TSTP Solution File: SYO633-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO633-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 01:41:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO633-1 : TPTP v8.1.0. Released v7.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 15:37:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(tptp_fun__E__type, type, (
% 0.19/0.41 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun__0__type, type, (
% 0.19/0.41 tptp_fun__0_: $i)).
% 0.19/0.41 tff(f_type, type, (
% 0.19/0.41 f: $i > $i)).
% 0.19/0.41 tff(tptp_fun__AP__type, type, (
% 0.19/0.41 tptp_fun__AP_: ( $i * $i ) > $i)).
% 0.19/0.41 tff(elem_0_type, type, (
% 0.19/0.41 elem_0: $i)).
% 0.19/0.41 tff(s_type, type, (
% 0.19/0.41 s: $i > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[B: $i] : refl(tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8_05')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (^[B_0: $i] : refl(tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6_04')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,(
% 0.19/0.41 ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (^[B_0: $i, A_0: $i] : rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.41 tff(24,axiom,(![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1_10')).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.41 tff(27,plain,(
% 0.19/0.41 ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))) <=> ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 28, 18, 9])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (^[A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (^[A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.41 tff(38,axiom,(![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4_12')).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.42 tff(41,plain,(
% 0.19/0.42 ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[40])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[45, 42, 18, 9, 32])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (^[A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (^[A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.42 tff(52,axiom,(![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_12_09')).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.42 tff(55,plain,(
% 0.19/0.42 ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[62, 56, 18, 9, 32, 46])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (^[A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (^[A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.43 tff(69,axiom,(![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2_07')).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.44 tff(72,plain,(
% 0.19/0.44 ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[71])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))) <=> ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[76, 73, 18, 9, 32, 63, 46])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (^[A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (^[A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_4), |'0'|))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.44 tff(83,axiom,(![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5_03')).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.45 tff(86,plain,(
% 0.19/0.45 ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[85])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(90,plain,
% 0.19/0.45 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.45 tff(91,plain,
% 0.19/0.45 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.45 tff(92,plain,
% 0.19/0.45 ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(93,plain,
% 0.19/0.45 ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.45 tff(94,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[93, 87, 18, 9, 32, 63, 46, 77])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------