))))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[505])).
% 0.61/0.69 tff(507,plain,
% 0.61/0.69 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.70 inference(transitivity,[status(thm)],[506, 504])).
% 0.61/0.70 tff(508,plain,
% 0.61/0.70 ((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(509,plain,
% 0.61/0.70 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.61/0.70 tff(510,plain,
% 0.61/0.70 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[509, 321])).
% 0.61/0.70 tff(511,plain,
% 0.61/0.70 ($false),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[510, 503, 497, 66])).
% 0.61/0.70 tff(512,plain,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.70 tff(513,plain,
% 0.61/0.70 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[512, 485])).
% 0.61/0.70 tff(514,plain,
% 0.61/0.70 (((~![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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(515,plain,
% 0.61/0.70 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(516,plain,
% 0.61/0.70 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[515])).
% 0.61/0.70 tff(517,plain,
% 0.61/0.70 (((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(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(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))),
% 0.61/0.70 inference(transitivity,[status(thm)],[516, 514])).
% 0.61/0.70 tff(518,plain,
% 0.61/0.70 ((~![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(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(519,plain,
% 0.61/0.70 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.61/0.70 tff(520,plain,
% 0.61/0.70 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[519, 287, 66])).
% 0.61/0.70 tff(521,plain,
% 0.61/0.70 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(elem!0))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[520, 513])).
% 0.61/0.70 tff(522,plain,
% 0.61/0.70 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[276, 521, 474])).
% 0.61/0.70 tff(523,plain,
% 0.61/0.70 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(elem!0)))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[308, 522])).
% 0.61/0.70 tff(524,plain,
% 0.61/0.70 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[364, 521, 474])).
% 0.61/0.70 tff(525,plain,
% 0.61/0.70 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(elem!0))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[356, 524])).
% 0.61/0.70 tff(526,plain,
% 0.61/0.70 ($false),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[351, 525, 523])).
% 0.61/0.70 tff(527,plain,(tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.70 tff(528,plain,
% 0.61/0.70 (^[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)))))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(529,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[528])).
% 0.61/0.70 tff(530,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(531,plain,
% 0.61/0.70 (^[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)))))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(532,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[531])).
% 0.61/0.70 tff(533,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')).
% 0.61/0.70 tff(534,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.61/0.70 tff(535,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[534, 530])).
% 0.61/0.70 tff(536,plain,(
% 0.61/0.70 ![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))))),
% 0.61/0.70 inference(skolemize,[status(sab)],[535])).
% 0.61/0.70 tff(537,plain,
% 0.61/0.70 (![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))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[536, 529])).
% 0.61/0.70 tff(538,plain,
% 0.61/0.70 (((~![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_(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)))))))))) <=> ((~![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_(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)))))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(539,plain,
% 0.61/0.70 ((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_(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)))))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(540,plain,
% 0.61/0.70 (((~![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_(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))))))))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[539])).
% 0.61/0.70 tff(541,plain,
% 0.61/0.70 (((~![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_(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)))))))))),
% 0.61/0.70 inference(transitivity,[status(thm)],[540, 538])).
% 0.61/0.70 tff(542,plain,
% 0.61/0.70 ((~![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))))))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(543,plain,
% 0.61/0.70 ((~![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_(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))))))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.61/0.70 tff(544,plain,
% 0.61/0.70 ((~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))))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[543, 537, 66])).
% 0.61/0.70 tff(545,plain,
% 0.61/0.70 (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(elem!0))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[544, 527])).
% 0.61/0.70 tff(546,plain,
% 0.61/0.70 (((~![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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), 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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(547,plain,
% 0.61/0.70 (((~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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(548,plain,
% 0.61/0.70 (((~![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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[547])).
% 0.61/0.70 tff(549,plain,
% 0.61/0.70 (((~![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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)))),
% 0.61/0.70 inference(transitivity,[status(thm)],[548, 546])).
% 0.61/0.70 tff(550,plain,
% 0.61/0.70 ((~![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'|)))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(551,plain,
% 0.61/0.70 ((~![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__E_(s(|'0'|), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.61/0.70 tff(552,plain,
% 0.61/0.70 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(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(|'0'|))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[551, 132, 198])).
% 0.61/0.70 tff(553,plain,
% 0.61/0.70 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[552, 545])).
% 0.61/0.70 tff(554,plain,
% 0.61/0.70 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[553, 85])).
% 0.61/0.70 tff(555,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.61/0.70 tff(556,plain,
% 0.61/0.70 (((~![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(|'0'|))) | tptp_fun__E_(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'|))))))) <=> ((~![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(|'0'|))) | tptp_fun__E_(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'|))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(557,plain,
% 0.61/0.70 ((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__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | tptp_fun__E_(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'|))))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(558,plain,
% 0.61/0.70 (((~![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__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | tptp_fun__E_(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'|)))))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[557])).
% 0.61/0.70 tff(559,plain,
% 0.61/0.70 (((~![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__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | tptp_fun__E_(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'|))))))),
% 0.61/0.70 inference(transitivity,[status(thm)],[558, 556])).
% 0.61/0.70 tff(560,plain,
% 0.61/0.70 ((~![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'|))))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(561,plain,
% 0.61/0.70 ((~![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(|'0'|))) | tptp_fun__E_(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'|)))))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.61/0.70 tff(562,plain,
% 0.61/0.70 (tptp_fun__LE_(f(g(g(g(elem!0)))), 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(s(|'0'|)))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[561, 150, 218])).
% 0.61/0.70 tff(563,plain,
% 0.61/0.70 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[562, 555, 554])).
% 0.61/0.70 tff(564,plain,
% 0.61/0.70 (((~![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__E_(s(|'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)))))) | (~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__E_(s(|'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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(565,plain,
% 0.61/0.70 (((~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__E_(s(|'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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(566,plain,
% 0.61/0.70 (((~![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__E_(s(|'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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[565])).
% 0.61/0.70 tff(567,plain,
% 0.61/0.70 (((~![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__E_(s(|'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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))))),
% 0.61/0.70 inference(transitivity,[status(thm)],[566, 564])).
% 0.61/0.70 tff(568,plain,
% 0.61/0.70 ((~![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'|)))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(569,plain,
% 0.61/0.71 ((~![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__E_(s(|'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)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.61/0.71 tff(570,plain,
% 0.61/0.71 (tptp_fun__E_(s(|'0'|), f(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(s(|'0'|))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[569, 132, 47])).
% 0.61/0.71 tff(571,plain,
% 0.61/0.71 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[570, 545])).
% 0.61/0.71 tff(572,plain,
% 0.61/0.71 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(|'0'|)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[571, 85])).
% 0.61/0.71 tff(573,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[443, 555, 572])).
% 0.61/0.71 tff(574,plain,
% 0.61/0.71 (((~![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_(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))))))))) <=> ((~![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_(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))))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(575,plain,
% 0.61/0.71 ((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_(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))))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(576,plain,
% 0.61/0.71 (((~![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_(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)))))))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[575])).
% 0.61/0.71 tff(577,plain,
% 0.61/0.71 (((~![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_(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))))))))),
% 0.61/0.71 inference(transitivity,[status(thm)],[576, 574])).
% 0.61/0.71 tff(578,plain,
% 0.61/0.71 ((~![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)))))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(579,plain,
% 0.61/0.71 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_11)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_11))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.61/0.71 tff(580,plain,
% 0.61/0.71 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0)))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[579, 181, 228])).
% 0.61/0.71 tff(581,plain,
% 0.61/0.71 ($false),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[580, 573, 563])).
% 0.61/0.71 tff(582,plain,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.71 tff(583,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.61/0.71 tff(584,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[384, 583, 582])).
% 0.61/0.71 tff(585,plain,
% 0.61/0.71 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(|'0'|))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[435, 582])).
% 0.61/0.71 tff(586,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(elem!0))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[154, 585, 572])).
% 0.61/0.71 tff(587,plain,
% 0.61/0.71 (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0)))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[580, 586])).
% 0.61/0.71 tff(588,plain,
% 0.61/0.71 (((~![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(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(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(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(589,plain,
% 0.61/0.71 ((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(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(590,plain,
% 0.61/0.71 (((~![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(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[589])).
% 0.61/0.71 tff(591,plain,
% 0.61/0.71 (((~![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(g(elem!0)))), s(s(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))))),
% 0.61/0.71 inference(transitivity,[status(thm)],[590, 588])).
% 0.61/0.71 tff(592,plain,
% 0.61/0.71 ((~![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'|))))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(593,plain,
% 0.61/0.71 ((~![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(|'0'|))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.61/0.71 tff(594,plain,
% 0.61/0.71 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|)))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[593, 150, 336])).
% 0.61/0.71 tff(595,plain,
% 0.61/0.71 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(|'0'|))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[594, 587, 554])).
% 0.61/0.71 tff(596,plain,
% 0.61/0.71 (((~![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)))) | 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)))))) <=> ((~![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)))) | 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)))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(597,plain,
% 0.61/0.71 ((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'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(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)))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(598,plain,
% 0.61/0.71 (((~![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'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(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))))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[597])).
% 0.61/0.71 tff(599,plain,
% 0.61/0.71 (((~![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'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(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)))))),
% 0.61/0.71 inference(transitivity,[status(thm)],[598, 596])).
% 0.61/0.71 tff(600,plain,
% 0.61/0.71 ((~![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'|)))))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(601,plain,
% 0.61/0.71 ((~![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)))) | 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))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.61/0.71 tff(602,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(s(|'0'|))), f(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'|))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[601, 208, 415])).
% 0.61/0.71 tff(603,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[602, 583, 595])).
% 0.61/0.71 tff(604,plain,
% 0.61/0.71 (((~![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_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'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_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(605,plain,
% 0.61/0.71 ((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_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(606,plain,
% 0.61/0.71 (((~![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_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[605])).
% 0.61/0.71 tff(607,plain,
% 0.61/0.71 (((~![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_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))))),
% 0.61/0.71 inference(transitivity,[status(thm)],[606, 604])).
% 0.61/0.71 tff(608,plain,
% 0.61/0.71 ((~![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))))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(609,plain,
% 0.61/0.71 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_8))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.61/0.71 tff(610,plain,
% 0.61/0.71 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[609, 238, 311])).
% 0.61/0.71 tff(611,plain,
% 0.61/0.71 ($false),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[610, 603, 584])).
% 0.61/0.71 tff(612,plain,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.71 tff(613,assumption,(~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))), introduced(assumption)).
% 0.61/0.71 tff(614,plain,
% 0.61/0.71 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[407, 613, 612])).
% 0.61/0.71 tff(615,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[412, 614])).
% 0.61/0.71 tff(616,plain,
% 0.61/0.71 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(|'0'|))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[422, 613, 612])).
% 0.61/0.71 tff(617,plain,
% 0.61/0.71 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(elem!0))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[333, 616])).
% 0.61/0.71 tff(618,plain,
% 0.61/0.71 ($false),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[433, 617, 615])).
% 0.61/0.71 tff(619,plain,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.71 tff(620,plain,
% 0.61/0.71 (((~![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))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(621,plain,
% 0.61/0.71 ((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))))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(622,plain,
% 0.61/0.71 (((~![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)))))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[621])).
% 0.61/0.71 tff(623,plain,
% 0.61/0.71 (((~![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))))))),
% 0.61/0.71 inference(transitivity,[status(thm)],[622, 620])).
% 0.61/0.71 tff(624,plain,
% 0.61/0.71 ((~![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)))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.72 tff(625,plain,
% 0.61/0.72 ((~![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)))))),
% 0.61/0.72 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.61/0.72 tff(626,plain,
% 0.61/0.72 ((~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)))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[625, 287, 426])).
% 0.61/0.72 tff(627,plain,
% 0.61/0.72 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(elem!0)))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[626, 619])).
% 0.61/0.72 tff(628,plain,
% 0.61/0.72 (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(elem!0)))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[400, 619])).
% 0.61/0.72 tff(629,plain,
% 0.61/0.72 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(|'0'|)))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[392, 628])).
% 0.61/0.72 tff(630,plain,
% 0.61/0.72 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(elem!0)))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[225, 629, 582])).
% 0.61/0.72 tff(631,plain,
% 0.61/0.72 (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(elem!0))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[610, 630])).
% 0.61/0.72 tff(632,plain,
% 0.61/0.72 (((~![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(elem!0), g(g(elem!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'|)))) | (~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'|)))))))) | (~iLEQ(g(elem!0), g(g(elem!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'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(633,plain,
% 0.61/0.72 ((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'|))))))) <=> ((~iLEQ(g(elem!0), g(g(elem!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'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(634,plain,
% 0.61/0.72 (((~![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'|)))))))) | ((~iLEQ(g(elem!0), g(g(elem!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'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))))))),
% 0.61/0.72 inference(monotonicity,[status(thm)],[633])).
% 0.61/0.72 tff(635,plain,
% 0.61/0.72 (((~![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'|)))))))) | (~iLEQ(g(elem!0), g(g(elem!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'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))))),
% 0.61/0.72 inference(transitivity,[status(thm)],[634, 632])).
% 0.61/0.72 tff(636,plain,
% 0.61/0.72 ((~![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'|)))))))),
% 0.61/0.72 inference(quant_inst,[status(thm)],[])).
% 0.61/0.72 tff(637,plain,
% 0.61/0.72 ((~![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(elem!0), g(g(elem!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'|)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|))))))),
% 0.61/0.72 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.61/0.72 tff(638,plain,
% 0.61/0.72 (tptp_fun__E_(s(s(s(|'0'|))), f(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'|))))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[637, 208, 403])).
% 0.61/0.72 tff(639,plain,
% 0.61/0.72 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(|'0'|)))))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[638, 631, 595])).
% 0.61/0.72 tff(640,plain,
% 0.61/0.72 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(elem!0), g(elem!0))),
% 0.61/0.72 inference(quant_inst,[status(thm)],[])).
% 0.61/0.72 tff(641,plain,
% 0.61/0.72 (iLEQ(g(elem!0), g(elem!0))),
% 0.61/0.72 inference(unit_resolution,[status(thm)],[640, 45])).
% 0.61/0.72 tff(642,plain,
% 0.61/0.72 (((~![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))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(elem!0), 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(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'|))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(643,plain,
% 0.61/0.72 (((~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))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(644,plain,
% 0.61/0.72 (((~![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))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(elem!0), g(elem!0)))))),
% 0.61/0.72 inference(monotonicity,[status(thm)],[643])).
% 0.61/0.72 tff(645,plain,
% 0.61/0.72 (((~![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))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 0.68/0.72 inference(transitivity,[status(thm)],[644, 642])).
% 0.68/0.72 tff(646,plain,
% 0.68/0.72 ((~![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'|))))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(647,plain,
% 0.68/0.72 ((~![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))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(elem!0), g(elem!0)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.68/0.72 tff(648,plain,
% 0.68/0.72 (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'|)))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[647, 261, 641])).
% 0.68/0.72 tff(649,plain,
% 0.68/0.72 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[648, 639, 627])).
% 0.68/0.72 tff(650,plain,
% 0.68/0.72 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[412, 649])).
% 0.68/0.72 tff(651,plain,
% 0.68/0.72 ((~![A_2: $i] : iLEQ(A_2, g(A_2))) | iLEQ(elem!0, g(elem!0))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(652,plain,
% 0.68/0.72 (iLEQ(elem!0, g(elem!0))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[651, 17])).
% 0.68/0.72 tff(653,plain,
% 0.68/0.72 (((~![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'|))))))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(654,plain,
% 0.68/0.72 ((~![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'|))))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(655,plain,
% 0.68/0.72 ((~![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'|)))))))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.68/0.72 tff(656,plain,
% 0.68/0.72 (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'|)))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[655, 261, 652])).
% 0.68/0.72 tff(657,plain,
% 0.68/0.72 (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[656, 639, 627])).
% 0.68/0.72 tff(658,plain,
% 0.68/0.72 (((~![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'|)))))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(659,plain,
% 0.68/0.72 ((~![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'|)))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(660,plain,
% 0.68/0.72 ((~![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'|))))))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.68/0.72 tff(661,plain,
% 0.68/0.72 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[660, 304])).
% 0.68/0.72 tff(662,plain,
% 0.68/0.72 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[661, 657])).
% 0.68/0.72 tff(663,plain,
% 0.68/0.72 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(elem!0), f(g(elem!0))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(664,plain,
% 0.68/0.72 (~tptp_fun__E_(f(elem!0), f(g(elem!0)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[663, 64])).
% 0.68/0.72 tff(665,plain,
% 0.68/0.72 (((~![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))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(666,plain,
% 0.68/0.72 ((~![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))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(667,plain,
% 0.68/0.72 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.68/0.72 tff(668,plain,
% 0.68/0.72 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(elem!0)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[667, 321, 664])).
% 0.68/0.72 tff(669,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[668, 662, 650])).
% 0.68/0.72 % SZS output end Proof
%------------------------------------------------------------------------------