TSTP Solution File: SYO614-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO614-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 01:41:04 EDT 2022
% Result : Unsatisfiable 2.30s 1.64s
% Output : Proof 2.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO614-1 : TPTP v8.1.0. Released v7.1.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n015.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Sep 5 15:33:42 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 2.30/1.64 % SZS status Unsatisfiable
% 2.30/1.64 % SZS output start Proof
% 2.30/1.64 tff(eq_type, type, (
% 2.30/1.64 eq: ( $i * $i ) > $o)).
% 2.30/1.64 tff(a1_type, type, (
% 2.30/1.64 a1: $i)).
% 2.30/1.64 tff(f_type, type, (
% 2.30/1.64 f: $i > $i)).
% 2.30/1.64 tff(max_type, type, (
% 2.30/1.64 max: ( $i * $i ) > $i)).
% 2.30/1.64 tff(s_type, type, (
% 2.30/1.64 s: $i > $i)).
% 2.30/1.64 tff(elem_0_type, type, (
% 2.30/1.64 elem_0: $i)).
% 2.30/1.64 tff(a0_type, type, (
% 2.30/1.64 a0: $i)).
% 2.30/1.64 tff(le_type, type, (
% 2.30/1.64 le: ( $i * $i ) > $o)).
% 2.30/1.64 tff(1,assumption,(eq(f(elem!0), a1)), introduced(assumption)).
% 2.30/1.64 tff(2,plain,
% 2.30/1.64 (^[A: $i] : refl(le(A, A) <=> le(A, A))),
% 2.30/1.64 inference(bind,[status(th)],[])).
% 2.30/1.64 tff(3,plain,
% 2.30/1.64 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 2.30/1.64 inference(quant_intro,[status(thm)],[2])).
% 2.30/1.64 tff(4,plain,
% 2.30/1.64 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 2.30/1.64 inference(rewrite,[status(thm)],[])).
% 2.30/1.64 tff(5,axiom,(![A: $i] : le(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_01')).
% 2.30/1.64 tff(6,plain,
% 2.30/1.64 (![A: $i] : le(A, A)),
% 2.30/1.64 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.30/1.64 tff(7,plain,(
% 2.30/1.64 ![A: $i] : le(A, A)),
% 2.30/1.64 inference(skolemize,[status(sab)],[6])).
% 2.30/1.64 tff(8,plain,
% 2.30/1.64 (![A: $i] : le(A, A)),
% 2.30/1.64 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.30/1.64 tff(9,plain,
% 2.30/1.64 ((~![A: $i] : le(A, A)) | le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.64 inference(quant_inst,[status(thm)],[])).
% 2.30/1.64 tff(10,plain,
% 2.30/1.64 (le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.64 inference(unit_resolution,[status(thm)],[9, 8])).
% 2.30/1.64 tff(11,plain,
% 2.30/1.64 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(A, C)) <=> ((~le(max(A, B), C)) | le(A, C)))),
% 2.30/1.64 inference(bind,[status(th)],[])).
% 2.30/1.64 tff(12,plain,
% 2.30/1.64 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 2.30/1.64 inference(quant_intro,[status(thm)],[11])).
% 2.30/1.64 tff(13,plain,
% 2.30/1.64 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 2.30/1.64 inference(rewrite,[status(thm)],[])).
% 2.30/1.64 tff(14,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_02')).
% 2.30/1.64 tff(15,plain,
% 2.30/1.64 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 2.30/1.64 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.30/1.64 tff(16,plain,(
% 2.30/1.64 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 2.30/1.64 inference(skolemize,[status(sab)],[15])).
% 2.30/1.64 tff(17,plain,
% 2.30/1.64 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 2.30/1.64 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.30/1.64 tff(18,plain,
% 2.30/1.64 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.64 inference(rewrite,[status(thm)],[])).
% 2.30/1.64 tff(19,plain,
% 2.30/1.64 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.65 inference(quant_inst,[status(thm)],[])).
% 2.30/1.65 tff(20,plain,
% 2.30/1.65 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.30/1.65 tff(21,plain,
% 2.30/1.65 (le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 2.30/1.65 tff(22,plain,
% 2.30/1.65 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(B, C)) <=> ((~le(max(A, B), C)) | le(B, C)))),
% 2.30/1.65 inference(bind,[status(th)],[])).
% 2.30/1.65 tff(23,plain,
% 2.30/1.65 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 2.30/1.65 inference(quant_intro,[status(thm)],[22])).
% 2.30/1.65 tff(24,plain,
% 2.30/1.65 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 2.30/1.65 inference(rewrite,[status(thm)],[])).
% 2.30/1.65 tff(25,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_03')).
% 2.30/1.65 tff(26,plain,
% 2.30/1.65 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 2.30/1.65 inference(modus_ponens,[status(thm)],[25, 24])).
% 2.30/1.65 tff(27,plain,(
% 2.30/1.65 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 2.30/1.65 inference(skolemize,[status(sab)],[26])).
% 2.30/1.65 tff(28,plain,
% 2.30/1.65 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 2.30/1.65 inference(modus_ponens,[status(thm)],[27, 23])).
% 2.30/1.65 tff(29,plain,
% 2.30/1.65 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.65 inference(rewrite,[status(thm)],[])).
% 2.30/1.65 tff(30,plain,
% 2.30/1.65 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.65 inference(quant_inst,[status(thm)],[])).
% 2.30/1.65 tff(31,plain,
% 2.30/1.65 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.30/1.65 tff(32,plain,
% 2.30/1.65 (le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(unit_resolution,[status(thm)],[31, 28, 21])).
% 2.30/1.65 tff(33,plain,
% 2.30/1.65 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.65 inference(rewrite,[status(thm)],[])).
% 2.30/1.65 tff(34,plain,
% 2.30/1.65 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.65 inference(quant_inst,[status(thm)],[])).
% 2.30/1.65 tff(35,plain,
% 2.30/1.65 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(s(elem!0), s(elem!0)), s(elem!0)), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.30/1.65 tff(36,plain,
% 2.30/1.65 (le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.65 inference(unit_resolution,[status(thm)],[35, 28, 32])).
% 2.30/1.65 tff(37,plain,
% 2.30/1.65 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))))),
% 2.30/1.65 inference(bind,[status(th)],[])).
% 2.30/1.65 tff(38,plain,
% 2.30/1.65 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.65 inference(quant_intro,[status(thm)],[37])).
% 2.30/1.65 tff(39,plain,
% 2.30/1.65 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.65 inference(rewrite,[status(thm)],[])).
% 2.30/1.65 tff(40,plain,
% 2.30/1.65 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a1)) | (~eq(f(A1), a1))) <=> ((~eq(f(A1), a1)) | (~eq(f(A0), a1)))), ((((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a1)) | (~eq(f(A0), a1))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a1)) | (~eq(f(A0), a1))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))), ((((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))))),
% 2.30/1.65 inference(bind,[status(th)],[])).
% 2.30/1.65 tff(41,plain,
% 2.30/1.65 (![A0: $i, A1: $i] : (((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.65 inference(quant_intro,[status(thm)],[40])).
% 2.30/1.65 tff(42,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_06')).
% 2.30/1.65 tff(43,plain,
% 2.30/1.65 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[42, 41])).
% 2.30/1.66 tff(44,plain,
% 2.30/1.66 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[43, 39])).
% 2.30/1.66 tff(45,plain,(
% 2.30/1.66 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.66 inference(skolemize,[status(sab)],[44])).
% 2.30/1.66 tff(46,plain,
% 2.30/1.66 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[45, 38])).
% 2.30/1.66 tff(47,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(48,plain,
% 2.30/1.66 (((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(49,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))))),
% 2.30/1.66 inference(monotonicity,[status(thm)],[48])).
% 2.30/1.66 tff(50,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)))),
% 2.30/1.66 inference(transitivity,[status(thm)],[49, 47])).
% 2.30/1.66 tff(51,plain,
% 2.30/1.66 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(52,plain,
% 2.30/1.66 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.30/1.66 tff(53,plain,
% 2.30/1.66 ((~eq(f(elem!0), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[52, 46, 36])).
% 2.30/1.66 tff(54,plain,
% 2.30/1.66 (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[53, 1])).
% 2.30/1.66 tff(55,plain,
% 2.30/1.66 ((~![A: $i] : le(A, A)) | le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(56,plain,
% 2.30/1.66 (le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[55, 8])).
% 2.30/1.66 tff(57,plain,
% 2.30/1.66 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))) | le(s(elem!0), max(s(elem!0), s(elem!0))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))) | le(s(elem!0), max(s(elem!0), s(elem!0))))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(58,plain,
% 2.30/1.66 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))) | le(s(elem!0), max(s(elem!0), s(elem!0))))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(59,plain,
% 2.30/1.66 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), s(elem!0)), max(s(elem!0), s(elem!0)))) | le(s(elem!0), max(s(elem!0), s(elem!0)))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[58, 57])).
% 2.30/1.66 tff(60,plain,
% 2.30/1.66 (le(s(elem!0), max(s(elem!0), s(elem!0)))),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[59, 17, 56])).
% 2.30/1.66 tff(61,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(62,plain,
% 2.30/1.66 (((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(63,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0))))))),
% 2.30/1.66 inference(monotonicity,[status(thm)],[62])).
% 2.30/1.66 tff(64,plain,
% 2.30/1.66 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))))),
% 2.30/1.66 inference(transitivity,[status(thm)],[63, 61])).
% 2.30/1.66 tff(65,plain,
% 2.30/1.66 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(elem!0), a1)))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(66,plain,
% 2.30/1.66 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~le(s(elem!0), max(s(elem!0), s(elem!0))))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.30/1.66 tff(67,plain,
% 2.30/1.66 ((~eq(f(elem!0), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1))),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[66, 46, 60])).
% 2.30/1.66 tff(68,plain,
% 2.30/1.66 (~eq(f(max(s(elem!0), s(elem!0))), a1)),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[67, 1])).
% 2.30/1.66 tff(69,plain,
% 2.30/1.66 (^[A: $i] : refl((eq(f(A), a0) | eq(f(A), a1)) <=> (eq(f(A), a0) | eq(f(A), a1)))),
% 2.30/1.66 inference(bind,[status(th)],[])).
% 2.30/1.66 tff(70,plain,
% 2.30/1.66 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1)) <=> ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 2.30/1.66 inference(quant_intro,[status(thm)],[69])).
% 2.30/1.66 tff(71,plain,
% 2.30/1.66 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1)) <=> ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(72,axiom,(![A: $i] : (eq(f(A), a0) | eq(f(A), a1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_04')).
% 2.30/1.66 tff(73,plain,
% 2.30/1.66 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[72, 71])).
% 2.30/1.66 tff(74,plain,(
% 2.30/1.66 ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 2.30/1.66 inference(skolemize,[status(sab)],[73])).
% 2.30/1.66 tff(75,plain,
% 2.30/1.66 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[74, 70])).
% 2.30/1.66 tff(76,plain,
% 2.30/1.66 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(s(elem!0), s(elem!0))), a0) | eq(f(max(s(elem!0), s(elem!0))), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(s(elem!0), s(elem!0))), a0) | eq(f(max(s(elem!0), s(elem!0))), a1))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(77,plain,
% 2.30/1.66 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(s(elem!0), s(elem!0))), a0) | eq(f(max(s(elem!0), s(elem!0))), a1))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(78,plain,
% 2.30/1.66 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(s(elem!0), s(elem!0))), a0) | eq(f(max(s(elem!0), s(elem!0))), a1)),
% 2.30/1.66 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.30/1.66 tff(79,plain,
% 2.30/1.66 (eq(f(max(s(elem!0), s(elem!0))), a0) | eq(f(max(s(elem!0), s(elem!0))), a1)),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[78, 75])).
% 2.30/1.66 tff(80,plain,
% 2.30/1.66 (eq(f(max(s(elem!0), s(elem!0))), a0)),
% 2.30/1.66 inference(unit_resolution,[status(thm)],[79, 68])).
% 2.30/1.66 tff(81,plain,
% 2.30/1.66 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.66 inference(rewrite,[status(thm)],[])).
% 2.30/1.66 tff(82,plain,
% 2.30/1.66 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.66 inference(quant_inst,[status(thm)],[])).
% 2.30/1.66 tff(83,plain,
% 2.30/1.66 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.67 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.30/1.67 tff(84,plain,
% 2.30/1.67 (le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))),
% 2.30/1.67 inference(unit_resolution,[status(thm)],[83, 28, 10])).
% 2.30/1.67 tff(85,plain,
% 2.30/1.67 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))))),
% 2.30/1.67 inference(bind,[status(th)],[])).
% 2.30/1.67 tff(86,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(quant_intro,[status(thm)],[85])).
% 2.30/1.67 tff(87,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(rewrite,[status(thm)],[])).
% 2.30/1.67 tff(88,plain,
% 2.30/1.67 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a0)) | (~eq(f(A1), a0))) <=> ((~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))))),
% 2.30/1.67 inference(bind,[status(th)],[])).
% 2.30/1.67 tff(89,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(quant_intro,[status(thm)],[88])).
% 2.30/1.67 tff(90,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_05')).
% 2.30/1.67 tff(91,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.30/1.67 tff(92,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(modus_ponens,[status(thm)],[91, 87])).
% 2.30/1.67 tff(93,plain,(
% 2.30/1.67 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(skolemize,[status(sab)],[92])).
% 2.30/1.67 tff(94,plain,
% 2.30/1.67 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 2.30/1.67 inference(modus_ponens,[status(thm)],[93, 86])).
% 2.30/1.67 tff(95,plain,
% 2.30/1.67 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.67 inference(rewrite,[status(thm)],[])).
% 2.30/1.67 tff(96,plain,
% 2.30/1.67 (((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(elem!0), s(elem!0))), a0))) <=> ((~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.67 inference(rewrite,[status(thm)],[])).
% 2.30/1.67 tff(97,plain,
% 2.30/1.67 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))))),
% 2.30/1.67 inference(monotonicity,[status(thm)],[96])).
% 2.30/1.67 tff(98,plain,
% 2.30/1.67 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.67 inference(transitivity,[status(thm)],[97, 95])).
% 2.30/1.67 tff(99,plain,
% 2.30/1.67 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))),
% 2.30/1.67 inference(quant_inst,[status(thm)],[])).
% 2.30/1.67 tff(100,plain,
% 2.30/1.67 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.67 inference(modus_ponens,[status(thm)],[99, 98])).
% 2.30/1.67 tff(101,plain,
% 2.30/1.67 ((~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0))),
% 2.30/1.67 inference(unit_resolution,[status(thm)],[100, 94, 84])).
% 2.30/1.67 tff(102,plain,
% 2.30/1.67 (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)),
% 2.30/1.67 inference(unit_resolution,[status(thm)],[101, 80])).
% 2.30/1.67 tff(103,plain,
% 2.30/1.67 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(104,plain,
% 2.30/1.68 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))),
% 2.30/1.68 inference(quant_inst,[status(thm)],[])).
% 2.30/1.68 tff(105,plain,
% 2.30/1.68 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0) | eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)),
% 2.30/1.68 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.30/1.68 tff(106,plain,
% 2.30/1.68 ($false),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[105, 75, 102, 54])).
% 2.30/1.68 tff(107,plain,(~eq(f(elem!0), a1)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.68 tff(108,plain,
% 2.30/1.68 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(elem!0), a0) | eq(f(elem!0), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(elem!0), a0) | eq(f(elem!0), a1))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(109,plain,
% 2.30/1.68 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(elem!0), a0) | eq(f(elem!0), a1))),
% 2.30/1.68 inference(quant_inst,[status(thm)],[])).
% 2.30/1.68 tff(110,plain,
% 2.30/1.68 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(elem!0), a0) | eq(f(elem!0), a1)),
% 2.30/1.68 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.30/1.68 tff(111,plain,
% 2.30/1.68 (eq(f(elem!0), a0) | eq(f(elem!0), a1)),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[110, 75])).
% 2.30/1.68 tff(112,plain,
% 2.30/1.68 (eq(f(elem!0), a0)),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[111, 107])).
% 2.30/1.68 tff(113,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(114,plain,
% 2.30/1.68 (((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(115,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0))))),
% 2.30/1.68 inference(monotonicity,[status(thm)],[114])).
% 2.30/1.68 tff(116,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)))),
% 2.30/1.68 inference(transitivity,[status(thm)],[115, 113])).
% 2.30/1.68 tff(117,plain,
% 2.30/1.68 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0)) | (~eq(f(elem!0), a0)))),
% 2.30/1.68 inference(quant_inst,[status(thm)],[])).
% 2.30/1.68 tff(118,plain,
% 2.30/1.68 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(elem!0), s(elem!0)))) | (~eq(f(max(s(elem!0), s(elem!0))), a0))),
% 2.30/1.68 inference(modus_ponens,[status(thm)],[117, 116])).
% 2.30/1.68 tff(119,plain,
% 2.30/1.68 ((~eq(f(elem!0), a0)) | (~eq(f(max(s(elem!0), s(elem!0))), a0))),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[118, 94, 60])).
% 2.30/1.68 tff(120,plain,
% 2.30/1.68 (~eq(f(max(s(elem!0), s(elem!0))), a0)),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[119, 112])).
% 2.30/1.68 tff(121,plain,
% 2.30/1.68 (eq(f(max(s(elem!0), s(elem!0))), a1)),
% 2.30/1.68 inference(unit_resolution,[status(thm)],[79, 120])).
% 2.30/1.68 tff(122,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(123,plain,
% 2.30/1.68 (((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1))) <=> ((~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.68 inference(rewrite,[status(thm)],[])).
% 2.30/1.68 tff(124,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))))),
% 2.30/1.68 inference(monotonicity,[status(thm)],[123])).
% 2.30/1.68 tff(125,plain,
% 2.30/1.68 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))))),
% 2.30/1.68 inference(transitivity,[status(thm)],[124, 122])).
% 2.30/1.68 tff(126,plain,
% 2.30/1.68 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(elem!0), s(elem!0))), a1)))),
% 2.30/1.69 inference(quant_inst,[status(thm)],[])).
% 2.30/1.69 tff(127,plain,
% 2.30/1.69 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)) | (~le(s(max(s(elem!0), s(elem!0))), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))))),
% 2.30/1.69 inference(modus_ponens,[status(thm)],[126, 125])).
% 2.30/1.69 tff(128,plain,
% 2.30/1.69 ((~eq(f(max(s(elem!0), s(elem!0))), a1)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1))),
% 2.30/1.69 inference(unit_resolution,[status(thm)],[127, 46, 84])).
% 2.30/1.69 tff(129,plain,
% 2.30/1.69 (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a1)),
% 2.30/1.69 inference(unit_resolution,[status(thm)],[128, 121])).
% 2.30/1.69 tff(130,plain,
% 2.30/1.69 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)))),
% 2.30/1.69 inference(rewrite,[status(thm)],[])).
% 2.30/1.69 tff(131,plain,
% 2.30/1.69 (((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)))),
% 2.30/1.69 inference(rewrite,[status(thm)],[])).
% 2.30/1.69 tff(132,plain,
% 2.30/1.69 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0))))),
% 2.30/1.69 inference(monotonicity,[status(thm)],[131])).
% 2.30/1.69 tff(133,plain,
% 2.30/1.69 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)))),
% 2.30/1.69 inference(transitivity,[status(thm)],[132, 130])).
% 2.30/1.69 tff(134,plain,
% 2.30/1.69 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))),
% 2.30/1.69 inference(quant_inst,[status(thm)],[])).
% 2.30/1.69 tff(135,plain,
% 2.30/1.69 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0)))))) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0))),
% 2.30/1.69 inference(modus_ponens,[status(thm)],[134, 133])).
% 2.30/1.69 tff(136,plain,
% 2.30/1.69 ((~eq(f(elem!0), a0)) | (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0))),
% 2.30/1.69 inference(unit_resolution,[status(thm)],[135, 94, 36])).
% 2.30/1.69 tff(137,plain,
% 2.30/1.69 (~eq(f(max(max(max(max(s(elem!0), elem!0), elem!0), max(max(s(elem!0), s(elem!0)), s(elem!0))), s(max(s(elem!0), s(elem!0))))), a0)),
% 2.30/1.69 inference(unit_resolution,[status(thm)],[136, 112])).
% 2.30/1.69 tff(138,plain,
% 2.30/1.69 ($false),
% 2.30/1.69 inference(unit_resolution,[status(thm)],[105, 75, 137, 129])).
% 2.30/1.69 % SZS output end Proof
%------------------------------------------------------------------------------