TSTP Solution File: ALG141+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG141+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Tue Sep 6 16:08:29 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG141+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.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 Aug 29 13:47:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(e2_type, type, (
% 0.20/0.45 e2: $i)).
% 0.20/0.45 tff(op_type, type, (
% 0.20/0.45 op: ( $i * $i ) > $i)).
% 0.20/0.45 tff(e0_type, type, (
% 0.20/0.45 e0: $i)).
% 0.20/0.45 tff(e1_type, type, (
% 0.20/0.45 e1: $i)).
% 0.20/0.45 tff(e3_type, type, (
% 0.20/0.45 e3: $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 ((e0 = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 ((e2 = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(3,assumption,(~(op(e2, e2) = e2)), introduced(assumption)).
% 0.20/0.45 tff(4,assumption,(~(op(e0, e0) = e2)), introduced(assumption)).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 ((e2 = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(6,assumption,(~(op(e2, e2) = e3)), introduced(assumption)).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 ((e2 = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(8,assumption,(~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))), introduced(assumption)).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(op(e2, e2), op(e2, e2)) = e2)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (op(op(e2, e2), op(e2, e2)) = e2),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(op(e2, e1), op(e2, e1)) = e1)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.45 tff(13,assumption,(~(op(e2, e1) = e2)), introduced(assumption)).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(op(e2, e3), op(e2, e3)) = e3)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (op(op(e2, e3), op(e2, e3)) = e3),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[14, 8])).
% 0.20/0.45 tff(16,assumption,(op(op(e2, e3), op(e2, e3)) = e3), introduced(assumption)).
% 0.20/0.45 tff(17,assumption,(op(e2, e3) = e2), introduced(assumption)).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (op(op(e2, e3), op(e2, e3)) = op(e2, e2)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[17, 17])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (op(e2, e2) = op(op(e2, e3), op(e2, e3))),
% 0.20/0.45 inference(symmetry,[status(thm)],[18])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (op(e2, e2) = e3),
% 0.20/0.45 inference(transitivity,[status(thm)],[19, 16])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[6, 20])).
% 0.20/0.45 tff(22,plain,((~(op(e2, e3) = e2)) | (op(e2, e2) = e3) | (~(op(op(e2, e3), op(e2, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (~(op(e2, e3) = e2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[22, 15, 6])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 ((((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> (((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.20/0.45 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.46 tff(29,axiom,(((((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))) & ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))) & ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))) & ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 ((((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))) & ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))) & ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))),
% 0.20/0.47 inference(and_elim,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))) & ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))),
% 0.20/0.48 inference(and_elim,[status(thm)],[30])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 ((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))),
% 0.20/0.48 inference(and_elim,[status(thm)],[31])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))),
% 0.20/0.49 inference(and_elim,[status(thm)],[32])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 ((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))),
% 0.20/0.49 inference(and_elim,[status(thm)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))),
% 0.20/0.49 inference(and_elim,[status(thm)],[34])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 ((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))),
% 0.20/0.50 inference(and_elim,[status(thm)],[35])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))),
% 0.20/0.50 inference(and_elim,[status(thm)],[36])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 ((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))),
% 0.20/0.50 inference(and_elim,[status(thm)],[38])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 ((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))),
% 0.20/0.51 inference(and_elim,[status(thm)],[39])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)),
% 0.20/0.51 inference(and_elim,[status(thm)],[40])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[41, 28])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[42, 24])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (op(e2, e0) = e2),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[43, 23, 13, 3])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (op(op(e2, e0), op(e2, e0)) = op(e2, e2)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[44, 44])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(op(e2, e0), op(e2, e0)) = e0)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 (op(op(e2, e0), op(e2, e0)) = e0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[46, 8])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (e0 = op(op(e2, e0), op(e2, e0))),
% 0.20/0.51 inference(symmetry,[status(thm)],[47])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (e0 = op(e2, e2)),
% 0.20/0.51 inference(transitivity,[status(thm)],[48, 45])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[49, 49])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (op(e0, e0) = e2),
% 0.20/0.51 inference(transitivity,[status(thm)],[50, 10])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[4, 51])).
% 0.20/0.51 tff(53,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e0, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (op(e2, e1) = e2),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[53, 8, 3, 4, 6])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 ((e2 = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(56,assumption,(op(e1, e1) = e2), introduced(assumption)).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.20/0.51 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = op(e2, e1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(61,axiom,((((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))) & (~(op(e3, e1) = op(e3, e3)))) & (~(op(e3, e2) = op(e3, e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))) & (~(op(e3, e1) = op(e3, e3)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[61])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 ((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[62])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[63])).
% 0.20/0.52 tff(65,plain,
% 0.20/0.52 ((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[64])).
% 0.20/0.52 tff(66,plain,
% 0.20/0.52 (((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[65])).
% 0.20/0.52 tff(67,plain,
% 0.20/0.52 ((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[66])).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 (((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[67])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 ((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))),
% 0.20/0.52 inference(and_elim,[status(thm)],[68])).
% 0.20/0.52 tff(70,plain,
% 0.20/0.52 (((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[69])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 ((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[70])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[71])).
% 0.20/0.53 tff(73,plain,
% 0.20/0.53 ((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[72])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 (((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[73])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 ((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[74])).
% 0.20/0.54 tff(76,plain,
% 0.20/0.54 (((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[75])).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 ((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[76])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 (((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[77])).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 ((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[78])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 (((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[79])).
% 0.20/0.55 tff(81,plain,
% 0.20/0.55 ((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[80])).
% 0.20/0.55 tff(82,plain,
% 0.20/0.55 (((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[81])).
% 0.20/0.55 tff(83,plain,
% 0.20/0.55 ((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[82])).
% 0.20/0.55 tff(84,plain,
% 0.20/0.55 (((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[83])).
% 0.20/0.55 tff(85,plain,
% 0.20/0.55 ((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[84])).
% 0.20/0.55 tff(86,plain,
% 0.20/0.55 (((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[85])).
% 0.20/0.55 tff(87,plain,
% 0.20/0.55 ((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[86])).
% 0.20/0.55 tff(88,plain,
% 0.20/0.55 (((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))),
% 0.20/0.55 inference(and_elim,[status(thm)],[87])).
% 0.20/0.55 tff(89,plain,
% 0.20/0.55 ((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[88])).
% 0.20/0.56 tff(90,plain,
% 0.20/0.56 (((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[89])).
% 0.20/0.56 tff(91,plain,
% 0.20/0.56 ((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[90])).
% 0.20/0.56 tff(92,plain,
% 0.20/0.56 (((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[91])).
% 0.20/0.56 tff(93,plain,
% 0.20/0.56 ((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[92])).
% 0.20/0.56 tff(94,plain,
% 0.20/0.56 (((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[93])).
% 0.20/0.56 tff(95,plain,
% 0.20/0.56 ((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))),
% 0.20/0.56 inference(and_elim,[status(thm)],[94])).
% 0.20/0.56 tff(96,plain,
% 0.20/0.56 (((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[95])).
% 0.42/0.56 tff(97,plain,
% 0.42/0.56 ((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[96])).
% 0.42/0.56 tff(98,plain,
% 0.42/0.56 (((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[97])).
% 0.42/0.56 tff(99,plain,
% 0.42/0.56 ((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[98])).
% 0.42/0.56 tff(100,plain,
% 0.42/0.56 (~(op(e1, e1) = op(e2, e1))),
% 0.42/0.56 inference(and_elim,[status(thm)],[99])).
% 0.42/0.56 tff(101,plain,
% 0.42/0.56 (~(op(e1, e1) = op(e2, e1))),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[100, 60])).
% 0.42/0.56 tff(102,plain,
% 0.42/0.56 (~(op(e2, e1) = e2)),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[101, 59])).
% 0.42/0.56 tff(103,plain,
% 0.42/0.56 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 0.42/0.56 inference(monotonicity,[status(thm)],[56])).
% 0.42/0.56 tff(104,plain,
% 0.42/0.56 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[103])).
% 0.42/0.56 tff(105,plain,
% 0.42/0.56 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = op(e1, e1)))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(106,plain,
% 0.42/0.56 (((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[99])).
% 0.42/0.56 tff(107,plain,
% 0.42/0.56 ((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[106])).
% 0.42/0.56 tff(108,plain,
% 0.42/0.56 (((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))),
% 0.42/0.56 inference(and_elim,[status(thm)],[107])).
% 0.42/0.56 tff(109,plain,
% 0.42/0.56 (~(op(e0, e1) = op(e1, e1))),
% 0.42/0.56 inference(and_elim,[status(thm)],[108])).
% 0.42/0.56 tff(110,plain,
% 0.42/0.56 (~(op(e0, e1) = op(e1, e1))),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.42/0.56 tff(111,plain,
% 0.42/0.56 (~(op(e0, e1) = e2)),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[110, 104])).
% 0.42/0.56 tff(112,assumption,(~(op(e0, e1) = e2)), introduced(assumption)).
% 0.42/0.56 tff(113,assumption,(~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))), introduced(assumption)).
% 0.42/0.56 tff(114,plain,
% 0.42/0.56 (((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(op(e0, e2), op(e0, e2)) = e2)),
% 0.42/0.56 inference(tautology,[status(thm)],[])).
% 0.42/0.56 tff(115,plain,
% 0.42/0.56 (op(op(e0, e2), op(e0, e2)) = e2),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.42/0.56 tff(116,assumption,(op(op(e0, e2), op(e0, e2)) = e2), introduced(assumption)).
% 0.42/0.56 tff(117,assumption,(op(e0, e2) = e2), introduced(assumption)).
% 0.42/0.56 tff(118,plain,
% 0.42/0.56 (e2 = op(e0, e2)),
% 0.42/0.56 inference(symmetry,[status(thm)],[117])).
% 0.42/0.56 tff(119,plain,
% 0.42/0.56 (op(e2, e2) = op(op(e0, e2), op(e0, e2))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[118, 118])).
% 0.42/0.56 tff(120,plain,
% 0.42/0.56 (op(e2, e2) = e2),
% 0.42/0.56 inference(transitivity,[status(thm)],[119, 116])).
% 0.42/0.56 tff(121,plain,
% 0.42/0.56 ((op(e0, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[117])).
% 0.42/0.56 tff(122,plain,
% 0.42/0.56 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.42/0.56 inference(transitivity,[status(thm)],[121, 7])).
% 0.42/0.56 tff(123,plain,
% 0.42/0.56 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[122])).
% 0.42/0.56 tff(124,plain,
% 0.42/0.56 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = op(e2, e2)))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(125,plain,
% 0.42/0.56 (~(op(e0, e2) = op(e2, e2))),
% 0.42/0.56 inference(and_elim,[status(thm)],[95])).
% 0.42/0.56 tff(126,plain,
% 0.42/0.56 (~(op(e0, e2) = op(e2, e2))),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.42/0.56 tff(127,plain,
% 0.42/0.56 (~(op(e2, e2) = e2)),
% 0.42/0.56 inference(modus_ponens,[status(thm)],[126, 123])).
% 0.42/0.56 tff(128,plain,
% 0.42/0.56 ($false),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[127, 120])).
% 0.42/0.56 tff(129,plain,((~(op(e0, e2) = e2)) | (~(op(op(e0, e2), op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.56 tff(130,plain,
% 0.42/0.56 (~(op(e0, e2) = e2)),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[129, 115])).
% 0.42/0.56 tff(131,plain,
% 0.42/0.56 (((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(op(e0, e3), op(e0, e3)) = e3)),
% 0.42/0.56 inference(tautology,[status(thm)],[])).
% 0.42/0.56 tff(132,plain,
% 0.42/0.56 (op(op(e0, e3), op(e0, e3)) = e3),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[131, 113])).
% 0.42/0.56 tff(133,assumption,(op(op(e0, e3), op(e0, e3)) = e3), introduced(assumption)).
% 0.42/0.56 tff(134,assumption,(op(e0, e3) = e2), introduced(assumption)).
% 0.42/0.56 tff(135,plain,
% 0.42/0.56 (e2 = op(e0, e3)),
% 0.42/0.56 inference(symmetry,[status(thm)],[134])).
% 0.42/0.56 tff(136,plain,
% 0.42/0.56 (op(e2, e2) = op(op(e0, e3), op(e0, e3))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[135, 135])).
% 0.42/0.56 tff(137,plain,
% 0.42/0.56 (op(e2, e2) = e3),
% 0.42/0.56 inference(transitivity,[status(thm)],[136, 133])).
% 0.42/0.56 tff(138,plain,
% 0.42/0.56 ($false),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[6, 137])).
% 0.42/0.56 tff(139,plain,((~(op(e0, e3) = e2)) | (op(e2, e2) = e3) | (~(op(op(e0, e3), op(e0, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.42/0.56 tff(140,plain,
% 0.42/0.56 (~(op(e0, e3) = e2)),
% 0.42/0.56 inference(unit_resolution,[status(thm)],[139, 132, 6])).
% 0.42/0.56 tff(141,plain,
% 0.42/0.56 (((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(142,plain,
% 0.42/0.56 ((((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(143,plain,
% 0.42/0.56 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2))),
% 0.42/0.56 inference(rewrite,[status(thm)],[])).
% 0.42/0.56 tff(144,plain,
% 0.42/0.56 (((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)) <=> (((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))),
% 0.42/0.56 inference(monotonicity,[status(thm)],[143])).
% 0.42/0.56 tff(145,plain,
% 0.42/0.56 (((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2))),
% 0.42/0.56 inference(transitivity,[status(thm)],[144, 142])).
% 0.42/0.56 tff(146,plain,
% 0.42/0.56 (((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))),
% 0.42/0.57 inference(and_elim,[status(thm)],[40])).
% 0.42/0.57 tff(147,plain,
% 0.42/0.57 ((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))),
% 0.42/0.57 inference(and_elim,[status(thm)],[146])).
% 0.42/0.57 tff(148,plain,
% 0.42/0.57 (((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))),
% 0.42/0.58 inference(and_elim,[status(thm)],[147])).
% 0.42/0.58 tff(149,plain,
% 0.42/0.58 ((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))),
% 0.42/0.58 inference(and_elim,[status(thm)],[148])).
% 0.42/0.58 tff(150,plain,
% 0.42/0.58 (((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))),
% 0.42/0.58 inference(and_elim,[status(thm)],[149])).
% 0.42/0.58 tff(151,plain,
% 0.42/0.58 ((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))),
% 0.44/0.58 inference(and_elim,[status(thm)],[150])).
% 0.44/0.58 tff(152,plain,
% 0.44/0.58 (((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))),
% 0.44/0.58 inference(and_elim,[status(thm)],[151])).
% 0.44/0.58 tff(153,plain,
% 0.44/0.58 ((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))),
% 0.44/0.58 inference(and_elim,[status(thm)],[152])).
% 0.44/0.58 tff(154,plain,
% 0.44/0.58 (((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))),
% 0.44/0.59 inference(and_elim,[status(thm)],[153])).
% 0.44/0.59 tff(155,plain,
% 0.44/0.59 ((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))),
% 0.44/0.59 inference(and_elim,[status(thm)],[154])).
% 0.44/0.59 tff(156,plain,
% 0.44/0.59 (((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))),
% 0.44/0.59 inference(and_elim,[status(thm)],[155])).
% 0.44/0.59 tff(157,plain,
% 0.44/0.59 ((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))),
% 0.44/0.59 inference(and_elim,[status(thm)],[156])).
% 0.44/0.59 tff(158,plain,
% 0.44/0.59 (((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))),
% 0.44/0.59 inference(and_elim,[status(thm)],[157])).
% 0.44/0.59 tff(159,plain,
% 0.44/0.59 ((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))),
% 0.44/0.59 inference(and_elim,[status(thm)],[158])).
% 0.44/0.59 tff(160,plain,
% 0.44/0.59 (((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))),
% 0.44/0.59 inference(and_elim,[status(thm)],[159])).
% 0.44/0.59 tff(161,plain,
% 0.44/0.59 ((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))),
% 0.44/0.59 inference(and_elim,[status(thm)],[160])).
% 0.44/0.59 tff(162,plain,
% 0.44/0.59 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)),
% 0.44/0.59 inference(and_elim,[status(thm)],[161])).
% 0.44/0.59 tff(163,plain,
% 0.44/0.59 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[162, 145])).
% 0.44/0.59 tff(164,plain,
% 0.44/0.59 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[163, 141])).
% 0.44/0.59 tff(165,plain,
% 0.44/0.59 ($false),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[164, 140, 130, 112, 4])).
% 0.44/0.59 tff(166,plain,(((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(e0, e1) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.59 tff(167,plain,
% 0.44/0.59 (op(e0, e0) = e2),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[166, 113, 112, 6])).
% 0.44/0.59 tff(168,assumption,(~(op(e0, e0) = e0)), introduced(assumption)).
% 0.44/0.59 tff(169,plain,
% 0.44/0.59 (((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(op(e0, e0), op(e0, e0)) = e0)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(170,plain,
% 0.44/0.59 (op(op(e0, e0), op(e0, e0)) = e0),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[169, 113])).
% 0.44/0.59 tff(171,plain,
% 0.44/0.59 (((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(op(e0, e1), op(e0, e1)) = e1)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(172,plain,
% 0.44/0.59 (op(op(e0, e1), op(e0, e1)) = e1),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[171, 113])).
% 0.44/0.59 tff(173,assumption,(op(e0, e0) = e2), introduced(assumption)).
% 0.44/0.59 tff(174,assumption,(op(op(e0, e0), op(e0, e0)) = e0), introduced(assumption)).
% 0.44/0.59 tff(175,plain,
% 0.44/0.59 (op(op(e0, e0), op(e0, e0)) = op(e2, e2)),
% 0.44/0.59 inference(monotonicity,[status(thm)],[173, 173])).
% 0.44/0.59 tff(176,plain,
% 0.44/0.59 (op(e2, e2) = op(op(e0, e0), op(e0, e0))),
% 0.44/0.59 inference(symmetry,[status(thm)],[175])).
% 0.44/0.59 tff(177,plain,
% 0.44/0.59 (op(e2, e2) = e0),
% 0.44/0.59 inference(transitivity,[status(thm)],[176, 174])).
% 0.44/0.59 tff(178,plain,
% 0.44/0.59 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.44/0.59 inference(monotonicity,[status(thm)],[177, 177])).
% 0.44/0.59 tff(179,plain,
% 0.44/0.59 (e0 = op(op(e0, e0), op(e0, e0))),
% 0.44/0.60 inference(symmetry,[status(thm)],[174])).
% 0.44/0.60 tff(180,plain,
% 0.44/0.60 (e0 = op(e2, e2)),
% 0.44/0.60 inference(transitivity,[status(thm)],[179, 175])).
% 0.44/0.60 tff(181,plain,
% 0.44/0.60 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e2, e2))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[180])).
% 0.44/0.60 tff(182,plain,
% 0.44/0.60 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 0.44/0.60 inference(symmetry,[status(thm)],[181])).
% 0.44/0.60 tff(183,plain,
% 0.44/0.60 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[182])).
% 0.44/0.60 tff(184,plain,
% 0.44/0.60 (~(op(e0, e2) = e0)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[126, 183])).
% 0.44/0.60 tff(185,assumption,(op(e0, e3) = e0), introduced(assumption)).
% 0.44/0.60 tff(186,plain,
% 0.44/0.60 (op(e0, e3) = op(e2, e2)),
% 0.44/0.60 inference(transitivity,[status(thm)],[185, 179, 175])).
% 0.44/0.60 tff(187,plain,
% 0.44/0.60 (op(op(e0, e3), op(e0, e3)) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[186, 186])).
% 0.44/0.60 tff(188,plain,
% 0.44/0.60 (op(op(e2, e2), op(e2, e2)) = op(op(e0, e3), op(e0, e3))),
% 0.44/0.60 inference(symmetry,[status(thm)],[187])).
% 0.44/0.60 tff(189,plain,
% 0.44/0.60 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.60 inference(symmetry,[status(thm)],[178])).
% 0.44/0.60 tff(190,plain,
% 0.44/0.60 (e2 = op(e0, e0)),
% 0.44/0.60 inference(symmetry,[status(thm)],[173])).
% 0.44/0.60 tff(191,plain,
% 0.44/0.60 (e2 = e3),
% 0.44/0.60 inference(transitivity,[status(thm)],[190, 189, 188, 133])).
% 0.44/0.60 tff(192,plain,
% 0.44/0.60 ((~(e2 = e3)) <=> (~(e2 = e3))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(193,axiom,((((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))) & (~(e2 = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.44/0.60 tff(194,plain,
% 0.44/0.60 (~(e2 = e3)),
% 0.44/0.60 inference(and_elim,[status(thm)],[193])).
% 0.44/0.60 tff(195,plain,
% 0.44/0.60 (~(e2 = e3)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[194, 192])).
% 0.44/0.60 tff(196,plain,
% 0.44/0.60 ($false),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[195, 191])).
% 0.44/0.60 tff(197,plain,((~(op(e0, e3) = e0)) | (~(op(op(e0, e3), op(e0, e3)) = e3)) | (~(op(e0, e0) = e2)) | (~(op(op(e0, e0), op(e0, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.60 tff(198,plain,
% 0.44/0.60 (~(op(e0, e3) = e0)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[197, 173, 133, 174])).
% 0.44/0.60 tff(199,plain,
% 0.44/0.60 (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(200,plain,
% 0.44/0.60 ((((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(201,plain,
% 0.44/0.60 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(202,plain,
% 0.44/0.60 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[201])).
% 0.44/0.60 tff(203,plain,
% 0.44/0.60 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.44/0.60 inference(transitivity,[status(thm)],[202, 200])).
% 0.44/0.60 tff(204,plain,
% 0.44/0.60 (((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))),
% 0.44/0.60 inference(and_elim,[status(thm)],[161])).
% 0.44/0.60 tff(205,plain,
% 0.44/0.60 ((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))),
% 0.44/0.60 inference(and_elim,[status(thm)],[204])).
% 0.44/0.60 tff(206,plain,
% 0.44/0.60 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))),
% 0.44/0.60 inference(and_elim,[status(thm)],[205])).
% 0.44/0.60 tff(207,plain,
% 0.44/0.60 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)),
% 0.44/0.60 inference(and_elim,[status(thm)],[206])).
% 0.44/0.60 tff(208,plain,
% 0.44/0.60 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.44/0.60 tff(209,plain,
% 0.44/0.60 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[208, 199])).
% 0.44/0.60 tff(210,plain,
% 0.44/0.60 (op(e0, e1) = e0),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[209, 198, 168, 184])).
% 0.44/0.60 tff(211,plain,
% 0.44/0.60 (op(e0, e1) = op(e2, e2)),
% 0.44/0.60 inference(transitivity,[status(thm)],[210, 179, 175])).
% 0.44/0.60 tff(212,plain,
% 0.44/0.60 (op(op(e0, e1), op(e0, e1)) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[211, 211])).
% 0.44/0.60 tff(213,assumption,(op(op(e0, e1), op(e0, e1)) = e1), introduced(assumption)).
% 0.44/0.60 tff(214,plain,
% 0.44/0.60 (e1 = op(op(e0, e1), op(e0, e1))),
% 0.44/0.60 inference(symmetry,[status(thm)],[213])).
% 0.44/0.60 tff(215,plain,
% 0.44/0.60 (e1 = e2),
% 0.44/0.60 inference(transitivity,[status(thm)],[214, 212, 178, 173])).
% 0.44/0.60 tff(216,plain,
% 0.44/0.60 ((~(e1 = e2)) <=> (~(e1 = e2))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(217,plain,
% 0.44/0.60 (((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))),
% 0.44/0.60 inference(and_elim,[status(thm)],[193])).
% 0.44/0.60 tff(218,plain,
% 0.44/0.60 ((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))),
% 0.44/0.60 inference(and_elim,[status(thm)],[217])).
% 0.44/0.60 tff(219,plain,
% 0.44/0.60 (~(e1 = e2)),
% 0.44/0.60 inference(and_elim,[status(thm)],[218])).
% 0.44/0.60 tff(220,plain,
% 0.44/0.60 (~(e1 = e2)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[219, 216])).
% 0.44/0.60 tff(221,plain,
% 0.44/0.60 ($false),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[220, 215])).
% 0.44/0.60 tff(222,plain,((~(op(e0, e0) = e2)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e0), op(e0, e0)) = e0)) | (op(e0, e0) = e0) | (~(op(op(e0, e3), op(e0, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.60 tff(223,plain,
% 0.44/0.60 (~(op(e0, e0) = e2)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[222, 172, 170, 168, 132])).
% 0.44/0.60 tff(224,assumption,(op(e0, e2) = e0), introduced(assumption)).
% 0.44/0.60 tff(225,plain,
% 0.44/0.60 (e0 = op(e0, e2)),
% 0.44/0.60 inference(symmetry,[status(thm)],[224])).
% 0.44/0.60 tff(226,plain,
% 0.44/0.60 (op(e0, e0) = op(op(e0, e2), op(e0, e2))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[225, 225])).
% 0.44/0.60 tff(227,plain,
% 0.44/0.60 (op(e0, e0) = e2),
% 0.44/0.60 inference(transitivity,[status(thm)],[226, 116])).
% 0.44/0.60 tff(228,plain,
% 0.44/0.60 ($false),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[4, 227])).
% 0.44/0.60 tff(229,plain,((~(op(e0, e2) = e0)) | (op(e0, e0) = e2) | (~(op(op(e0, e2), op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.60 tff(230,plain,
% 0.44/0.60 (~(op(e0, e2) = e0)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[229, 223, 115])).
% 0.44/0.60 tff(231,assumption,(~(op(e0, e2) = e2)), introduced(assumption)).
% 0.44/0.60 tff(232,assumption,(~(op(e0, e2) = e0)), introduced(assumption)).
% 0.44/0.60 tff(233,plain,
% 0.44/0.60 (op(e0, e3) = e2),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[164, 231, 4, 112])).
% 0.44/0.60 tff(234,plain,
% 0.44/0.60 (op(e2, e2) = e3),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[139, 233, 133])).
% 0.44/0.60 tff(235,plain,
% 0.44/0.60 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[234])).
% 0.44/0.60 tff(236,plain,
% 0.44/0.60 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[235])).
% 0.44/0.60 tff(237,plain,
% 0.44/0.60 (~(op(e0, e2) = e3)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[126, 236])).
% 0.44/0.60 tff(238,plain,
% 0.44/0.60 (((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(239,plain,
% 0.44/0.60 ((((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(240,plain,
% 0.44/0.60 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(241,plain,
% 0.44/0.60 (((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)) <=> (((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[240])).
% 0.44/0.60 tff(242,plain,
% 0.44/0.60 (((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3))),
% 0.44/0.60 inference(transitivity,[status(thm)],[241, 239])).
% 0.44/0.60 tff(243,axiom,(((((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))) & ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))) & ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 0.44/0.60 tff(244,plain,
% 0.44/0.60 ((((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))) & ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))),
% 0.44/0.60 inference(and_elim,[status(thm)],[243])).
% 0.44/0.60 tff(245,plain,
% 0.44/0.60 (((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))),
% 0.44/0.61 inference(and_elim,[status(thm)],[244])).
% 0.44/0.61 tff(246,plain,
% 0.44/0.61 ((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))),
% 0.44/0.61 inference(and_elim,[status(thm)],[245])).
% 0.44/0.61 tff(247,plain,
% 0.44/0.61 (((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))),
% 0.44/0.61 inference(and_elim,[status(thm)],[246])).
% 0.44/0.61 tff(248,plain,
% 0.44/0.61 ((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))),
% 0.44/0.61 inference(and_elim,[status(thm)],[247])).
% 0.44/0.61 tff(249,plain,
% 0.44/0.61 (((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[248])).
% 0.44/0.62 tff(250,plain,
% 0.44/0.62 ((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[249])).
% 0.44/0.62 tff(251,plain,
% 0.44/0.62 (((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[250])).
% 0.44/0.62 tff(252,plain,
% 0.44/0.62 ((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[251])).
% 0.44/0.62 tff(253,plain,
% 0.44/0.62 (((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[252])).
% 0.44/0.62 tff(254,plain,
% 0.44/0.62 ((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[253])).
% 0.44/0.62 tff(255,plain,
% 0.44/0.62 (((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[254])).
% 0.44/0.62 tff(256,plain,
% 0.44/0.62 ((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[255])).
% 0.44/0.62 tff(257,plain,
% 0.44/0.62 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)),
% 0.44/0.62 inference(and_elim,[status(thm)],[256])).
% 0.44/0.62 tff(258,plain,
% 0.44/0.62 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[257, 242])).
% 0.44/0.62 tff(259,plain,
% 0.44/0.62 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[258, 238])).
% 0.44/0.62 tff(260,plain,
% 0.44/0.62 (op(e0, e2) = e1),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[259, 237, 232, 231])).
% 0.44/0.62 tff(261,plain,
% 0.44/0.62 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[260])).
% 0.44/0.62 tff(262,plain,
% 0.44/0.62 ((op(e0, e0) = e1) <=> (op(e0, e0) = op(e0, e2))),
% 0.44/0.62 inference(symmetry,[status(thm)],[261])).
% 0.44/0.62 tff(263,plain,
% 0.44/0.62 ((e2 = e0) <=> (e0 = e2)),
% 0.44/0.62 inference(commutativity,[status(thm)],[])).
% 0.44/0.62 tff(264,plain,
% 0.44/0.62 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[233])).
% 0.44/0.62 tff(265,plain,
% 0.44/0.62 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.44/0.62 inference(transitivity,[status(thm)],[264, 263])).
% 0.44/0.62 tff(266,plain,
% 0.44/0.62 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.44/0.62 inference(symmetry,[status(thm)],[265])).
% 0.44/0.62 tff(267,plain,
% 0.44/0.62 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[266])).
% 0.44/0.62 tff(268,plain,
% 0.44/0.62 ((~(e0 = e2)) <=> (~(e0 = e2))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(269,plain,
% 0.44/0.62 (((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))),
% 0.44/0.62 inference(and_elim,[status(thm)],[218])).
% 0.44/0.62 tff(270,plain,
% 0.44/0.62 ((~(e0 = e1)) & (~(e0 = e2))),
% 0.44/0.62 inference(and_elim,[status(thm)],[269])).
% 0.44/0.62 tff(271,plain,
% 0.44/0.62 (~(e0 = e2)),
% 0.44/0.62 inference(and_elim,[status(thm)],[270])).
% 0.44/0.62 tff(272,plain,
% 0.44/0.62 (~(e0 = e2)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[271, 268])).
% 0.44/0.62 tff(273,plain,
% 0.44/0.62 (~(op(e0, e3) = e0)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[272, 267])).
% 0.44/0.62 tff(274,plain,
% 0.44/0.62 (op(e0, e1) = e0),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[209, 273, 168, 232])).
% 0.44/0.62 tff(275,plain,
% 0.44/0.62 (e0 = op(e0, e1)),
% 0.44/0.62 inference(symmetry,[status(thm)],[274])).
% 0.44/0.62 tff(276,plain,
% 0.44/0.62 (op(e0, e0) = op(op(e0, e1), op(e0, e1))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[275, 275])).
% 0.44/0.62 tff(277,plain,
% 0.44/0.62 (op(e0, e0) = e1),
% 0.44/0.62 inference(transitivity,[status(thm)],[276, 213])).
% 0.44/0.62 tff(278,plain,
% 0.44/0.62 (op(e0, e0) = op(e0, e2)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[277, 262])).
% 0.44/0.62 tff(279,plain,
% 0.44/0.62 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = op(e0, e2)))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(280,plain,
% 0.44/0.62 (~(op(e0, e0) = op(e0, e2))),
% 0.44/0.62 inference(and_elim,[status(thm)],[83])).
% 0.44/0.62 tff(281,plain,
% 0.44/0.62 (~(op(e0, e0) = op(e0, e2))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.44/0.62 tff(282,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[281, 278])).
% 0.44/0.62 tff(283,plain,((op(e0, e2) = e2) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (op(e0, e2) = e0) | (op(e0, e0) = e0) | (~(op(op(e0, e3), op(e0, e3)) = e3)) | (op(e0, e0) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.62 tff(284,plain,
% 0.44/0.62 (op(e0, e1) = e2),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[283, 130, 230, 168, 132, 223, 172])).
% 0.44/0.62 tff(285,plain,
% 0.44/0.62 (e2 = op(e0, e1)),
% 0.44/0.62 inference(symmetry,[status(thm)],[284])).
% 0.44/0.62 tff(286,plain,
% 0.44/0.62 (op(e2, e2) = op(op(e0, e1), op(e0, e1))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[285, 285])).
% 0.44/0.62 tff(287,plain,
% 0.44/0.62 (op(e2, e2) = e1),
% 0.44/0.62 inference(transitivity,[status(thm)],[286, 172])).
% 0.44/0.62 tff(288,plain,
% 0.44/0.62 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[287])).
% 0.44/0.62 tff(289,plain,
% 0.44/0.62 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[288])).
% 0.44/0.62 tff(290,plain,
% 0.44/0.62 (~(op(e0, e2) = e1)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[126, 289])).
% 0.44/0.62 tff(291,plain,
% 0.44/0.62 (op(e0, e2) = e3),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[259, 290, 230, 130])).
% 0.44/0.62 tff(292,plain,
% 0.44/0.62 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[291])).
% 0.44/0.62 tff(293,plain,
% 0.44/0.62 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e2))),
% 0.44/0.62 inference(symmetry,[status(thm)],[292])).
% 0.44/0.62 tff(294,plain,
% 0.44/0.62 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[284])).
% 0.44/0.62 tff(295,plain,
% 0.44/0.62 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 0.44/0.62 inference(transitivity,[status(thm)],[294, 263])).
% 0.44/0.62 tff(296,plain,
% 0.44/0.62 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 0.44/0.62 inference(symmetry,[status(thm)],[295])).
% 0.44/0.62 tff(297,plain,
% 0.44/0.62 ((~(e0 = e2)) <=> (~(op(e0, e1) = e0))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[296])).
% 0.44/0.62 tff(298,plain,
% 0.44/0.62 (~(op(e0, e1) = e0)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[272, 297])).
% 0.44/0.62 tff(299,plain,
% 0.44/0.62 (op(e0, e3) = e0),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[209, 298, 168, 230])).
% 0.44/0.62 tff(300,plain,
% 0.44/0.62 (e0 = op(e0, e3)),
% 0.44/0.62 inference(symmetry,[status(thm)],[299])).
% 0.44/0.62 tff(301,plain,
% 0.44/0.62 (op(e0, e0) = op(op(e0, e3), op(e0, e3))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[300, 300])).
% 0.44/0.62 tff(302,plain,
% 0.44/0.62 (op(e0, e0) = e3),
% 0.44/0.62 inference(transitivity,[status(thm)],[301, 132])).
% 0.44/0.62 tff(303,plain,
% 0.44/0.62 (op(e0, e0) = op(e0, e2)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[302, 293])).
% 0.44/0.62 tff(304,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[281, 303])).
% 0.44/0.62 tff(305,plain,(((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.62 tff(306,plain,
% 0.44/0.62 (op(e0, e0) = e0),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[305, 113])).
% 0.44/0.62 tff(307,plain,
% 0.44/0.62 (e0 = op(e0, e0)),
% 0.44/0.62 inference(symmetry,[status(thm)],[306])).
% 0.44/0.62 tff(308,plain,
% 0.44/0.62 (e0 = e2),
% 0.44/0.62 inference(transitivity,[status(thm)],[307, 167])).
% 0.44/0.62 tff(309,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[272, 308])).
% 0.44/0.62 tff(310,plain,(((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(e0, e1) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.62 tff(311,plain,
% 0.44/0.62 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[310, 6, 111])).
% 0.44/0.62 tff(312,assumption,(~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))), introduced(assumption)).
% 0.44/0.62 tff(313,plain,
% 0.44/0.62 (((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(op(e1, e3), op(e1, e3)) = e3)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(314,plain,
% 0.44/0.62 (op(op(e1, e3), op(e1, e3)) = e3),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.44/0.62 tff(315,plain,
% 0.44/0.62 (op(op(e1, e1), op(e1, e1)) = op(e2, e2)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[56, 56])).
% 0.44/0.62 tff(316,plain,
% 0.44/0.62 (((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(op(e1, e1), op(e1, e1)) = e1)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(317,plain,
% 0.44/0.62 (op(op(e1, e1), op(e1, e1)) = e1),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[316, 312])).
% 0.44/0.62 tff(318,plain,
% 0.44/0.62 (e1 = op(op(e1, e1), op(e1, e1))),
% 0.44/0.62 inference(symmetry,[status(thm)],[317])).
% 0.44/0.62 tff(319,plain,
% 0.44/0.62 ((e2 = e1) <=> (e1 = e2)),
% 0.44/0.62 inference(commutativity,[status(thm)],[])).
% 0.44/0.62 tff(320,plain,
% 0.44/0.62 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[56])).
% 0.44/0.62 tff(321,plain,
% 0.44/0.62 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 0.44/0.62 inference(transitivity,[status(thm)],[320, 319])).
% 0.44/0.62 tff(322,plain,
% 0.44/0.62 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 0.44/0.62 inference(symmetry,[status(thm)],[321])).
% 0.44/0.62 tff(323,plain,
% 0.44/0.62 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[322])).
% 0.44/0.62 tff(324,plain,
% 0.44/0.62 (~(op(e1, e1) = e1)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[220, 323])).
% 0.44/0.62 tff(325,plain,
% 0.44/0.62 (e1 = op(e2, e2)),
% 0.44/0.62 inference(transitivity,[status(thm)],[318, 315])).
% 0.44/0.62 tff(326,plain,
% 0.44/0.62 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e2, e2))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[325])).
% 0.44/0.62 tff(327,plain,
% 0.44/0.62 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 0.44/0.62 inference(symmetry,[status(thm)],[326])).
% 0.44/0.62 tff(328,plain,
% 0.44/0.62 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[327])).
% 0.44/0.62 tff(329,plain,
% 0.44/0.62 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = op(e2, e2)))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(330,plain,
% 0.44/0.62 (~(op(e1, e2) = op(e2, e2))),
% 0.44/0.62 inference(and_elim,[status(thm)],[93])).
% 0.44/0.62 tff(331,plain,
% 0.44/0.62 (~(op(e1, e2) = op(e2, e2))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.44/0.62 tff(332,plain,
% 0.44/0.62 (~(op(e1, e2) = e1)),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[331, 328])).
% 0.44/0.62 tff(333,plain,
% 0.44/0.62 (((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(op(e1, e0), op(e1, e0)) = e0)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(334,plain,
% 0.44/0.62 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[333, 312])).
% 0.44/0.62 tff(335,assumption,(op(op(e1, e1), op(e1, e1)) = e1), introduced(assumption)).
% 0.44/0.62 tff(336,plain,
% 0.44/0.62 (op(e2, e2) = op(op(e1, e1), op(e1, e1))),
% 0.44/0.62 inference(symmetry,[status(thm)],[315])).
% 0.44/0.62 tff(337,plain,
% 0.44/0.62 (op(e2, e2) = e1),
% 0.44/0.62 inference(transitivity,[status(thm)],[336, 335])).
% 0.44/0.62 tff(338,plain,
% 0.44/0.62 (op(op(e2, e2), op(e2, e2)) = op(e1, e1)),
% 0.44/0.62 inference(monotonicity,[status(thm)],[337, 337])).
% 0.44/0.62 tff(339,plain,
% 0.44/0.62 (e1 = op(op(e1, e1), op(e1, e1))),
% 0.44/0.62 inference(symmetry,[status(thm)],[335])).
% 0.44/0.62 tff(340,assumption,(op(e1, e0) = e1), introduced(assumption)).
% 0.44/0.62 tff(341,plain,
% 0.44/0.62 (op(e1, e0) = op(e2, e2)),
% 0.44/0.62 inference(transitivity,[status(thm)],[340, 339, 315])).
% 0.44/0.62 tff(342,plain,
% 0.44/0.62 (op(op(e1, e0), op(e1, e0)) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[341, 341])).
% 0.44/0.62 tff(343,assumption,(op(op(e1, e0), op(e1, e0)) = e0), introduced(assumption)).
% 0.44/0.62 tff(344,plain,
% 0.44/0.62 (e0 = op(op(e1, e0), op(e1, e0))),
% 0.44/0.62 inference(symmetry,[status(thm)],[343])).
% 0.44/0.62 tff(345,plain,
% 0.44/0.62 (e0 = e2),
% 0.44/0.62 inference(transitivity,[status(thm)],[344, 342, 338, 56])).
% 0.44/0.62 tff(346,plain,
% 0.44/0.62 ($false),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[272, 345])).
% 0.44/0.62 tff(347,plain,((~(op(e1, e0) = e1)) | (~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(e1, e1) = e2)) | (~(op(op(e1, e1), op(e1, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.62 tff(348,plain,
% 0.44/0.62 (~(op(e1, e0) = e1)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[347, 334, 56, 317])).
% 0.44/0.62 tff(349,plain,
% 0.44/0.62 (((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(350,plain,
% 0.44/0.62 ((((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(351,plain,
% 0.44/0.62 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(352,plain,
% 0.44/0.63 (((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> (((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[351])).
% 0.44/0.63 tff(353,plain,
% 0.44/0.63 (((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.44/0.63 inference(transitivity,[status(thm)],[352, 350])).
% 0.44/0.63 tff(354,plain,
% 0.44/0.63 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)),
% 0.44/0.63 inference(and_elim,[status(thm)],[155])).
% 0.44/0.63 tff(355,plain,
% 0.44/0.63 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.44/0.63 tff(356,plain,
% 0.44/0.63 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[355, 349])).
% 0.44/0.63 tff(357,plain,
% 0.44/0.63 (op(e1, e3) = e1),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[356, 348, 332, 324])).
% 0.44/0.63 tff(358,plain,
% 0.44/0.63 (op(e1, e3) = op(e2, e2)),
% 0.44/0.63 inference(transitivity,[status(thm)],[357, 318, 315])).
% 0.44/0.63 tff(359,plain,
% 0.44/0.63 (op(op(e1, e3), op(e1, e3)) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[358, 358])).
% 0.44/0.63 tff(360,plain,
% 0.44/0.63 (op(op(e2, e2), op(e2, e2)) = op(op(e1, e3), op(e1, e3))),
% 0.44/0.63 inference(symmetry,[status(thm)],[359])).
% 0.44/0.63 tff(361,plain,
% 0.44/0.63 (op(e2, e2) = e1),
% 0.44/0.63 inference(transitivity,[status(thm)],[336, 317])).
% 0.44/0.63 tff(362,plain,
% 0.44/0.63 (op(op(e2, e2), op(e2, e2)) = op(e1, e1)),
% 0.44/0.63 inference(monotonicity,[status(thm)],[361, 361])).
% 0.44/0.63 tff(363,plain,
% 0.44/0.63 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.44/0.63 inference(symmetry,[status(thm)],[362])).
% 0.44/0.63 tff(364,plain,
% 0.44/0.63 (e2 = op(e1, e1)),
% 0.44/0.63 inference(symmetry,[status(thm)],[56])).
% 0.44/0.63 tff(365,plain,
% 0.44/0.63 (e2 = e3),
% 0.44/0.63 inference(transitivity,[status(thm)],[364, 363, 360, 314])).
% 0.44/0.63 tff(366,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[195, 365])).
% 0.44/0.63 tff(367,plain,(((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.63 tff(368,plain,
% 0.44/0.63 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[367, 56])).
% 0.44/0.63 tff(369,plain,
% 0.44/0.63 ((e1 = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(370,plain,
% 0.44/0.63 ((e2 = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(371,plain,
% 0.44/0.63 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[56])).
% 0.44/0.63 tff(372,plain,
% 0.44/0.63 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.44/0.63 inference(transitivity,[status(thm)],[371, 370])).
% 0.44/0.63 tff(373,plain,
% 0.44/0.63 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[372])).
% 0.44/0.63 tff(374,plain,
% 0.44/0.63 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = op(e3, e1)))),
% 0.44/0.63 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(375,plain,
% 0.44/0.63 (~(op(e1, e1) = op(e3, e1))),
% 0.44/0.63 inference(and_elim,[status(thm)],[98])).
% 0.44/0.63 tff(376,plain,
% 0.44/0.63 (~(op(e1, e1) = op(e3, e1))),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.44/0.63 tff(377,plain,
% 0.44/0.63 (~(op(e3, e1) = e2)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[376, 373])).
% 0.44/0.63 tff(378,plain,
% 0.44/0.63 ((e2 = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(379,plain,
% 0.44/0.63 ((e2 = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(380,plain,
% 0.44/0.63 (op(e0, e0) = e2),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[53, 8, 3, 6, 13])).
% 0.44/0.63 tff(381,plain,
% 0.44/0.63 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[380])).
% 0.44/0.63 tff(382,plain,
% 0.44/0.63 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.44/0.63 inference(transitivity,[status(thm)],[381, 379])).
% 0.44/0.63 tff(383,plain,
% 0.44/0.63 ((op(e2, e0) = e2) <=> (op(e0, e0) = op(e2, e0))),
% 0.49/0.63 inference(symmetry,[status(thm)],[382])).
% 0.49/0.63 tff(384,plain,
% 0.49/0.63 (op(e0, e0) = op(e2, e0)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[44, 383])).
% 0.49/0.63 tff(385,plain,
% 0.49/0.63 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = op(e2, e0)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(386,plain,
% 0.49/0.63 ((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[108])).
% 0.49/0.63 tff(387,plain,
% 0.49/0.63 (((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[386])).
% 0.49/0.63 tff(388,plain,
% 0.49/0.63 ((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[387])).
% 0.49/0.63 tff(389,plain,
% 0.49/0.63 (((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[388])).
% 0.49/0.63 tff(390,plain,
% 0.49/0.63 ((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))),
% 0.49/0.63 inference(and_elim,[status(thm)],[389])).
% 0.49/0.63 tff(391,plain,
% 0.49/0.63 (~(op(e0, e0) = op(e2, e0))),
% 0.49/0.63 inference(and_elim,[status(thm)],[390])).
% 0.49/0.63 tff(392,plain,
% 0.49/0.63 (~(op(e0, e0) = op(e2, e0))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[391, 385])).
% 0.49/0.63 tff(393,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[392, 384])).
% 0.49/0.63 tff(394,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(395,plain,
% 0.49/0.63 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[394, 3, 102, 6])).
% 0.49/0.63 tff(396,plain,
% 0.49/0.63 ((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))) <=> ((~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(397,plain,
% 0.49/0.63 ((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(398,plain,
% 0.49/0.64 (((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3))) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(399,plain,
% 0.49/0.64 ((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3)) <=> ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(400,plain,
% 0.49/0.64 ((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) <=> ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(401,plain,
% 0.49/0.64 (((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3)) <=> (((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[400])).
% 0.49/0.64 tff(402,plain,
% 0.49/0.64 (((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3)) <=> ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))),
% 0.49/0.64 inference(transitivity,[status(thm)],[401, 399])).
% 0.49/0.64 tff(403,plain,
% 0.49/0.64 (((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(404,plain,
% 0.49/0.64 ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3)) <=> ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(405,plain,
% 0.49/0.64 ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) <=> ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(406,plain,
% 0.49/0.64 (((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3)) <=> (((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[405])).
% 0.49/0.64 tff(407,plain,
% 0.49/0.64 (((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3)) <=> ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3))),
% 0.49/0.64 inference(transitivity,[status(thm)],[406, 404])).
% 0.49/0.64 tff(408,plain,
% 0.49/0.64 ((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(409,plain,
% 0.49/0.64 (((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))) <=> ((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[408, 407])).
% 0.49/0.64 tff(410,plain,
% 0.49/0.64 (((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[409, 403])).
% 0.49/0.64 tff(411,plain,
% 0.49/0.64 ((((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))) | ((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3))) <=> ((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3))) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[410, 402])).
% 0.51/0.65 tff(412,plain,
% 0.51/0.65 ((((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))) | ((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3))) <=> (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.51/0.65 inference(transitivity,[status(thm)],[411, 398])).
% 0.51/0.65 tff(413,axiom,(((((((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1)) & (op(op(e0, e2), op(e0, e2)) = e2)) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1)) & (op(op(e1, e2), op(e1, e2)) = e2)) & (op(op(e1, e3), op(e1, e3)) = e3))) | ((((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1)) & (op(op(e2, e2), op(e2, e2)) = e2)) & (op(op(e2, e3), op(e2, e3)) = e3))) | ((((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1)) & (op(op(e3, e2), op(e3, e2)) = e2)) & (op(op(e3, e3), op(e3, e3)) = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax5')).
% 0.51/0.65 tff(414,plain,
% 0.51/0.65 (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.51/0.65 tff(415,plain,
% 0.51/0.65 (((op(op(e0, e0), op(e0, e0)) = e0) & (op(op(e0, e1), op(e0, e1)) = e1) & (op(op(e0, e2), op(e0, e2)) = e2) & (op(op(e0, e3), op(e0, e3)) = e3)) | ((op(op(e1, e0), op(e1, e0)) = e0) & (op(op(e1, e1), op(e1, e1)) = e1) & (op(op(e1, e2), op(e1, e2)) = e2) & (op(op(e1, e3), op(e1, e3)) = e3)) | ((op(op(e2, e0), op(e2, e0)) = e0) & (op(op(e2, e1), op(e2, e1)) = e1) & (op(op(e2, e2), op(e2, e2)) = e2) & (op(op(e2, e3), op(e2, e3)) = e3)) | ((op(op(e3, e0), op(e3, e0)) = e0) & (op(op(e3, e1), op(e3, e1)) = e1) & (op(op(e3, e2), op(e3, e2)) = e2) & (op(op(e3, e3), op(e3, e3)) = e3))),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[414, 397])).
% 0.51/0.65 tff(416,plain,
% 0.51/0.65 ((~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))))),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[415, 396])).
% 0.51/0.65 tff(417,plain,
% 0.51/0.65 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[416, 395, 368, 311])).
% 0.51/0.65 tff(418,assumption,(~(op(e3, e3) = e2)), introduced(assumption)).
% 0.51/0.65 tff(419,plain,
% 0.51/0.65 (((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(op(e1, e2), op(e1, e2)) = e2)),
% 0.51/0.65 inference(tautology,[status(thm)],[])).
% 0.51/0.65 tff(420,plain,
% 0.51/0.65 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[419, 312])).
% 0.51/0.65 tff(421,plain,
% 0.51/0.65 ((e2 = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.51/0.65 inference(commutativity,[status(thm)],[])).
% 0.51/0.65 tff(422,plain,
% 0.51/0.65 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[56])).
% 0.51/0.65 tff(423,plain,
% 0.51/0.65 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.51/0.65 inference(transitivity,[status(thm)],[422, 421])).
% 0.51/0.65 tff(424,plain,
% 0.51/0.65 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[423])).
% 0.51/0.65 tff(425,plain,
% 0.51/0.65 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = op(e1, e2)))),
% 0.51/0.65 inference(rewrite,[status(thm)],[])).
% 0.51/0.65 tff(426,plain,
% 0.51/0.65 (~(op(e1, e1) = op(e1, e2))),
% 0.51/0.65 inference(and_elim,[status(thm)],[75])).
% 0.51/0.65 tff(427,plain,
% 0.51/0.65 (~(op(e1, e1) = op(e1, e2))),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.51/0.65 tff(428,plain,
% 0.51/0.65 (~(op(e1, e2) = e2)),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[427, 424])).
% 0.51/0.65 tff(429,assumption,(op(op(e1, e2), op(e1, e2)) = e2), introduced(assumption)).
% 0.51/0.65 tff(430,assumption,(op(e1, e2) = e0), introduced(assumption)).
% 0.51/0.65 tff(431,plain,
% 0.51/0.65 (e0 = op(e1, e2)),
% 0.51/0.65 inference(symmetry,[status(thm)],[430])).
% 0.51/0.65 tff(432,plain,
% 0.51/0.65 (op(e0, e0) = op(op(e1, e2), op(e1, e2))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[431, 431])).
% 0.51/0.65 tff(433,plain,
% 0.51/0.65 (op(e0, e0) = e2),
% 0.51/0.65 inference(transitivity,[status(thm)],[432, 429])).
% 0.51/0.65 tff(434,plain,
% 0.51/0.65 ($false),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[4, 433])).
% 0.51/0.65 tff(435,plain,((~(op(e1, e2) = e0)) | (op(e0, e0) = e2) | (~(op(op(e1, e2), op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.65 tff(436,plain,
% 0.51/0.65 (~(op(e1, e2) = e0)),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[435, 420, 4])).
% 0.51/0.65 tff(437,plain,
% 0.51/0.65 (op(e2, e2) = op(op(e1, e1), op(e1, e1))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[364, 364])).
% 0.51/0.65 tff(438,plain,
% 0.51/0.65 (op(e2, e2) = e1),
% 0.51/0.65 inference(transitivity,[status(thm)],[437, 317])).
% 0.51/0.65 tff(439,plain,
% 0.51/0.65 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 0.51/0.65 inference(monotonicity,[status(thm)],[438])).
% 0.51/0.65 tff(440,plain,
% 0.51/0.65 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[439])).
% 0.51/0.65 tff(441,plain,
% 0.51/0.65 (~(op(e1, e2) = e1)),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[331, 440])).
% 0.51/0.65 tff(442,plain,
% 0.51/0.65 (((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3))),
% 0.51/0.65 inference(rewrite,[status(thm)],[])).
% 0.51/0.65 tff(443,plain,
% 0.51/0.65 ((((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3))),
% 0.51/0.65 inference(rewrite,[status(thm)],[])).
% 0.51/0.65 tff(444,plain,
% 0.51/0.65 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2))),
% 0.51/0.65 inference(rewrite,[status(thm)],[])).
% 0.51/0.65 tff(445,plain,
% 0.51/0.65 (((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)) <=> (((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[444])).
% 0.51/0.65 tff(446,plain,
% 0.51/0.65 (((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3))),
% 0.51/0.65 inference(transitivity,[status(thm)],[445, 443])).
% 0.51/0.65 tff(447,plain,
% 0.51/0.65 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)),
% 0.51/0.65 inference(and_elim,[status(thm)],[252])).
% 0.51/0.65 tff(448,plain,
% 0.51/0.65 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.51/0.65 tff(449,plain,
% 0.51/0.65 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.51/0.65 inference(modus_ponens,[status(thm)],[448, 442])).
% 0.51/0.65 tff(450,plain,
% 0.51/0.65 (op(e1, e2) = e3),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[449, 441, 436, 428])).
% 0.51/0.65 tff(451,plain,
% 0.51/0.65 (e3 = op(e1, e2)),
% 0.51/0.65 inference(symmetry,[status(thm)],[450])).
% 0.51/0.65 tff(452,plain,
% 0.51/0.65 (op(e3, e3) = op(op(e1, e2), op(e1, e2))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[451, 451])).
% 0.51/0.65 tff(453,plain,
% 0.51/0.65 (op(e3, e3) = e2),
% 0.51/0.65 inference(transitivity,[status(thm)],[452, 420])).
% 0.51/0.65 tff(454,plain,
% 0.51/0.65 ($false),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[418, 453])).
% 0.51/0.65 tff(455,plain,(((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(e3, e3) = e2) | (~(op(e1, e1) = e2)) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.65 tff(456,plain,
% 0.51/0.65 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[455, 4, 56, 418])).
% 0.51/0.65 tff(457,plain,
% 0.51/0.65 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[166, 4, 111, 6])).
% 0.51/0.65 tff(458,plain,
% 0.51/0.65 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[416, 457, 456, 395])).
% 0.51/0.65 tff(459,plain,
% 0.51/0.65 (((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.51/0.65 inference(tautology,[status(thm)],[])).
% 0.51/0.65 tff(460,plain,
% 0.51/0.65 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[459, 458])).
% 0.51/0.65 tff(461,assumption,(op(op(e3, e2), op(e3, e2)) = e2), introduced(assumption)).
% 0.51/0.65 tff(462,assumption,(op(e3, e2) = e3), introduced(assumption)).
% 0.51/0.65 tff(463,plain,
% 0.51/0.65 (e3 = op(e3, e2)),
% 0.51/0.65 inference(symmetry,[status(thm)],[462])).
% 0.51/0.65 tff(464,plain,
% 0.51/0.65 (op(e3, e3) = op(op(e3, e2), op(e3, e2))),
% 0.51/0.65 inference(monotonicity,[status(thm)],[463, 463])).
% 0.51/0.65 tff(465,plain,
% 0.51/0.65 (op(e3, e3) = e2),
% 0.51/0.65 inference(transitivity,[status(thm)],[464, 461])).
% 0.51/0.65 tff(466,plain,
% 0.51/0.65 ($false),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[418, 465])).
% 0.51/0.65 tff(467,plain,((~(op(e3, e2) = e3)) | (op(e3, e3) = e2) | (~(op(op(e3, e2), op(e3, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.65 tff(468,plain,
% 0.51/0.65 (~(op(e3, e2) = e3)),
% 0.51/0.65 inference(unit_resolution,[status(thm)],[467, 460, 418])).
% 0.51/0.65 tff(469,assumption,(op(e3, e2) = e0), introduced(assumption)).
% 0.51/0.66 tff(470,plain,
% 0.51/0.66 (e0 = op(e3, e2)),
% 0.51/0.66 inference(symmetry,[status(thm)],[469])).
% 0.51/0.66 tff(471,plain,
% 0.51/0.66 (op(e0, e0) = op(op(e3, e2), op(e3, e2))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[470, 470])).
% 0.51/0.66 tff(472,plain,
% 0.51/0.66 (op(e0, e0) = e2),
% 0.51/0.66 inference(transitivity,[status(thm)],[471, 461])).
% 0.51/0.66 tff(473,plain,
% 0.51/0.66 ($false),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[4, 472])).
% 0.51/0.66 tff(474,plain,((~(op(e3, e2) = e0)) | (op(e0, e0) = e2) | (~(op(op(e3, e2), op(e3, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.66 tff(475,plain,
% 0.51/0.66 (~(op(e3, e2) = e0)),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[474, 460, 4])).
% 0.51/0.66 tff(476,plain,
% 0.51/0.66 (((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(op(e3, e0), op(e3, e0)) = e0)),
% 0.51/0.66 inference(tautology,[status(thm)],[])).
% 0.51/0.66 tff(477,plain,
% 0.51/0.66 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[476, 458])).
% 0.51/0.66 tff(478,plain,
% 0.51/0.66 (((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(op(e3, e1), op(e3, e1)) = e1)),
% 0.51/0.66 inference(tautology,[status(thm)],[])).
% 0.51/0.66 tff(479,plain,
% 0.51/0.66 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[478, 458])).
% 0.51/0.66 tff(480,assumption,(op(op(e3, e1), op(e3, e1)) = e1), introduced(assumption)).
% 0.51/0.66 tff(481,assumption,(~(op(e3, e2) = e0)), introduced(assumption)).
% 0.51/0.66 tff(482,assumption,(~(op(e3, e2) = e3)), introduced(assumption)).
% 0.51/0.66 tff(483,assumption,(~(op(e3, e2) = e2)), introduced(assumption)).
% 0.51/0.66 tff(484,plain,
% 0.51/0.66 (((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(485,plain,
% 0.51/0.66 ((((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(486,plain,
% 0.51/0.66 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(487,plain,
% 0.51/0.66 (((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)) <=> (((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[486])).
% 0.51/0.66 tff(488,plain,
% 0.51/0.66 (((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(transitivity,[status(thm)],[487, 485])).
% 0.51/0.66 tff(489,plain,
% 0.51/0.66 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(and_elim,[status(thm)],[244])).
% 0.51/0.66 tff(490,plain,
% 0.51/0.66 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.51/0.66 tff(491,plain,
% 0.51/0.66 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[490, 484])).
% 0.51/0.66 tff(492,plain,
% 0.51/0.66 (op(e3, e2) = e1),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[491, 483, 482, 481])).
% 0.51/0.66 tff(493,plain,
% 0.51/0.66 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e1)),
% 0.51/0.66 inference(monotonicity,[status(thm)],[492])).
% 0.51/0.66 tff(494,plain,
% 0.51/0.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e1))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[493])).
% 0.51/0.66 tff(495,plain,
% 0.51/0.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e3, e2)))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(496,plain,
% 0.51/0.66 (~(op(e3, e1) = op(e3, e2))),
% 0.51/0.66 inference(and_elim,[status(thm)],[63])).
% 0.51/0.66 tff(497,plain,
% 0.51/0.66 (~(op(e3, e1) = op(e3, e2))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.51/0.66 tff(498,plain,
% 0.51/0.66 (~(op(e3, e1) = e1)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.51/0.66 tff(499,plain,
% 0.51/0.66 ((e0 = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.51/0.66 inference(commutativity,[status(thm)],[])).
% 0.51/0.66 tff(500,plain,
% 0.51/0.66 (((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(501,plain,
% 0.51/0.66 ((((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(502,plain,
% 0.51/0.66 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(503,plain,
% 0.51/0.66 (((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)) <=> (((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[502])).
% 0.51/0.66 tff(504,plain,
% 0.51/0.66 (((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2))),
% 0.51/0.66 inference(transitivity,[status(thm)],[503, 501])).
% 0.51/0.66 tff(505,plain,
% 0.51/0.66 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)),
% 0.51/0.66 inference(and_elim,[status(thm)],[39])).
% 0.51/0.66 tff(506,plain,
% 0.51/0.66 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.51/0.66 tff(507,plain,
% 0.51/0.66 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[506, 500])).
% 0.51/0.66 tff(508,plain,
% 0.51/0.66 (op(e0, e2) = e2),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[507, 483, 428, 3])).
% 0.51/0.66 tff(509,plain,
% 0.51/0.66 ((op(e0, e2) = e3) <=> (e2 = e3)),
% 0.51/0.66 inference(monotonicity,[status(thm)],[508])).
% 0.51/0.66 tff(510,plain,
% 0.51/0.66 ((e2 = e3) <=> (op(e0, e2) = e3)),
% 0.51/0.66 inference(symmetry,[status(thm)],[509])).
% 0.51/0.66 tff(511,plain,
% 0.51/0.66 ((~(e2 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[510])).
% 0.51/0.66 tff(512,plain,
% 0.51/0.66 (~(op(e0, e2) = e3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[195, 511])).
% 0.51/0.66 tff(513,plain,
% 0.51/0.66 (((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(514,plain,
% 0.51/0.66 ((((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(515,plain,
% 0.51/0.66 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(516,plain,
% 0.51/0.66 (((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)) <=> (((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[515])).
% 0.51/0.66 tff(517,plain,
% 0.51/0.66 (((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3))),
% 0.51/0.66 inference(transitivity,[status(thm)],[516, 514])).
% 0.51/0.66 tff(518,plain,
% 0.51/0.66 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(and_elim,[status(thm)],[37])).
% 0.51/0.66 tff(519,plain,
% 0.51/0.66 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.51/0.66 tff(520,plain,
% 0.51/0.66 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[519, 513])).
% 0.51/0.66 tff(521,plain,
% 0.51/0.66 (op(e1, e2) = e3),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[520, 512, 6, 482])).
% 0.51/0.66 tff(522,plain,
% 0.51/0.66 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.51/0.66 inference(monotonicity,[status(thm)],[56])).
% 0.51/0.66 tff(523,plain,
% 0.51/0.66 (op(e1, op(e1, e1)) = e3),
% 0.51/0.66 inference(transitivity,[status(thm)],[522, 521])).
% 0.51/0.66 tff(524,plain,
% 0.51/0.66 (op(op(e1, op(e1, e1)), e1) = op(e3, e1)),
% 0.51/0.66 inference(monotonicity,[status(thm)],[523])).
% 0.51/0.66 tff(525,plain,
% 0.51/0.66 ((e0 = op(op(e1, op(e1, e1)), e1)) <=> (e0 = op(e3, e1))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[524])).
% 0.51/0.66 tff(526,plain,
% 0.51/0.66 ((e0 = op(op(e1, op(e1, e1)), e1)) <=> (op(e3, e1) = e0)),
% 0.51/0.66 inference(transitivity,[status(thm)],[525, 499])).
% 0.51/0.66 tff(527,plain,
% 0.51/0.66 ((~(e0 = op(op(e1, op(e1, e1)), e1))) <=> (~(op(e3, e1) = e0))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[526])).
% 0.51/0.66 tff(528,plain,
% 0.51/0.66 ((e2 = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.51/0.66 inference(commutativity,[status(thm)],[])).
% 0.51/0.66 tff(529,plain,
% 0.51/0.66 ((op(e1, e1) = e2) <=> (e2 = op(e1, e1))),
% 0.51/0.66 inference(symmetry,[status(thm)],[528])).
% 0.51/0.66 tff(530,plain,
% 0.51/0.66 (e2 = op(e1, e1)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[56, 529])).
% 0.51/0.66 tff(531,plain,
% 0.51/0.66 ((e3 = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.51/0.66 inference(commutativity,[status(thm)],[])).
% 0.51/0.66 tff(532,plain,
% 0.51/0.66 ((e3 = op(e1, op(e1, e1))) <=> (e3 = op(e1, e2))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[522])).
% 0.51/0.66 tff(533,plain,
% 0.51/0.66 ((e3 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e3)),
% 0.51/0.66 inference(transitivity,[status(thm)],[532, 531])).
% 0.51/0.66 tff(534,plain,
% 0.51/0.66 ((op(e1, e2) = e3) <=> (e3 = op(e1, op(e1, e1)))),
% 0.51/0.66 inference(symmetry,[status(thm)],[533])).
% 0.51/0.66 tff(535,plain,
% 0.51/0.66 (e3 = op(e1, op(e1, e1))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[521, 534])).
% 0.51/0.66 tff(536,plain,
% 0.51/0.66 ((~(~((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1))))))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(537,plain,
% 0.51/0.66 (((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1))) <=> (~((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1))))))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(538,plain,
% 0.51/0.66 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1)))) <=> (~(~((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1)))))))),
% 0.51/0.66 inference(monotonicity,[status(thm)],[537])).
% 0.51/0.66 tff(539,plain,
% 0.51/0.66 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1)))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.51/0.66 inference(transitivity,[status(thm)],[538, 536])).
% 0.51/0.66 tff(540,plain,
% 0.51/0.66 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1)))) <=> (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1))))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(541,plain,
% 0.51/0.66 ((~(((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), e1)))) <=> (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1))))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(542,axiom,(~(((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), e1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax28')).
% 0.51/0.66 tff(543,plain,
% 0.51/0.66 (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1)))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.51/0.66 tff(544,plain,
% 0.51/0.66 (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(op(e1, op(e1, e1)), e1)))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[543, 540])).
% 0.51/0.66 tff(545,plain,
% 0.51/0.66 ((~(e2 = op(e1, e1))) | (~(e0 = op(op(e1, op(e1, e1)), e1))) | (~(e3 = op(e1, op(e1, e1))))),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[544, 539])).
% 0.51/0.66 tff(546,plain,
% 0.51/0.66 (~(e0 = op(op(e1, op(e1, e1)), e1))),
% 0.51/0.66 inference(unit_resolution,[status(thm)],[545, 535, 530])).
% 0.51/0.66 tff(547,plain,
% 0.51/0.66 (~(op(e3, e1) = e0)),
% 0.51/0.66 inference(modus_ponens,[status(thm)],[546, 527])).
% 0.51/0.66 tff(548,plain,
% 0.51/0.66 (((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(549,plain,
% 0.51/0.66 ((((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(550,plain,
% 0.51/0.67 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(551,plain,
% 0.51/0.67 (((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)) <=> (((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[550])).
% 0.51/0.67 tff(552,plain,
% 0.51/0.67 (((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3))),
% 0.51/0.67 inference(transitivity,[status(thm)],[551, 549])).
% 0.51/0.67 tff(553,plain,
% 0.51/0.67 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)),
% 0.51/0.67 inference(and_elim,[status(thm)],[245])).
% 0.51/0.67 tff(554,plain,
% 0.51/0.67 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.51/0.67 tff(555,plain,
% 0.51/0.67 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[554, 548])).
% 0.51/0.67 tff(556,plain,
% 0.51/0.67 (op(e3, e1) = e3),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[555, 547, 377, 498])).
% 0.51/0.67 tff(557,plain,
% 0.51/0.67 (op(op(e3, e1), op(e3, e1)) = op(e3, e3)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[556, 556])).
% 0.51/0.67 tff(558,plain,
% 0.51/0.67 (op(e3, e3) = op(op(e3, e1), op(e3, e1))),
% 0.51/0.67 inference(symmetry,[status(thm)],[557])).
% 0.51/0.67 tff(559,plain,
% 0.51/0.67 (((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(560,plain,
% 0.51/0.67 ((((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(561,plain,
% 0.51/0.67 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(562,plain,
% 0.51/0.67 (((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)) <=> (((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[561])).
% 0.51/0.67 tff(563,plain,
% 0.51/0.67 (((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2))),
% 0.51/0.67 inference(transitivity,[status(thm)],[562, 560])).
% 0.51/0.67 tff(564,plain,
% 0.51/0.67 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)),
% 0.51/0.67 inference(and_elim,[status(thm)],[32])).
% 0.51/0.67 tff(565,plain,
% 0.51/0.67 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.51/0.67 tff(566,plain,
% 0.51/0.67 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[565, 559])).
% 0.51/0.67 tff(567,plain,
% 0.51/0.67 (op(e3, e0) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[566, 483, 418, 377])).
% 0.51/0.67 tff(568,plain,
% 0.51/0.67 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[567])).
% 0.51/0.67 tff(569,plain,
% 0.51/0.67 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.51/0.67 inference(transitivity,[status(thm)],[568, 263])).
% 0.51/0.67 tff(570,plain,
% 0.51/0.67 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.51/0.67 inference(symmetry,[status(thm)],[569])).
% 0.51/0.67 tff(571,plain,
% 0.51/0.67 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[570])).
% 0.51/0.67 tff(572,plain,
% 0.51/0.67 (~(op(e3, e0) = e0)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[272, 571])).
% 0.51/0.67 tff(573,plain,
% 0.51/0.67 (((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(574,plain,
% 0.51/0.67 ((((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(575,plain,
% 0.51/0.67 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(576,plain,
% 0.51/0.67 (((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> (((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[575])).
% 0.51/0.67 tff(577,plain,
% 0.51/0.67 (((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.51/0.67 inference(transitivity,[status(thm)],[576, 574])).
% 0.51/0.67 tff(578,plain,
% 0.51/0.67 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)),
% 0.51/0.67 inference(and_elim,[status(thm)],[36])).
% 0.51/0.67 tff(579,plain,
% 0.51/0.67 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.51/0.67 tff(580,plain,
% 0.51/0.67 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[579, 573])).
% 0.51/0.67 tff(581,plain,
% 0.51/0.67 (op(e3, e3) = e0),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[580, 547, 481, 572])).
% 0.51/0.67 tff(582,plain,
% 0.51/0.67 (e0 = op(e3, e3)),
% 0.51/0.67 inference(symmetry,[status(thm)],[581])).
% 0.51/0.67 tff(583,assumption,(op(op(e3, e0), op(e3, e0)) = e0), introduced(assumption)).
% 0.51/0.67 tff(584,plain,
% 0.51/0.67 (op(op(e3, e0), op(e3, e0)) = op(e2, e2)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[567, 567])).
% 0.51/0.67 tff(585,plain,
% 0.51/0.67 (op(e2, e2) = op(op(e3, e0), op(e3, e0))),
% 0.51/0.67 inference(symmetry,[status(thm)],[584])).
% 0.51/0.67 tff(586,plain,
% 0.51/0.67 (op(e2, e2) = e1),
% 0.51/0.67 inference(transitivity,[status(thm)],[585, 583, 582, 558, 480])).
% 0.51/0.67 tff(587,plain,
% 0.51/0.67 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[492])).
% 0.51/0.67 tff(588,plain,
% 0.51/0.67 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[587])).
% 0.51/0.67 tff(589,plain,
% 0.51/0.67 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = op(e3, e2)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(590,plain,
% 0.51/0.67 (~(op(e2, e2) = op(e3, e2))),
% 0.51/0.67 inference(and_elim,[status(thm)],[91])).
% 0.51/0.67 tff(591,plain,
% 0.51/0.67 (~(op(e2, e2) = op(e3, e2))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.51/0.67 tff(592,plain,
% 0.51/0.67 (~(op(e2, e2) = e1)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[591, 588])).
% 0.51/0.67 tff(593,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[592, 586])).
% 0.51/0.67 tff(594,plain,((op(e3, e2) = e2) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e0), op(e3, e0)) = e0)) | (op(e3, e2) = e0) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e2) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(595,plain,
% 0.51/0.67 (op(e3, e2) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[594, 479, 477, 475, 56, 6, 468, 418, 3])).
% 0.51/0.67 tff(596,plain,
% 0.51/0.67 (e2 = op(e3, e2)),
% 0.51/0.67 inference(symmetry,[status(thm)],[595])).
% 0.51/0.67 tff(597,plain,
% 0.51/0.67 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[596, 596])).
% 0.51/0.67 tff(598,plain,
% 0.51/0.67 (op(e2, e2) = e2),
% 0.51/0.67 inference(transitivity,[status(thm)],[597, 460])).
% 0.51/0.67 tff(599,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[3, 598])).
% 0.51/0.67 tff(600,plain,((op(e0, e0) = e2) | (op(e2, e2) = e2) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e3) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(601,plain,
% 0.51/0.67 (op(e0, e0) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[600, 418, 56, 6, 3])).
% 0.51/0.67 tff(602,plain,
% 0.51/0.67 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[601])).
% 0.51/0.67 tff(603,plain,
% 0.51/0.67 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 0.51/0.67 inference(transitivity,[status(thm)],[602, 263])).
% 0.51/0.67 tff(604,plain,
% 0.51/0.67 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 0.51/0.67 inference(symmetry,[status(thm)],[603])).
% 0.51/0.67 tff(605,plain,
% 0.51/0.67 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[604])).
% 0.51/0.67 tff(606,plain,
% 0.51/0.67 (~(op(e0, e0) = e0)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[272, 605])).
% 0.51/0.67 tff(607,plain,
% 0.51/0.67 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[305, 606])).
% 0.51/0.67 tff(608,plain,
% 0.51/0.67 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[416, 607, 368, 395])).
% 0.51/0.67 tff(609,plain,
% 0.51/0.67 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[459, 608])).
% 0.51/0.67 tff(610,plain,
% 0.51/0.67 ((e2 = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.51/0.67 inference(commutativity,[status(thm)],[])).
% 0.51/0.67 tff(611,plain,
% 0.51/0.67 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[601])).
% 0.51/0.67 tff(612,plain,
% 0.51/0.67 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.51/0.67 inference(transitivity,[status(thm)],[611, 610])).
% 0.51/0.67 tff(613,plain,
% 0.51/0.67 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[612])).
% 0.51/0.67 tff(614,plain,
% 0.51/0.67 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = op(e3, e0)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(615,plain,
% 0.51/0.67 (~(op(e0, e0) = op(e3, e0))),
% 0.51/0.67 inference(and_elim,[status(thm)],[389])).
% 0.51/0.67 tff(616,plain,
% 0.51/0.67 (~(op(e0, e0) = op(e3, e0))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.51/0.67 tff(617,plain,
% 0.51/0.67 (~(op(e3, e0) = e2)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[616, 613])).
% 0.51/0.67 tff(618,plain,
% 0.51/0.67 (op(e3, e2) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[566, 617, 418, 377])).
% 0.51/0.67 tff(619,plain,
% 0.51/0.67 (e2 = op(e3, e2)),
% 0.51/0.67 inference(symmetry,[status(thm)],[618])).
% 0.51/0.67 tff(620,plain,
% 0.51/0.67 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[619, 619])).
% 0.51/0.67 tff(621,plain,
% 0.51/0.67 (op(e2, e2) = e2),
% 0.51/0.67 inference(transitivity,[status(thm)],[620, 609])).
% 0.51/0.67 tff(622,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[3, 621])).
% 0.51/0.67 tff(623,plain,((op(e3, e3) = e2) | (op(e2, e2) = e2) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(624,plain,
% 0.51/0.67 (op(e3, e3) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[623, 3, 56, 6])).
% 0.51/0.67 tff(625,assumption,(op(op(e3, e3), op(e3, e3)) = e3), introduced(assumption)).
% 0.51/0.67 tff(626,assumption,(op(e3, e3) = e2), introduced(assumption)).
% 0.51/0.67 tff(627,plain,
% 0.51/0.67 (e2 = op(e3, e3)),
% 0.51/0.67 inference(symmetry,[status(thm)],[626])).
% 0.51/0.67 tff(628,plain,
% 0.51/0.67 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[627, 627])).
% 0.51/0.67 tff(629,plain,
% 0.51/0.67 (op(e2, e2) = e3),
% 0.51/0.67 inference(transitivity,[status(thm)],[628, 625])).
% 0.51/0.67 tff(630,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[6, 629])).
% 0.51/0.67 tff(631,plain,((~(op(e3, e3) = e2)) | (op(e2, e2) = e3) | (~(op(op(e3, e3), op(e3, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(632,plain,
% 0.51/0.67 (~(op(op(e3, e3), op(e3, e3)) = e3)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[631, 624, 6])).
% 0.51/0.67 tff(633,plain,
% 0.51/0.67 (((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(op(e3, e3), op(e3, e3)) = e3)),
% 0.51/0.67 inference(tautology,[status(thm)],[])).
% 0.51/0.67 tff(634,plain,
% 0.51/0.67 ($false),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[633, 632, 417])).
% 0.51/0.67 tff(635,plain,((op(e2, e2) = e2) | (op(e2, e2) = e3) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.67 tff(636,plain,
% 0.51/0.67 (op(e2, e2) = e2),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[635, 6, 56])).
% 0.51/0.67 tff(637,plain,
% 0.51/0.67 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[636])).
% 0.51/0.67 tff(638,plain,
% 0.51/0.67 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.51/0.67 inference(transitivity,[status(thm)],[637, 378])).
% 0.51/0.67 tff(639,plain,
% 0.51/0.67 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[638])).
% 0.51/0.67 tff(640,plain,
% 0.51/0.67 (~(op(e3, e2) = e2)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[591, 639])).
% 0.51/0.68 tff(641,plain,
% 0.51/0.68 (op(e3, e0) = e2),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[566, 418, 640, 377])).
% 0.51/0.68 tff(642,plain,
% 0.51/0.68 (op(op(e3, e0), op(e3, e0)) = op(e2, e2)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[641, 641])).
% 0.51/0.68 tff(643,plain,
% 0.51/0.68 (op(op(e3, e0), op(e3, e0)) = e2),
% 0.51/0.68 inference(transitivity,[status(thm)],[642, 636])).
% 0.51/0.68 tff(644,plain,
% 0.51/0.68 ((op(op(e3, e0), op(e3, e0)) = e0) <=> (e2 = e0)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[643])).
% 0.51/0.68 tff(645,plain,
% 0.51/0.68 ((op(op(e3, e0), op(e3, e0)) = e0) <=> (e0 = e2)),
% 0.51/0.68 inference(transitivity,[status(thm)],[644, 263])).
% 0.51/0.68 tff(646,plain,
% 0.51/0.68 ((e0 = e2) <=> (op(op(e3, e0), op(e3, e0)) = e0)),
% 0.51/0.68 inference(symmetry,[status(thm)],[645])).
% 0.51/0.68 tff(647,plain,
% 0.51/0.68 ((~(e0 = e2)) <=> (~(op(op(e3, e0), op(e3, e0)) = e0))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[646])).
% 0.51/0.68 tff(648,plain,
% 0.51/0.68 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[272, 647])).
% 0.51/0.68 tff(649,plain,
% 0.51/0.68 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[476, 648])).
% 0.51/0.68 tff(650,plain,
% 0.51/0.68 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[416, 649, 368, 311])).
% 0.51/0.68 tff(651,assumption,(op(e3, e3) = e3), introduced(assumption)).
% 0.51/0.68 tff(652,plain,
% 0.51/0.68 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[651])).
% 0.51/0.68 tff(653,plain,
% 0.51/0.68 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[652])).
% 0.51/0.68 tff(654,plain,
% 0.51/0.68 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = op(e3, e3)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(655,plain,
% 0.51/0.68 (~(op(e2, e3) = op(e3, e3))),
% 0.51/0.68 inference(and_elim,[status(thm)],[85])).
% 0.51/0.68 tff(656,plain,
% 0.51/0.68 (~(op(e2, e3) = op(e3, e3))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.51/0.68 tff(657,plain,
% 0.51/0.68 (~(op(e2, e3) = e3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[656, 653])).
% 0.51/0.68 tff(658,assumption,(op(op(e2, e1), op(e2, e1)) = e1), introduced(assumption)).
% 0.51/0.68 tff(659,assumption,(op(e2, e1) = e3), introduced(assumption)).
% 0.51/0.68 tff(660,plain,
% 0.51/0.68 (op(op(e2, e1), op(e2, e1)) = op(e3, e3)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[659, 659])).
% 0.51/0.68 tff(661,plain,
% 0.51/0.68 (e1 = op(op(e2, e1), op(e2, e1))),
% 0.51/0.68 inference(symmetry,[status(thm)],[658])).
% 0.51/0.68 tff(662,plain,
% 0.51/0.68 (e1 = e3),
% 0.51/0.68 inference(transitivity,[status(thm)],[661, 660, 651])).
% 0.51/0.68 tff(663,plain,
% 0.51/0.68 ((~(e1 = e3)) <=> (~(e1 = e3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(664,plain,
% 0.51/0.68 (~(e1 = e3)),
% 0.51/0.68 inference(and_elim,[status(thm)],[217])).
% 0.51/0.68 tff(665,plain,
% 0.51/0.68 (~(e1 = e3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.51/0.68 tff(666,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[665, 662])).
% 0.51/0.68 tff(667,plain,((~(op(e2, e1) = e3)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(e3, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(668,plain,
% 0.51/0.68 (~(op(e2, e1) = e3)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[667, 651, 658])).
% 0.51/0.68 tff(669,plain,
% 0.51/0.68 (((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(670,plain,
% 0.51/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(671,plain,
% 0.51/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(672,plain,
% 0.51/0.68 (((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> (((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[671])).
% 0.51/0.68 tff(673,plain,
% 0.51/0.68 (((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.51/0.68 inference(transitivity,[status(thm)],[672, 670])).
% 0.51/0.68 tff(674,plain,
% 0.51/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)),
% 0.51/0.68 inference(and_elim,[status(thm)],[38])).
% 0.51/0.68 tff(675,plain,
% 0.51/0.68 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.51/0.68 tff(676,plain,
% 0.51/0.68 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[675, 669])).
% 0.51/0.68 tff(677,plain,
% 0.51/0.68 (op(e2, e0) = e3),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[676, 668, 6, 657])).
% 0.51/0.68 tff(678,plain,
% 0.51/0.68 (op(op(e2, e0), op(e2, e0)) = op(e3, e3)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[677, 677])).
% 0.51/0.68 tff(679,assumption,(op(op(e2, e0), op(e2, e0)) = e0), introduced(assumption)).
% 0.51/0.68 tff(680,plain,
% 0.51/0.68 (e0 = op(op(e2, e0), op(e2, e0))),
% 0.51/0.68 inference(symmetry,[status(thm)],[679])).
% 0.51/0.68 tff(681,plain,
% 0.51/0.68 (e0 = e3),
% 0.51/0.68 inference(transitivity,[status(thm)],[680, 678, 651])).
% 0.51/0.68 tff(682,plain,
% 0.51/0.68 ((~(e0 = e3)) <=> (~(e0 = e3))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(683,plain,
% 0.51/0.68 (~(e0 = e3)),
% 0.51/0.68 inference(and_elim,[status(thm)],[269])).
% 0.51/0.68 tff(684,plain,
% 0.51/0.68 (~(e0 = e3)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.51/0.68 tff(685,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[684, 681])).
% 0.51/0.68 tff(686,plain,((~(op(e3, e3) = e3)) | (~(op(op(e2, e0), op(e2, e0)) = e0)) | (op(e2, e2) = e3) | (~(op(op(e2, e1), op(e2, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(687,plain,
% 0.51/0.68 ($false),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[686, 12, 47, 6, 651])).
% 0.51/0.68 tff(688,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e2, e2) = e3) | (~(op(e3, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.68 tff(689,plain,
% 0.51/0.68 (~(op(e3, e3) = e3)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[688, 650, 6])).
% 0.51/0.68 tff(690,plain,
% 0.51/0.68 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[641])).
% 0.51/0.68 tff(691,plain,
% 0.51/0.68 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.51/0.68 inference(transitivity,[status(thm)],[690, 263])).
% 0.51/0.68 tff(692,plain,
% 0.51/0.68 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.51/0.68 inference(symmetry,[status(thm)],[691])).
% 0.51/0.68 tff(693,plain,
% 0.51/0.68 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[692])).
% 0.51/0.68 tff(694,plain,
% 0.51/0.68 (~(op(e3, e0) = e0)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[272, 693])).
% 0.51/0.68 tff(695,plain,
% 0.51/0.68 ((e2 = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.51/0.68 inference(commutativity,[status(thm)],[])).
% 0.51/0.68 tff(696,plain,
% 0.51/0.68 ((op(e1, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[56])).
% 0.51/0.68 tff(697,plain,
% 0.51/0.68 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.51/0.68 inference(transitivity,[status(thm)],[696, 695])).
% 0.51/0.68 tff(698,plain,
% 0.51/0.68 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[697])).
% 0.51/0.68 tff(699,plain,
% 0.51/0.68 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = op(e1, e3)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(700,plain,
% 0.51/0.68 (~(op(e1, e1) = op(e1, e3))),
% 0.51/0.68 inference(and_elim,[status(thm)],[74])).
% 0.51/0.68 tff(701,plain,
% 0.51/0.68 (~(op(e1, e1) = op(e1, e3))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.51/0.68 tff(702,plain,
% 0.51/0.68 (~(op(e1, e3) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[701, 698])).
% 0.51/0.68 tff(703,plain,
% 0.51/0.68 ((e2 = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.51/0.68 inference(commutativity,[status(thm)],[])).
% 0.51/0.68 tff(704,plain,
% 0.51/0.68 ((op(e2, e2) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[636])).
% 0.51/0.68 tff(705,plain,
% 0.51/0.68 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.51/0.68 inference(transitivity,[status(thm)],[704, 703])).
% 0.51/0.68 tff(706,plain,
% 0.51/0.68 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[705])).
% 0.51/0.68 tff(707,plain,
% 0.51/0.68 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = op(e2, e3)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(708,plain,
% 0.51/0.68 (~(op(e2, e2) = op(e2, e3))),
% 0.51/0.68 inference(and_elim,[status(thm)],[67])).
% 0.51/0.68 tff(709,plain,
% 0.51/0.68 (~(op(e2, e2) = op(e2, e3))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.51/0.68 tff(710,plain,
% 0.51/0.68 (~(op(e2, e3) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[709, 706])).
% 0.51/0.68 tff(711,plain,
% 0.51/0.68 (((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(712,plain,
% 0.51/0.68 ((((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(713,plain,
% 0.51/0.68 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(714,plain,
% 0.51/0.68 (((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)) <=> (((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[713])).
% 0.51/0.68 tff(715,plain,
% 0.51/0.68 (((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2))),
% 0.51/0.68 inference(transitivity,[status(thm)],[714, 712])).
% 0.51/0.68 tff(716,plain,
% 0.51/0.68 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)),
% 0.51/0.68 inference(and_elim,[status(thm)],[31])).
% 0.51/0.68 tff(717,plain,
% 0.51/0.68 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.51/0.68 tff(718,plain,
% 0.51/0.68 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[717, 711])).
% 0.51/0.68 tff(719,plain,
% 0.51/0.68 (op(e0, e3) = e2),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[718, 418, 710, 702])).
% 0.51/0.68 tff(720,plain,
% 0.51/0.68 ((e3 = e0) <=> (e0 = e3)),
% 0.51/0.68 inference(commutativity,[status(thm)],[])).
% 0.51/0.68 tff(721,plain,
% 0.51/0.68 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[11, 650])).
% 0.51/0.68 tff(722,plain,
% 0.51/0.68 ((e1 = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.51/0.68 inference(commutativity,[status(thm)],[])).
% 0.51/0.68 tff(723,plain,
% 0.51/0.68 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[719])).
% 0.51/0.68 tff(724,plain,
% 0.51/0.68 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[723])).
% 0.51/0.68 tff(725,plain,
% 0.51/0.68 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = op(e0, e3)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(726,plain,
% 0.51/0.68 (~(op(e0, e0) = op(e0, e3))),
% 0.51/0.68 inference(and_elim,[status(thm)],[82])).
% 0.51/0.68 tff(727,plain,
% 0.51/0.68 (~(op(e0, e0) = op(e0, e3))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.51/0.68 tff(728,plain,
% 0.51/0.68 (~(op(e0, e0) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[727, 724])).
% 0.51/0.68 tff(729,assumption,(~(op(e0, e1) = e1)), introduced(assumption)).
% 0.51/0.68 tff(730,plain,
% 0.51/0.68 ((e3 = e1) <=> (e1 = e3)),
% 0.51/0.68 inference(commutativity,[status(thm)],[])).
% 0.51/0.68 tff(731,plain,
% 0.51/0.68 (~(op(e3, e3) = e3)),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[688, 8, 6])).
% 0.51/0.68 tff(732,plain,
% 0.51/0.68 (op(e2, e2) = e2),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[53, 8, 4, 6, 102])).
% 0.51/0.68 tff(733,plain,
% 0.51/0.68 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[732])).
% 0.51/0.68 tff(734,plain,
% 0.51/0.68 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.51/0.68 inference(transitivity,[status(thm)],[733, 378])).
% 0.51/0.68 tff(735,plain,
% 0.51/0.68 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[734])).
% 0.51/0.68 tff(736,plain,
% 0.51/0.68 (~(op(e3, e2) = e2)),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[591, 735])).
% 0.51/0.68 tff(737,plain,
% 0.51/0.68 (op(e3, e0) = e2),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[566, 736, 418, 377])).
% 0.51/0.68 tff(738,plain,
% 0.51/0.68 ((op(e3, e0) = e3) <=> (e2 = e3)),
% 0.51/0.68 inference(monotonicity,[status(thm)],[737])).
% 0.51/0.69 tff(739,plain,
% 0.51/0.69 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 0.51/0.69 inference(symmetry,[status(thm)],[738])).
% 0.51/0.69 tff(740,plain,
% 0.51/0.69 ((~(e2 = e3)) <=> (~(op(e3, e0) = e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[739])).
% 0.51/0.69 tff(741,plain,
% 0.51/0.69 (~(op(e3, e0) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[195, 740])).
% 0.51/0.69 tff(742,plain,
% 0.51/0.69 (((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(743,plain,
% 0.51/0.69 ((((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(744,plain,
% 0.51/0.69 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(745,plain,
% 0.51/0.69 (((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> (((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[744])).
% 0.51/0.69 tff(746,plain,
% 0.51/0.69 (((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(transitivity,[status(thm)],[745, 743])).
% 0.51/0.69 tff(747,plain,
% 0.51/0.69 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)),
% 0.51/0.69 inference(and_elim,[status(thm)],[30])).
% 0.51/0.69 tff(748,plain,
% 0.51/0.69 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.51/0.69 tff(749,plain,
% 0.51/0.69 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[748, 742])).
% 0.51/0.69 tff(750,plain,
% 0.51/0.69 (op(e3, e1) = e3),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[749, 741, 482, 731])).
% 0.51/0.69 tff(751,plain,
% 0.51/0.69 ((op(e3, e1) = e1) <=> (e3 = e1)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[750])).
% 0.51/0.69 tff(752,plain,
% 0.51/0.69 ((op(e3, e1) = e1) <=> (e1 = e3)),
% 0.51/0.69 inference(transitivity,[status(thm)],[751, 730])).
% 0.51/0.69 tff(753,plain,
% 0.51/0.69 ((e1 = e3) <=> (op(e3, e1) = e1)),
% 0.51/0.69 inference(symmetry,[status(thm)],[752])).
% 0.51/0.69 tff(754,plain,
% 0.51/0.69 ((~(e1 = e3)) <=> (~(op(e3, e1) = e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[753])).
% 0.51/0.69 tff(755,plain,
% 0.51/0.69 (~(op(e3, e1) = e1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[665, 754])).
% 0.51/0.69 tff(756,plain,
% 0.51/0.69 (((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(757,plain,
% 0.51/0.69 ((((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(758,plain,
% 0.51/0.69 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(759,plain,
% 0.51/0.69 (((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)) <=> (((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[758])).
% 0.51/0.69 tff(760,plain,
% 0.51/0.69 (((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1))),
% 0.51/0.69 inference(transitivity,[status(thm)],[759, 757])).
% 0.51/0.69 tff(761,plain,
% 0.51/0.69 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)),
% 0.51/0.69 inference(and_elim,[status(thm)],[154])).
% 0.51/0.69 tff(762,plain,
% 0.51/0.69 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[761, 760])).
% 0.51/0.69 tff(763,plain,
% 0.51/0.69 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[762, 756])).
% 0.51/0.69 tff(764,plain,
% 0.51/0.69 (op(e2, e1) = e1),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[763, 755, 729, 324])).
% 0.51/0.69 tff(765,plain,
% 0.51/0.69 (op(op(e2, e1), op(e2, e1)) = op(e1, e1)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[764, 764])).
% 0.51/0.69 tff(766,plain,
% 0.51/0.69 (e1 = op(op(e2, e1), op(e2, e1))),
% 0.51/0.69 inference(symmetry,[status(thm)],[12])).
% 0.51/0.69 tff(767,plain,
% 0.51/0.69 (e1 = e2),
% 0.51/0.69 inference(transitivity,[status(thm)],[766, 765, 56])).
% 0.51/0.69 tff(768,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[220, 767])).
% 0.51/0.69 tff(769,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (~(op(e1, e1) = e2)) | (op(e0, e1) = e1) | (op(e3, e2) = e3) | (op(e3, e3) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(770,plain,
% 0.51/0.69 (op(e0, e1) = e1),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[769, 482, 56, 6, 418, 728, 650])).
% 0.51/0.69 tff(771,plain,
% 0.51/0.69 ((op(e0, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[770])).
% 0.51/0.69 tff(772,plain,
% 0.51/0.69 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.51/0.69 inference(transitivity,[status(thm)],[771, 722])).
% 0.51/0.69 tff(773,plain,
% 0.51/0.69 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[772])).
% 0.51/0.69 tff(774,plain,
% 0.51/0.69 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = op(e2, e1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(775,plain,
% 0.51/0.69 (~(op(e0, e1) = op(e2, e1))),
% 0.51/0.69 inference(and_elim,[status(thm)],[107])).
% 0.51/0.69 tff(776,plain,
% 0.51/0.69 (~(op(e0, e1) = op(e2, e1))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.51/0.69 tff(777,plain,
% 0.51/0.69 (~(op(e2, e1) = e1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[776, 773])).
% 0.51/0.69 tff(778,plain,
% 0.51/0.69 ((op(e3, e0) = e3) <=> (e2 = e3)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[641])).
% 0.51/0.69 tff(779,plain,
% 0.51/0.69 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 0.51/0.69 inference(symmetry,[status(thm)],[778])).
% 0.51/0.69 tff(780,plain,
% 0.51/0.69 ((~(e2 = e3)) <=> (~(op(e3, e0) = e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[779])).
% 0.51/0.69 tff(781,plain,
% 0.51/0.69 (~(op(e3, e0) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[195, 780])).
% 0.51/0.69 tff(782,plain,
% 0.51/0.69 (op(e3, e1) = e3),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[749, 482, 781, 689])).
% 0.51/0.69 tff(783,plain,
% 0.51/0.69 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[782])).
% 0.51/0.69 tff(784,plain,
% 0.51/0.69 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[783])).
% 0.51/0.69 tff(785,plain,
% 0.51/0.69 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e3, e1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(786,plain,
% 0.51/0.69 (~(op(e2, e1) = op(e3, e1))),
% 0.51/0.69 inference(and_elim,[status(thm)],[97])).
% 0.51/0.69 tff(787,plain,
% 0.51/0.69 (~(op(e2, e1) = op(e3, e1))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.51/0.69 tff(788,plain,
% 0.51/0.69 (~(op(e2, e1) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[787, 784])).
% 0.51/0.69 tff(789,plain,
% 0.51/0.69 (((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(790,plain,
% 0.51/0.69 ((((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(791,plain,
% 0.51/0.69 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(792,plain,
% 0.51/0.69 (((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)) <=> (((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[791])).
% 0.51/0.69 tff(793,plain,
% 0.51/0.69 (((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3))),
% 0.51/0.69 inference(transitivity,[status(thm)],[792, 790])).
% 0.51/0.69 tff(794,plain,
% 0.51/0.69 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)),
% 0.51/0.69 inference(and_elim,[status(thm)],[249])).
% 0.51/0.69 tff(795,plain,
% 0.51/0.69 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.51/0.69 tff(796,plain,
% 0.51/0.69 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[795, 789])).
% 0.51/0.69 tff(797,plain,
% 0.51/0.69 (op(e2, e1) = e0),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[796, 788, 102, 777])).
% 0.51/0.69 tff(798,plain,
% 0.51/0.69 (e0 = op(e2, e1)),
% 0.51/0.69 inference(symmetry,[status(thm)],[797])).
% 0.51/0.69 tff(799,plain,
% 0.51/0.69 (op(e0, e0) = op(op(e2, e1), op(e2, e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[798, 798])).
% 0.51/0.69 tff(800,plain,
% 0.51/0.69 (op(e0, e0) = e1),
% 0.51/0.69 inference(transitivity,[status(thm)],[799, 721])).
% 0.51/0.69 tff(801,plain,
% 0.51/0.69 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e1)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[770])).
% 0.51/0.69 tff(802,plain,
% 0.51/0.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e1))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[801])).
% 0.51/0.69 tff(803,plain,
% 0.51/0.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = op(e0, e1)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(804,plain,
% 0.51/0.69 (~(op(e0, e0) = op(e0, e1))),
% 0.51/0.69 inference(and_elim,[status(thm)],[84])).
% 0.51/0.69 tff(805,plain,
% 0.51/0.69 (~(op(e0, e0) = op(e0, e1))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.51/0.69 tff(806,plain,
% 0.51/0.69 (~(op(e0, e0) = e1)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[805, 802])).
% 0.51/0.69 tff(807,plain,
% 0.51/0.69 ($false),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[806, 800])).
% 0.51/0.69 tff(808,plain,((op(e3, e2) = e3) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e3) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.69 tff(809,plain,
% 0.51/0.69 (op(e3, e2) = e3),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[808, 418, 6, 56])).
% 0.51/0.69 tff(810,plain,
% 0.51/0.69 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[809])).
% 0.51/0.69 tff(811,plain,
% 0.51/0.69 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.51/0.69 inference(transitivity,[status(thm)],[810, 720])).
% 0.51/0.69 tff(812,plain,
% 0.51/0.69 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.51/0.69 inference(symmetry,[status(thm)],[811])).
% 0.51/0.69 tff(813,plain,
% 0.51/0.69 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[812])).
% 0.51/0.69 tff(814,plain,
% 0.51/0.69 (~(op(e3, e2) = e0)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[684, 813])).
% 0.51/0.69 tff(815,plain,
% 0.51/0.69 ((e1 = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.51/0.69 inference(commutativity,[status(thm)],[])).
% 0.51/0.69 tff(816,plain,
% 0.51/0.69 ((op(e3, e3) = e1) <=> (e1 = op(e3, e3))),
% 0.51/0.69 inference(symmetry,[status(thm)],[815])).
% 0.51/0.69 tff(817,assumption,(~(op(e3, e3) = e3)), introduced(assumption)).
% 0.51/0.69 tff(818,plain,
% 0.51/0.69 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[134])).
% 0.51/0.69 tff(819,plain,
% 0.51/0.69 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.51/0.69 inference(transitivity,[status(thm)],[818, 5])).
% 0.51/0.69 tff(820,plain,
% 0.51/0.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[819])).
% 0.51/0.69 tff(821,plain,
% 0.51/0.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = op(e3, e3)))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(822,plain,
% 0.51/0.69 (~(op(e0, e3) = op(e3, e3))),
% 0.51/0.69 inference(and_elim,[status(thm)],[88])).
% 0.51/0.69 tff(823,plain,
% 0.51/0.69 (~(op(e0, e3) = op(e3, e3))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.51/0.69 tff(824,plain,
% 0.51/0.69 (~(op(e3, e3) = e2)),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[823, 820])).
% 0.51/0.69 tff(825,assumption,(~(op(e3, e3) = e0)), introduced(assumption)).
% 0.51/0.69 tff(826,plain,
% 0.51/0.69 (((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(827,plain,
% 0.51/0.69 ((((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(828,plain,
% 0.51/0.69 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(829,plain,
% 0.51/0.70 (((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)) <=> (((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2)) | (op(e3, e3) = e3))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[828])).
% 0.51/0.70 tff(830,plain,
% 0.51/0.70 (((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3))),
% 0.51/0.70 inference(transitivity,[status(thm)],[829, 827])).
% 0.51/0.70 tff(831,plain,
% 0.51/0.70 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)),
% 0.51/0.70 inference(and_elim,[status(thm)],[243])).
% 0.51/0.70 tff(832,plain,
% 0.51/0.70 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.51/0.70 tff(833,plain,
% 0.51/0.70 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[832, 826])).
% 0.51/0.70 tff(834,plain,
% 0.51/0.70 (op(e3, e3) = e1),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[833, 825, 824, 817])).
% 0.51/0.70 tff(835,plain,
% 0.51/0.70 (e1 = op(e3, e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[834, 816])).
% 0.51/0.70 tff(836,plain,
% 0.51/0.70 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[834])).
% 0.51/0.70 tff(837,plain,
% 0.51/0.70 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[836])).
% 0.51/0.70 tff(838,assumption,(~(op(e3, e0) = e0)), introduced(assumption)).
% 0.51/0.70 tff(839,plain,
% 0.51/0.70 (op(e3, e1) = e0),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[580, 825, 481, 838])).
% 0.51/0.70 tff(840,plain,
% 0.51/0.70 (e0 = op(e3, e1)),
% 0.51/0.70 inference(symmetry,[status(thm)],[839])).
% 0.51/0.70 tff(841,plain,
% 0.51/0.70 (e0 = op(e3, op(e3, e3))),
% 0.51/0.70 inference(transitivity,[status(thm)],[840, 837])).
% 0.51/0.70 tff(842,plain,
% 0.51/0.70 (op(e3, op(e3, e3)) = e0),
% 0.51/0.70 inference(transitivity,[status(thm)],[836, 839])).
% 0.51/0.70 tff(843,plain,
% 0.51/0.70 (op(op(e3, op(e3, e3)), e3) = op(e0, e3)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[842])).
% 0.51/0.70 tff(844,plain,
% 0.51/0.70 (op(e0, e3) = op(op(e3, op(e3, e3)), e3)),
% 0.51/0.70 inference(symmetry,[status(thm)],[843])).
% 0.51/0.70 tff(845,plain,
% 0.51/0.70 (e2 = op(op(e3, op(e3, e3)), e3)),
% 0.51/0.70 inference(transitivity,[status(thm)],[135, 844])).
% 0.51/0.70 tff(846,plain,
% 0.51/0.70 ((~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3)))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(847,plain,
% 0.51/0.70 (((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3))) <=> (~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(848,plain,
% 0.51/0.70 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3)))) <=> (~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[847])).
% 0.51/0.70 tff(849,plain,
% 0.51/0.70 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3)))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[848, 846])).
% 0.51/0.70 tff(850,plain,
% 0.51/0.70 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(851,plain,
% 0.51/0.70 ((~(((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(852,axiom,(~(((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax6')).
% 0.51/0.70 tff(853,plain,
% 0.51/0.70 (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.51/0.70 tff(854,plain,
% 0.51/0.70 (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(op(e3, op(e3, e3)), e3)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[853, 850])).
% 0.51/0.70 tff(855,plain,
% 0.51/0.70 ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(op(e3, op(e3, e3)), e3)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[854, 849])).
% 0.51/0.70 tff(856,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[855, 845, 841, 835])).
% 0.51/0.70 tff(857,plain,((op(e3, e3) = e0) | (~(op(e0, e3) = e2)) | (op(e3, e2) = e0) | (op(e3, e0) = e0) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(858,plain,
% 0.51/0.70 (op(e3, e3) = e0),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[857, 814, 719, 694, 689])).
% 0.51/0.70 tff(859,plain,
% 0.51/0.70 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[858])).
% 0.51/0.70 tff(860,plain,
% 0.51/0.70 (op(e3, op(e3, e3)) = e2),
% 0.51/0.70 inference(transitivity,[status(thm)],[859, 641])).
% 0.51/0.70 tff(861,plain,
% 0.51/0.70 (op(op(e3, op(e3, e3)), e3) = op(e2, e3)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[860])).
% 0.51/0.70 tff(862,plain,
% 0.51/0.70 ((e1 = op(op(e3, op(e3, e3)), e3)) <=> (e1 = op(e2, e3))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[861])).
% 0.51/0.70 tff(863,plain,
% 0.51/0.70 ((e1 = op(op(e3, op(e3, e3)), e3)) <=> (op(e2, e3) = e1)),
% 0.51/0.70 inference(transitivity,[status(thm)],[862, 369])).
% 0.51/0.70 tff(864,plain,
% 0.51/0.70 ((~(e1 = op(op(e3, op(e3, e3)), e3))) <=> (~(op(e2, e3) = e1))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[863])).
% 0.51/0.70 tff(865,plain,
% 0.51/0.70 (op(e3, e0) = op(e3, op(e3, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[859])).
% 0.51/0.70 tff(866,plain,
% 0.51/0.70 (e2 = op(e3, e0)),
% 0.51/0.70 inference(symmetry,[status(thm)],[641])).
% 0.51/0.70 tff(867,plain,
% 0.51/0.70 (e2 = op(e3, op(e3, e3))),
% 0.51/0.70 inference(transitivity,[status(thm)],[866, 865])).
% 0.51/0.70 tff(868,plain,
% 0.51/0.70 ((e0 = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.51/0.70 inference(commutativity,[status(thm)],[])).
% 0.51/0.70 tff(869,plain,
% 0.51/0.70 ((op(e3, e3) = e0) <=> (e0 = op(e3, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[868])).
% 0.51/0.70 tff(870,plain,
% 0.51/0.70 (e0 = op(e3, e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[858, 869])).
% 0.51/0.70 tff(871,plain,
% 0.51/0.70 ((~(~((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))))) <=> ((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(872,plain,
% 0.51/0.70 (((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))) <=> (~((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(873,plain,
% 0.51/0.70 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~(~((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[872])).
% 0.51/0.70 tff(874,plain,
% 0.51/0.70 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> ((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[873, 871])).
% 0.51/0.70 tff(875,plain,
% 0.51/0.70 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(876,plain,
% 0.51/0.70 ((~(((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(877,axiom,(~(((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax18')).
% 0.51/0.70 tff(878,plain,
% 0.51/0.70 (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.51/0.70 tff(879,plain,
% 0.51/0.70 (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[878, 875])).
% 0.51/0.70 tff(880,plain,
% 0.51/0.70 ((~(e1 = op(op(e3, op(e3, e3)), e3))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[879, 874])).
% 0.51/0.70 tff(881,plain,
% 0.51/0.70 (~(e1 = op(op(e3, op(e3, e3)), e3))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[880, 870, 867])).
% 0.51/0.70 tff(882,plain,
% 0.51/0.70 (~(op(e2, e3) = e1)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[881, 864])).
% 0.51/0.70 tff(883,plain,
% 0.51/0.70 (op(op(e2, e3), op(e2, e3)) = e3),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[14, 650])).
% 0.51/0.70 tff(884,assumption,(op(e2, e3) = e3), introduced(assumption)).
% 0.51/0.70 tff(885,plain,
% 0.51/0.70 (op(op(e2, e3), op(e2, e3)) = op(e3, e3)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[884, 884])).
% 0.51/0.70 tff(886,plain,
% 0.51/0.70 (op(e3, e3) = op(op(e2, e3), op(e2, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[885])).
% 0.51/0.70 tff(887,assumption,(op(e3, e3) = e0), introduced(assumption)).
% 0.51/0.70 tff(888,plain,
% 0.51/0.70 (e0 = op(e3, e3)),
% 0.51/0.70 inference(symmetry,[status(thm)],[887])).
% 0.51/0.70 tff(889,plain,
% 0.51/0.70 (e0 = e3),
% 0.51/0.70 inference(transitivity,[status(thm)],[888, 886, 16])).
% 0.51/0.70 tff(890,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[684, 889])).
% 0.51/0.70 tff(891,plain,((~(op(e2, e3) = e3)) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(892,plain,
% 0.51/0.70 (~(op(e2, e3) = e3)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[891, 858, 883])).
% 0.51/0.70 tff(893,plain,
% 0.51/0.70 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[858])).
% 0.51/0.70 tff(894,plain,
% 0.51/0.70 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[893])).
% 0.51/0.70 tff(895,plain,
% 0.51/0.70 (~(op(e2, e3) = e0)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[656, 894])).
% 0.51/0.70 tff(896,plain,
% 0.51/0.70 (((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(897,plain,
% 0.51/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(898,plain,
% 0.51/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(899,plain,
% 0.51/0.70 (((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> (((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[898])).
% 0.51/0.70 tff(900,plain,
% 0.51/0.70 (((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.51/0.70 inference(transitivity,[status(thm)],[899, 897])).
% 0.51/0.70 tff(901,plain,
% 0.51/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)),
% 0.51/0.70 inference(and_elim,[status(thm)],[247])).
% 0.51/0.70 tff(902,plain,
% 0.51/0.70 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.51/0.70 tff(903,plain,
% 0.51/0.70 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[902, 896])).
% 0.51/0.70 tff(904,plain,
% 0.51/0.70 (op(e2, e3) = e1),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[903, 895, 710, 892])).
% 0.51/0.70 tff(905,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[904, 882])).
% 0.51/0.70 tff(906,plain,((op(e3, e3) = e2) | (op(e2, e2) = e3) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(907,plain,
% 0.51/0.70 (op(e3, e3) = e2),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[906, 6, 56])).
% 0.51/0.70 tff(908,plain,
% 0.51/0.70 (~(op(op(e3, e3), op(e3, e3)) = e3)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[631, 907, 6])).
% 0.51/0.70 tff(909,plain,
% 0.51/0.70 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[633, 908])).
% 0.51/0.70 tff(910,plain,
% 0.51/0.70 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[416, 909, 368, 311])).
% 0.51/0.70 tff(911,plain,
% 0.51/0.70 (op(op(e2, e3), op(e2, e3)) = e3),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[14, 910])).
% 0.51/0.70 tff(912,plain,
% 0.51/0.70 (e2 = e3),
% 0.51/0.70 inference(transitivity,[status(thm)],[627, 886, 16])).
% 0.51/0.70 tff(913,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[195, 912])).
% 0.51/0.70 tff(914,plain,((~(op(e2, e3) = e3)) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(915,plain,
% 0.51/0.70 (~(op(e2, e3) = e3)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[914, 911, 907])).
% 0.51/0.70 tff(916,plain,
% 0.51/0.70 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[636])).
% 0.51/0.70 tff(917,plain,
% 0.51/0.70 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[916])).
% 0.51/0.70 tff(918,plain,
% 0.51/0.70 (~(op(e0, e2) = e2)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[126, 917])).
% 0.51/0.70 tff(919,plain,
% 0.51/0.70 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[907])).
% 0.51/0.70 tff(920,plain,
% 0.51/0.70 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[919])).
% 0.51/0.70 tff(921,plain,
% 0.51/0.70 (~(op(e0, e3) = e2)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[823, 920])).
% 0.51/0.70 tff(922,plain,
% 0.51/0.70 (op(e0, e0) = e2),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[164, 921, 111, 918])).
% 0.51/0.70 tff(923,assumption,(op(e2, e3) = e0), introduced(assumption)).
% 0.51/0.70 tff(924,plain,
% 0.51/0.70 (op(op(e2, e3), op(e2, e3)) = op(e0, e0)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[923, 923])).
% 0.51/0.70 tff(925,plain,
% 0.51/0.70 (op(e0, e0) = op(op(e2, e3), op(e2, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[924])).
% 0.51/0.70 tff(926,plain,
% 0.51/0.70 (e2 = e3),
% 0.51/0.70 inference(transitivity,[status(thm)],[190, 925, 16])).
% 0.51/0.70 tff(927,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[195, 926])).
% 0.51/0.70 tff(928,plain,((~(op(e2, e3) = e0)) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (~(op(e0, e0) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(929,plain,
% 0.51/0.70 (~(op(e2, e3) = e0)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[928, 911, 922])).
% 0.51/0.70 tff(930,plain,
% 0.51/0.70 (op(e2, e3) = e1),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[903, 929, 710, 915])).
% 0.51/0.70 tff(931,plain,
% 0.51/0.70 (op(op(e2, e3), op(e2, e3)) = op(e1, e1)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[930, 930])).
% 0.51/0.70 tff(932,plain,
% 0.51/0.70 (op(e1, e1) = op(op(e2, e3), op(e2, e3))),
% 0.51/0.70 inference(symmetry,[status(thm)],[931])).
% 0.51/0.70 tff(933,plain,
% 0.51/0.70 (e2 = e3),
% 0.51/0.70 inference(transitivity,[status(thm)],[364, 932, 911])).
% 0.51/0.70 tff(934,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[195, 933])).
% 0.51/0.70 tff(935,plain,((op(e2, e2) = e3) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(936,plain,
% 0.51/0.70 (op(e2, e2) = e3),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[935, 56])).
% 0.51/0.70 tff(937,plain,
% 0.51/0.70 ((e3 = e2) <=> (e2 = e3)),
% 0.51/0.70 inference(commutativity,[status(thm)],[])).
% 0.51/0.70 tff(938,plain,
% 0.51/0.70 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[936])).
% 0.51/0.70 tff(939,plain,
% 0.51/0.70 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.51/0.70 inference(transitivity,[status(thm)],[938, 937])).
% 0.51/0.70 tff(940,plain,
% 0.51/0.70 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.51/0.70 inference(symmetry,[status(thm)],[939])).
% 0.51/0.70 tff(941,plain,
% 0.51/0.70 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[940])).
% 0.51/0.70 tff(942,plain,
% 0.51/0.70 (~(op(e2, e2) = e2)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[195, 941])).
% 0.51/0.70 tff(943,assumption,(op(e2, e2) = e3), introduced(assumption)).
% 0.51/0.70 tff(944,plain,
% 0.51/0.70 (e3 = op(e2, e2)),
% 0.51/0.70 inference(symmetry,[status(thm)],[943])).
% 0.51/0.70 tff(945,plain,
% 0.51/0.70 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[944, 944])).
% 0.51/0.70 tff(946,plain,
% 0.51/0.70 (op(e3, e3) = e2),
% 0.51/0.70 inference(transitivity,[status(thm)],[945, 10])).
% 0.51/0.70 tff(947,plain,
% 0.51/0.70 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 0.51/0.70 inference(monotonicity,[status(thm)],[946])).
% 0.51/0.70 tff(948,plain,
% 0.51/0.70 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[947])).
% 0.51/0.70 tff(949,plain,
% 0.51/0.70 (~(op(e2, e3) = e2)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[656, 948])).
% 0.51/0.71 tff(950,plain,
% 0.51/0.71 (op(e2, e0) = e2),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[43, 949, 13, 3])).
% 0.51/0.71 tff(951,plain,
% 0.51/0.71 (op(op(e2, e0), op(e2, e0)) = op(e2, e2)),
% 0.51/0.71 inference(monotonicity,[status(thm)],[950, 950])).
% 0.51/0.71 tff(952,plain,
% 0.51/0.71 (op(e2, e2) = op(op(e2, e0), op(e2, e0))),
% 0.51/0.71 inference(symmetry,[status(thm)],[951])).
% 0.51/0.71 tff(953,plain,
% 0.51/0.71 (op(e2, e2) = e0),
% 0.51/0.71 inference(transitivity,[status(thm)],[952, 47])).
% 0.51/0.71 tff(954,plain,
% 0.51/0.71 ((e0 = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.51/0.71 inference(commutativity,[status(thm)],[])).
% 0.51/0.71 tff(955,plain,
% 0.51/0.71 ((e0 = e3) <=> (e0 = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[944])).
% 0.51/0.71 tff(956,plain,
% 0.51/0.71 ((e0 = e3) <=> (op(e2, e2) = e0)),
% 0.51/0.71 inference(transitivity,[status(thm)],[955, 954])).
% 0.51/0.71 tff(957,plain,
% 0.51/0.71 ((~(e0 = e3)) <=> (~(op(e2, e2) = e0))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[956])).
% 0.51/0.71 tff(958,plain,
% 0.51/0.71 (~(op(e2, e2) = e0)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[684, 957])).
% 0.51/0.71 tff(959,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[958, 953])).
% 0.51/0.71 tff(960,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (~(op(e2, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(961,plain,
% 0.51/0.71 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[960, 942, 936, 102])).
% 0.51/0.71 tff(962,plain,
% 0.51/0.71 ((op(e3, e2) = op(e2, e2)) <=> (op(e2, e2) = op(e3, e2))),
% 0.51/0.71 inference(commutativity,[status(thm)],[])).
% 0.51/0.71 tff(963,plain,
% 0.51/0.71 (e3 = op(e2, e2)),
% 0.51/0.71 inference(symmetry,[status(thm)],[936])).
% 0.51/0.71 tff(964,plain,
% 0.51/0.71 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[963])).
% 0.51/0.71 tff(965,plain,
% 0.51/0.71 ((op(e3, e2) = e3) <=> (op(e2, e2) = op(e3, e2))),
% 0.51/0.71 inference(transitivity,[status(thm)],[964, 962])).
% 0.51/0.71 tff(966,plain,
% 0.51/0.71 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.51/0.71 inference(symmetry,[status(thm)],[965])).
% 0.51/0.71 tff(967,plain,
% 0.51/0.71 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[966])).
% 0.51/0.71 tff(968,plain,
% 0.51/0.71 (~(op(e3, e2) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[591, 967])).
% 0.51/0.71 tff(969,plain,
% 0.51/0.71 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[522])).
% 0.51/0.71 tff(970,plain,
% 0.51/0.71 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 0.51/0.71 inference(transitivity,[status(thm)],[969, 1])).
% 0.51/0.71 tff(971,plain,
% 0.51/0.71 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 0.51/0.71 inference(symmetry,[status(thm)],[970])).
% 0.51/0.71 tff(972,plain,
% 0.51/0.71 ((e0 = e3) <=> (e0 = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[963])).
% 0.51/0.71 tff(973,plain,
% 0.51/0.71 ((e0 = e3) <=> (op(e2, e2) = e0)),
% 0.51/0.71 inference(transitivity,[status(thm)],[972, 954])).
% 0.51/0.71 tff(974,plain,
% 0.51/0.71 ((~(e0 = e3)) <=> (~(op(e2, e2) = e0))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[973])).
% 0.51/0.71 tff(975,plain,
% 0.51/0.71 (~(op(e2, e2) = e0)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[684, 974])).
% 0.51/0.71 tff(976,plain,
% 0.51/0.71 (~(op(e0, e2) = e0)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[229, 115, 4])).
% 0.51/0.71 tff(977,assumption,(~(op(e1, e2) = e2)), introduced(assumption)).
% 0.51/0.71 tff(978,plain,
% 0.51/0.71 (op(e0, e2) = e2),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[507, 3, 977, 483])).
% 0.51/0.71 tff(979,plain,
% 0.51/0.71 (e2 = op(e0, e2)),
% 0.51/0.71 inference(symmetry,[status(thm)],[978])).
% 0.51/0.71 tff(980,plain,
% 0.51/0.71 (op(e2, e2) = op(op(e0, e2), op(e0, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[979, 979])).
% 0.51/0.71 tff(981,plain,
% 0.51/0.71 (op(e2, e2) = e2),
% 0.51/0.71 inference(transitivity,[status(thm)],[980, 116])).
% 0.51/0.71 tff(982,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[3, 981])).
% 0.51/0.71 tff(983,plain,((op(e2, e2) = e2) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (op(e1, e2) = e2) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(984,plain,
% 0.51/0.71 (op(e3, e2) = e2),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[983, 115, 428, 942])).
% 0.51/0.71 tff(985,plain,
% 0.51/0.71 ((op(e3, e2) = e0) <=> (e2 = e0)),
% 0.51/0.71 inference(monotonicity,[status(thm)],[984])).
% 0.51/0.71 tff(986,plain,
% 0.51/0.71 ((op(e3, e2) = e0) <=> (e0 = e2)),
% 0.51/0.71 inference(transitivity,[status(thm)],[985, 263])).
% 0.51/0.71 tff(987,plain,
% 0.51/0.71 ((e0 = e2) <=> (op(e3, e2) = e0)),
% 0.51/0.71 inference(symmetry,[status(thm)],[986])).
% 0.51/0.71 tff(988,plain,
% 0.51/0.71 ((~(e0 = e2)) <=> (~(op(e3, e2) = e0))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[987])).
% 0.51/0.71 tff(989,plain,
% 0.51/0.71 (~(op(e3, e2) = e0)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[272, 988])).
% 0.51/0.71 tff(990,plain,
% 0.51/0.71 (((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(991,plain,
% 0.51/0.71 ((((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(992,plain,
% 0.51/0.71 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(993,plain,
% 0.51/0.71 (((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)) <=> (((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[992])).
% 0.51/0.71 tff(994,plain,
% 0.51/0.71 (((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0))),
% 0.51/0.71 inference(transitivity,[status(thm)],[993, 991])).
% 0.51/0.71 tff(995,plain,
% 0.51/0.71 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)),
% 0.51/0.71 inference(and_elim,[status(thm)],[148])).
% 0.51/0.71 tff(996,plain,
% 0.51/0.71 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.51/0.71 tff(997,plain,
% 0.51/0.71 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[996, 990])).
% 0.51/0.71 tff(998,plain,
% 0.51/0.71 (op(e1, e2) = e0),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[997, 989, 976, 975])).
% 0.51/0.71 tff(999,plain,
% 0.51/0.71 (e0 = op(e1, op(e1, e1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[998, 971])).
% 0.51/0.71 tff(1000,plain,
% 0.51/0.71 (op(e1, op(e1, e1)) = e0),
% 0.51/0.71 inference(transitivity,[status(thm)],[522, 998])).
% 0.51/0.71 tff(1001,plain,
% 0.51/0.71 (op(op(e1, op(e1, e1)), e1) = op(e0, e1)),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1000])).
% 0.51/0.71 tff(1002,plain,
% 0.51/0.71 (op(e0, e1) = op(op(e1, op(e1, e1)), e1)),
% 0.51/0.71 inference(symmetry,[status(thm)],[1001])).
% 0.51/0.71 tff(1003,plain,
% 0.51/0.71 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[963])).
% 0.51/0.71 tff(1004,plain,
% 0.51/0.71 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.51/0.71 inference(symmetry,[status(thm)],[1003])).
% 0.51/0.71 tff(1005,plain,
% 0.51/0.71 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1004])).
% 0.51/0.71 tff(1006,plain,
% 0.51/0.71 (~(op(e0, e2) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[126, 1005])).
% 0.51/0.71 tff(1007,plain,
% 0.51/0.71 ((op(e0, e0) = e3) <=> (e0 = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[306, 963])).
% 0.51/0.71 tff(1008,plain,
% 0.51/0.71 ((op(e0, e0) = e3) <=> (op(e2, e2) = e0)),
% 0.51/0.71 inference(transitivity,[status(thm)],[1007, 954])).
% 0.51/0.71 tff(1009,plain,
% 0.51/0.71 ((op(e2, e2) = e0) <=> (op(e0, e0) = e3)),
% 0.51/0.71 inference(symmetry,[status(thm)],[1008])).
% 0.51/0.71 tff(1010,plain,
% 0.51/0.71 ((~(op(e2, e2) = e0)) <=> (~(op(e0, e0) = e3))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1009])).
% 0.51/0.71 tff(1011,plain,
% 0.51/0.71 (~(op(e0, e0) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[975, 1010])).
% 0.51/0.71 tff(1012,plain,
% 0.51/0.71 (op(e0, e3) = e2),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[164, 130, 111, 4])).
% 0.51/0.71 tff(1013,plain,
% 0.51/0.71 ((op(e0, e3) = e3) <=> (e2 = op(e2, e2))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1012, 963])).
% 0.51/0.71 tff(1014,plain,
% 0.51/0.71 ((op(e0, e3) = e3) <=> (op(e2, e2) = e2)),
% 0.51/0.71 inference(transitivity,[status(thm)],[1013, 7])).
% 0.51/0.71 tff(1015,plain,
% 0.51/0.71 ((op(e2, e2) = e2) <=> (op(e0, e3) = e3)),
% 0.51/0.71 inference(symmetry,[status(thm)],[1014])).
% 0.51/0.71 tff(1016,plain,
% 0.51/0.71 ((~(op(e2, e2) = e2)) <=> (~(op(e0, e3) = e3))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1015])).
% 0.51/0.71 tff(1017,plain,
% 0.51/0.71 (~(op(e0, e3) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[942, 1016])).
% 0.51/0.71 tff(1018,plain,
% 0.51/0.71 (((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1019,plain,
% 0.51/0.71 ((((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1020,plain,
% 0.51/0.71 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(1021,plain,
% 0.51/0.71 (((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)) <=> (((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[1020])).
% 0.51/0.71 tff(1022,plain,
% 0.51/0.71 (((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3))),
% 0.51/0.71 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.51/0.71 tff(1023,plain,
% 0.51/0.71 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)),
% 0.51/0.71 inference(and_elim,[status(thm)],[159])).
% 0.51/0.71 tff(1024,plain,
% 0.51/0.71 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.51/0.71 tff(1025,plain,
% 0.51/0.71 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[1024, 1018])).
% 0.51/0.71 tff(1026,plain,
% 0.51/0.71 (op(e0, e1) = e3),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[1025, 1017, 1011, 1006])).
% 0.51/0.71 tff(1027,plain,
% 0.51/0.71 (e3 = op(e0, e1)),
% 0.51/0.71 inference(symmetry,[status(thm)],[1026])).
% 0.51/0.71 tff(1028,plain,
% 0.51/0.71 (e3 = op(op(e1, op(e1, e1)), e1)),
% 0.58/0.71 inference(transitivity,[status(thm)],[1027, 1002])).
% 0.58/0.71 tff(1029,plain,
% 0.58/0.71 ((~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1)))))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1))))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1030,plain,
% 0.58/0.71 (((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1))) <=> (~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1)))))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1031,plain,
% 0.58/0.71 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1)))) <=> (~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1))))))),
% 0.58/0.71 inference(monotonicity,[status(thm)],[1030])).
% 0.58/0.71 tff(1032,plain,
% 0.58/0.71 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1)))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1))))),
% 0.58/0.71 inference(transitivity,[status(thm)],[1031, 1029])).
% 0.58/0.71 tff(1033,plain,
% 0.58/0.71 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1)))) <=> (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1))))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1034,plain,
% 0.58/0.71 ((~(((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), e1)))) <=> (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1))))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(1035,axiom,(~(((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), e1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax9')).
% 0.58/0.71 tff(1036,plain,
% 0.58/0.71 (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1)))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.58/0.71 tff(1037,plain,
% 0.58/0.71 (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(op(e1, op(e1, e1)), e1)))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1036, 1033])).
% 0.58/0.72 tff(1038,plain,
% 0.58/0.72 ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(op(e1, op(e1, e1)), e1)))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1037, 1032])).
% 0.58/0.72 tff(1039,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1038, 1028, 999, 530])).
% 0.58/0.72 tff(1040,plain,(((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (~(op(e1, e1) = e2)) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1041,plain,
% 0.58/0.72 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1040, 4, 56])).
% 0.58/0.72 tff(1042,plain,
% 0.58/0.72 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[416, 1041, 368, 961])).
% 0.58/0.72 tff(1043,plain,
% 0.58/0.72 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[459, 1042])).
% 0.58/0.72 tff(1044,plain,
% 0.58/0.72 (~(op(e3, e2) = e0)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[474, 1043, 4])).
% 0.58/0.72 tff(1045,assumption,(op(e3, e2) = e2), introduced(assumption)).
% 0.58/0.72 tff(1046,plain,
% 0.58/0.72 (e2 = op(e3, e2)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1045])).
% 0.58/0.72 tff(1047,plain,
% 0.58/0.72 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1046, 1046])).
% 0.58/0.72 tff(1048,plain,
% 0.58/0.72 (op(e2, e2) = e2),
% 0.58/0.72 inference(transitivity,[status(thm)],[1047, 461])).
% 0.58/0.72 tff(1049,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[3, 1048])).
% 0.58/0.72 tff(1050,plain,((~(op(e3, e2) = e2)) | (op(e2, e2) = e2) | (~(op(op(e3, e2), op(e3, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1051,plain,
% 0.58/0.72 (~(op(e3, e2) = e2)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1050, 1043, 942])).
% 0.58/0.72 tff(1052,plain,
% 0.58/0.72 (op(e3, e2) = e1),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[491, 1051, 1044, 968])).
% 0.58/0.72 tff(1053,plain,
% 0.58/0.72 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1052])).
% 0.58/0.72 tff(1054,plain,
% 0.58/0.72 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1053])).
% 0.58/0.72 tff(1055,plain,
% 0.58/0.72 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = op(e3, e2)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1056,plain,
% 0.58/0.72 (~(op(e3, e0) = op(e3, e2))),
% 0.58/0.72 inference(and_elim,[status(thm)],[65])).
% 0.58/0.72 tff(1057,plain,
% 0.58/0.72 (~(op(e3, e0) = op(e3, e2))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.58/0.72 tff(1058,plain,
% 0.58/0.72 (~(op(e3, e0) = e1)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 0.58/0.72 tff(1059,plain,
% 0.58/0.72 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[476, 1042])).
% 0.58/0.72 tff(1060,assumption,(op(e3, e0) = e2), introduced(assumption)).
% 0.58/0.72 tff(1061,plain,
% 0.58/0.72 (op(op(e3, e0), op(e3, e0)) = op(e2, e2)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1060, 1060])).
% 0.58/0.72 tff(1062,plain,
% 0.58/0.72 (op(e2, e2) = op(op(e3, e0), op(e3, e0))),
% 0.58/0.72 inference(symmetry,[status(thm)],[1061])).
% 0.58/0.72 tff(1063,plain,
% 0.58/0.72 (op(e2, e2) = e0),
% 0.58/0.72 inference(transitivity,[status(thm)],[1062, 583])).
% 0.58/0.72 tff(1064,assumption,(~(op(e2, e2) = e0)), introduced(assumption)).
% 0.58/0.72 tff(1065,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1064, 1063])).
% 0.58/0.72 tff(1066,plain,((~(op(e3, e0) = e2)) | (op(e2, e2) = e0) | (~(op(op(e3, e0), op(e3, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1067,plain,
% 0.58/0.72 (~(op(e3, e0) = e2)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1066, 1059, 975])).
% 0.58/0.72 tff(1068,plain,
% 0.58/0.72 (op(e3, e3) = e2),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[566, 1051, 1067, 377])).
% 0.58/0.72 tff(1069,plain,
% 0.58/0.72 ((op(e3, e3) = e0) <=> (e2 = e0)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1068])).
% 0.58/0.72 tff(1070,plain,
% 0.58/0.72 ((op(e3, e3) = e0) <=> (e0 = e2)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1069, 263])).
% 0.58/0.72 tff(1071,plain,
% 0.58/0.72 ((e0 = e2) <=> (op(e3, e3) = e0)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1070])).
% 0.58/0.72 tff(1072,plain,
% 0.58/0.72 ((~(e0 = e2)) <=> (~(op(e3, e3) = e0))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1071])).
% 0.58/0.72 tff(1073,plain,
% 0.58/0.72 (~(op(e3, e3) = e0)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[272, 1072])).
% 0.58/0.72 tff(1074,assumption,(op(e3, e0) = e3), introduced(assumption)).
% 0.58/0.72 tff(1075,plain,
% 0.58/0.72 (e3 = op(e3, e0)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1074])).
% 0.58/0.72 tff(1076,plain,
% 0.58/0.72 (op(e3, e3) = op(op(e3, e0), op(e3, e0))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1075, 1075])).
% 0.58/0.72 tff(1077,plain,
% 0.58/0.72 (op(e3, e3) = e0),
% 0.58/0.72 inference(transitivity,[status(thm)],[1076, 583])).
% 0.58/0.72 tff(1078,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[825, 1077])).
% 0.58/0.72 tff(1079,plain,((~(op(e3, e0) = e3)) | (op(e3, e3) = e0) | (~(op(op(e3, e0), op(e3, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1080,plain,
% 0.58/0.72 (~(op(e3, e0) = e3)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1079, 1073, 1059])).
% 0.58/0.72 tff(1081,plain,
% 0.58/0.72 (((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1082,plain,
% 0.58/0.72 ((((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1083,plain,
% 0.58/0.72 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1084,plain,
% 0.58/0.72 (((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> (((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1083])).
% 0.58/0.72 tff(1085,plain,
% 0.58/0.72 (((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.58/0.72 inference(transitivity,[status(thm)],[1084, 1082])).
% 0.58/0.72 tff(1086,plain,
% 0.58/0.72 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)),
% 0.58/0.72 inference(and_elim,[status(thm)],[246])).
% 0.58/0.72 tff(1087,plain,
% 0.58/0.72 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.58/0.72 tff(1088,plain,
% 0.58/0.72 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1087, 1081])).
% 0.58/0.72 tff(1089,plain,
% 0.58/0.72 (op(e3, e0) = e0),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1088, 1080, 1067, 1058])).
% 0.58/0.72 tff(1090,plain,
% 0.58/0.72 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e0)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1089])).
% 0.58/0.72 tff(1091,plain,
% 0.58/0.72 ((op(e0, e0) = e0) <=> (op(e0, e0) = op(e3, e0))),
% 0.58/0.72 inference(symmetry,[status(thm)],[1090])).
% 0.58/0.72 tff(1092,assumption,(op(e3, e0) = e0), introduced(assumption)).
% 0.58/0.72 tff(1093,plain,
% 0.58/0.72 (e0 = op(e3, e0)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1092])).
% 0.58/0.72 tff(1094,plain,
% 0.58/0.72 (op(e0, e0) = op(op(e3, e0), op(e3, e0))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1093, 1093])).
% 0.58/0.72 tff(1095,plain,
% 0.58/0.72 (op(e0, e0) = e0),
% 0.58/0.72 inference(transitivity,[status(thm)],[1094, 583])).
% 0.58/0.72 tff(1096,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[168, 1095])).
% 0.58/0.72 tff(1097,plain,((~(op(e3, e0) = e0)) | (op(e0, e0) = e0) | (~(op(op(e3, e0), op(e3, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1098,plain,
% 0.58/0.72 (op(e0, e0) = e0),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1097, 1089, 1059])).
% 0.58/0.72 tff(1099,plain,
% 0.58/0.72 (op(e0, e0) = op(e3, e0)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1098, 1091])).
% 0.58/0.72 tff(1100,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[616, 1099])).
% 0.58/0.72 tff(1101,plain,((op(e0, e0) = e2) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1102,plain,
% 0.58/0.72 (op(e0, e0) = e2),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1101, 56])).
% 0.58/0.72 tff(1103,plain,
% 0.58/0.72 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1102])).
% 0.58/0.72 tff(1104,plain,
% 0.58/0.72 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1103, 263])).
% 0.58/0.72 tff(1105,plain,
% 0.58/0.72 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1104])).
% 0.58/0.72 tff(1106,plain,
% 0.58/0.72 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1105])).
% 0.58/0.72 tff(1107,plain,
% 0.58/0.72 (~(op(e0, e0) = e0)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[272, 1106])).
% 0.58/0.72 tff(1108,plain,
% 0.58/0.72 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[305, 1107])).
% 0.58/0.72 tff(1109,plain,
% 0.58/0.72 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[416, 1108, 368, 961])).
% 0.58/0.72 tff(1110,plain,
% 0.58/0.72 ((op(e0, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1102])).
% 0.58/0.72 tff(1111,plain,
% 0.58/0.72 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1110, 2])).
% 0.58/0.72 tff(1112,plain,
% 0.58/0.72 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1111])).
% 0.58/0.72 tff(1113,plain,
% 0.58/0.72 (~(op(e0, e2) = e2)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[281, 1112])).
% 0.58/0.72 tff(1114,plain,
% 0.58/0.72 (op(e3, e2) = e2),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[507, 1113, 428, 942])).
% 0.58/0.72 tff(1115,plain,
% 0.58/0.72 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1050, 1114, 942])).
% 0.58/0.72 tff(1116,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[459, 1115, 1109])).
% 0.58/0.72 tff(1117,plain,(~(op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1118,assumption,(op(op(e2, e2), op(e2, e2)) = e2), introduced(assumption)).
% 0.58/0.72 tff(1119,assumption,(op(e2, e1) = e2), introduced(assumption)).
% 0.58/0.72 tff(1120,plain,
% 0.58/0.72 (op(op(e2, e1), op(e2, e1)) = op(e2, e2)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1119, 1119])).
% 0.58/0.72 tff(1121,plain,
% 0.58/0.72 (e1 = op(e2, e2)),
% 0.58/0.72 inference(transitivity,[status(thm)],[661, 1120])).
% 0.58/0.72 tff(1122,plain,
% 0.58/0.72 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1121, 1121])).
% 0.58/0.72 tff(1123,plain,
% 0.58/0.72 (op(e1, e1) = e2),
% 0.58/0.72 inference(transitivity,[status(thm)],[1122, 1118])).
% 0.58/0.72 tff(1124,assumption,(~(op(e1, e1) = e2)), introduced(assumption)).
% 0.58/0.72 tff(1125,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1124, 1123])).
% 0.58/0.72 tff(1126,plain,((~(op(e2, e1) = e2)) | (op(e1, e1) = e2) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e1), op(e2, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1127,plain,
% 0.58/0.72 ((~(op(e2, e1) = e2)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e1), op(e2, e1)) = e1))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1126, 1117])).
% 0.58/0.72 tff(1128,plain,
% 0.58/0.72 ($false),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1127, 54, 12, 10])).
% 0.58/0.72 tff(1129,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e2, e2) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.72 tff(1130,plain,
% 0.58/0.72 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[1129, 6, 4, 3])).
% 0.58/0.72 tff(1131,plain,
% 0.58/0.72 ((op(e3, e3) = e2) <=> (e2 = op(e3, e3))),
% 0.58/0.72 inference(symmetry,[status(thm)],[5])).
% 0.58/0.72 tff(1132,plain,
% 0.58/0.72 (op(e0, e1) = e2),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[166, 113, 6, 4])).
% 0.58/0.72 tff(1133,plain,
% 0.58/0.72 (e2 = op(e0, e1)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1132])).
% 0.58/0.72 tff(1134,plain,
% 0.58/0.72 (op(e2, e2) = op(op(e0, e1), op(e0, e1))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1133, 1133])).
% 0.58/0.72 tff(1135,plain,
% 0.58/0.72 (op(e2, e2) = e1),
% 0.58/0.72 inference(transitivity,[status(thm)],[1134, 172])).
% 0.58/0.72 tff(1136,plain,
% 0.58/0.72 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1135])).
% 0.58/0.72 tff(1137,plain,
% 0.58/0.72 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1136])).
% 0.58/0.72 tff(1138,plain,
% 0.58/0.72 (~(op(e0, e2) = e1)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[126, 1137])).
% 0.58/0.72 tff(1139,plain,
% 0.58/0.72 (op(e0, e2) = e3),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[259, 1138, 976, 130])).
% 0.58/0.72 tff(1140,plain,
% 0.58/0.72 (e3 = op(e0, e2)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1139])).
% 0.58/0.72 tff(1141,plain,
% 0.58/0.72 (op(e3, e3) = op(op(e0, e2), op(e0, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1140, 1140])).
% 0.58/0.72 tff(1142,plain,
% 0.58/0.72 (op(e3, e3) = e2),
% 0.58/0.72 inference(transitivity,[status(thm)],[1141, 115])).
% 0.58/0.72 tff(1143,plain,
% 0.58/0.72 (e2 = op(e3, e3)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1142, 1131])).
% 0.58/0.72 tff(1144,plain,
% 0.58/0.72 ((e0 = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.58/0.72 inference(commutativity,[status(thm)],[])).
% 0.58/0.72 tff(1145,plain,
% 0.58/0.72 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1142])).
% 0.58/0.72 tff(1146,plain,
% 0.58/0.72 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1145])).
% 0.58/0.72 tff(1147,plain,
% 0.58/0.72 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e0)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1146, 1144])).
% 0.58/0.72 tff(1148,plain,
% 0.58/0.72 ((op(e3, e2) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 0.58/0.72 inference(symmetry,[status(thm)],[1147])).
% 0.58/0.72 tff(1149,plain,
% 0.58/0.72 ((e3 = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.58/0.72 inference(commutativity,[status(thm)],[])).
% 0.58/0.72 tff(1150,plain,
% 0.58/0.72 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1139])).
% 0.58/0.72 tff(1151,plain,
% 0.58/0.72 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1150, 1149])).
% 0.58/0.72 tff(1152,plain,
% 0.58/0.72 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1151])).
% 0.58/0.72 tff(1153,plain,
% 0.58/0.72 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = op(e3, e2)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1154,plain,
% 0.58/0.72 (~(op(e0, e2) = op(e3, e2))),
% 0.58/0.72 inference(and_elim,[status(thm)],[94])).
% 0.58/0.72 tff(1155,plain,
% 0.58/0.72 (~(op(e0, e2) = op(e3, e2))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.58/0.72 tff(1156,plain,
% 0.58/0.72 (~(op(e3, e2) = e3)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1155, 1152])).
% 0.58/0.72 tff(1157,plain,
% 0.58/0.72 ((e1 = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.58/0.72 inference(commutativity,[status(thm)],[])).
% 0.58/0.72 tff(1158,plain,
% 0.58/0.72 ((op(e2, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1135])).
% 0.58/0.72 tff(1159,plain,
% 0.58/0.72 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.58/0.72 inference(transitivity,[status(thm)],[1158, 1157])).
% 0.58/0.72 tff(1160,plain,
% 0.58/0.72 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1159])).
% 0.58/0.72 tff(1161,plain,
% 0.58/0.72 (~(op(e3, e2) = e1)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[591, 1160])).
% 0.58/0.72 tff(1162,plain,
% 0.58/0.72 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e2)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1142])).
% 0.58/0.72 tff(1163,plain,
% 0.58/0.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e2))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1162])).
% 0.58/0.72 tff(1164,plain,
% 0.58/0.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = op(e3, e3)))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(1165,plain,
% 0.58/0.72 (~(op(e3, e2) = op(e3, e3))),
% 0.58/0.72 inference(and_elim,[status(thm)],[61])).
% 0.58/0.72 tff(1166,plain,
% 0.58/0.72 (~(op(e3, e2) = op(e3, e3))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.58/0.72 tff(1167,plain,
% 0.58/0.72 (~(op(e3, e2) = e2)),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1166, 1163])).
% 0.58/0.72 tff(1168,plain,
% 0.58/0.72 (op(e3, e2) = e0),
% 0.58/0.72 inference(unit_resolution,[status(thm)],[491, 1167, 1161, 1156])).
% 0.58/0.72 tff(1169,plain,
% 0.58/0.72 (e0 = op(e3, op(e3, e3))),
% 0.58/0.72 inference(modus_ponens,[status(thm)],[1168, 1148])).
% 0.58/0.72 tff(1170,plain,
% 0.58/0.72 (op(e3, op(e3, e3)) = e0),
% 0.58/0.72 inference(transitivity,[status(thm)],[1145, 1168])).
% 0.58/0.72 tff(1171,plain,
% 0.58/0.72 (op(op(e3, op(e3, e3)), e3) = op(e0, e3)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1170])).
% 0.58/0.72 tff(1172,plain,
% 0.58/0.72 (op(e0, e3) = op(op(e3, op(e3, e3)), e3)),
% 0.58/0.72 inference(symmetry,[status(thm)],[1171])).
% 0.58/0.72 tff(1173,plain,
% 0.58/0.72 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 0.58/0.72 inference(monotonicity,[status(thm)],[1132])).
% 0.58/0.73 tff(1174,plain,
% 0.58/0.73 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 0.58/0.73 inference(transitivity,[status(thm)],[1173, 319])).
% 0.58/0.73 tff(1175,plain,
% 0.58/0.73 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 0.58/0.73 inference(symmetry,[status(thm)],[1174])).
% 0.58/0.73 tff(1176,plain,
% 0.58/0.73 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1175])).
% 0.58/0.73 tff(1177,plain,
% 0.58/0.73 (~(op(e0, e1) = e1)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[220, 1176])).
% 0.58/0.73 tff(1178,plain,
% 0.58/0.73 ((e0 = e1) <=> (op(e0, e0) = e1)),
% 0.58/0.73 inference(monotonicity,[status(thm)],[307])).
% 0.58/0.73 tff(1179,plain,
% 0.58/0.73 ((~(e0 = e1)) <=> (~(op(e0, e0) = e1))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1178])).
% 0.58/0.73 tff(1180,plain,
% 0.58/0.73 ((~(e0 = e1)) <=> (~(e0 = e1))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1181,plain,
% 0.58/0.73 (~(e0 = e1)),
% 0.58/0.73 inference(and_elim,[status(thm)],[270])).
% 0.58/0.73 tff(1182,plain,
% 0.58/0.73 (~(e0 = e1)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.58/0.73 tff(1183,plain,
% 0.58/0.73 (~(op(e0, e0) = e1)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1182, 1179])).
% 0.58/0.73 tff(1184,plain,
% 0.58/0.73 (((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1185,plain,
% 0.58/0.73 ((((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1186,plain,
% 0.58/0.73 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1187,plain,
% 0.58/0.73 (((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)) <=> (((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1186])).
% 0.58/0.73 tff(1188,plain,
% 0.58/0.73 (((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1))),
% 0.58/0.73 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.58/0.73 tff(1189,plain,
% 0.58/0.73 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)),
% 0.58/0.73 inference(and_elim,[status(thm)],[205])).
% 0.58/0.73 tff(1190,plain,
% 0.58/0.73 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.58/0.73 tff(1191,plain,
% 0.58/0.73 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1190, 1184])).
% 0.58/0.73 tff(1192,plain,
% 0.58/0.73 (op(e0, e3) = e1),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1191, 1138, 1183, 1177])).
% 0.58/0.73 tff(1193,plain,
% 0.58/0.73 (e1 = op(e0, e3)),
% 0.58/0.73 inference(symmetry,[status(thm)],[1192])).
% 0.58/0.73 tff(1194,plain,
% 0.58/0.73 (e1 = op(op(e3, op(e3, e3)), e3)),
% 0.58/0.73 inference(transitivity,[status(thm)],[1193, 1172])).
% 0.58/0.73 tff(1195,plain,
% 0.58/0.73 ((~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3)))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1196,plain,
% 0.58/0.73 (((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))) <=> (~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3)))))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1197,plain,
% 0.58/0.73 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3))))))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1196])).
% 0.58/0.73 tff(1198,plain,
% 0.58/0.73 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.73 inference(transitivity,[status(thm)],[1197, 1195])).
% 0.58/0.73 tff(1199,plain,
% 0.58/0.73 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1200,plain,
% 0.58/0.73 ((~(((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1201,axiom,(~(((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax8')).
% 0.58/0.73 tff(1202,plain,
% 0.58/0.73 (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.58/0.73 tff(1203,plain,
% 0.58/0.73 (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1202, 1199])).
% 0.58/0.73 tff(1204,plain,
% 0.58/0.73 ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1203, 1198])).
% 0.58/0.73 tff(1205,plain,
% 0.58/0.73 ($false),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1204, 1194, 1169, 1143])).
% 0.58/0.73 tff(1206,plain,(((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))) | (op(e0, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.73 tff(1207,plain,
% 0.58/0.73 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1206, 6, 4])).
% 0.58/0.73 tff(1208,assumption,(~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))), introduced(assumption)).
% 0.58/0.73 tff(1209,plain,
% 0.58/0.73 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[459, 1208])).
% 0.58/0.73 tff(1210,plain,
% 0.58/0.73 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[633, 1208])).
% 0.58/0.73 tff(1211,plain,
% 0.58/0.73 (~(op(e3, e3) = e2)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[631, 1210, 6])).
% 0.58/0.73 tff(1212,plain,
% 0.58/0.73 (~(op(e3, e2) = e3)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[467, 1211, 1209])).
% 0.58/0.73 tff(1213,plain,
% 0.58/0.73 (~(op(e3, e2) = e0)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[474, 1209, 4])).
% 0.58/0.73 tff(1214,plain,
% 0.58/0.73 (op(e3, e2) = e1),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[491, 1213, 483, 1212])).
% 0.58/0.73 tff(1215,plain,
% 0.58/0.73 (e1 = op(e3, e2)),
% 0.58/0.73 inference(symmetry,[status(thm)],[1214])).
% 0.58/0.73 tff(1216,plain,
% 0.58/0.73 (op(e1, e1) = op(op(e3, e2), op(e3, e2))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1215, 1215])).
% 0.58/0.73 tff(1217,plain,
% 0.58/0.73 (op(e1, e1) = e2),
% 0.58/0.73 inference(transitivity,[status(thm)],[1216, 1209])).
% 0.58/0.73 tff(1218,plain,
% 0.58/0.73 ($false),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1124, 1217])).
% 0.58/0.73 tff(1219,plain,(((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(e1, e1) = e2) | (op(e3, e2) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.73 tff(1220,plain,
% 0.58/0.73 (((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(e3, e2) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1219, 1117])).
% 0.58/0.73 tff(1221,plain,
% 0.58/0.73 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1220, 483, 4, 6])).
% 0.58/0.73 tff(1222,plain,
% 0.58/0.73 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[416, 1221, 1207, 1130])).
% 0.58/0.73 tff(1223,assumption,(~(op(e1, e0) = e2)), introduced(assumption)).
% 0.58/0.73 tff(1224,assumption,(op(op(e1, e3), op(e1, e3)) = e3), introduced(assumption)).
% 0.58/0.73 tff(1225,assumption,(op(e1, e3) = e2), introduced(assumption)).
% 0.58/0.73 tff(1226,plain,
% 0.58/0.73 (op(op(e1, e3), op(e1, e3)) = op(e2, e2)),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1225, 1225])).
% 0.58/0.73 tff(1227,plain,
% 0.58/0.73 (op(e2, e2) = op(op(e1, e3), op(e1, e3))),
% 0.58/0.73 inference(symmetry,[status(thm)],[1226])).
% 0.58/0.73 tff(1228,plain,
% 0.58/0.73 (op(e2, e2) = e3),
% 0.58/0.73 inference(transitivity,[status(thm)],[1227, 1224])).
% 0.58/0.73 tff(1229,plain,
% 0.58/0.73 ($false),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[6, 1228])).
% 0.58/0.73 tff(1230,plain,((~(op(e1, e3) = e2)) | (op(e2, e2) = e3) | (~(op(op(e1, e3), op(e1, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.73 tff(1231,plain,
% 0.58/0.73 (~(op(e1, e3) = e2)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1230, 314, 6])).
% 0.58/0.73 tff(1232,plain,
% 0.58/0.73 (((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1233,plain,
% 0.58/0.73 ((((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1234,plain,
% 0.58/0.73 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(1235,plain,
% 0.58/0.73 (((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)) <=> (((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1234])).
% 0.58/0.73 tff(1236,plain,
% 0.58/0.73 (((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2))),
% 0.58/0.73 inference(transitivity,[status(thm)],[1235, 1233])).
% 0.58/0.73 tff(1237,plain,
% 0.58/0.73 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)),
% 0.58/0.73 inference(and_elim,[status(thm)],[153])).
% 0.58/0.73 tff(1238,plain,
% 0.58/0.73 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.58/0.73 tff(1239,plain,
% 0.58/0.73 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[1238, 1232])).
% 0.58/0.73 tff(1240,plain,
% 0.58/0.73 (op(e1, e2) = e2),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1239, 1231, 1124, 1223])).
% 0.58/0.73 tff(1241,plain,
% 0.58/0.73 (e2 = op(e1, e2)),
% 0.58/0.73 inference(symmetry,[status(thm)],[1240])).
% 0.58/0.73 tff(1242,plain,
% 0.58/0.73 (op(e2, e2) = op(op(e1, e2), op(e1, e2))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1241, 1241])).
% 0.58/0.73 tff(1243,plain,
% 0.58/0.73 (op(e2, e2) = e2),
% 0.58/0.73 inference(transitivity,[status(thm)],[1242, 420])).
% 0.58/0.73 tff(1244,plain,
% 0.58/0.73 ($false),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[3, 1243])).
% 0.58/0.73 tff(1245,plain,(((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(e2, e2) = e2) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.73 tff(1246,plain,
% 0.58/0.73 (((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(e2, e2) = e2) | (op(e1, e0) = e2) | (op(e2, e2) = e3)),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1245, 1117])).
% 0.58/0.73 tff(1247,plain,
% 0.58/0.73 (op(e1, e0) = e2),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[1246, 1222, 6, 3])).
% 0.58/0.73 tff(1248,plain,
% 0.58/0.73 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.58/0.73 inference(monotonicity,[status(thm)],[1247, 1247])).
% 0.58/0.73 tff(1249,plain,
% 0.58/0.73 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[333, 1222])).
% 0.58/0.73 tff(1250,plain,
% 0.58/0.73 (e0 = op(op(e1, e0), op(e1, e0))),
% 0.58/0.73 inference(symmetry,[status(thm)],[1249])).
% 0.58/0.73 tff(1251,plain,
% 0.58/0.73 (e0 = op(e2, e2)),
% 0.58/0.73 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.58/0.73 tff(1252,plain,
% 0.58/0.73 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[419, 1222])).
% 0.58/0.74 tff(1253,plain,
% 0.58/0.74 (~(op(e1, e2) = e0)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[435, 1252, 4])).
% 0.58/0.74 tff(1254,assumption,(op(e1, e2) = e2), introduced(assumption)).
% 0.58/0.74 tff(1255,plain,
% 0.58/0.74 (e2 = op(e1, e2)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1254])).
% 0.58/0.74 tff(1256,plain,
% 0.58/0.74 (op(e2, e2) = op(op(e1, e2), op(e1, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1255, 1255])).
% 0.58/0.74 tff(1257,plain,
% 0.58/0.74 (op(e2, e2) = e2),
% 0.58/0.74 inference(transitivity,[status(thm)],[1256, 429])).
% 0.58/0.74 tff(1258,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[3, 1257])).
% 0.58/0.74 tff(1259,plain,((~(op(e1, e2) = e2)) | (op(e2, e2) = e2) | (~(op(op(e1, e2), op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1260,plain,
% 0.58/0.74 (~(op(e1, e2) = e2)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1259, 1252, 3])).
% 0.58/0.74 tff(1261,assumption,(op(e1, e2) = e1), introduced(assumption)).
% 0.58/0.74 tff(1262,plain,
% 0.58/0.74 (e1 = op(e1, e2)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1261])).
% 0.58/0.74 tff(1263,plain,
% 0.58/0.74 (op(e1, e1) = op(op(e1, e2), op(e1, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1262, 1262])).
% 0.58/0.74 tff(1264,plain,
% 0.58/0.74 (op(e1, e1) = e2),
% 0.58/0.74 inference(transitivity,[status(thm)],[1263, 429])).
% 0.58/0.74 tff(1265,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1117, 1264])).
% 0.58/0.74 tff(1266,plain,((~(op(e1, e2) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1267,plain,
% 0.58/0.74 (~(op(e1, e2) = e1)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1266, 1252])).
% 0.58/0.74 tff(1268,plain,
% 0.58/0.74 (op(e1, e2) = e3),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[449, 1267, 1260, 1253])).
% 0.58/0.74 tff(1269,assumption,(op(e1, e2) = e3), introduced(assumption)).
% 0.58/0.74 tff(1270,plain,
% 0.58/0.74 (e3 = op(e1, e2)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1269])).
% 0.58/0.74 tff(1271,plain,
% 0.58/0.74 (op(e3, e3) = op(op(e1, e2), op(e1, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1270, 1270])).
% 0.58/0.74 tff(1272,plain,
% 0.58/0.74 (op(e3, e3) = e2),
% 0.58/0.74 inference(transitivity,[status(thm)],[1271, 429])).
% 0.58/0.74 tff(1273,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[418, 1272])).
% 0.58/0.74 tff(1274,plain,((~(op(e1, e2) = e3)) | (op(e3, e3) = e2) | (~(op(op(e1, e2), op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1275,plain,
% 0.58/0.74 (op(e3, e3) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1274, 1268, 1252])).
% 0.58/0.74 tff(1276,plain,
% 0.58/0.74 ((op(e3, e3) = e0) <=> (e2 = op(e2, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1275, 1251])).
% 0.58/0.74 tff(1277,plain,
% 0.58/0.74 ((op(e3, e3) = e0) <=> (op(e2, e2) = e2)),
% 0.58/0.74 inference(transitivity,[status(thm)],[1276, 7])).
% 0.58/0.74 tff(1278,plain,
% 0.58/0.74 ((op(e2, e2) = e2) <=> (op(e3, e3) = e0)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1277])).
% 0.58/0.74 tff(1279,plain,
% 0.58/0.74 ((~(op(e2, e2) = e2)) <=> (~(op(e3, e3) = e0))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1278])).
% 0.58/0.74 tff(1280,plain,
% 0.58/0.74 (~(op(e3, e3) = e0)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[3, 1279])).
% 0.58/0.74 tff(1281,plain,
% 0.58/0.74 ((op(e2, e3) = op(e2, e2)) <=> (op(e2, e2) = op(e2, e3))),
% 0.58/0.74 inference(commutativity,[status(thm)],[])).
% 0.58/0.74 tff(1282,plain,
% 0.58/0.74 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e2, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1251])).
% 0.58/0.74 tff(1283,plain,
% 0.58/0.74 ((op(e2, e3) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 0.58/0.74 inference(transitivity,[status(thm)],[1282, 1281])).
% 0.58/0.74 tff(1284,plain,
% 0.58/0.74 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1283])).
% 0.58/0.74 tff(1285,plain,
% 0.58/0.74 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1284])).
% 0.58/0.74 tff(1286,plain,
% 0.58/0.74 (~(op(e2, e3) = e0)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[709, 1285])).
% 0.58/0.74 tff(1287,plain,
% 0.58/0.74 ((e0 = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.58/0.74 inference(commutativity,[status(thm)],[])).
% 0.58/0.74 tff(1288,assumption,((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))), introduced(assumption)).
% 0.58/0.74 tff(1289,assumption,((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))), introduced(assumption)).
% 0.58/0.74 tff(1290,plain,
% 0.58/0.74 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1219, 483, 1124, 4, 6])).
% 0.58/0.74 tff(1291,plain,
% 0.58/0.74 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1219, 483, 6, 4, 1124])).
% 0.58/0.74 tff(1292,plain,
% 0.58/0.74 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[416, 1291, 1289, 1288])).
% 0.58/0.74 tff(1293,plain,
% 0.58/0.74 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[419, 1292])).
% 0.58/0.74 tff(1294,plain,
% 0.58/0.74 (op(e1, e2) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[507, 483, 231, 3])).
% 0.58/0.74 tff(1295,plain,
% 0.58/0.74 (e2 = op(e1, e2)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1294])).
% 0.58/0.74 tff(1296,plain,
% 0.58/0.74 (op(e2, e2) = op(op(e1, e2), op(e1, e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1295, 1295])).
% 0.58/0.74 tff(1297,plain,
% 0.58/0.74 (op(e2, e2) = e2),
% 0.58/0.74 inference(transitivity,[status(thm)],[1296, 1293])).
% 0.58/0.74 tff(1298,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[3, 1297])).
% 0.58/0.74 tff(1299,plain,((op(e3, e2) = e2) | (op(e2, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e2, e2) = e3) | (op(e0, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1300,plain,
% 0.58/0.74 (op(e2, e2) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1299, 483, 1289, 1288, 6, 4, 1124, 231])).
% 0.58/0.74 tff(1301,assumption,(op(e2, e2) = e2), introduced(assumption)).
% 0.58/0.74 tff(1302,plain,
% 0.58/0.74 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1301])).
% 0.58/0.74 tff(1303,plain,
% 0.58/0.74 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1302])).
% 0.58/0.74 tff(1304,plain,
% 0.58/0.74 (~(op(e1, e2) = e2)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[331, 1303])).
% 0.58/0.74 tff(1305,plain,
% 0.58/0.74 (op(e1, e0) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1239, 1231, 1124, 1304])).
% 0.58/0.74 tff(1306,plain,
% 0.58/0.74 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1305, 1305])).
% 0.58/0.74 tff(1307,plain,
% 0.58/0.74 (e0 = op(op(e1, e0), op(e1, e0))),
% 0.58/0.74 inference(symmetry,[status(thm)],[334])).
% 0.58/0.74 tff(1308,plain,
% 0.58/0.74 (e0 = e2),
% 0.58/0.74 inference(transitivity,[status(thm)],[1307, 1306, 1301])).
% 0.58/0.74 tff(1309,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[272, 1308])).
% 0.58/0.74 tff(1310,plain,(((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (~(op(e2, e2) = e2)) | (op(e1, e1) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1311,plain,
% 0.58/0.74 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1310, 1300, 1124, 6])).
% 0.58/0.74 tff(1312,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[416, 1311, 1290, 1289, 1288])).
% 0.58/0.74 tff(1313,plain,((op(e3, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e2, e2) = e3) | (op(e0, e0) = e2) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(1314,plain,
% 0.58/0.74 ((op(e3, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e2, e2) = e3) | (op(e0, e0) = e2) | (op(e0, e2) = e2)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1313, 1117])).
% 0.58/0.74 tff(1315,plain,
% 0.58/0.74 (op(e0, e2) = e2),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1314, 483, 4, 6, 1207, 1130])).
% 0.58/0.74 tff(1316,plain,
% 0.58/0.74 ((op(e0, e2) = e1) <=> (e2 = e1)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1315])).
% 0.58/0.74 tff(1317,plain,
% 0.58/0.74 ((op(e0, e2) = e1) <=> (e1 = e2)),
% 0.58/0.74 inference(transitivity,[status(thm)],[1316, 319])).
% 0.58/0.74 tff(1318,plain,
% 0.58/0.74 ((e1 = e2) <=> (op(e0, e2) = e1)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1317])).
% 0.58/0.74 tff(1319,plain,
% 0.58/0.74 ((~(e1 = e2)) <=> (~(op(e0, e2) = e1))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1318])).
% 0.58/0.74 tff(1320,plain,
% 0.58/0.74 (~(op(e0, e2) = e1)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[220, 1319])).
% 0.58/0.74 tff(1321,plain,
% 0.58/0.74 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1251])).
% 0.58/0.74 tff(1322,plain,
% 0.58/0.74 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1321])).
% 0.58/0.74 tff(1323,plain,
% 0.58/0.74 (~(op(e2, e2) = e1)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[1182, 1322])).
% 0.58/0.74 tff(1324,plain,
% 0.58/0.74 (((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(1325,plain,
% 0.58/0.74 ((((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(1326,plain,
% 0.58/0.74 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(1327,plain,
% 0.58/0.74 (((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> (((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1326])).
% 0.58/0.74 tff(1328,plain,
% 0.58/0.74 (((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.58/0.74 inference(transitivity,[status(thm)],[1327, 1325])).
% 0.58/0.74 tff(1329,plain,
% 0.58/0.74 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)),
% 0.58/0.74 inference(and_elim,[status(thm)],[146])).
% 0.58/0.74 tff(1330,plain,
% 0.58/0.74 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.58/0.74 tff(1331,plain,
% 0.58/0.74 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[1330, 1324])).
% 0.58/0.74 tff(1332,plain,
% 0.58/0.74 (op(e3, e2) = e1),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[1331, 1267, 1323, 1320])).
% 0.58/0.74 tff(1333,plain,
% 0.58/0.74 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1275])).
% 0.58/0.74 tff(1334,plain,
% 0.58/0.74 (op(e3, op(e3, e3)) = e1),
% 0.58/0.74 inference(transitivity,[status(thm)],[1333, 1332])).
% 0.58/0.74 tff(1335,plain,
% 0.58/0.74 (op(op(e3, op(e3, e3)), e3) = op(e1, e3)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1334])).
% 0.58/0.74 tff(1336,plain,
% 0.58/0.74 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (e0 = op(e1, e3))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1335])).
% 0.58/0.74 tff(1337,plain,
% 0.58/0.74 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (op(e1, e3) = e0)),
% 0.58/0.74 inference(transitivity,[status(thm)],[1336, 1287])).
% 0.58/0.74 tff(1338,plain,
% 0.58/0.74 ((~(e0 = op(op(e3, op(e3, e3)), e3))) <=> (~(op(e1, e3) = e0))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[1337])).
% 0.58/0.74 tff(1339,plain,
% 0.58/0.74 (e2 = op(e3, e3)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[1275, 1131])).
% 0.58/0.74 tff(1340,plain,
% 0.58/0.74 (op(e3, e2) = op(e3, op(e3, e3))),
% 0.58/0.74 inference(symmetry,[status(thm)],[1333])).
% 0.58/0.74 tff(1341,plain,
% 0.58/0.74 (e1 = op(e3, e2)),
% 0.58/0.74 inference(symmetry,[status(thm)],[1332])).
% 0.58/0.75 tff(1342,plain,
% 0.58/0.75 (e1 = op(e3, op(e3, e3))),
% 0.58/0.75 inference(transitivity,[status(thm)],[1341, 1340])).
% 0.58/0.75 tff(1343,plain,
% 0.58/0.75 ((~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3)))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1344,plain,
% 0.58/0.75 (((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))) <=> (~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3)))))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1345,plain,
% 0.58/0.75 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3))))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1344])).
% 0.58/0.75 tff(1346,plain,
% 0.58/0.75 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.75 inference(transitivity,[status(thm)],[1345, 1343])).
% 0.58/0.75 tff(1347,plain,
% 0.58/0.75 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1348,plain,
% 0.58/0.75 ((~(((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1349,axiom,(~(((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax14')).
% 0.58/0.75 tff(1350,plain,
% 0.58/0.75 (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.58/0.75 tff(1351,plain,
% 0.58/0.75 (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1350, 1347])).
% 0.58/0.75 tff(1352,plain,
% 0.58/0.75 ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), e3)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1351, 1346])).
% 0.58/0.75 tff(1353,plain,
% 0.58/0.75 (~(e0 = op(op(e3, op(e3, e3)), e3))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1352, 1342, 1339])).
% 0.58/0.75 tff(1354,plain,
% 0.58/0.75 (~(op(e1, e3) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1353, 1338])).
% 0.58/0.75 tff(1355,plain,
% 0.58/0.75 ((e0 = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.58/0.75 inference(commutativity,[status(thm)],[])).
% 0.58/0.75 tff(1356,plain,
% 0.58/0.75 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1315])).
% 0.58/0.75 tff(1357,plain,
% 0.58/0.75 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1356])).
% 0.58/0.75 tff(1358,plain,
% 0.58/0.75 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = op(e0, e2)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1359,plain,
% 0.58/0.75 (~(op(e0, e1) = op(e0, e2))),
% 0.58/0.75 inference(and_elim,[status(thm)],[81])).
% 0.58/0.75 tff(1360,plain,
% 0.58/0.75 (~(op(e0, e1) = op(e0, e2))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.58/0.75 tff(1361,plain,
% 0.58/0.75 (~(op(e0, e1) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1360, 1357])).
% 0.58/0.75 tff(1362,plain,
% 0.58/0.75 ((e2 = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.58/0.75 inference(commutativity,[status(thm)],[])).
% 0.58/0.75 tff(1363,plain,
% 0.58/0.75 ((op(e0, e2) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1315])).
% 0.58/0.75 tff(1364,plain,
% 0.58/0.75 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.58/0.75 inference(transitivity,[status(thm)],[1363, 1362])).
% 0.58/0.75 tff(1365,plain,
% 0.58/0.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1364])).
% 0.58/0.75 tff(1366,plain,
% 0.58/0.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e0, e3)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1367,plain,
% 0.58/0.75 (~(op(e0, e2) = op(e0, e3))),
% 0.58/0.75 inference(and_elim,[status(thm)],[79])).
% 0.58/0.75 tff(1368,plain,
% 0.58/0.75 (~(op(e0, e2) = op(e0, e3))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.58/0.75 tff(1369,plain,
% 0.58/0.75 (~(op(e0, e3) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1368, 1365])).
% 0.58/0.75 tff(1370,plain,
% 0.58/0.75 ((op(e0, e2) = e0) <=> (e2 = e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1315])).
% 0.58/0.75 tff(1371,plain,
% 0.58/0.75 ((op(e0, e2) = e0) <=> (e0 = e2)),
% 0.58/0.75 inference(transitivity,[status(thm)],[1370, 263])).
% 0.58/0.75 tff(1372,plain,
% 0.58/0.75 ((e0 = e2) <=> (op(e0, e2) = e0)),
% 0.58/0.75 inference(symmetry,[status(thm)],[1371])).
% 0.58/0.75 tff(1373,plain,
% 0.58/0.75 ((~(e0 = e2)) <=> (~(op(e0, e2) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1372])).
% 0.58/0.75 tff(1374,plain,
% 0.58/0.75 (~(op(e0, e2) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[272, 1373])).
% 0.58/0.75 tff(1375,plain,
% 0.58/0.75 ((op(e2, e2) = op(e2, e0)) <=> (op(e2, e0) = op(e2, e2))),
% 0.58/0.75 inference(commutativity,[status(thm)],[])).
% 0.58/0.75 tff(1376,plain,
% 0.58/0.75 (op(e2, e0) = op(e2, op(e2, e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1251])).
% 0.58/0.75 tff(1377,plain,
% 0.58/0.75 (op(e2, op(e2, e2)) = op(e2, e0)),
% 0.58/0.75 inference(symmetry,[status(thm)],[1376])).
% 0.58/0.75 tff(1378,plain,
% 0.58/0.75 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e2) = op(e2, e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1251, 1377])).
% 0.58/0.75 tff(1379,plain,
% 0.58/0.75 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e0) = op(e2, e2))),
% 0.58/0.75 inference(transitivity,[status(thm)],[1378, 1375])).
% 0.58/0.75 tff(1380,plain,
% 0.58/0.75 ((op(e2, e0) = op(e2, e2)) <=> (e0 = op(e2, op(e2, e2)))),
% 0.58/0.75 inference(symmetry,[status(thm)],[1379])).
% 0.58/0.75 tff(1381,plain,
% 0.58/0.75 ((~(op(e2, e0) = op(e2, e2))) <=> (~(e0 = op(e2, op(e2, e2))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1380])).
% 0.58/0.75 tff(1382,plain,
% 0.58/0.75 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = op(e2, e2)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1383,plain,
% 0.58/0.75 (~(op(e2, e0) = op(e2, e2))),
% 0.58/0.75 inference(and_elim,[status(thm)],[71])).
% 0.58/0.75 tff(1384,plain,
% 0.58/0.75 (~(op(e2, e0) = op(e2, e2))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 0.58/0.75 tff(1385,plain,
% 0.58/0.75 (~(e0 = op(e2, op(e2, e2)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1384, 1381])).
% 0.58/0.75 tff(1386,plain,
% 0.58/0.75 ((op(e0, e2) = e3) <=> (e2 = e3)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1315])).
% 0.58/0.75 tff(1387,plain,
% 0.58/0.75 ((e2 = e3) <=> (op(e0, e2) = e3)),
% 0.58/0.75 inference(symmetry,[status(thm)],[1386])).
% 0.58/0.75 tff(1388,plain,
% 0.58/0.75 ((~(e2 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1387])).
% 0.58/0.75 tff(1389,plain,
% 0.58/0.75 (~(op(e0, e2) = e3)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[195, 1388])).
% 0.58/0.75 tff(1390,plain,
% 0.58/0.75 ((e2 = op(e3, op(e3, e3))) <=> (e2 = e1)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1334])).
% 0.58/0.75 tff(1391,plain,
% 0.58/0.75 ((e2 = op(e3, op(e3, e3))) <=> (e1 = e2)),
% 0.58/0.75 inference(transitivity,[status(thm)],[1390, 319])).
% 0.58/0.75 tff(1392,plain,
% 0.58/0.75 ((e1 = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.58/0.75 inference(symmetry,[status(thm)],[1391])).
% 0.58/0.75 tff(1393,plain,
% 0.58/0.75 ((~(e1 = e2)) <=> (~(e2 = op(e3, op(e3, e3))))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1392])).
% 0.58/0.75 tff(1394,plain,
% 0.58/0.75 (~(e2 = op(e3, op(e3, e3)))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[220, 1393])).
% 0.58/0.75 tff(1395,assumption,(~(op(e0, e3) = e2)), introduced(assumption)).
% 0.58/0.75 tff(1396,assumption,(~(op(e0, e2) = e3)), introduced(assumption)).
% 0.58/0.75 tff(1397,assumption,(~(e2 = op(e3, op(e3, e3)))), introduced(assumption)).
% 0.58/0.75 tff(1398,assumption,(~(op(e0, e2) = e1)), introduced(assumption)).
% 0.58/0.75 tff(1399,plain,
% 0.58/0.75 ((op(e0, e3) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e3))),
% 0.58/0.75 inference(commutativity,[status(thm)],[])).
% 0.58/0.75 tff(1400,plain,
% 0.58/0.75 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1219, 1124, 483, 4, 6])).
% 0.58/0.75 tff(1401,plain,
% 0.58/0.75 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[305, 168])).
% 0.58/0.75 tff(1402,plain,
% 0.58/0.75 (~(op(e2, e1) = e2)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1126, 10, 1124, 12])).
% 0.58/0.75 tff(1403,plain,
% 0.58/0.75 (((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1404,plain,
% 0.58/0.75 ((((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1405,plain,
% 0.58/0.75 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1406,plain,
% 0.58/0.75 (((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)) <=> (((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1405])).
% 0.58/0.75 tff(1407,plain,
% 0.58/0.75 (((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2))),
% 0.58/0.75 inference(transitivity,[status(thm)],[1406, 1404])).
% 0.58/0.75 tff(1408,plain,
% 0.58/0.75 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)),
% 0.58/0.75 inference(and_elim,[status(thm)],[152])).
% 0.58/0.75 tff(1409,plain,
% 0.58/0.75 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.58/0.75 tff(1410,plain,
% 0.58/0.75 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1409, 1403])).
% 0.58/0.75 tff(1411,plain,
% 0.58/0.75 (op(e3, e1) = e2),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1410, 1402, 112, 1124])).
% 0.58/0.75 tff(1412,plain,
% 0.58/0.75 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1411])).
% 0.58/0.75 tff(1413,plain,
% 0.58/0.75 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.58/0.75 inference(transitivity,[status(thm)],[1412, 5])).
% 0.58/0.75 tff(1414,plain,
% 0.58/0.75 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1413])).
% 0.58/0.75 tff(1415,plain,
% 0.58/0.75 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = op(e3, e3)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1416,plain,
% 0.58/0.75 (~(op(e3, e1) = op(e3, e3))),
% 0.58/0.75 inference(and_elim,[status(thm)],[62])).
% 0.58/0.75 tff(1417,plain,
% 0.58/0.75 (~(op(e3, e1) = op(e3, e3))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.58/0.75 tff(1418,plain,
% 0.58/0.75 (~(op(e3, e3) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1417, 1414])).
% 0.58/0.75 tff(1419,plain,
% 0.58/0.75 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1411])).
% 0.58/0.75 tff(1420,plain,
% 0.58/0.75 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1419])).
% 0.58/0.75 tff(1421,plain,
% 0.58/0.75 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = op(e3, e1)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1422,plain,
% 0.58/0.75 (~(op(e3, e0) = op(e3, e1))),
% 0.58/0.75 inference(and_elim,[status(thm)],[66])).
% 0.58/0.75 tff(1423,plain,
% 0.58/0.75 (~(op(e3, e0) = op(e3, e1))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 0.58/0.75 tff(1424,plain,
% 0.58/0.75 (~(op(e3, e0) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1423, 1420])).
% 0.58/0.75 tff(1425,plain,
% 0.58/0.75 (op(e3, e3) = e1),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[833, 418, 817, 825])).
% 0.58/0.75 tff(1426,plain,
% 0.58/0.75 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1425])).
% 0.58/0.75 tff(1427,plain,
% 0.58/0.75 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.58/0.75 inference(symmetry,[status(thm)],[1426])).
% 0.58/0.75 tff(1428,assumption,(~(op(e3, e0) = e2)), introduced(assumption)).
% 0.58/0.75 tff(1429,plain,
% 0.58/0.75 (op(e3, e1) = e2),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[566, 418, 1428, 483])).
% 0.58/0.75 tff(1430,plain,
% 0.58/0.75 (e2 = op(e3, e1)),
% 0.58/0.75 inference(symmetry,[status(thm)],[1429])).
% 0.58/0.75 tff(1431,plain,
% 0.58/0.75 (e2 = op(e3, op(e3, e3))),
% 0.58/0.75 inference(transitivity,[status(thm)],[1430, 1427])).
% 0.58/0.75 tff(1432,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1397, 1431])).
% 0.58/0.75 tff(1433,plain,((op(e3, e3) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e3, e3) = e3) | (op(e3, e3) = e0) | (op(e3, e0) = e2) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.75 tff(1434,plain,
% 0.58/0.75 (op(e3, e3) = e0),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[1433, 1424, 731, 1418, 1397, 483])).
% 0.58/0.75 tff(1435,plain,
% 0.58/0.75 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1434])).
% 0.58/0.75 tff(1436,plain,
% 0.58/0.75 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1435])).
% 0.58/0.75 tff(1437,plain,
% 0.58/0.75 (~(op(e2, e3) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[656, 1436])).
% 0.58/0.75 tff(1438,plain,
% 0.58/0.75 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1434])).
% 0.58/0.75 tff(1439,plain,
% 0.58/0.75 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1438])).
% 0.58/0.75 tff(1440,plain,
% 0.58/0.75 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = op(e3, e3)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(1441,plain,
% 0.58/0.75 (~(op(e1, e3) = op(e3, e3))),
% 0.58/0.75 inference(and_elim,[status(thm)],[86])).
% 0.58/0.75 tff(1442,plain,
% 0.58/0.75 (~(op(e1, e3) = op(e3, e3))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 0.58/0.75 tff(1443,plain,
% 0.58/0.75 (~(op(e1, e3) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[1442, 1439])).
% 0.58/0.75 tff(1444,plain,
% 0.58/0.75 ((e0 = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.58/0.75 inference(commutativity,[status(thm)],[])).
% 0.58/0.75 tff(1445,plain,
% 0.58/0.75 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1434])).
% 0.58/0.75 tff(1446,plain,
% 0.58/0.75 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1445])).
% 0.58/0.75 tff(1447,plain,
% 0.58/0.75 (~(op(e0, e3) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[823, 1446])).
% 0.58/0.75 tff(1448,plain,
% 0.58/0.75 (op(e0, e1) = e0),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[209, 1447, 168, 232])).
% 0.58/0.75 tff(1449,plain,
% 0.58/0.75 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1448])).
% 0.58/0.75 tff(1450,plain,
% 0.58/0.75 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.58/0.75 inference(transitivity,[status(thm)],[1449, 1444])).
% 0.58/0.75 tff(1451,plain,
% 0.58/0.75 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1450])).
% 0.58/0.75 tff(1452,plain,
% 0.58/0.75 (~(op(e1, e1) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[110, 1451])).
% 0.58/0.75 tff(1453,assumption,((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))), introduced(assumption)).
% 0.58/0.75 tff(1454,assumption,(op(e2, e2) = e0), introduced(assumption)).
% 0.58/0.75 tff(1455,plain,
% 0.58/0.75 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1454, 1454])).
% 0.58/0.75 tff(1456,plain,
% 0.58/0.75 ((op(op(e2, e2), op(e2, e2)) = e2) <=> (op(e0, e0) = e2)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1455])).
% 0.58/0.75 tff(1457,plain,
% 0.58/0.75 ((op(e0, e0) = e2) <=> (op(op(e2, e2), op(e2, e2)) = e2)),
% 0.58/0.75 inference(symmetry,[status(thm)],[1456])).
% 0.58/0.75 tff(1458,plain,
% 0.58/0.75 ((~(op(e0, e0) = e2)) <=> (~(op(op(e2, e2), op(e2, e2)) = e2))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1457])).
% 0.58/0.75 tff(1459,plain,
% 0.58/0.75 (~(op(op(e2, e2), op(e2, e2)) = e2)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[4, 1458])).
% 0.58/0.75 tff(1460,plain,
% 0.58/0.75 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[9, 1459])).
% 0.58/0.75 tff(1461,plain,
% 0.58/0.75 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[416, 1460, 1401, 1453])).
% 0.58/0.75 tff(1462,plain,
% 0.58/0.75 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[333, 1461])).
% 0.58/0.75 tff(1463,assumption,(~(op(e1, e1) = e0)), introduced(assumption)).
% 0.58/0.75 tff(1464,assumption,(~(op(e1, e3) = e0)), introduced(assumption)).
% 0.58/0.75 tff(1465,plain,
% 0.58/0.75 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e0)),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1454])).
% 0.58/0.75 tff(1466,plain,
% 0.58/0.75 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e0))),
% 0.58/0.75 inference(monotonicity,[status(thm)],[1465])).
% 0.58/0.75 tff(1467,plain,
% 0.58/0.75 (~(op(e1, e2) = e0)),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[331, 1466])).
% 0.58/0.75 tff(1468,plain,
% 0.58/0.75 (((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1469,plain,
% 0.58/0.76 ((((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1470,plain,
% 0.58/0.76 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1471,plain,
% 0.58/0.76 (((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)) <=> (((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1470])).
% 0.58/0.76 tff(1472,plain,
% 0.58/0.76 (((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0))),
% 0.58/0.76 inference(transitivity,[status(thm)],[1471, 1469])).
% 0.58/0.76 tff(1473,plain,
% 0.58/0.76 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)),
% 0.58/0.76 inference(and_elim,[status(thm)],[157])).
% 0.58/0.76 tff(1474,plain,
% 0.58/0.76 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.58/0.76 tff(1475,plain,
% 0.58/0.76 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1474, 1468])).
% 0.58/0.76 tff(1476,plain,
% 0.58/0.76 (op(e1, e0) = e0),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1475, 1467, 1464, 1463])).
% 0.58/0.76 tff(1477,plain,
% 0.58/0.76 (e0 = op(e1, e0)),
% 0.58/0.76 inference(symmetry,[status(thm)],[1476])).
% 0.58/0.76 tff(1478,plain,
% 0.58/0.76 (op(e0, e0) = op(op(e1, e0), op(e1, e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1477, 1477])).
% 0.58/0.76 tff(1479,plain,
% 0.58/0.76 (op(e0, e0) = e0),
% 0.58/0.76 inference(transitivity,[status(thm)],[1478, 1462])).
% 0.58/0.76 tff(1480,plain,
% 0.58/0.76 ($false),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[168, 1479])).
% 0.58/0.76 tff(1481,plain,((~(op(e2, e2) = e0)) | (op(e0, e0) = e0) | (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.76 tff(1482,plain,
% 0.58/0.76 (~(op(e2, e2) = e0)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1481, 1452, 168, 1400, 1443, 4])).
% 0.58/0.76 tff(1483,plain,
% 0.58/0.76 ((e0 = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.58/0.76 inference(commutativity,[status(thm)],[])).
% 0.58/0.76 tff(1484,plain,
% 0.58/0.76 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1448])).
% 0.58/0.76 tff(1485,plain,
% 0.58/0.76 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.58/0.76 inference(transitivity,[status(thm)],[1484, 1483])).
% 0.58/0.76 tff(1486,plain,
% 0.58/0.76 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1485])).
% 0.58/0.76 tff(1487,plain,
% 0.58/0.76 (~(op(e2, e1) = e0)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[776, 1486])).
% 0.58/0.76 tff(1488,plain,
% 0.58/0.76 (((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1489,plain,
% 0.58/0.76 ((((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1490,plain,
% 0.58/0.76 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1491,plain,
% 0.58/0.76 (((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)) <=> (((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1490])).
% 0.58/0.76 tff(1492,plain,
% 0.58/0.76 (((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0))),
% 0.58/0.76 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.58/0.76 tff(1493,plain,
% 0.58/0.76 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)),
% 0.58/0.76 inference(and_elim,[status(thm)],[149])).
% 0.58/0.76 tff(1494,plain,
% 0.58/0.76 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.58/0.76 tff(1495,plain,
% 0.58/0.76 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1494, 1488])).
% 0.58/0.76 tff(1496,plain,
% 0.58/0.76 (op(e2, e0) = e0),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1495, 1487, 1482, 1437])).
% 0.58/0.76 tff(1497,plain,
% 0.58/0.76 (e0 = op(e2, e0)),
% 0.58/0.76 inference(symmetry,[status(thm)],[1496])).
% 0.58/0.76 tff(1498,plain,
% 0.58/0.76 (op(e0, e0) = op(op(e2, e0), op(e2, e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1497, 1497])).
% 0.58/0.76 tff(1499,plain,
% 0.58/0.76 (op(e0, e0) = e0),
% 0.58/0.76 inference(transitivity,[status(thm)],[1498, 47])).
% 0.58/0.76 tff(1500,plain,
% 0.58/0.76 ($false),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[168, 1499])).
% 0.58/0.76 tff(1501,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e0, e0) = e0) | (op(e0, e0) = e2) | (op(e0, e2) = e0) | (e2 = op(e3, op(e3, e3))) | (op(e3, e2) = e2) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.76 tff(1502,plain,
% 0.58/0.76 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1501, 1124, 4, 232, 1397, 483, 112, 168, 6])).
% 0.58/0.76 tff(1503,plain,
% 0.58/0.76 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[416, 1502, 1401, 1400])).
% 0.58/0.76 tff(1504,plain,
% 0.58/0.76 (op(op(e1, e3), op(e1, e3)) = e3),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[313, 1503])).
% 0.58/0.76 tff(1505,plain,
% 0.58/0.76 (~(op(e1, e3) = e2)),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1230, 1504, 6])).
% 0.58/0.76 tff(1506,plain,
% 0.58/0.76 (op(e1, e0) = e2),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[1239, 1505, 977, 1124])).
% 0.58/0.76 tff(1507,plain,
% 0.58/0.76 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1506, 1506])).
% 0.58/0.76 tff(1508,plain,
% 0.58/0.76 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.58/0.76 inference(unit_resolution,[status(thm)],[333, 1503])).
% 0.58/0.76 tff(1509,plain,
% 0.58/0.76 (e0 = op(op(e1, e0), op(e1, e0))),
% 0.58/0.76 inference(symmetry,[status(thm)],[1508])).
% 0.58/0.76 tff(1510,plain,
% 0.58/0.76 (e0 = op(e2, e2)),
% 0.58/0.76 inference(transitivity,[status(thm)],[1509, 1507])).
% 0.58/0.76 tff(1511,plain,
% 0.58/0.76 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1510, 1510])).
% 0.58/0.76 tff(1512,plain,
% 0.58/0.76 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.58/0.76 inference(symmetry,[status(thm)],[1511])).
% 0.58/0.76 tff(1513,plain,
% 0.58/0.76 (op(e2, e2) = op(op(e1, e0), op(e1, e0))),
% 0.58/0.76 inference(symmetry,[status(thm)],[1507])).
% 0.58/0.76 tff(1514,plain,
% 0.58/0.76 (op(e2, e2) = e0),
% 0.58/0.76 inference(transitivity,[status(thm)],[1513, 1508])).
% 0.58/0.76 tff(1515,plain,
% 0.58/0.76 ((op(e1, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1506])).
% 0.58/0.76 tff(1516,plain,
% 0.58/0.76 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.58/0.76 inference(transitivity,[status(thm)],[1515, 379])).
% 0.58/0.76 tff(1517,plain,
% 0.58/0.76 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1516])).
% 0.58/0.76 tff(1518,plain,
% 0.58/0.76 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = op(e2, e0)))),
% 0.58/0.76 inference(rewrite,[status(thm)],[])).
% 0.58/0.76 tff(1519,plain,
% 0.58/0.76 (~(op(e1, e0) = op(e2, e0))),
% 0.58/0.76 inference(and_elim,[status(thm)],[388])).
% 0.58/0.76 tff(1520,plain,
% 0.58/0.76 (~(op(e1, e0) = op(e2, e0))),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 0.58/0.76 tff(1521,plain,
% 0.58/0.76 (~(op(e2, e0) = e2)),
% 0.58/0.76 inference(modus_ponens,[status(thm)],[1520, 1517])).
% 0.58/0.76 tff(1522,plain,
% 0.58/0.76 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 0.58/0.76 inference(monotonicity,[status(thm)],[1506])).
% 0.63/0.76 tff(1523,plain,
% 0.63/0.76 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 0.63/0.76 inference(transitivity,[status(thm)],[1522, 263])).
% 0.63/0.76 tff(1524,plain,
% 0.63/0.76 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 0.63/0.76 inference(symmetry,[status(thm)],[1523])).
% 0.63/0.76 tff(1525,plain,
% 0.63/0.76 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1524])).
% 0.63/0.76 tff(1526,plain,
% 0.63/0.76 (~(op(e1, e0) = e0)),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[272, 1525])).
% 0.63/0.76 tff(1527,plain,
% 0.63/0.76 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e2))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1510])).
% 0.63/0.76 tff(1528,plain,
% 0.63/0.76 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e0)),
% 0.63/0.76 inference(symmetry,[status(thm)],[1527])).
% 0.63/0.76 tff(1529,plain,
% 0.63/0.76 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e0))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1528])).
% 0.63/0.76 tff(1530,plain,
% 0.63/0.76 (~(op(e2, e0) = e0)),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[1384, 1529])).
% 0.63/0.76 tff(1531,plain,
% 0.63/0.76 (((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0))),
% 0.63/0.76 inference(rewrite,[status(thm)],[])).
% 0.63/0.76 tff(1532,plain,
% 0.63/0.76 ((((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0))),
% 0.63/0.76 inference(rewrite,[status(thm)],[])).
% 0.63/0.76 tff(1533,plain,
% 0.63/0.76 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0))),
% 0.63/0.76 inference(rewrite,[status(thm)],[])).
% 0.63/0.76 tff(1534,plain,
% 0.63/0.76 (((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)) <=> (((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1533])).
% 0.63/0.76 tff(1535,plain,
% 0.63/0.76 (((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0))),
% 0.63/0.76 inference(transitivity,[status(thm)],[1534, 1532])).
% 0.63/0.76 tff(1536,plain,
% 0.63/0.76 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)),
% 0.63/0.76 inference(and_elim,[status(thm)],[206])).
% 0.63/0.76 tff(1537,plain,
% 0.63/0.76 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 0.63/0.76 tff(1538,plain,
% 0.63/0.76 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[1537, 1531])).
% 0.63/0.76 tff(1539,plain,
% 0.63/0.76 (op(e3, e0) = e0),
% 0.63/0.76 inference(unit_resolution,[status(thm)],[1538, 1530, 168, 1526])).
% 0.63/0.76 tff(1540,plain,
% 0.63/0.76 ((op(e3, e0) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1539])).
% 0.63/0.76 tff(1541,plain,
% 0.63/0.76 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.63/0.76 inference(transitivity,[status(thm)],[1540, 868])).
% 0.63/0.76 tff(1542,plain,
% 0.63/0.76 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1541])).
% 0.63/0.76 tff(1543,plain,
% 0.63/0.76 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = op(e3, e3)))),
% 0.63/0.76 inference(rewrite,[status(thm)],[])).
% 0.63/0.76 tff(1544,plain,
% 0.63/0.76 (~(op(e3, e0) = op(e3, e3))),
% 0.63/0.76 inference(and_elim,[status(thm)],[64])).
% 0.63/0.76 tff(1545,plain,
% 0.63/0.76 (~(op(e3, e0) = op(e3, e3))),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 0.63/0.76 tff(1546,plain,
% 0.63/0.76 (~(op(e3, e3) = e0)),
% 0.63/0.76 inference(modus_ponens,[status(thm)],[1545, 1542])).
% 0.63/0.76 tff(1547,plain,
% 0.63/0.76 ((op(e1, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1506])).
% 0.63/0.76 tff(1548,plain,
% 0.63/0.76 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.63/0.76 inference(transitivity,[status(thm)],[1547, 610])).
% 0.63/0.76 tff(1549,plain,
% 0.63/0.76 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.63/0.76 inference(monotonicity,[status(thm)],[1548])).
% 0.63/0.76 tff(1550,plain,
% 0.63/0.76 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e3, e0)))),
% 0.63/0.76 inference(rewrite,[status(thm)],[])).
% 0.63/0.76 tff(1551,plain,
% 0.63/0.76 (~(op(e1, e0) = op(e3, e0))),
% 0.63/0.76 inference(and_elim,[status(thm)],[387])).
% 0.63/0.76 tff(1552,plain,
% 0.63/0.76 (~(op(e1, e0) = op(e3, e0))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 0.63/0.77 tff(1553,plain,
% 0.63/0.77 (~(op(e3, e0) = e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1552, 1549])).
% 0.63/0.77 tff(1554,plain,
% 0.63/0.77 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[419, 1503])).
% 0.63/0.77 tff(1555,plain,
% 0.63/0.77 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[651])).
% 0.63/0.77 tff(1556,plain,
% 0.63/0.77 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1555])).
% 0.63/0.77 tff(1557,plain,
% 0.63/0.77 (~(op(e3, e2) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1166, 1556])).
% 0.63/0.77 tff(1558,plain,
% 0.63/0.77 (op(e1, e2) = e3),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[520, 1557, 1396, 6])).
% 0.63/0.77 tff(1559,plain,
% 0.63/0.77 (op(op(e1, e2), op(e1, e2)) = op(e3, e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1558, 1558])).
% 0.63/0.77 tff(1560,plain,
% 0.63/0.77 (e2 = op(op(e1, e2), op(e1, e2))),
% 0.63/0.77 inference(symmetry,[status(thm)],[429])).
% 0.63/0.77 tff(1561,plain,
% 0.63/0.77 (e2 = e3),
% 0.63/0.77 inference(transitivity,[status(thm)],[1560, 1559, 651])).
% 0.63/0.77 tff(1562,plain,
% 0.63/0.77 ($false),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[195, 1561])).
% 0.63/0.77 tff(1563,plain,((~(op(e3, e3) = e3)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (op(e0, e2) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.77 tff(1564,plain,
% 0.63/0.77 (~(op(e3, e3) = e3)),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1563, 1554, 1396, 6])).
% 0.63/0.77 tff(1565,plain,
% 0.63/0.77 (op(e3, e3) = e2),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1433, 1564, 1553, 1546, 1397, 483])).
% 0.63/0.77 tff(1566,plain,
% 0.63/0.77 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1565])).
% 0.63/0.77 tff(1567,plain,
% 0.63/0.77 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1566])).
% 0.63/0.77 tff(1568,plain,
% 0.63/0.77 (~(op(e2, e3) = e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[656, 1567])).
% 0.63/0.77 tff(1569,plain,
% 0.63/0.77 (op(e2, e1) = e2),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[43, 1568, 1521, 3])).
% 0.63/0.77 tff(1570,plain,
% 0.63/0.77 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1569])).
% 0.63/0.77 tff(1571,plain,
% 0.63/0.77 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1570, 319])).
% 0.63/0.77 tff(1572,plain,
% 0.63/0.77 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1571])).
% 0.63/0.77 tff(1573,plain,
% 0.63/0.77 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1572])).
% 0.63/0.77 tff(1574,plain,
% 0.63/0.77 (~(op(e2, e1) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[220, 1573])).
% 0.63/0.77 tff(1575,plain,
% 0.63/0.77 (op(op(e1, e1), op(e1, e1)) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[316, 1503])).
% 0.63/0.77 tff(1576,assumption,(op(e1, e0) = e2), introduced(assumption)).
% 0.63/0.77 tff(1577,plain,
% 0.63/0.77 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1576, 1576])).
% 0.63/0.77 tff(1578,plain,
% 0.63/0.77 (e0 = op(e2, e2)),
% 0.63/0.77 inference(transitivity,[status(thm)],[344, 1577])).
% 0.63/0.77 tff(1579,plain,
% 0.63/0.77 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1578, 1578])).
% 0.63/0.77 tff(1580,plain,
% 0.63/0.77 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1579])).
% 0.63/0.77 tff(1581,assumption,(op(e1, e1) = e0), introduced(assumption)).
% 0.63/0.77 tff(1582,plain,
% 0.63/0.77 (op(e1, e1) = op(e2, e2)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1581, 344, 1577])).
% 0.63/0.77 tff(1583,plain,
% 0.63/0.77 (op(op(e1, e1), op(e1, e1)) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1582, 1582])).
% 0.63/0.77 tff(1584,plain,
% 0.63/0.77 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1578])).
% 0.63/0.77 tff(1585,plain,
% 0.63/0.77 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1584])).
% 0.63/0.77 tff(1586,plain,
% 0.63/0.77 (~(op(e2, e2) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1182, 1585])).
% 0.63/0.77 tff(1587,plain,
% 0.63/0.77 ((op(e1, e1) = e1) <=> (op(e2, e2) = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1582])).
% 0.63/0.77 tff(1588,plain,
% 0.63/0.77 ((op(e2, e2) = e1) <=> (op(e1, e1) = e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1587])).
% 0.63/0.77 tff(1589,plain,
% 0.63/0.77 ((~(op(e2, e2) = e1)) <=> (~(op(e1, e1) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1588])).
% 0.63/0.77 tff(1590,plain,
% 0.63/0.77 (~(op(e1, e1) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1586, 1589])).
% 0.63/0.77 tff(1591,assumption,(~(op(e2, e1) = e1)), introduced(assumption)).
% 0.63/0.77 tff(1592,plain,
% 0.63/0.77 ((op(e0, e1) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e1))),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1593,plain,
% 0.63/0.77 (e1 = op(e0, e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[339, 1583, 1580])).
% 0.63/0.77 tff(1594,plain,
% 0.63/0.77 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e0, e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1593])).
% 0.63/0.77 tff(1595,plain,
% 0.63/0.77 ((op(e0, e1) = e1) <=> (op(e0, e0) = op(e0, e1))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1594, 1592])).
% 0.63/0.77 tff(1596,plain,
% 0.63/0.77 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1595])).
% 0.63/0.77 tff(1597,plain,
% 0.63/0.77 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1596])).
% 0.63/0.77 tff(1598,plain,
% 0.63/0.77 (~(op(e0, e1) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[805, 1597])).
% 0.63/0.77 tff(1599,plain,
% 0.63/0.77 (op(e3, e1) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[763, 1598, 1591, 1590])).
% 0.63/0.77 tff(1600,plain,
% 0.63/0.77 ((op(e3, e1) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1599])).
% 0.63/0.77 tff(1601,plain,
% 0.63/0.77 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1600, 1157])).
% 0.63/0.77 tff(1602,plain,
% 0.63/0.77 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1601])).
% 0.63/0.77 tff(1603,plain,
% 0.63/0.77 (~(op(e3, e2) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[497, 1602])).
% 0.63/0.77 tff(1604,plain,
% 0.63/0.77 (op(e1, e2) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1331, 1603, 1398, 1586])).
% 0.63/0.77 tff(1605,plain,
% 0.63/0.77 (op(e1, e2) = op(e0, e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1604, 339, 1583, 1580])).
% 0.63/0.77 tff(1606,plain,
% 0.63/0.77 (op(op(e1, e2), op(e1, e2)) = op(op(e0, e0), op(e0, e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1605, 1605])).
% 0.63/0.77 tff(1607,plain,
% 0.63/0.77 (op(op(e0, e0), op(e0, e0)) = op(op(e1, e2), op(e1, e2))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1606])).
% 0.63/0.77 tff(1608,plain,
% 0.63/0.77 (op(op(e2, e2), op(e2, e2)) = op(op(e1, e1), op(e1, e1))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1583])).
% 0.63/0.77 tff(1609,plain,
% 0.63/0.77 (op(e0, e0) = e1),
% 0.63/0.77 inference(transitivity,[status(thm)],[1579, 1608, 335])).
% 0.63/0.77 tff(1610,plain,
% 0.63/0.77 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1609, 1609])).
% 0.63/0.77 tff(1611,plain,
% 0.63/0.77 (op(e1, e1) = op(op(e0, e0), op(e0, e0))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1610])).
% 0.63/0.77 tff(1612,plain,
% 0.63/0.77 (e0 = op(e1, e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1581])).
% 0.63/0.77 tff(1613,plain,
% 0.63/0.77 (op(e2, e2) = op(op(e1, e0), op(e1, e0))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1577])).
% 0.63/0.77 tff(1614,plain,
% 0.63/0.77 (op(e2, e2) = e2),
% 0.63/0.77 inference(transitivity,[status(thm)],[1613, 343, 1612, 1611, 1607, 429])).
% 0.63/0.77 tff(1615,plain,
% 0.63/0.77 ($false),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[3, 1614])).
% 0.63/0.77 tff(1616,plain,((~(op(e1, e1) = e0)) | (op(e2, e2) = e2) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(e1, e0) = e2)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (op(e0, e2) = e1) | (op(e2, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.77 tff(1617,plain,
% 0.63/0.77 (~(op(e1, e1) = e0)),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1616, 1554, 3, 1508, 1506, 1575, 1398, 1574])).
% 0.63/0.77 tff(1618,plain,
% 0.63/0.77 (op(e1, e3) = e0),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1481, 1617, 168, 1400, 1514, 4])).
% 0.63/0.77 tff(1619,plain,
% 0.63/0.77 (op(e1, e3) = op(e2, e2)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1618, 1509, 1507])).
% 0.63/0.77 tff(1620,plain,
% 0.63/0.77 (op(op(e1, e3), op(e1, e3)) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1619, 1619])).
% 0.63/0.77 tff(1621,plain,
% 0.63/0.77 (e3 = op(op(e1, e3), op(e1, e3))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1504])).
% 0.63/0.77 tff(1622,plain,
% 0.63/0.77 (e3 = op(e0, e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1621, 1620, 1512])).
% 0.63/0.77 tff(1623,plain,
% 0.63/0.77 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e0, e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1622])).
% 0.63/0.77 tff(1624,plain,
% 0.63/0.77 ((op(e0, e3) = e3) <=> (op(e0, e0) = op(e0, e3))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1623, 1399])).
% 0.63/0.77 tff(1625,plain,
% 0.63/0.77 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1624])).
% 0.63/0.77 tff(1626,plain,
% 0.63/0.77 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1625])).
% 0.63/0.77 tff(1627,plain,
% 0.63/0.77 (~(op(e0, e3) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[727, 1626])).
% 0.63/0.77 tff(1628,plain,
% 0.63/0.77 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1618])).
% 0.63/0.77 tff(1629,plain,
% 0.63/0.77 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1628])).
% 0.63/0.77 tff(1630,plain,
% 0.63/0.77 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = op(e1, e3)))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1631,plain,
% 0.63/0.77 (~(op(e0, e3) = op(e1, e3))),
% 0.63/0.77 inference(and_elim,[status(thm)],[90])).
% 0.63/0.77 tff(1632,plain,
% 0.63/0.77 (~(op(e0, e3) = op(e1, e3))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.63/0.77 tff(1633,plain,
% 0.63/0.77 (~(op(e0, e3) = e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1632, 1629])).
% 0.63/0.77 tff(1634,plain,
% 0.63/0.77 (((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1635,plain,
% 0.63/0.77 ((((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1636,plain,
% 0.63/0.77 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1637,plain,
% 0.63/0.77 (((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)) <=> (((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1636])).
% 0.63/0.77 tff(1638,plain,
% 0.63/0.77 (((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1637, 1635])).
% 0.63/0.77 tff(1639,plain,
% 0.63/0.77 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)),
% 0.63/0.77 inference(and_elim,[status(thm)],[255])).
% 0.63/0.77 tff(1640,plain,
% 0.63/0.77 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 0.63/0.77 tff(1641,plain,
% 0.63/0.77 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1640, 1634])).
% 0.63/0.77 tff(1642,plain,
% 0.63/0.77 (op(e0, e3) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1641, 1633, 1395, 1627])).
% 0.63/0.77 tff(1643,plain,
% 0.63/0.77 (op(op(e2, e2), op(e2, e2)) = op(op(e1, e3), op(e1, e3))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1620])).
% 0.63/0.77 tff(1644,plain,
% 0.63/0.77 (op(e0, e0) = e3),
% 0.63/0.77 inference(transitivity,[status(thm)],[1511, 1643, 1504])).
% 0.63/0.77 tff(1645,plain,
% 0.63/0.77 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1644])).
% 0.63/0.77 tff(1646,plain,
% 0.63/0.77 (op(e0, op(e0, e0)) = e1),
% 0.63/0.77 inference(transitivity,[status(thm)],[1645, 1642])).
% 0.63/0.77 tff(1647,plain,
% 0.63/0.77 (op(op(e0, op(e0, e0)), e0) = op(e1, e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1646])).
% 0.63/0.77 tff(1648,plain,
% 0.63/0.77 (op(e1, e0) = op(op(e0, op(e0, e0)), e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1647])).
% 0.63/0.77 tff(1649,plain,
% 0.63/0.77 (e2 = op(e1, e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1506])).
% 0.63/0.77 tff(1650,plain,
% 0.63/0.77 (e2 = op(op(e0, op(e0, e0)), e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1649, 1648])).
% 0.63/0.77 tff(1651,plain,
% 0.63/0.77 ((e3 = op(e0, e0)) <=> (op(e0, e0) = e3)),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1652,plain,
% 0.63/0.77 ((op(e0, e0) = e3) <=> (e3 = op(e0, e0))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1651])).
% 0.63/0.77 tff(1653,plain,
% 0.63/0.77 (e3 = op(e0, e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1644, 1652])).
% 0.63/0.77 tff(1654,plain,
% 0.63/0.77 ((op(e0, op(e0, e0)) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1655,plain,
% 0.63/0.77 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1645])).
% 0.63/0.77 tff(1656,plain,
% 0.63/0.77 ((op(e0, e3) = e1) <=> (op(e0, op(e0, e0)) = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1655])).
% 0.63/0.77 tff(1657,plain,
% 0.63/0.77 ((op(e0, e3) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1656, 1654])).
% 0.63/0.77 tff(1658,plain,
% 0.63/0.77 (e1 = op(e0, op(e0, e0))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1642, 1657])).
% 0.63/0.77 tff(1659,plain,
% 0.63/0.77 ((~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0)))))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1660,plain,
% 0.63/0.77 (((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0))) <=> (~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0)))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1661,plain,
% 0.63/0.77 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0)))) <=> (~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0))))))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1660])).
% 0.63/0.77 tff(1662,plain,
% 0.63/0.77 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0)))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0))))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1661, 1659])).
% 0.63/0.77 tff(1663,plain,
% 0.63/0.77 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0)))) <=> (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1664,plain,
% 0.63/0.77 ((~(((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), e0)))) <=> (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1665,axiom,(~(((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), e0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax17')).
% 0.63/0.77 tff(1666,plain,
% 0.63/0.77 (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0)))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.63/0.77 tff(1667,plain,
% 0.63/0.77 (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(op(e0, op(e0, e0)), e0)))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1666, 1663])).
% 0.63/0.77 tff(1668,plain,
% 0.63/0.77 ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, op(e0, e0)), e0)))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1667, 1662])).
% 0.63/0.77 tff(1669,plain,
% 0.63/0.77 ($false),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1668, 1658, 1653, 1650])).
% 0.63/0.77 tff(1670,plain,((op(e1, e1) = e2) | (op(e0, e3) = e2) | (op(e0, e0) = e0) | (op(e0, e0) = e2) | (op(e2, e2) = e2) | (op(e0, e2) = e1) | (e2 = op(e3, op(e3, e3))) | (op(e3, e2) = e2) | (op(e0, e2) = e3) | (op(e2, e2) = e3) | (op(e1, e2) = e2) | (op(e0, e2) = e0) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.77 tff(1671,plain,
% 0.63/0.77 (op(e1, e1) = e2),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1670, 6, 168, 4, 3, 1398, 1397, 483, 1396, 1395, 977, 232, 112])).
% 0.63/0.77 tff(1672,plain,
% 0.63/0.77 (e2 = op(e1, e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1671, 529])).
% 0.63/0.77 tff(1673,plain,
% 0.63/0.77 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1671])).
% 0.63/0.77 tff(1674,plain,
% 0.63/0.77 ((e3 = op(e1, op(e1, e1))) <=> (e3 = op(e1, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1673])).
% 0.63/0.77 tff(1675,plain,
% 0.63/0.77 ((e3 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1674, 531])).
% 0.63/0.77 tff(1676,plain,
% 0.63/0.77 ((op(e1, e2) = e3) <=> (e3 = op(e1, op(e1, e1)))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1675])).
% 0.63/0.77 tff(1677,assumption,(~(e0 = op(e2, op(e2, e2)))), introduced(assumption)).
% 0.63/0.77 tff(1678,plain,
% 0.63/0.77 ((e0 = e1) <=> (e0 = op(e2, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[325])).
% 0.63/0.77 tff(1679,plain,
% 0.63/0.77 ((e0 = e1) <=> (op(e2, e2) = e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1678, 954])).
% 0.63/0.78 tff(1680,plain,
% 0.63/0.78 ((~(e0 = e1)) <=> (~(op(e2, e2) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1679])).
% 0.63/0.78 tff(1681,plain,
% 0.63/0.78 (~(op(e2, e2) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1182, 1680])).
% 0.63/0.78 tff(1682,plain,
% 0.63/0.78 ((op(e2, op(e2, e2)) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.63/0.78 inference(commutativity,[status(thm)],[])).
% 0.63/0.78 tff(1683,plain,
% 0.63/0.78 (op(e2, op(e2, e2)) = op(e2, e1)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[361])).
% 0.63/0.78 tff(1684,plain,
% 0.63/0.78 (op(e2, e1) = op(e2, op(e2, e2))),
% 0.63/0.78 inference(symmetry,[status(thm)],[1683])).
% 0.63/0.78 tff(1685,plain,
% 0.63/0.78 ((op(e2, e1) = e0) <=> (op(e2, op(e2, e2)) = e0)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1684])).
% 0.63/0.78 tff(1686,plain,
% 0.63/0.78 ((op(e2, e1) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1685, 1682])).
% 0.63/0.78 tff(1687,plain,
% 0.63/0.78 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e0)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1686])).
% 0.63/0.78 tff(1688,plain,
% 0.63/0.78 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e1) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1687])).
% 0.63/0.78 tff(1689,plain,
% 0.63/0.78 (~(op(e2, e1) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1677, 1688])).
% 0.63/0.78 tff(1690,plain,
% 0.63/0.78 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[325])).
% 0.63/0.78 tff(1691,plain,
% 0.63/0.78 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1690])).
% 0.63/0.78 tff(1692,plain,
% 0.63/0.78 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1691])).
% 0.63/0.78 tff(1693,plain,
% 0.63/0.78 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = op(e2, e2)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1694,plain,
% 0.63/0.78 (~(op(e2, e1) = op(e2, e2))),
% 0.63/0.78 inference(and_elim,[status(thm)],[69])).
% 0.63/0.78 tff(1695,plain,
% 0.63/0.78 (~(op(e2, e1) = op(e2, e2))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 0.63/0.78 tff(1696,plain,
% 0.63/0.78 (~(op(e2, e1) = e1)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1695, 1692])).
% 0.63/0.78 tff(1697,plain,
% 0.63/0.78 (op(e2, e1) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[796, 1696, 102, 1689])).
% 0.63/0.78 tff(1698,plain,
% 0.63/0.78 (op(e2, op(e2, e2)) = e3),
% 0.63/0.78 inference(transitivity,[status(thm)],[1683, 1697])).
% 0.63/0.78 tff(1699,plain,
% 0.63/0.78 (op(op(e2, op(e2, e2)), e2) = op(e3, e2)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1698])).
% 0.63/0.78 tff(1700,plain,
% 0.63/0.78 ((e0 = op(op(e2, op(e2, e2)), e2)) <=> (e0 = op(e3, e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1699])).
% 0.63/0.78 tff(1701,plain,
% 0.63/0.78 ((e0 = op(op(e2, op(e2, e2)), e2)) <=> (op(e3, e2) = e0)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1700, 1144])).
% 0.63/0.78 tff(1702,plain,
% 0.63/0.78 ((~(e0 = op(op(e2, op(e2, e2)), e2))) <=> (~(op(e3, e2) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1701])).
% 0.63/0.78 tff(1703,plain,
% 0.63/0.78 ((e1 = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.63/0.78 inference(commutativity,[status(thm)],[])).
% 0.63/0.78 tff(1704,plain,
% 0.63/0.78 ((op(e2, e2) = e1) <=> (e1 = op(e2, e2))),
% 0.63/0.78 inference(symmetry,[status(thm)],[1703])).
% 0.63/0.78 tff(1705,plain,
% 0.63/0.78 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (op(e2, e2) = e1)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[315])).
% 0.63/0.78 tff(1706,plain,
% 0.63/0.78 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (e1 = op(e2, e2))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1705, 1704])).
% 0.63/0.78 tff(1707,plain,
% 0.63/0.78 (e1 = op(e2, e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[317, 1706])).
% 0.63/0.78 tff(1708,plain,
% 0.63/0.78 ((op(e2, op(e2, e2)) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 0.63/0.78 inference(commutativity,[status(thm)],[])).
% 0.63/0.78 tff(1709,plain,
% 0.63/0.78 ((op(e2, e1) = e3) <=> (op(e2, op(e2, e2)) = e3)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1684])).
% 0.63/0.78 tff(1710,plain,
% 0.63/0.78 ((op(e2, e1) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1709, 1708])).
% 0.63/0.78 tff(1711,plain,
% 0.63/0.78 (e3 = op(e2, op(e2, e2))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1697, 1710])).
% 0.63/0.78 tff(1712,plain,
% 0.63/0.78 ((~(~((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2))))))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1713,plain,
% 0.63/0.78 (((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))) <=> (~((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1714,plain,
% 0.63/0.78 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~(~((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2)))))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1713])).
% 0.63/0.78 tff(1715,plain,
% 0.63/0.78 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1714, 1712])).
% 0.63/0.78 tff(1716,plain,
% 0.63/0.78 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1717,plain,
% 0.63/0.78 ((~(((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1718,axiom,(~(((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(op(e2, op(e2, e2)), e2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax26')).
% 0.63/0.78 tff(1719,plain,
% 0.63/0.78 (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 0.63/0.78 tff(1720,plain,
% 0.63/0.78 (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1719, 1716])).
% 0.63/0.78 tff(1721,plain,
% 0.63/0.78 ((~(e1 = op(e2, e2))) | (~(e0 = op(op(e2, op(e2, e2)), e2))) | (~(e3 = op(e2, op(e2, e2))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1720, 1715])).
% 0.63/0.78 tff(1722,plain,
% 0.63/0.78 (~(e0 = op(op(e2, op(e2, e2)), e2))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1721, 1711, 1707])).
% 0.63/0.78 tff(1723,plain,
% 0.63/0.78 (~(op(e3, e2) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1722, 1702])).
% 0.63/0.78 tff(1724,plain,
% 0.63/0.78 (op(e1, e2) = e0),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[997, 1723, 232, 1681])).
% 0.63/0.78 tff(1725,plain,
% 0.63/0.78 (e0 = op(e1, e2)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1724])).
% 0.63/0.78 tff(1726,plain,
% 0.63/0.78 (op(e0, e0) = op(op(e1, e2), op(e1, e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1725, 1725])).
% 0.63/0.78 tff(1727,plain,
% 0.63/0.78 (op(e0, e0) = e2),
% 0.63/0.78 inference(transitivity,[status(thm)],[1726, 420])).
% 0.63/0.78 tff(1728,plain,
% 0.63/0.78 ($false),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[4, 1727])).
% 0.63/0.78 tff(1729,plain,(((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))) | (op(e0, e0) = e2) | (op(e0, e2) = e0) | (~(op(e1, e1) = e2)) | (e0 = op(e2, op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.78 tff(1730,plain,
% 0.63/0.78 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1729, 1671, 232, 4, 1677])).
% 0.63/0.78 tff(1731,plain,
% 0.63/0.78 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1671])).
% 0.63/0.78 tff(1732,plain,
% 0.63/0.78 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1731, 55])).
% 0.63/0.78 tff(1733,plain,
% 0.63/0.78 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1732])).
% 0.63/0.78 tff(1734,plain,
% 0.63/0.78 (~(op(e2, e1) = e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[101, 1733])).
% 0.63/0.78 tff(1735,plain,
% 0.63/0.78 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[53, 1734, 4, 3, 6])).
% 0.63/0.78 tff(1736,plain,
% 0.63/0.78 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[416, 1735, 1401, 1730])).
% 0.63/0.78 tff(1737,plain,
% 0.63/0.78 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[459, 1736])).
% 0.63/0.78 tff(1738,plain,
% 0.63/0.78 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[633, 1736])).
% 0.63/0.78 tff(1739,plain,
% 0.63/0.78 (~(op(e3, e3) = e2)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[631, 1738, 6])).
% 0.63/0.78 tff(1740,plain,
% 0.63/0.78 (~(op(e3, e2) = e3)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[467, 1739, 1737])).
% 0.63/0.78 tff(1741,plain,
% 0.63/0.78 (op(e1, e2) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[520, 1740, 1396, 6])).
% 0.63/0.78 tff(1742,plain,
% 0.63/0.78 (e3 = op(e1, op(e1, e1))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1741, 1676])).
% 0.63/0.78 tff(1743,plain,
% 0.63/0.78 (op(e1, op(e1, e1)) = e3),
% 0.63/0.78 inference(transitivity,[status(thm)],[1673, 1741])).
% 0.63/0.78 tff(1744,plain,
% 0.63/0.78 (op(op(e1, op(e1, e1)), e1) = op(e3, e1)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1743])).
% 0.63/0.78 tff(1745,plain,
% 0.63/0.78 (op(e3, e1) = op(op(e1, op(e1, e1)), e1)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1744])).
% 0.63/0.78 tff(1746,plain,
% 0.63/0.78 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[476, 1736])).
% 0.63/0.78 tff(1747,plain,
% 0.63/0.78 (~(op(e3, e0) = e0)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1097, 1746, 168])).
% 0.63/0.78 tff(1748,plain,
% 0.63/0.78 (~(op(e3, e2) = e0)),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[474, 1737, 4])).
% 0.63/0.78 tff(1749,plain,
% 0.63/0.78 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[887])).
% 0.63/0.78 tff(1750,plain,
% 0.63/0.78 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1749])).
% 0.63/0.78 tff(1751,plain,
% 0.63/0.78 (~(op(e0, e3) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[823, 1750])).
% 0.63/0.78 tff(1752,plain,
% 0.63/0.78 ((e3 = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.63/0.78 inference(commutativity,[status(thm)],[])).
% 0.63/0.78 tff(1753,plain,
% 0.63/0.78 (op(e0, e0) = op(op(e3, e3), op(e3, e3))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[888, 888])).
% 0.63/0.78 tff(1754,plain,
% 0.63/0.78 (op(e0, e0) = e3),
% 0.63/0.78 inference(transitivity,[status(thm)],[1753, 625])).
% 0.63/0.78 tff(1755,plain,
% 0.63/0.78 ((op(e0, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1754])).
% 0.63/0.78 tff(1756,plain,
% 0.63/0.78 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1755, 1752])).
% 0.63/0.78 tff(1757,plain,
% 0.63/0.78 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1756])).
% 0.63/0.78 tff(1758,plain,
% 0.63/0.78 (~(op(e3, e0) = e3)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[616, 1757])).
% 0.63/0.78 tff(1759,assumption,(~(op(e3, e0) = e1)), introduced(assumption)).
% 0.63/0.78 tff(1760,plain,
% 0.63/0.78 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[887])).
% 0.63/0.78 tff(1761,plain,
% 0.63/0.78 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1760])).
% 0.63/0.78 tff(1762,plain,
% 0.63/0.78 (~(op(e3, e0) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1545, 1761])).
% 0.63/0.78 tff(1763,plain,
% 0.63/0.78 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[887])).
% 0.63/0.78 tff(1764,plain,
% 0.63/0.78 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1763])).
% 0.63/0.78 tff(1765,plain,
% 0.63/0.78 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1764, 610])).
% 0.63/0.78 tff(1766,plain,
% 0.63/0.78 ((~(e2 = op(e3, op(e3, e3)))) <=> (~(op(e3, e0) = e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1765])).
% 0.63/0.78 tff(1767,plain,
% 0.63/0.78 (~(op(e3, e0) = e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1397, 1766])).
% 0.63/0.78 tff(1768,plain,
% 0.63/0.78 ($false),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1088, 1767, 1762, 1759, 1758])).
% 0.63/0.78 tff(1769,plain,((~(op(e3, e3) = e0)) | (op(e3, e0) = e1) | (e2 = op(e3, op(e3, e3))) | (~(op(op(e3, e3), op(e3, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.78 tff(1770,plain,
% 0.63/0.78 (op(e3, e0) = e1),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1769, 887, 1397, 625])).
% 0.63/0.78 tff(1771,plain,
% 0.63/0.78 (e1 = op(e3, e0)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1770])).
% 0.63/0.78 tff(1772,plain,
% 0.63/0.78 (op(e1, e1) = op(op(e3, e0), op(e3, e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1771, 1771])).
% 0.63/0.78 tff(1773,plain,
% 0.63/0.78 (op(e1, e1) = e0),
% 0.63/0.78 inference(transitivity,[status(thm)],[1772, 583])).
% 0.63/0.79 tff(1774,plain,
% 0.63/0.79 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1773])).
% 0.63/0.79 tff(1775,plain,
% 0.63/0.79 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1774])).
% 0.63/0.79 tff(1776,plain,
% 0.63/0.79 (~(op(e0, e1) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[110, 1775])).
% 0.63/0.79 tff(1777,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[209, 1776, 1751, 168, 232])).
% 0.63/0.79 tff(1778,plain,((~(op(e3, e3) = e0)) | (op(e0, e0) = e0) | (op(e0, e2) = e0) | (~(op(op(e3, e0), op(e3, e0)) = e0)) | (e2 = op(e3, op(e3, e3))) | (~(op(op(e3, e3), op(e3, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1779,plain,
% 0.63/0.79 (~(op(e3, e3) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1778, 1738, 232, 168, 1397, 1746])).
% 0.63/0.79 tff(1780,plain,
% 0.63/0.79 (op(e3, e1) = e0),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[580, 1779, 1748, 1747])).
% 0.63/0.79 tff(1781,plain,
% 0.63/0.79 (e0 = op(e3, e1)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1780])).
% 0.63/0.79 tff(1782,plain,
% 0.63/0.79 (e0 = op(op(e1, op(e1, e1)), e1)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1781, 1745])).
% 0.63/0.79 tff(1783,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[545, 1782, 1742, 1672])).
% 0.63/0.79 tff(1784,plain,((op(e2, e2) = e3) | (op(e0, e2) = e3) | (op(e0, e2) = e0) | (op(e0, e0) = e0) | (e2 = op(e3, op(e3, e3))) | (op(e0, e0) = e2) | (op(e2, e2) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e0, e2) = e1) | (op(e3, e2) = e2) | (op(e0, e3) = e2) | (op(e1, e2) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1785,plain,
% 0.63/0.79 (op(e0, e0) = e0),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1784, 1394, 4, 6, 1389, 1320, 3, 1385, 1374, 483, 1369, 1260, 1361])).
% 0.63/0.79 tff(1786,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1785])).
% 0.63/0.79 tff(1787,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1786, 1355])).
% 0.63/0.79 tff(1788,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1787])).
% 0.63/0.79 tff(1789,plain,
% 0.63/0.79 (~(op(e0, e3) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[727, 1788])).
% 0.63/0.79 tff(1790,plain,
% 0.63/0.79 (((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1791,plain,
% 0.63/0.79 ((((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1792,plain,
% 0.63/0.79 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1793,plain,
% 0.63/0.79 (((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)) <=> (((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1792])).
% 0.63/0.79 tff(1794,plain,
% 0.63/0.79 (((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1793, 1791])).
% 0.63/0.79 tff(1795,plain,
% 0.63/0.79 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)),
% 0.63/0.79 inference(and_elim,[status(thm)],[35])).
% 0.63/0.79 tff(1796,plain,
% 0.63/0.79 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 0.63/0.79 tff(1797,plain,
% 0.63/0.79 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1796, 1790])).
% 0.63/0.79 tff(1798,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1797, 1789, 1354, 1286, 1280])).
% 0.63/0.79 tff(1799,plain,((op(e3, e2) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1800,plain,
% 0.63/0.79 (op(e3, e2) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1799, 6, 4, 3])).
% 0.63/0.79 tff(1801,plain,
% 0.63/0.79 ((op(e3, e2) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1800])).
% 0.63/0.79 tff(1802,plain,
% 0.63/0.79 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1801, 5])).
% 0.63/0.79 tff(1803,plain,
% 0.63/0.79 ((op(e3, e3) = e2) <=> (op(e3, e2) = op(e3, e3))),
% 0.63/0.79 inference(symmetry,[status(thm)],[1802])).
% 0.63/0.79 tff(1804,plain,
% 0.63/0.79 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1050, 1800, 3])).
% 0.63/0.79 tff(1805,plain,
% 0.63/0.79 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[459, 1804])).
% 0.63/0.79 tff(1806,plain,
% 0.63/0.79 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[416, 1805, 1207, 1130])).
% 0.63/0.79 tff(1807,plain,
% 0.63/0.79 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[419, 1806])).
% 0.63/0.79 tff(1808,plain,
% 0.63/0.79 (~(op(e1, e2) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[435, 1807, 4])).
% 0.63/0.79 tff(1809,plain,
% 0.63/0.79 (~(op(e1, e2) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1259, 1807, 3])).
% 0.63/0.79 tff(1810,plain,
% 0.63/0.79 (~(op(e1, e2) = e1)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1266, 1807])).
% 0.63/0.79 tff(1811,plain,
% 0.63/0.79 (op(e1, e2) = e3),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[449, 1810, 1809, 1808])).
% 0.63/0.79 tff(1812,plain,
% 0.63/0.79 (op(e3, e3) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1274, 1811, 1807])).
% 0.63/0.79 tff(1813,plain,
% 0.63/0.79 (op(e3, e2) = op(e3, e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1812, 1803])).
% 0.63/0.79 tff(1814,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1166, 1813])).
% 0.63/0.79 tff(1815,plain,((op(e2, e2) = e3) | (op(e0, e0) = e2) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1816,plain,
% 0.63/0.79 (op(e2, e2) = e3),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1815, 4, 3])).
% 0.63/0.79 tff(1817,plain,
% 0.63/0.79 (~(op(e1, e2) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[435, 429, 4])).
% 0.63/0.79 tff(1818,plain,
% 0.63/0.79 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1816])).
% 0.63/0.79 tff(1819,plain,
% 0.63/0.79 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1818])).
% 0.63/0.79 tff(1820,plain,
% 0.63/0.79 (~(op(e1, e2) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[331, 1819])).
% 0.63/0.79 tff(1821,plain,
% 0.63/0.79 (~(op(e1, e2) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1259, 429, 3])).
% 0.63/0.79 tff(1822,plain,
% 0.63/0.79 (~(op(e1, e2) = e1)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1266, 429])).
% 0.63/0.79 tff(1823,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[449, 1822, 1821, 1820, 1817])).
% 0.63/0.79 tff(1824,plain,((~(op(op(e1, e2), op(e1, e2)) = e2)) | (op(e0, e0) = e2) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1825,plain,
% 0.63/0.79 (~(op(op(e1, e2), op(e1, e2)) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1824, 4, 3])).
% 0.63/0.79 tff(1826,plain,
% 0.63/0.79 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[419, 1825])).
% 0.63/0.79 tff(1827,plain,
% 0.63/0.79 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1816])).
% 0.63/0.79 tff(1828,plain,
% 0.63/0.79 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1827])).
% 0.63/0.79 tff(1829,plain,
% 0.63/0.79 (~(op(e0, e2) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[126, 1828])).
% 0.63/0.79 tff(1830,plain,
% 0.63/0.79 (~(op(e0, e2) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[129, 116])).
% 0.63/0.79 tff(1831,plain,
% 0.63/0.79 (~(op(e0, e2) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[229, 116, 4])).
% 0.63/0.79 tff(1832,plain,
% 0.63/0.79 (op(e0, e2) = e1),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[259, 1831, 1396, 1830])).
% 0.63/0.79 tff(1833,plain,
% 0.63/0.79 (e1 = op(e0, e2)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1832])).
% 0.63/0.79 tff(1834,plain,
% 0.63/0.79 (op(e1, e1) = op(op(e0, e2), op(e0, e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1833, 1833])).
% 0.63/0.79 tff(1835,plain,
% 0.63/0.79 (op(e1, e1) = e2),
% 0.63/0.79 inference(transitivity,[status(thm)],[1834, 116])).
% 0.63/0.79 tff(1836,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1117, 1835])).
% 0.63/0.79 tff(1837,plain,((~(op(op(e0, e2), op(e0, e2)) = e2)) | (op(e0, e2) = e3) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1838,plain,
% 0.63/0.79 (~(op(op(e0, e2), op(e0, e2)) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1837, 1829, 4])).
% 0.63/0.79 tff(1839,plain,
% 0.63/0.79 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[114, 1838])).
% 0.63/0.79 tff(1840,plain,
% 0.63/0.79 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1816])).
% 0.63/0.79 tff(1841,plain,
% 0.63/0.79 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1840, 1149])).
% 0.63/0.79 tff(1842,plain,
% 0.63/0.79 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1841])).
% 0.63/0.79 tff(1843,plain,
% 0.63/0.79 (~(op(e3, e2) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[591, 1842])).
% 0.63/0.79 tff(1844,plain,
% 0.63/0.79 (~(op(e3, e2) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1050, 461, 3])).
% 0.63/0.79 tff(1845,plain,
% 0.63/0.79 (~(op(e3, e2) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[474, 461, 4])).
% 0.63/0.79 tff(1846,plain,
% 0.63/0.79 (op(e3, e2) = e1),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[491, 1845, 483, 482])).
% 0.63/0.79 tff(1847,plain,
% 0.63/0.79 (e1 = op(e3, e2)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1846])).
% 0.63/0.79 tff(1848,plain,
% 0.63/0.79 (op(e1, e1) = op(op(e3, e2), op(e3, e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1847, 1847])).
% 0.63/0.79 tff(1849,plain,
% 0.63/0.79 (op(e1, e1) = e2),
% 0.63/0.79 inference(transitivity,[status(thm)],[1848, 461])).
% 0.63/0.79 tff(1850,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1124, 1849])).
% 0.63/0.79 tff(1851,plain,((~(op(op(e3, e2), op(e3, e2)) = e2)) | (op(e1, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e2) = e3) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1852,plain,
% 0.63/0.79 ((~(op(op(e3, e2), op(e3, e2)) = e2)) | (op(e3, e2) = e2) | (op(e3, e2) = e3) | (op(e0, e0) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1851, 1117])).
% 0.63/0.79 tff(1853,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1852, 1844, 461, 4, 1843])).
% 0.63/0.79 tff(1854,plain,((~(op(op(e3, e2), op(e3, e2)) = e2)) | (op(e0, e0) = e2) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1855,plain,
% 0.63/0.79 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1854, 4, 3])).
% 0.63/0.79 tff(1856,plain,
% 0.63/0.79 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[459, 1855])).
% 0.63/0.79 tff(1857,plain,
% 0.63/0.79 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[416, 1856, 1839, 1826])).
% 0.63/0.79 tff(1858,plain,
% 0.63/0.79 (op(e2, e1) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[960, 1857, 3, 1816])).
% 0.63/0.79 tff(1859,plain,
% 0.63/0.79 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[11, 1857])).
% 0.63/0.79 tff(1860,plain,
% 0.63/0.79 (op(op(e2, e2), op(e2, e2)) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[9, 1857])).
% 0.63/0.79 tff(1861,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1127, 1860, 1859, 1858])).
% 0.63/0.79 tff(1862,plain,((op(e0, e0) = e2) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1863,plain,
% 0.63/0.79 (op(e0, e0) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1862, 3])).
% 0.63/0.79 tff(1864,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.79 tff(1865,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1864, 2])).
% 0.63/0.79 tff(1866,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1865])).
% 0.63/0.79 tff(1867,plain,
% 0.63/0.79 (~(op(e0, e2) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[281, 1866])).
% 0.63/0.79 tff(1868,plain,
% 0.63/0.79 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.79 tff(1869,plain,
% 0.63/0.79 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1868, 263])).
% 0.63/0.79 tff(1870,plain,
% 0.63/0.79 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1869])).
% 0.63/0.79 tff(1871,plain,
% 0.63/0.79 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1870])).
% 0.63/0.79 tff(1872,plain,
% 0.63/0.79 (~(op(e0, e0) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[272, 1871])).
% 0.63/0.79 tff(1873,plain,
% 0.63/0.79 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[305, 1872])).
% 0.63/0.79 tff(1874,plain,
% 0.63/0.79 ((e2 = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.63/0.79 inference(commutativity,[status(thm)],[])).
% 0.63/0.79 tff(1875,plain,
% 0.63/0.79 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[173])).
% 0.63/0.79 tff(1876,plain,
% 0.63/0.79 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1875, 1874])).
% 0.63/0.79 tff(1877,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1876])).
% 0.63/0.79 tff(1878,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = op(e1, e0)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1879,plain,
% 0.63/0.79 (~(op(e0, e0) = op(e1, e0))),
% 0.63/0.79 inference(and_elim,[status(thm)],[390])).
% 0.63/0.79 tff(1880,plain,
% 0.63/0.79 (~(op(e0, e0) = op(e1, e0))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 0.63/0.79 tff(1881,plain,
% 0.63/0.79 (~(op(e1, e0) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1880, 1877])).
% 0.63/0.79 tff(1882,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[173])).
% 0.63/0.79 tff(1883,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1882, 1362])).
% 0.63/0.79 tff(1884,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1883])).
% 0.63/0.79 tff(1885,plain,
% 0.63/0.79 (~(op(e0, e3) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[727, 1884])).
% 0.63/0.79 tff(1886,plain,
% 0.63/0.79 ((e2 = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.63/0.79 inference(commutativity,[status(thm)],[])).
% 0.63/0.79 tff(1887,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[173])).
% 0.63/0.79 tff(1888,plain,
% 0.63/0.79 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1887, 1886])).
% 0.63/0.79 tff(1889,plain,
% 0.63/0.79 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1888])).
% 0.63/0.79 tff(1890,plain,
% 0.63/0.79 (~(op(e0, e1) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[805, 1889])).
% 0.63/0.79 tff(1891,plain,
% 0.63/0.79 (op(e3, e1) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1410, 1402, 1890, 1124])).
% 0.63/0.79 tff(1892,plain,
% 0.63/0.79 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1891])).
% 0.63/0.79 tff(1893,plain,
% 0.63/0.79 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1892, 5])).
% 0.63/0.79 tff(1894,plain,
% 0.63/0.79 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1893])).
% 0.63/0.79 tff(1895,plain,
% 0.63/0.79 (~(op(e3, e3) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1417, 1894])).
% 0.63/0.79 tff(1896,assumption,(~(op(e2, e3) = e2)), introduced(assumption)).
% 0.63/0.79 tff(1897,plain,
% 0.63/0.79 (op(e1, e3) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[718, 418, 1395, 1896])).
% 0.63/0.79 tff(1898,plain,
% 0.63/0.79 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1897])).
% 0.63/0.79 tff(1899,plain,
% 0.63/0.79 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1898, 263])).
% 0.63/0.79 tff(1900,plain,
% 0.63/0.79 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1899])).
% 0.63/0.79 tff(1901,plain,
% 0.63/0.79 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1900])).
% 0.63/0.79 tff(1902,plain,
% 0.63/0.80 (~(op(e1, e3) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[272, 1901])).
% 0.63/0.80 tff(1903,plain,
% 0.63/0.80 ((e0 = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.63/0.80 inference(commutativity,[status(thm)],[])).
% 0.63/0.80 tff(1904,plain,
% 0.63/0.80 ((op(e0, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[185])).
% 0.63/0.80 tff(1905,plain,
% 0.63/0.80 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.63/0.80 inference(transitivity,[status(thm)],[1904, 1903])).
% 0.63/0.80 tff(1906,plain,
% 0.63/0.80 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1905])).
% 0.63/0.80 tff(1907,plain,
% 0.63/0.80 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = op(e2, e3)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1908,plain,
% 0.63/0.80 (~(op(e0, e3) = op(e2, e3))),
% 0.63/0.80 inference(and_elim,[status(thm)],[89])).
% 0.63/0.80 tff(1909,plain,
% 0.63/0.80 (~(op(e0, e3) = op(e2, e3))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 0.63/0.80 tff(1910,plain,
% 0.63/0.80 (~(op(e2, e3) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1909, 1906])).
% 0.63/0.80 tff(1911,plain,
% 0.63/0.80 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[185])).
% 0.63/0.80 tff(1912,plain,
% 0.63/0.80 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.63/0.80 inference(transitivity,[status(thm)],[1911, 868])).
% 0.63/0.80 tff(1913,plain,
% 0.63/0.80 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1912])).
% 0.63/0.80 tff(1914,plain,
% 0.63/0.80 (~(op(e3, e3) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[823, 1913])).
% 0.63/0.80 tff(1915,plain,
% 0.63/0.80 ((op(e0, e3) = e3) <=> (e0 = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[185])).
% 0.63/0.80 tff(1916,plain,
% 0.63/0.80 ((e0 = e3) <=> (op(e0, e3) = e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1915])).
% 0.63/0.80 tff(1917,plain,
% 0.63/0.80 ((~(e0 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1916])).
% 0.63/0.80 tff(1918,plain,
% 0.63/0.80 (~(op(e0, e3) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[684, 1917])).
% 0.63/0.80 tff(1919,assumption,(~(op(e0, e3) = e3)), introduced(assumption)).
% 0.63/0.80 tff(1920,plain,
% 0.63/0.80 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1897])).
% 0.63/0.80 tff(1921,plain,
% 0.63/0.80 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1920])).
% 0.63/0.80 tff(1922,plain,
% 0.63/0.80 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1921])).
% 0.63/0.80 tff(1923,plain,
% 0.63/0.80 (~(op(e1, e3) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[195, 1922])).
% 0.63/0.80 tff(1924,plain,
% 0.63/0.80 (((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1925,plain,
% 0.63/0.80 ((((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1926,plain,
% 0.63/0.80 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1927,plain,
% 0.63/0.80 (((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)) <=> (((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3)) | (op(e3, e3) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1926])).
% 0.63/0.80 tff(1928,plain,
% 0.63/0.80 (((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3))),
% 0.63/0.80 inference(transitivity,[status(thm)],[1927, 1925])).
% 0.63/0.80 tff(1929,plain,
% 0.63/0.80 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)),
% 0.63/0.80 inference(and_elim,[status(thm)],[29])).
% 0.63/0.80 tff(1930,plain,
% 0.63/0.80 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 0.63/0.80 tff(1931,plain,
% 0.63/0.80 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1930, 1924])).
% 0.63/0.80 tff(1932,plain,
% 0.63/0.80 (op(e2, e3) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1931, 1923, 1919, 817])).
% 0.63/0.80 tff(1933,plain,
% 0.63/0.80 (op(op(e2, e3), op(e2, e3)) = op(e3, e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1932, 1932])).
% 0.63/0.80 tff(1934,plain,
% 0.63/0.80 (op(e3, e3) = op(op(e2, e3), op(e2, e3))),
% 0.63/0.80 inference(symmetry,[status(thm)],[1933])).
% 0.63/0.80 tff(1935,plain,
% 0.63/0.80 (op(e3, e3) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[833, 418, 825, 817])).
% 0.63/0.80 tff(1936,plain,
% 0.63/0.80 (e1 = op(e3, e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1935])).
% 0.63/0.80 tff(1937,plain,
% 0.63/0.80 (e1 = e3),
% 0.63/0.80 inference(transitivity,[status(thm)],[1936, 1934, 16])).
% 0.63/0.80 tff(1938,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[665, 1937])).
% 0.63/0.80 tff(1939,plain,((op(e3, e3) = e2) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e0, e3) = e3) | (op(e3, e3) = e3) | (op(e3, e3) = e0) | (op(e0, e3) = e2) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1940,plain,
% 0.63/0.80 (op(e3, e3) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1939, 1918, 16, 817, 1914, 1395, 1896])).
% 0.63/0.80 tff(1941,plain,
% 0.63/0.80 (~(op(e2, e3) = e3)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[914, 1940, 16])).
% 0.63/0.80 tff(1942,plain,
% 0.63/0.80 (op(e2, e3) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[903, 1941, 1896, 1910])).
% 0.63/0.80 tff(1943,plain,
% 0.63/0.80 (e1 = op(e2, e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1942])).
% 0.63/0.80 tff(1944,plain,
% 0.63/0.80 (op(e1, e1) = op(op(e2, e3), op(e2, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1943, 1943])).
% 0.63/0.80 tff(1945,plain,
% 0.63/0.80 (op(e1, e1) = e3),
% 0.63/0.80 inference(transitivity,[status(thm)],[1944, 16])).
% 0.63/0.80 tff(1946,plain,
% 0.63/0.80 (op(e1, e3) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1931, 1941, 1918, 817])).
% 0.63/0.80 tff(1947,plain,
% 0.63/0.80 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1946])).
% 0.63/0.80 tff(1948,plain,
% 0.63/0.80 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1947])).
% 0.63/0.80 tff(1949,plain,
% 0.63/0.80 (~(op(e1, e1) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[701, 1948])).
% 0.63/0.80 tff(1950,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1949, 1945])).
% 0.63/0.80 tff(1951,plain,((~(op(e0, e3) = e0)) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e2, e3) = e2) | (op(e3, e3) = e3) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1952,plain,
% 0.63/0.80 (~(op(e0, e3) = e0)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1951, 16, 1896, 817, 1395])).
% 0.63/0.80 tff(1953,plain,
% 0.63/0.80 (op(e2, e3) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1797, 825, 1952, 1902])).
% 0.63/0.80 tff(1954,plain,
% 0.63/0.80 (e0 = op(e2, e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1953])).
% 0.63/0.80 tff(1955,plain,
% 0.63/0.80 (op(e0, e0) = op(op(e2, e3), op(e2, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1954, 1954])).
% 0.63/0.80 tff(1956,plain,
% 0.63/0.80 (op(e0, e0) = e3),
% 0.63/0.80 inference(transitivity,[status(thm)],[1955, 16])).
% 0.63/0.80 tff(1957,plain,
% 0.63/0.80 (op(e0, e3) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1939, 825, 16, 817, 418, 1395, 1896])).
% 0.63/0.80 tff(1958,plain,
% 0.63/0.80 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1957])).
% 0.63/0.80 tff(1959,plain,
% 0.63/0.80 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1958])).
% 0.63/0.80 tff(1960,plain,
% 0.63/0.80 (~(op(e0, e0) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[727, 1959])).
% 0.63/0.80 tff(1961,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1960, 1956])).
% 0.63/0.80 tff(1962,plain,((op(e3, e3) = e0) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e3, e3) = e3) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1963,plain,
% 0.63/0.80 (op(e3, e3) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1962, 1895, 1885, 15, 731, 23])).
% 0.63/0.80 tff(1964,plain,
% 0.63/0.80 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1963])).
% 0.63/0.80 tff(1965,plain,
% 0.63/0.80 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1964])).
% 0.63/0.80 tff(1966,plain,
% 0.63/0.80 (~(op(e2, e3) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[656, 1965])).
% 0.63/0.80 tff(1967,plain,
% 0.63/0.80 (~(op(e2, e3) = e3)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[891, 15, 1963])).
% 0.63/0.80 tff(1968,plain,
% 0.63/0.80 (op(e2, e3) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[903, 1967, 23, 1966])).
% 0.63/0.80 tff(1969,plain,
% 0.63/0.80 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1968])).
% 0.63/0.80 tff(1970,plain,
% 0.63/0.80 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1969])).
% 0.63/0.80 tff(1971,plain,
% 0.63/0.80 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e2, e3)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(1972,plain,
% 0.63/0.80 (~(op(e2, e1) = op(e2, e3))),
% 0.63/0.80 inference(and_elim,[status(thm)],[68])).
% 0.63/0.80 tff(1973,plain,
% 0.63/0.80 (~(op(e2, e1) = op(e2, e3))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.63/0.80 tff(1974,plain,
% 0.63/0.80 (~(op(e2, e1) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1973, 1970])).
% 0.63/0.80 tff(1975,plain,
% 0.63/0.80 ((e3 = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.63/0.80 inference(commutativity,[status(thm)],[])).
% 0.63/0.80 tff(1976,plain,
% 0.63/0.80 (e1 = op(e2, e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[1968])).
% 0.63/0.80 tff(1977,plain,
% 0.63/0.80 (op(e1, e1) = op(op(e2, e3), op(e2, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1976, 1976])).
% 0.63/0.80 tff(1978,plain,
% 0.63/0.80 (op(e1, e1) = e3),
% 0.63/0.80 inference(transitivity,[status(thm)],[1977, 15])).
% 0.63/0.80 tff(1979,plain,
% 0.63/0.80 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1978])).
% 0.63/0.80 tff(1980,plain,
% 0.63/0.80 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.63/0.80 inference(transitivity,[status(thm)],[1979, 1975])).
% 0.63/0.80 tff(1981,plain,
% 0.63/0.80 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1980])).
% 0.63/0.80 tff(1982,plain,
% 0.63/0.80 (~(op(e2, e1) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[101, 1981])).
% 0.63/0.80 tff(1983,plain,
% 0.63/0.80 (op(e2, e1) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[796, 1982, 1974, 1402])).
% 0.63/0.80 tff(1984,plain,
% 0.63/0.80 (op(op(e2, e1), op(e2, e1)) = op(e0, e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1983, 1983])).
% 0.63/0.80 tff(1985,plain,
% 0.63/0.80 (e1 = e2),
% 0.63/0.80 inference(transitivity,[status(thm)],[766, 1984, 173])).
% 0.63/0.80 tff(1986,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[220, 1985])).
% 0.63/0.80 tff(1987,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (~(op(e0, e0) = e2)) | (op(e1, e1) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(1988,plain,
% 0.63/0.80 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1987, 6, 1124, 173])).
% 0.63/0.80 tff(1989,plain,
% 0.63/0.80 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[173])).
% 0.63/0.80 tff(1990,plain,
% 0.63/0.80 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[1989, 610])).
% 0.63/0.80 tff(1991,plain,
% 0.63/0.80 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1990])).
% 0.63/0.80 tff(1992,plain,
% 0.63/0.80 (~(op(e3, e0) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[616, 1991])).
% 0.63/0.80 tff(1993,plain,
% 0.63/0.80 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1245, 3, 1124, 1223, 6])).
% 0.63/0.80 tff(1994,plain,
% 0.63/0.80 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[416, 1993, 1289, 1288])).
% 0.63/0.80 tff(1995,plain,
% 0.63/0.80 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[459, 1994])).
% 0.63/0.80 tff(1996,plain,
% 0.63/0.80 (~(op(e3, e2) = e3)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[467, 1995, 418])).
% 0.63/0.80 tff(1997,plain,
% 0.63/0.80 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[478, 1994])).
% 0.63/0.80 tff(1998,plain,
% 0.63/0.80 (op(e3, e1) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[566, 483, 1428, 418])).
% 0.63/0.80 tff(1999,plain,
% 0.63/0.80 (op(op(e3, e1), op(e3, e1)) = op(e2, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1998, 1998])).
% 0.63/0.80 tff(2000,plain,
% 0.63/0.80 (op(e2, e2) = op(op(e3, e1), op(e3, e1))),
% 0.63/0.80 inference(symmetry,[status(thm)],[1999])).
% 0.63/0.80 tff(2001,plain,
% 0.63/0.80 (op(e2, e2) = e1),
% 0.63/0.80 inference(transitivity,[status(thm)],[2000, 480])).
% 0.63/0.80 tff(2002,plain,
% 0.63/0.80 (e1 = op(e2, e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2001, 1704])).
% 0.63/0.80 tff(2003,plain,
% 0.63/0.80 (op(e2, op(e2, e2)) = op(e2, e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2001])).
% 0.63/0.80 tff(2004,plain,
% 0.63/0.80 (op(e2, e1) = op(e2, op(e2, e2))),
% 0.63/0.80 inference(symmetry,[status(thm)],[2003])).
% 0.63/0.80 tff(2005,plain,
% 0.63/0.80 ((op(e2, e1) = e3) <=> (op(e2, op(e2, e2)) = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2004])).
% 0.63/0.80 tff(2006,plain,
% 0.63/0.80 ((op(e2, e1) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2005, 1708])).
% 0.63/0.80 tff(2007,plain,
% 0.63/0.80 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1998])).
% 0.63/0.80 tff(2008,plain,
% 0.63/0.80 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2007])).
% 0.63/0.80 tff(2009,plain,
% 0.63/0.80 (~(op(e2, e1) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[787, 2008])).
% 0.63/0.80 tff(2010,plain,
% 0.63/0.80 (e1 = op(op(e3, e1), op(e3, e1))),
% 0.63/0.80 inference(symmetry,[status(thm)],[480])).
% 0.63/0.80 tff(2011,plain,
% 0.63/0.80 (e1 = op(e2, e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2010, 1999])).
% 0.63/0.80 tff(2012,plain,
% 0.63/0.80 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2011])).
% 0.63/0.80 tff(2013,plain,
% 0.63/0.80 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2012])).
% 0.63/0.80 tff(2014,plain,
% 0.63/0.80 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2013])).
% 0.63/0.80 tff(2015,plain,
% 0.63/0.80 (~(op(e2, e1) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1695, 2014])).
% 0.63/0.80 tff(2016,plain,
% 0.63/0.80 ((op(e2, e1) = e0) <=> (op(e2, op(e2, e2)) = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2004])).
% 0.63/0.80 tff(2017,plain,
% 0.63/0.80 ((op(e2, e1) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2016, 1682])).
% 0.63/0.80 tff(2018,plain,
% 0.63/0.80 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e0)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2017])).
% 0.63/0.80 tff(2019,plain,
% 0.63/0.80 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e1) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2018])).
% 0.63/0.80 tff(2020,plain,
% 0.63/0.80 (~(op(e2, e1) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1677, 2019])).
% 0.63/0.80 tff(2021,plain,
% 0.63/0.80 (op(e2, e1) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[796, 2020, 2015, 2009])).
% 0.63/0.80 tff(2022,plain,
% 0.63/0.80 (e3 = op(e2, op(e2, e2))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2021, 2006])).
% 0.63/0.80 tff(2023,plain,
% 0.63/0.80 (op(e2, op(e2, e2)) = e3),
% 0.63/0.80 inference(transitivity,[status(thm)],[2003, 2021])).
% 0.63/0.80 tff(2024,plain,
% 0.63/0.80 (op(op(e2, op(e2, e2)), e2) = op(e3, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2023])).
% 0.63/0.80 tff(2025,plain,
% 0.63/0.80 (op(e3, e2) = op(op(e2, op(e2, e2)), e2)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2024])).
% 0.63/0.80 tff(2026,plain,
% 0.63/0.80 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2011])).
% 0.63/0.80 tff(2027,plain,
% 0.63/0.80 ((op(e3, e2) = e1) <=> (op(e2, e2) = op(e3, e2))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2026, 962])).
% 0.63/0.80 tff(2028,plain,
% 0.63/0.80 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2027])).
% 0.63/0.80 tff(2029,plain,
% 0.63/0.80 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2028])).
% 0.63/0.80 tff(2030,plain,
% 0.63/0.80 (~(op(e3, e2) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[591, 2029])).
% 0.63/0.80 tff(2031,plain,
% 0.63/0.80 (op(e3, e2) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[491, 2030, 482, 483])).
% 0.63/0.80 tff(2032,plain,
% 0.63/0.80 (e0 = op(e3, e2)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2031])).
% 0.63/0.80 tff(2033,plain,
% 0.63/0.80 (e0 = op(op(e2, op(e2, e2)), e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2032, 2025])).
% 0.63/0.80 tff(2034,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1721, 2033, 2022, 2002])).
% 0.63/0.80 tff(2035,plain,((op(e3, e2) = e2) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (op(e3, e2) = e3) | (e0 = op(e2, op(e2, e2))) | (op(e3, e0) = e2) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2036,plain,
% 0.63/0.81 (op(e3, e2) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2035, 1997, 1996, 1677, 1428, 418])).
% 0.63/0.81 tff(2037,plain,
% 0.63/0.81 (e2 = op(e3, e2)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2036])).
% 0.63/0.81 tff(2038,plain,
% 0.63/0.81 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2037, 2037])).
% 0.63/0.81 tff(2039,plain,
% 0.63/0.81 (op(e2, e2) = e2),
% 0.63/0.81 inference(transitivity,[status(thm)],[2038, 1995])).
% 0.63/0.81 tff(2040,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[3, 2039])).
% 0.63/0.81 tff(2041,plain,((op(e2, e2) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e3, e0) = e2) | (op(e3, e3) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2042,plain,
% 0.63/0.81 (op(e2, e2) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2041, 418, 1428, 1677, 1289, 1288, 1124, 1223, 6])).
% 0.63/0.81 tff(2043,plain,
% 0.63/0.81 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2042])).
% 0.63/0.81 tff(2044,plain,
% 0.63/0.81 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2043, 378])).
% 0.63/0.81 tff(2045,plain,
% 0.63/0.81 ((op(e3, e2) = e2) <=> (op(e2, e2) = op(e3, e2))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2044])).
% 0.63/0.81 tff(2046,plain,
% 0.63/0.81 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1310, 2042, 1124, 6])).
% 0.63/0.81 tff(2047,plain,
% 0.63/0.81 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[416, 2046, 1289, 1288])).
% 0.63/0.81 tff(2048,plain,
% 0.63/0.81 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[478, 2047])).
% 0.63/0.81 tff(2049,plain,
% 0.63/0.81 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[459, 2047])).
% 0.63/0.81 tff(2050,plain,
% 0.63/0.81 (~(op(e3, e2) = e3)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[467, 2049, 418])).
% 0.63/0.81 tff(2051,plain,
% 0.63/0.81 (op(e3, e2) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2035, 2050, 2048, 1677, 1428, 418])).
% 0.63/0.81 tff(2052,plain,
% 0.63/0.81 (op(e2, e2) = op(e3, e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2051, 2045])).
% 0.63/0.81 tff(2053,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[591, 2052])).
% 0.63/0.81 tff(2054,plain,((op(e3, e3) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e3, e0) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e2, e2) = e3) | (op(e1, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2055,plain,
% 0.63/0.81 (op(e3, e3) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2054, 1988, 1992, 1289, 1677, 1124, 6, 1881])).
% 0.63/0.81 tff(2056,plain,
% 0.63/0.81 (~(op(op(e3, e3), op(e3, e3)) = e3)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[631, 2055, 6])).
% 0.63/0.81 tff(2057,plain,
% 0.63/0.81 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[633, 2056])).
% 0.63/0.81 tff(2058,plain,
% 0.63/0.81 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[416, 2057, 1289, 1988])).
% 0.63/0.81 tff(2059,plain,
% 0.63/0.81 (~(op(e2, e2) = e2)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1310, 2058, 1124, 6])).
% 0.63/0.81 tff(2060,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1245, 2059, 2058, 1124, 1881, 6])).
% 0.63/0.81 tff(2061,plain,((op(e2, e2) = e3) | (op(e1, e1) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (e0 = op(e2, op(e2, e2))) | (~(op(e0, e0) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2062,plain,
% 0.63/0.81 (op(e2, e2) = e3),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2061, 1124, 1289, 1677, 173])).
% 0.63/0.81 tff(2063,plain,
% 0.63/0.81 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2062])).
% 0.63/0.81 tff(2064,plain,
% 0.63/0.81 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2063, 937])).
% 0.63/0.81 tff(2065,plain,
% 0.63/0.81 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2064])).
% 0.63/0.81 tff(2066,plain,
% 0.63/0.81 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2065])).
% 0.63/0.81 tff(2067,plain,
% 0.63/0.81 (~(op(e2, e2) = e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[195, 2066])).
% 0.63/0.81 tff(2068,plain,
% 0.63/0.81 (e3 = op(e2, e2)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2062])).
% 0.63/0.81 tff(2069,plain,
% 0.63/0.81 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2068])).
% 0.63/0.81 tff(2070,plain,
% 0.63/0.81 ((op(e3, e2) = e3) <=> (op(e2, e2) = op(e3, e2))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2069, 962])).
% 0.63/0.81 tff(2071,plain,
% 0.63/0.81 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2070])).
% 0.63/0.81 tff(2072,plain,
% 0.63/0.81 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2071])).
% 0.63/0.81 tff(2073,plain,
% 0.63/0.81 (~(op(e3, e2) = e3)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[591, 2072])).
% 0.63/0.81 tff(2074,plain,
% 0.63/0.81 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[946])).
% 0.63/0.81 tff(2075,plain,
% 0.63/0.81 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e3, e3))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2074])).
% 0.63/0.81 tff(2076,plain,
% 0.63/0.81 (op(e3, e1) = op(e3, e3)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1411, 2075])).
% 0.63/0.81 tff(2077,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1417, 2076])).
% 0.63/0.81 tff(2078,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (~(op(e2, e2) = e3)) | (op(e0, e1) = e2) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2079,plain,
% 0.63/0.81 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2078, 2062, 1890, 1124])).
% 0.63/0.81 tff(2080,plain,
% 0.63/0.81 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[173])).
% 0.63/0.81 tff(2081,plain,
% 0.63/0.81 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2080, 379])).
% 0.63/0.81 tff(2082,plain,
% 0.63/0.81 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2081])).
% 0.63/0.81 tff(2083,plain,
% 0.63/0.81 (~(op(e2, e0) = e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[392, 2082])).
% 0.63/0.81 tff(2084,plain,
% 0.63/0.81 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2062])).
% 0.63/0.81 tff(2085,plain,
% 0.63/0.81 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2084])).
% 0.63/0.81 tff(2086,plain,
% 0.63/0.81 ((op(e2, e3) = e0) <=> (op(e2, op(e2, e2)) = e0)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2085])).
% 0.63/0.81 tff(2087,plain,
% 0.63/0.81 ((op(e2, e3) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2086, 1682])).
% 0.63/0.81 tff(2088,plain,
% 0.63/0.81 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e3) = e0)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2087])).
% 0.63/0.81 tff(2089,plain,
% 0.63/0.81 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e3) = e0))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2088])).
% 0.63/0.81 tff(2090,plain,
% 0.63/0.81 (~(op(e2, e3) = e0)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[1677, 2089])).
% 0.63/0.81 tff(2091,plain,
% 0.63/0.81 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[943])).
% 0.63/0.81 tff(2092,plain,
% 0.63/0.81 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2091, 937])).
% 0.63/0.81 tff(2093,plain,
% 0.63/0.81 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2092])).
% 0.63/0.81 tff(2094,plain,
% 0.63/0.81 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2093])).
% 0.63/0.81 tff(2095,plain,
% 0.63/0.81 (~(op(e2, e2) = e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[195, 2094])).
% 0.63/0.81 tff(2096,plain,
% 0.63/0.81 (~(op(e1, e2) = e2)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1259, 429, 2095])).
% 0.63/0.81 tff(2097,plain,
% 0.63/0.81 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[944])).
% 0.63/0.81 tff(2098,plain,
% 0.63/0.81 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2097])).
% 0.63/0.81 tff(2099,plain,
% 0.63/0.81 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2098])).
% 0.63/0.81 tff(2100,plain,
% 0.63/0.81 (~(op(e1, e2) = e3)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[331, 2099])).
% 0.63/0.81 tff(2101,assumption,(~(op(e2, e3) = e0)), introduced(assumption)).
% 0.63/0.81 tff(2102,plain,
% 0.63/0.81 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e2, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[944])).
% 0.63/0.81 tff(2103,plain,
% 0.63/0.81 ((op(e2, e3) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2102, 1281])).
% 0.63/0.81 tff(2104,plain,
% 0.63/0.81 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2103])).
% 0.63/0.81 tff(2105,plain,
% 0.63/0.81 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2104])).
% 0.63/0.81 tff(2106,plain,
% 0.63/0.81 (~(op(e2, e3) = e3)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[709, 2105])).
% 0.63/0.81 tff(2107,plain,
% 0.63/0.81 (op(e1, e3) = e2),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1239, 2096, 1124, 1223])).
% 0.63/0.81 tff(2108,plain,
% 0.63/0.81 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2107])).
% 0.63/0.81 tff(2109,plain,
% 0.63/0.81 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2108, 703])).
% 0.63/0.81 tff(2110,plain,
% 0.63/0.81 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2109])).
% 0.63/0.81 tff(2111,plain,
% 0.63/0.81 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = op(e2, e3)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2112,plain,
% 0.63/0.81 (~(op(e1, e3) = op(e2, e3))),
% 0.63/0.81 inference(and_elim,[status(thm)],[87])).
% 0.63/0.81 tff(2113,plain,
% 0.63/0.81 (~(op(e1, e3) = op(e2, e3))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 0.63/0.81 tff(2114,plain,
% 0.63/0.81 (~(op(e2, e3) = e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2113, 2110])).
% 0.63/0.81 tff(2115,plain,
% 0.63/0.81 (op(e2, e3) = e1),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[903, 2114, 2106, 2101])).
% 0.63/0.81 tff(2116,plain,
% 0.63/0.81 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[943])).
% 0.63/0.81 tff(2117,plain,
% 0.63/0.81 (op(e2, op(e2, e2)) = e1),
% 0.63/0.81 inference(transitivity,[status(thm)],[2116, 2115])).
% 0.63/0.81 tff(2118,plain,
% 0.63/0.81 (op(op(e2, op(e2, e2)), e2) = op(e1, e2)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2117])).
% 0.63/0.81 tff(2119,plain,
% 0.63/0.81 ((e0 = op(op(e2, op(e2, e2)), e2)) <=> (e0 = op(e1, e2))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2118])).
% 0.63/0.81 tff(2120,plain,
% 0.63/0.81 ((e0 = op(op(e2, op(e2, e2)), e2)) <=> (op(e1, e2) = e0)),
% 0.63/0.81 inference(transitivity,[status(thm)],[2119, 1])).
% 0.63/0.81 tff(2121,plain,
% 0.63/0.81 ((~(e0 = op(op(e2, op(e2, e2)), e2))) <=> (~(op(e1, e2) = e0))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2120])).
% 0.63/0.81 tff(2122,plain,
% 0.63/0.81 ((e3 = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.63/0.81 inference(commutativity,[status(thm)],[])).
% 0.63/0.81 tff(2123,plain,
% 0.63/0.81 ((op(e2, e2) = e3) <=> (e3 = op(e2, e2))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2122])).
% 0.63/0.81 tff(2124,plain,
% 0.63/0.81 (e3 = op(e2, e2)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[943, 2123])).
% 0.63/0.81 tff(2125,plain,
% 0.63/0.81 ((op(e2, op(e2, e2)) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 0.63/0.81 inference(commutativity,[status(thm)],[])).
% 0.63/0.81 tff(2126,plain,
% 0.63/0.81 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2116])).
% 0.63/0.81 tff(2127,plain,
% 0.63/0.81 ((op(e2, e3) = e1) <=> (op(e2, op(e2, e2)) = e1)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2126])).
% 0.63/0.81 tff(2128,plain,
% 0.63/0.81 ((op(e2, e3) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2127, 2125])).
% 0.63/0.82 tff(2129,plain,
% 0.63/0.82 (e1 = op(e2, op(e2, e2))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2115, 2128])).
% 0.63/0.82 tff(2130,plain,
% 0.63/0.82 ((~(~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2)))))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2131,plain,
% 0.63/0.82 (((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))) <=> (~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2132,plain,
% 0.63/0.82 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~(~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2131])).
% 0.63/0.82 tff(2133,plain,
% 0.63/0.82 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2132, 2130])).
% 0.63/0.82 tff(2134,plain,
% 0.63/0.82 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2135,plain,
% 0.63/0.82 ((~(((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2136,axiom,(~(((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(op(e2, op(e2, e2)), e2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax16')).
% 0.63/0.82 tff(2137,plain,
% 0.63/0.82 (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 0.63/0.82 tff(2138,plain,
% 0.63/0.82 (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2137, 2134])).
% 0.63/0.82 tff(2139,plain,
% 0.63/0.82 ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2138, 2133])).
% 0.63/0.82 tff(2140,plain,
% 0.63/0.82 (~(e0 = op(op(e2, op(e2, e2)), e2))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2139, 2129, 2124])).
% 0.63/0.82 tff(2141,plain,
% 0.63/0.82 (~(op(e1, e2) = e0)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2140, 2121])).
% 0.63/0.82 tff(2142,plain,
% 0.63/0.82 (op(e1, e2) = e1),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[449, 2141, 2100, 2096])).
% 0.63/0.82 tff(2143,plain,
% 0.63/0.82 (op(op(e1, e2), op(e1, e2)) = op(e1, e1)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2142, 2142])).
% 0.63/0.82 tff(2144,plain,
% 0.63/0.82 (op(e1, e1) = op(op(e1, e2), op(e1, e2))),
% 0.63/0.82 inference(symmetry,[status(thm)],[2143])).
% 0.63/0.82 tff(2145,plain,
% 0.63/0.82 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2107])).
% 0.63/0.82 tff(2146,plain,
% 0.63/0.82 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2145, 263])).
% 0.63/0.82 tff(2147,plain,
% 0.63/0.82 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2146])).
% 0.63/0.82 tff(2148,plain,
% 0.63/0.82 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2147])).
% 0.63/0.82 tff(2149,plain,
% 0.63/0.82 (~(op(e1, e3) = e0)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[272, 2148])).
% 0.63/0.82 tff(2150,assumption,(~(op(e2, e0) = e2)), introduced(assumption)).
% 0.63/0.82 tff(2151,plain,
% 0.63/0.82 (op(e2, e1) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[43, 2114, 2150, 2095])).
% 0.63/0.82 tff(2152,plain,
% 0.63/0.82 ((op(e2, e1) = e0) <=> (e2 = e0)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2151])).
% 0.63/0.82 tff(2153,plain,
% 0.63/0.82 ((op(e2, e1) = e0) <=> (e0 = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2152, 263])).
% 0.63/0.82 tff(2154,plain,
% 0.63/0.82 ((e0 = e2) <=> (op(e2, e1) = e0)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2153])).
% 0.63/0.82 tff(2155,plain,
% 0.63/0.82 ((~(e0 = e2)) <=> (~(op(e2, e1) = e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2154])).
% 0.63/0.82 tff(2156,plain,
% 0.63/0.82 (~(op(e2, e1) = e0)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[272, 2155])).
% 0.63/0.82 tff(2157,plain,
% 0.63/0.82 (op(e2, e0) = e0),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1495, 2156, 2101, 958])).
% 0.63/0.82 tff(2158,plain,
% 0.63/0.82 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2157])).
% 0.63/0.82 tff(2159,plain,
% 0.63/0.82 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2158])).
% 0.63/0.82 tff(2160,plain,
% 0.63/0.82 (~(op(e1, e0) = e0)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1520, 2159])).
% 0.63/0.82 tff(2161,plain,
% 0.63/0.82 (op(e1, e1) = e0),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1475, 2160, 2149, 2141])).
% 0.63/0.82 tff(2162,plain,
% 0.63/0.82 (e0 = op(e1, e1)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2161])).
% 0.63/0.82 tff(2163,plain,
% 0.63/0.82 (e0 = e2),
% 0.63/0.82 inference(transitivity,[status(thm)],[2162, 2144, 429])).
% 0.63/0.82 tff(2164,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[272, 2163])).
% 0.63/0.82 tff(2165,plain,((~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(e2, e2) = e3)) | (op(e2, e3) = e0) | (op(e2, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2166,plain,
% 0.63/0.82 (~(op(op(e1, e2), op(e1, e2)) = e2)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2165, 2062, 2090, 2083, 1124, 1881])).
% 0.63/0.82 tff(2167,plain,
% 0.63/0.82 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[419, 2166])).
% 0.63/0.82 tff(2168,plain,
% 0.63/0.82 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[416, 2167, 1289, 2079])).
% 0.63/0.82 tff(2169,plain,
% 0.63/0.82 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[478, 1208])).
% 0.63/0.82 tff(2170,plain,
% 0.63/0.82 (op(e3, e2) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2035, 2169, 482, 1677, 1428, 418])).
% 0.63/0.82 tff(2171,plain,
% 0.63/0.82 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2170, 2170])).
% 0.63/0.82 tff(2172,plain,
% 0.63/0.82 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.63/0.82 inference(symmetry,[status(thm)],[2171])).
% 0.63/0.82 tff(2173,plain,
% 0.63/0.82 (op(e2, e2) = e2),
% 0.63/0.82 inference(transitivity,[status(thm)],[2172, 1209])).
% 0.63/0.82 tff(2174,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[3, 2173])).
% 0.63/0.82 tff(2175,plain,(((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))) | (op(e2, e2) = e2) | (op(e3, e2) = e3) | (e0 = op(e2, op(e2, e2))) | (op(e3, e0) = e2) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2176,plain,
% 0.63/0.82 (op(e3, e3) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2175, 2168, 2073, 1677, 1992, 2067])).
% 0.63/0.82 tff(2177,plain,
% 0.63/0.82 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2062, 2062])).
% 0.63/0.82 tff(2178,plain,
% 0.63/0.82 ((op(e3, e3) = e3) <=> (e2 = op(e2, e2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2176, 2068])).
% 0.63/0.82 tff(2179,plain,
% 0.63/0.82 ((op(e3, e3) = e3) <=> (op(e2, e2) = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2178, 7])).
% 0.63/0.82 tff(2180,plain,
% 0.63/0.82 ((op(e2, e2) = e2) <=> (op(e3, e3) = e3)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2179])).
% 0.63/0.82 tff(2181,plain,
% 0.63/0.82 ((~(op(e2, e2) = e2)) <=> (~(op(e3, e3) = e3))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2180])).
% 0.63/0.82 tff(2182,plain,
% 0.63/0.82 (~(op(e3, e3) = e3)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2067, 2181])).
% 0.63/0.82 tff(2183,plain,
% 0.63/0.82 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[476, 2168])).
% 0.63/0.82 tff(2184,plain,
% 0.63/0.82 ((op(e3, e3) = e0) <=> (e2 = e0)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2176])).
% 0.63/0.82 tff(2185,plain,
% 0.63/0.82 ((op(e3, e3) = e0) <=> (e0 = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2184, 263])).
% 0.63/0.82 tff(2186,plain,
% 0.63/0.82 ((e0 = e2) <=> (op(e3, e3) = e0)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2185])).
% 0.63/0.82 tff(2187,plain,
% 0.63/0.82 ((~(e0 = e2)) <=> (~(op(e3, e3) = e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2186])).
% 0.63/0.82 tff(2188,plain,
% 0.63/0.82 (~(op(e3, e3) = e0)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[272, 2187])).
% 0.63/0.82 tff(2189,plain,
% 0.63/0.82 (~(op(e3, e0) = e3)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1079, 2188, 2183])).
% 0.63/0.82 tff(2190,plain,
% 0.63/0.82 (op(e3, e1) = e3),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[749, 2189, 2073, 2182])).
% 0.63/0.82 tff(2191,plain,
% 0.63/0.82 (op(e3, e1) = op(e2, e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2190, 2068])).
% 0.63/0.82 tff(2192,plain,
% 0.63/0.82 (op(op(e3, e1), op(e3, e1)) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2191, 2191])).
% 0.63/0.82 tff(2193,plain,
% 0.63/0.82 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[478, 2168])).
% 0.63/0.82 tff(2194,plain,
% 0.63/0.82 (e1 = op(op(e3, e1), op(e3, e1))),
% 0.63/0.82 inference(symmetry,[status(thm)],[2193])).
% 0.63/0.82 tff(2195,plain,
% 0.63/0.82 (e1 = e2),
% 0.63/0.82 inference(transitivity,[status(thm)],[2194, 2192, 2177, 2176])).
% 0.63/0.82 tff(2196,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[220, 2195])).
% 0.63/0.82 tff(2197,plain,((op(e1, e1) = e2) | (e0 = op(e2, op(e2, e2))) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~(op(e0, e0) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2198,plain,
% 0.63/0.82 ((e0 = op(e2, op(e2, e2))) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~(op(e0, e0) = e2))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2197, 1117])).
% 0.63/0.82 tff(2199,plain,
% 0.63/0.82 (e0 = op(e2, op(e2, e2))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2198, 1873, 1863])).
% 0.63/0.82 tff(2200,plain,
% 0.63/0.82 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.82 tff(2201,plain,
% 0.63/0.82 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2200, 1874])).
% 0.63/0.82 tff(2202,plain,
% 0.63/0.82 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2201])).
% 0.63/0.82 tff(2203,plain,
% 0.63/0.82 (~(op(e1, e0) = e2)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[1880, 2202])).
% 0.63/0.82 tff(2204,plain,
% 0.63/0.82 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1246, 6, 2203, 3])).
% 0.63/0.82 tff(2205,plain,
% 0.63/0.82 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (~(op(e0, e0) = e2)) | (op(e2, e2) = e3)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1987, 1117])).
% 0.63/0.82 tff(2206,plain,
% 0.63/0.82 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2205, 6, 1863])).
% 0.63/0.82 tff(2207,plain,
% 0.63/0.82 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[416, 2206, 1873, 2204])).
% 0.63/0.82 tff(2208,plain,
% 0.63/0.82 (op(op(e3, e1), op(e3, e1)) = e1),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[478, 2207])).
% 0.63/0.82 tff(2209,plain,
% 0.63/0.82 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[459, 2207])).
% 0.63/0.82 tff(2210,plain,
% 0.63/0.82 (~(op(e3, e2) = e2)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1050, 2209, 3])).
% 0.63/0.82 tff(2211,plain,
% 0.63/0.82 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.82 tff(2212,plain,
% 0.63/0.82 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2211, 610])).
% 0.63/0.82 tff(2213,plain,
% 0.63/0.82 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2212])).
% 0.63/0.82 tff(2214,plain,
% 0.63/0.82 (~(op(e3, e0) = e2)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[616, 2213])).
% 0.63/0.82 tff(2215,plain,
% 0.63/0.82 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[633, 2207])).
% 0.63/0.82 tff(2216,plain,
% 0.63/0.82 (~(op(e3, e3) = e2)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[631, 2215, 6])).
% 0.63/0.82 tff(2217,plain,
% 0.63/0.82 (op(e3, e1) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[566, 2216, 2214, 2210])).
% 0.63/0.82 tff(2218,plain,
% 0.63/0.82 (op(op(e3, e1), op(e3, e1)) = op(e2, e2)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2217, 2217])).
% 0.63/0.82 tff(2219,plain,
% 0.63/0.82 (op(e2, e2) = op(op(e3, e1), op(e3, e1))),
% 0.63/0.82 inference(symmetry,[status(thm)],[2218])).
% 0.63/0.82 tff(2220,plain,
% 0.63/0.82 (op(e2, e2) = e1),
% 0.63/0.82 inference(transitivity,[status(thm)],[2219, 2208])).
% 0.63/0.82 tff(2221,plain,
% 0.63/0.82 (e1 = op(e2, e2)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2220, 1704])).
% 0.63/0.82 tff(2222,plain,
% 0.63/0.82 ((e3 = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.63/0.82 inference(commutativity,[status(thm)],[])).
% 0.63/0.82 tff(2223,plain,
% 0.63/0.82 (op(e2, op(e2, e2)) = e0),
% 0.63/0.82 inference(symmetry,[status(thm)],[2199])).
% 0.63/0.82 tff(2224,plain,
% 0.63/0.82 (op(op(e2, op(e2, e2)), e2) = op(e0, e2)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2223])).
% 0.63/0.82 tff(2225,plain,
% 0.63/0.82 ((e3 = op(op(e2, op(e2, e2)), e2)) <=> (e3 = op(e0, e2))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2224])).
% 0.63/0.82 tff(2226,plain,
% 0.63/0.82 ((e3 = op(op(e2, op(e2, e2)), e2)) <=> (op(e0, e2) = e3)),
% 0.63/0.82 inference(transitivity,[status(thm)],[2225, 2222])).
% 0.63/0.82 tff(2227,plain,
% 0.63/0.82 ((op(e0, e2) = e3) <=> (e3 = op(op(e2, op(e2, e2)), e2))),
% 0.63/0.82 inference(symmetry,[status(thm)],[2226])).
% 0.63/0.82 tff(2228,plain,
% 0.63/0.82 (~(op(e3, e2) = e3)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[467, 2216, 2209])).
% 0.63/0.82 tff(2229,plain,
% 0.63/0.82 (op(e1, e2) = e2),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[507, 2210, 1867, 3])).
% 0.63/0.82 tff(2230,plain,
% 0.63/0.82 ((op(e1, e2) = e3) <=> (e2 = e3)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2229])).
% 0.63/0.82 tff(2231,plain,
% 0.63/0.82 ((e2 = e3) <=> (op(e1, e2) = e3)),
% 0.63/0.82 inference(symmetry,[status(thm)],[2230])).
% 0.63/0.82 tff(2232,plain,
% 0.63/0.82 ((~(e2 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2231])).
% 0.63/0.82 tff(2233,plain,
% 0.63/0.82 (~(op(e1, e2) = e3)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[195, 2232])).
% 0.63/0.82 tff(2234,plain,
% 0.63/0.82 (op(e0, e2) = e3),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[520, 2233, 6, 2228])).
% 0.63/0.82 tff(2235,plain,
% 0.63/0.82 (e3 = op(op(e2, op(e2, e2)), e2)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2234, 2227])).
% 0.63/0.82 tff(2236,plain,
% 0.63/0.82 ((~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2)))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2237,plain,
% 0.63/0.82 (((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2))) <=> (~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2238,plain,
% 0.63/0.82 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2)))) <=> (~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2237])).
% 0.63/0.82 tff(2239,plain,
% 0.63/0.82 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2)))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2238, 2236])).
% 0.63/0.82 tff(2240,plain,
% 0.63/0.82 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2241,plain,
% 0.63/0.82 ((~(((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2242,axiom,(~(((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(op(e2, op(e2, e2)), e2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax7')).
% 0.63/0.82 tff(2243,plain,
% 0.63/0.82 (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 0.63/0.82 tff(2244,plain,
% 0.63/0.82 (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2243, 2240])).
% 0.63/0.83 tff(2245,plain,
% 0.63/0.83 ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2244, 2239])).
% 0.63/0.83 tff(2246,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2245, 2235, 2221, 2199])).
% 0.63/0.83 tff(2247,plain,((op(e2, e2) = e3) | (op(e2, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2248,plain,
% 0.63/0.83 (op(e2, e2) = e3),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2247, 3])).
% 0.63/0.83 tff(2249,plain,
% 0.63/0.83 (e3 = op(e2, e2)),
% 0.63/0.83 inference(symmetry,[status(thm)],[2248])).
% 0.63/0.83 tff(2250,plain,
% 0.63/0.83 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2249])).
% 0.63/0.83 tff(2251,plain,
% 0.63/0.83 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.63/0.83 inference(symmetry,[status(thm)],[2250])).
% 0.63/0.83 tff(2252,plain,
% 0.63/0.83 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2251])).
% 0.63/0.83 tff(2253,plain,
% 0.63/0.83 (~(op(e0, e2) = e3)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[126, 2252])).
% 0.63/0.83 tff(2254,plain,
% 0.63/0.83 ((e1 = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.63/0.83 inference(commutativity,[status(thm)],[])).
% 0.63/0.83 tff(2255,plain,
% 0.63/0.83 ((e1 = op(op(e2, op(e2, e2)), e2)) <=> (e1 = op(e0, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2224])).
% 0.63/0.83 tff(2256,plain,
% 0.63/0.83 ((e1 = op(op(e2, op(e2, e2)), e2)) <=> (op(e0, e2) = e1)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2255, 2254])).
% 0.63/0.83 tff(2257,plain,
% 0.63/0.83 ((~(e1 = op(op(e2, op(e2, e2)), e2))) <=> (~(op(e0, e2) = e1))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2256])).
% 0.63/0.83 tff(2258,plain,
% 0.63/0.83 (e3 = op(e2, e2)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2248, 2123])).
% 0.63/0.83 tff(2259,plain,
% 0.63/0.83 ((~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2)))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2260,plain,
% 0.63/0.83 (((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2))) <=> (~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2261,plain,
% 0.63/0.83 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2)))) <=> (~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2260])).
% 0.63/0.83 tff(2262,plain,
% 0.63/0.83 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2)))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[2261, 2259])).
% 0.63/0.83 tff(2263,plain,
% 0.63/0.83 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2264,plain,
% 0.63/0.83 ((~(((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(op(e2, op(e2, e2)), e2)))) <=> (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2265,axiom,(~(((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(op(e2, op(e2, e2)), e2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax10')).
% 0.63/0.83 tff(2266,plain,
% 0.63/0.83 (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 0.63/0.83 tff(2267,plain,
% 0.63/0.83 (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2266, 2263])).
% 0.63/0.83 tff(2268,plain,
% 0.63/0.83 ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, op(e2, e2)), e2)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2267, 2262])).
% 0.63/0.83 tff(2269,plain,
% 0.63/0.83 (~(e1 = op(op(e2, op(e2, e2)), e2))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2268, 2258, 2199])).
% 0.63/0.83 tff(2270,plain,
% 0.63/0.83 (~(op(e0, e2) = e1)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2269, 2257])).
% 0.63/0.83 tff(2271,plain,
% 0.63/0.83 (op(e0, e2) = e0),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[259, 2270, 2253, 1867])).
% 0.63/0.83 tff(2272,plain,
% 0.63/0.83 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2271])).
% 0.63/0.83 tff(2273,plain,
% 0.63/0.83 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2272, 1])).
% 0.63/0.83 tff(2274,plain,
% 0.63/0.83 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2273])).
% 0.63/0.83 tff(2275,plain,
% 0.63/0.83 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = op(e1, e2)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2276,plain,
% 0.63/0.83 (~(op(e0, e2) = op(e1, e2))),
% 0.63/0.83 inference(and_elim,[status(thm)],[96])).
% 0.63/0.83 tff(2277,plain,
% 0.63/0.83 (~(op(e0, e2) = op(e1, e2))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2276, 2275])).
% 0.63/0.83 tff(2278,plain,
% 0.63/0.83 (~(op(e1, e2) = e0)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2277, 2274])).
% 0.63/0.83 tff(2279,plain,
% 0.63/0.83 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2249])).
% 0.63/0.83 tff(2280,plain,
% 0.63/0.83 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.63/0.83 inference(symmetry,[status(thm)],[2279])).
% 0.63/0.83 tff(2281,plain,
% 0.63/0.83 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2280])).
% 0.63/0.83 tff(2282,plain,
% 0.63/0.83 (~(op(e1, e2) = e3)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[331, 2281])).
% 0.63/0.83 tff(2283,plain,
% 0.63/0.83 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.83 tff(2284,plain,
% 0.63/0.83 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2283, 1886])).
% 0.63/0.83 tff(2285,plain,
% 0.63/0.83 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2284])).
% 0.63/0.83 tff(2286,plain,
% 0.63/0.83 (~(op(e0, e1) = e2)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[805, 2285])).
% 0.63/0.83 tff(2287,plain,
% 0.63/0.83 (((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (~(op(e2, e2) = e3)) | (op(e0, e1) = e2)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2078, 1117])).
% 0.63/0.83 tff(2288,plain,
% 0.63/0.83 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2287, 2248, 2286])).
% 0.63/0.83 tff(2289,plain,
% 0.63/0.83 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2249])).
% 0.63/0.83 tff(2290,plain,
% 0.63/0.83 (op(e2, e3) = e0),
% 0.63/0.83 inference(transitivity,[status(thm)],[2289, 2223])).
% 0.63/0.83 tff(2291,plain,
% 0.63/0.83 ((op(e2, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2290])).
% 0.63/0.83 tff(2292,plain,
% 0.63/0.83 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2291, 868])).
% 0.63/0.83 tff(2293,plain,
% 0.63/0.83 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2292])).
% 0.63/0.83 tff(2294,plain,
% 0.63/0.83 (~(op(e3, e3) = e0)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[656, 2293])).
% 0.63/0.83 tff(2295,plain,
% 0.63/0.83 ((e1 = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.63/0.83 inference(commutativity,[status(thm)],[])).
% 0.63/0.83 tff(2296,plain,
% 0.63/0.83 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[1863])).
% 0.63/0.83 tff(2297,plain,
% 0.63/0.83 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2296, 379])).
% 0.63/0.83 tff(2298,plain,
% 0.63/0.83 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2297])).
% 0.63/0.83 tff(2299,plain,
% 0.63/0.83 (~(op(e2, e0) = e2)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[392, 2298])).
% 0.63/0.83 tff(2300,plain,
% 0.63/0.83 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e2, e2))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2249])).
% 0.63/0.83 tff(2301,plain,
% 0.63/0.83 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 0.63/0.83 inference(symmetry,[status(thm)],[2300])).
% 0.63/0.83 tff(2302,plain,
% 0.63/0.83 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2301])).
% 0.63/0.83 tff(2303,plain,
% 0.63/0.83 (~(op(e2, e0) = e3)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[1384, 2302])).
% 0.63/0.83 tff(2304,plain,
% 0.63/0.83 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2290])).
% 0.63/0.83 tff(2305,plain,
% 0.63/0.83 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2304])).
% 0.63/0.83 tff(2306,plain,
% 0.63/0.83 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = op(e2, e3)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2307,plain,
% 0.63/0.83 (~(op(e2, e0) = op(e2, e3))),
% 0.63/0.83 inference(and_elim,[status(thm)],[70])).
% 0.63/0.83 tff(2308,plain,
% 0.63/0.83 (~(op(e2, e0) = op(e2, e3))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 0.63/0.83 tff(2309,plain,
% 0.63/0.83 (~(op(e2, e0) = e0)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2308, 2305])).
% 0.63/0.83 tff(2310,plain,
% 0.63/0.83 (((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2311,plain,
% 0.63/0.83 ((((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2312,plain,
% 0.63/0.83 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2313,plain,
% 0.63/0.83 (((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)) <=> (((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2312])).
% 0.63/0.83 tff(2314,plain,
% 0.63/0.83 (((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3))),
% 0.63/0.83 inference(transitivity,[status(thm)],[2313, 2311])).
% 0.63/0.83 tff(2315,plain,
% 0.63/0.83 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)),
% 0.63/0.83 inference(and_elim,[status(thm)],[250])).
% 0.63/0.83 tff(2316,plain,
% 0.63/0.83 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 0.63/0.83 tff(2317,plain,
% 0.63/0.83 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2316, 2310])).
% 0.63/0.83 tff(2318,plain,
% 0.63/0.83 (op(e2, e0) = e1),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2317, 2309, 2303, 2299])).
% 0.63/0.83 tff(2319,plain,
% 0.63/0.83 ((op(e2, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2318])).
% 0.63/0.83 tff(2320,plain,
% 0.63/0.83 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.63/0.83 inference(transitivity,[status(thm)],[2319, 2295])).
% 0.63/0.83 tff(2321,plain,
% 0.63/0.83 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2320])).
% 0.63/0.83 tff(2322,plain,
% 0.63/0.83 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = op(e3, e0)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2323,plain,
% 0.63/0.83 (~(op(e2, e0) = op(e3, e0))),
% 0.63/0.83 inference(and_elim,[status(thm)],[386])).
% 0.63/0.83 tff(2324,plain,
% 0.63/0.83 (~(op(e2, e0) = op(e3, e0))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 0.63/0.83 tff(2325,plain,
% 0.63/0.83 (~(op(e3, e0) = e1)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2324, 2321])).
% 0.63/0.83 tff(2326,plain,
% 0.63/0.83 (~(op(e3, e0) = e0)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1097, 583, 168])).
% 0.63/0.83 tff(2327,plain,
% 0.63/0.83 (~(op(e3, e0) = e3)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1079, 583, 825])).
% 0.63/0.83 tff(2328,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1088, 2327, 2326, 1759, 1428])).
% 0.63/0.83 tff(2329,plain,((~(op(op(e3, e0), op(e3, e0)) = e0)) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2330,plain,
% 0.63/0.83 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2329, 2325, 2214, 2294, 1872])).
% 0.63/0.83 tff(2331,plain,
% 0.63/0.83 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[476, 2330])).
% 0.63/0.83 tff(2332,plain,
% 0.63/0.83 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[416, 2331, 1873, 2288])).
% 0.63/0.84 tff(2333,plain,
% 0.63/0.84 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[419, 2332])).
% 0.63/0.84 tff(2334,plain,
% 0.63/0.84 (~(op(e1, e2) = e2)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1259, 2333, 3])).
% 0.63/0.84 tff(2335,plain,
% 0.63/0.84 (~(op(e1, e2) = e1)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1266, 2333])).
% 0.63/0.84 tff(2336,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[449, 2335, 2334, 2282, 2278])).
% 0.63/0.84 tff(2337,plain,(op(e2, e2) = e2), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2338,plain,
% 0.63/0.84 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2337])).
% 0.63/0.84 tff(2339,plain,
% 0.63/0.84 (op(e2, op(e2, e2)) = e2),
% 0.63/0.84 inference(transitivity,[status(thm)],[2338, 2337])).
% 0.63/0.84 tff(2340,plain,
% 0.63/0.84 ((e0 = op(e2, op(e2, e2))) <=> (e0 = e2)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2339])).
% 0.63/0.84 tff(2341,plain,
% 0.63/0.84 ((e0 = e2) <=> (e0 = op(e2, op(e2, e2)))),
% 0.63/0.84 inference(symmetry,[status(thm)],[2340])).
% 0.63/0.84 tff(2342,plain,
% 0.63/0.84 ((~(e0 = e2)) <=> (~(e0 = op(e2, op(e2, e2))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2341])).
% 0.63/0.84 tff(2343,plain,
% 0.63/0.84 (~(e0 = op(e2, op(e2, e2)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[272, 2342])).
% 0.63/0.84 tff(2344,plain,
% 0.63/0.84 (e2 = op(e2, e2)),
% 0.63/0.84 inference(symmetry,[status(thm)],[2337])).
% 0.63/0.84 tff(2345,plain,
% 0.63/0.84 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2344])).
% 0.63/0.84 tff(2346,plain,
% 0.63/0.84 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2345])).
% 0.63/0.84 tff(2347,plain,
% 0.63/0.84 (~(op(e2, e2) = e3)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[195, 2346])).
% 0.63/0.84 tff(2348,plain,
% 0.63/0.84 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2337])).
% 0.63/0.84 tff(2349,plain,
% 0.63/0.84 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2348, 378])).
% 0.63/0.84 tff(2350,plain,
% 0.63/0.84 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2349])).
% 0.63/0.84 tff(2351,plain,
% 0.63/0.84 (~(op(e3, e2) = e2)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[591, 2350])).
% 0.63/0.84 tff(2352,plain,
% 0.63/0.84 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2337])).
% 0.63/0.84 tff(2353,plain,
% 0.63/0.84 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2352])).
% 0.63/0.84 tff(2354,plain,
% 0.63/0.84 (~(op(e0, e2) = e2)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[126, 2353])).
% 0.63/0.84 tff(2355,plain,
% 0.63/0.84 ((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1206, 4, 2347])).
% 0.63/0.84 tff(2356,plain,
% 0.63/0.84 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1314, 2355, 2347, 2354, 2351, 4])).
% 0.63/0.84 tff(2357,plain,
% 0.63/0.84 (op(op(e2, e3), op(e2, e3)) = e3),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[14, 2356])).
% 0.63/0.84 tff(2358,plain,
% 0.63/0.84 ((e0 = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 0.63/0.84 inference(commutativity,[status(thm)],[])).
% 0.63/0.84 tff(2359,plain,
% 0.63/0.84 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[11, 2356])).
% 0.63/0.84 tff(2360,plain,
% 0.63/0.84 (~(op(e3, e3) = e3)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[688, 2356, 2347])).
% 0.63/0.84 tff(2361,assumption,(e2 = op(e3, op(e3, e3))), introduced(assumption)).
% 0.63/0.84 tff(2362,plain,
% 0.63/0.84 (op(e3, op(e3, e3)) = e2),
% 0.63/0.84 inference(symmetry,[status(thm)],[2361])).
% 0.63/0.84 tff(2363,plain,
% 0.63/0.84 (op(op(e3, op(e3, e3)), e3) = op(e2, e3)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2362])).
% 0.63/0.84 tff(2364,plain,
% 0.63/0.84 ((e1 = op(op(e3, op(e3, e3)), e3)) <=> (e1 = op(e2, e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2363])).
% 0.63/0.84 tff(2365,plain,
% 0.63/0.84 ((e1 = op(op(e3, op(e3, e3)), e3)) <=> (op(e2, e3) = e1)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2364, 369])).
% 0.63/0.84 tff(2366,plain,
% 0.63/0.84 ((~(e1 = op(op(e3, op(e3, e3)), e3))) <=> (~(op(e2, e3) = e1))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2365])).
% 0.63/0.84 tff(2367,assumption,(op(e3, e3) = e1), introduced(assumption)).
% 0.63/0.84 tff(2368,plain,
% 0.63/0.84 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e1)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2367])).
% 0.63/0.84 tff(2369,plain,
% 0.63/0.84 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e1))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2368])).
% 0.63/0.84 tff(2370,plain,
% 0.63/0.84 (~(op(e2, e3) = e1)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[656, 2369])).
% 0.63/0.84 tff(2371,plain,
% 0.63/0.84 ((op(e2, e2) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2337])).
% 0.63/0.84 tff(2372,plain,
% 0.63/0.84 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2371, 703])).
% 0.63/0.84 tff(2373,plain,
% 0.63/0.84 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2372])).
% 0.63/0.84 tff(2374,plain,
% 0.63/0.84 (~(op(e2, e3) = e2)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[709, 2373])).
% 0.63/0.84 tff(2375,plain,
% 0.63/0.84 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (e0 = op(e2, e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2363])).
% 0.63/0.84 tff(2376,plain,
% 0.63/0.84 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (op(e2, e3) = e0)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2375, 1903])).
% 0.63/0.84 tff(2377,plain,
% 0.63/0.84 ((~(e0 = op(op(e3, op(e3, e3)), e3))) <=> (~(op(e2, e3) = e0))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2376])).
% 0.63/0.84 tff(2378,plain,
% 0.63/0.84 (e1 = op(e3, e3)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2367, 816])).
% 0.63/0.84 tff(2379,plain,
% 0.63/0.84 ((~(~((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3))))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2380,plain,
% 0.63/0.84 (((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))) <=> (~((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2381,plain,
% 0.63/0.84 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~(~((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3)))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2380])).
% 0.63/0.84 tff(2382,plain,
% 0.63/0.84 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[2381, 2379])).
% 0.63/0.84 tff(2383,plain,
% 0.63/0.84 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2384,plain,
% 0.63/0.84 ((~(((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), e3)))) <=> (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2385,axiom,(~(((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax20')).
% 0.63/0.84 tff(2386,plain,
% 0.63/0.84 (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 0.63/0.84 tff(2387,plain,
% 0.63/0.84 (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(op(e3, op(e3, e3)), e3)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2386, 2383])).
% 0.63/0.84 tff(2388,plain,
% 0.63/0.84 ((~(e1 = op(e3, e3))) | (~(e0 = op(op(e3, op(e3, e3)), e3))) | (~(e2 = op(e3, op(e3, e3))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2387, 2382])).
% 0.63/0.84 tff(2389,plain,
% 0.63/0.84 (~(e0 = op(op(e3, op(e3, e3)), e3))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2388, 2378, 2361])).
% 0.63/0.84 tff(2390,plain,
% 0.63/0.84 (~(op(e2, e3) = e0)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2389, 2377])).
% 0.63/0.84 tff(2391,plain,
% 0.63/0.84 (op(e2, e3) = e3),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[903, 2390, 2374, 2370])).
% 0.63/0.84 tff(2392,plain,
% 0.63/0.84 (op(op(e2, e3), op(e2, e3)) = op(e3, e3)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2391, 2391])).
% 0.63/0.84 tff(2393,plain,
% 0.63/0.84 (op(e3, e3) = op(op(e2, e3), op(e2, e3))),
% 0.63/0.84 inference(symmetry,[status(thm)],[2392])).
% 0.63/0.84 tff(2394,plain,
% 0.63/0.84 (e1 = op(e3, e3)),
% 0.63/0.84 inference(symmetry,[status(thm)],[2367])).
% 0.63/0.84 tff(2395,plain,
% 0.63/0.84 (e1 = e3),
% 0.63/0.84 inference(transitivity,[status(thm)],[2394, 2393, 16])).
% 0.63/0.84 tff(2396,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[665, 2395])).
% 0.63/0.84 tff(2397,plain,((~(op(e3, e3) = e1)) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (~(e2 = op(e3, op(e3, e3))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2398,plain,
% 0.63/0.84 (~(op(e3, e3) = e1)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2397, 2361, 16])).
% 0.63/0.84 tff(2399,plain,
% 0.63/0.84 (op(e3, e3) = e0),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[833, 2398, 418, 817])).
% 0.63/0.84 tff(2400,plain,
% 0.63/0.84 (e0 = op(e3, e3)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2399, 869])).
% 0.63/0.84 tff(2401,plain,
% 0.63/0.84 (~(e1 = op(op(e3, op(e3, e3)), e3))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[880, 2400, 2361])).
% 0.63/0.84 tff(2402,plain,
% 0.63/0.84 (~(op(e2, e3) = e1)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2401, 2366])).
% 0.63/0.84 tff(2403,plain,
% 0.63/0.84 (~(op(e2, e3) = e3)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[891, 2399, 16])).
% 0.63/0.84 tff(2404,plain,
% 0.63/0.84 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2399])).
% 0.63/0.84 tff(2405,plain,
% 0.63/0.84 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2404])).
% 0.63/0.84 tff(2406,plain,
% 0.63/0.84 (~(op(e2, e3) = e0)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[656, 2405])).
% 0.63/0.84 tff(2407,plain,
% 0.63/0.84 (op(e2, e3) = e1),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[903, 2406, 2374, 2403])).
% 0.63/0.84 tff(2408,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2407, 2402])).
% 0.63/0.84 tff(2409,plain,((~(e2 = op(e3, op(e3, e3)))) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e3, e3) = e2) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2410,plain,
% 0.63/0.84 (~(e2 = op(e3, op(e3, e3)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2409, 418, 2357, 2360])).
% 0.63/0.84 tff(2411,assumption,(op(e0, e1) = e2), introduced(assumption)).
% 0.63/0.84 tff(2412,plain,
% 0.63/0.84 ((op(e0, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.63/0.84 tff(2413,plain,
% 0.63/0.84 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2412, 55])).
% 0.63/0.84 tff(2414,plain,
% 0.63/0.84 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2413])).
% 0.63/0.84 tff(2415,plain,
% 0.63/0.84 (~(op(e2, e1) = e2)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[776, 2414])).
% 0.63/0.84 tff(2416,plain,
% 0.63/0.84 ((op(e0, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.63/0.84 tff(2417,plain,
% 0.63/0.84 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2416, 370])).
% 0.63/0.84 tff(2418,plain,
% 0.63/0.84 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2417])).
% 0.63/0.84 tff(2419,plain,
% 0.63/0.84 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = op(e3, e1)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2420,plain,
% 0.63/0.84 (~(op(e0, e1) = op(e3, e1))),
% 0.63/0.84 inference(and_elim,[status(thm)],[106])).
% 0.63/0.84 tff(2421,plain,
% 0.63/0.84 (~(op(e0, e1) = op(e3, e1))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 0.63/0.84 tff(2422,plain,
% 0.63/0.84 (~(op(e3, e1) = e2)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2421, 2418])).
% 0.63/0.84 tff(2423,plain,
% 0.63/0.84 ((op(e0, e1) = e3) <=> (e2 = e3)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.63/0.84 tff(2424,plain,
% 0.63/0.84 ((e2 = e3) <=> (op(e0, e1) = e3)),
% 0.63/0.84 inference(symmetry,[status(thm)],[2423])).
% 0.63/0.84 tff(2425,plain,
% 0.63/0.84 ((~(e2 = e3)) <=> (~(op(e0, e1) = e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2424])).
% 0.63/0.84 tff(2426,plain,
% 0.63/0.84 (~(op(e0, e1) = e3)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[195, 2425])).
% 0.63/0.84 tff(2427,plain,
% 0.63/0.84 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.63/0.84 tff(2428,plain,
% 0.63/0.84 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2427, 319])).
% 0.63/0.84 tff(2429,plain,
% 0.63/0.84 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 0.63/0.84 inference(symmetry,[status(thm)],[2428])).
% 0.63/0.84 tff(2430,plain,
% 0.63/0.84 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2429])).
% 0.63/0.84 tff(2431,plain,
% 0.63/0.84 (~(op(e0, e1) = e1)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[220, 2430])).
% 0.63/0.84 tff(2432,plain,
% 0.63/0.84 ((op(e0, e1) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.63/0.84 tff(2433,plain,
% 0.63/0.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.63/0.84 inference(transitivity,[status(thm)],[2432, 1362])).
% 0.63/0.84 tff(2434,plain,
% 0.63/0.84 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2433])).
% 0.63/0.84 tff(2435,plain,
% 0.63/0.84 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e0, e3)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2436,plain,
% 0.63/0.84 (~(op(e0, e1) = op(e0, e3))),
% 0.63/0.84 inference(and_elim,[status(thm)],[80])).
% 0.63/0.84 tff(2437,plain,
% 0.63/0.84 (~(op(e0, e1) = op(e0, e3))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 0.63/0.84 tff(2438,plain,
% 0.63/0.84 (~(op(e0, e3) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2437, 2434])).
% 0.71/0.84 tff(2439,plain,
% 0.71/0.84 ((op(e0, e1) = op(e1, e1)) <=> (e2 = op(e1, e1))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.71/0.84 tff(2440,plain,
% 0.71/0.84 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2439, 528])).
% 0.71/0.84 tff(2441,plain,
% 0.71/0.84 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2440])).
% 0.71/0.84 tff(2442,plain,
% 0.71/0.84 (~(op(e1, e1) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[110, 2441])).
% 0.71/0.84 tff(2443,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.71/0.84 tff(2444,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2443, 2])).
% 0.71/0.84 tff(2445,plain,
% 0.71/0.84 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2444])).
% 0.71/0.84 tff(2446,plain,
% 0.71/0.84 (~(op(e0, e2) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1360, 2445])).
% 0.71/0.84 tff(2447,plain,
% 0.71/0.84 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2411])).
% 0.71/0.84 tff(2448,plain,
% 0.71/0.84 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2447, 263])).
% 0.71/0.84 tff(2449,plain,
% 0.71/0.84 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2448])).
% 0.71/0.84 tff(2450,plain,
% 0.71/0.84 ((~(e0 = e2)) <=> (~(op(e0, e1) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2449])).
% 0.71/0.84 tff(2451,plain,
% 0.71/0.84 (~(op(e0, e1) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[272, 2450])).
% 0.71/0.84 tff(2452,assumption,(~(op(e0, e1) = e0)), introduced(assumption)).
% 0.71/0.84 tff(2453,assumption,(~(op(e3, e1) = e2)), introduced(assumption)).
% 0.71/0.84 tff(2454,assumption,(~(op(e0, e1) = e3)), introduced(assumption)).
% 0.71/0.84 tff(2455,plain,
% 0.71/0.84 (op(e2, e2) = e2),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[53, 8, 4, 6, 13])).
% 0.71/0.84 tff(2456,plain,
% 0.71/0.84 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2455])).
% 0.71/0.84 tff(2457,plain,
% 0.71/0.84 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2456, 378])).
% 0.71/0.84 tff(2458,plain,
% 0.71/0.84 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2457])).
% 0.71/0.84 tff(2459,plain,
% 0.71/0.84 (~(op(e3, e2) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[591, 2458])).
% 0.71/0.84 tff(2460,plain,
% 0.71/0.84 (op(e3, e3) = e0),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[1962, 418, 817, 16, 1395, 1896])).
% 0.71/0.84 tff(2461,plain,
% 0.71/0.84 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2460])).
% 0.71/0.84 tff(2462,plain,
% 0.71/0.84 (op(e3, e0) = op(e3, op(e3, e3))),
% 0.71/0.84 inference(symmetry,[status(thm)],[2461])).
% 0.71/0.84 tff(2463,plain,
% 0.71/0.84 (op(e3, e0) = e2),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[566, 418, 483, 2453])).
% 0.71/0.84 tff(2464,plain,
% 0.71/0.84 (e2 = op(e3, e0)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2463])).
% 0.71/0.84 tff(2465,plain,
% 0.71/0.84 (e2 = op(e3, op(e3, e3))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2464, 2462])).
% 0.71/0.84 tff(2466,plain,
% 0.71/0.84 ($false),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[1397, 2465])).
% 0.71/0.84 tff(2467,plain,((op(e3, e3) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e3, e3) = e3) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e0, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e2) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2468,plain,
% 0.71/0.85 (op(e3, e3) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2467, 731, 1397, 15, 1395, 23, 2459, 2453])).
% 0.71/0.85 tff(2469,plain,
% 0.71/0.85 (~(op(e0, e3) = e0)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1951, 15, 23, 731, 1395])).
% 0.71/0.85 tff(2470,plain,
% 0.71/0.85 (op(e0, e2) = e0),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[209, 2469, 168, 2452])).
% 0.71/0.85 tff(2471,plain,
% 0.71/0.85 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2470])).
% 0.71/0.85 tff(2472,plain,
% 0.71/0.85 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2471])).
% 0.71/0.85 tff(2473,plain,
% 0.71/0.85 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2472])).
% 0.71/0.85 tff(2474,plain,
% 0.71/0.85 (~(op(e0, e2) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[684, 2473])).
% 0.71/0.85 tff(2475,plain,
% 0.71/0.85 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2470])).
% 0.71/0.85 tff(2476,plain,
% 0.71/0.85 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2475, 1144])).
% 0.71/0.85 tff(2477,plain,
% 0.71/0.85 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2476])).
% 0.71/0.85 tff(2478,plain,
% 0.71/0.85 (~(op(e3, e2) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1155, 2477])).
% 0.71/0.85 tff(2479,plain,
% 0.71/0.85 ((op(e0, e2) = e1) <=> (e0 = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2470])).
% 0.71/0.85 tff(2480,plain,
% 0.71/0.85 ((e0 = e1) <=> (op(e0, e2) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2479])).
% 0.71/0.85 tff(2481,plain,
% 0.71/0.85 ((~(e0 = e1)) <=> (~(op(e0, e2) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2480])).
% 0.71/0.85 tff(2482,plain,
% 0.71/0.85 (~(op(e0, e2) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1182, 2481])).
% 0.71/0.85 tff(2483,plain,
% 0.71/0.85 ((op(e3, e3) = e0) <=> (e2 = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[626])).
% 0.71/0.85 tff(2484,plain,
% 0.71/0.85 ((op(e3, e3) = e0) <=> (e0 = e2)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2483, 263])).
% 0.71/0.85 tff(2485,plain,
% 0.71/0.85 ((e0 = e2) <=> (op(e3, e3) = e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2484])).
% 0.71/0.85 tff(2486,plain,
% 0.71/0.85 ((~(e0 = e2)) <=> (~(op(e3, e3) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2485])).
% 0.71/0.85 tff(2487,plain,
% 0.71/0.85 (~(op(e3, e3) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[272, 2486])).
% 0.71/0.85 tff(2488,assumption,(~(op(e0, e3) = e0)), introduced(assumption)).
% 0.71/0.85 tff(2489,plain,
% 0.71/0.85 (op(e3, e2) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[491, 482, 483, 481])).
% 0.71/0.85 tff(2490,plain,
% 0.71/0.85 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[626])).
% 0.71/0.85 tff(2491,plain,
% 0.71/0.85 (op(e3, op(e3, e3)) = e1),
% 0.71/0.85 inference(transitivity,[status(thm)],[2490, 2489])).
% 0.71/0.85 tff(2492,plain,
% 0.71/0.85 (op(op(e3, op(e3, e3)), e3) = op(e1, e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2491])).
% 0.71/0.85 tff(2493,plain,
% 0.71/0.85 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (e0 = op(e1, e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2492])).
% 0.71/0.85 tff(2494,plain,
% 0.71/0.85 ((e0 = op(op(e3, op(e3, e3)), e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2493, 1287])).
% 0.71/0.85 tff(2495,plain,
% 0.71/0.85 ((~(e0 = op(op(e3, op(e3, e3)), e3))) <=> (~(op(e1, e3) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2494])).
% 0.71/0.85 tff(2496,plain,
% 0.71/0.85 (e2 = op(e3, e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[626, 1131])).
% 0.71/0.85 tff(2497,plain,
% 0.71/0.85 ((e1 = op(e3, op(e3, e3))) <=> (e1 = op(e3, e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2490])).
% 0.71/0.85 tff(2498,plain,
% 0.71/0.85 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e1)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2497, 1157])).
% 0.71/0.85 tff(2499,plain,
% 0.71/0.85 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2498])).
% 0.71/0.85 tff(2500,plain,
% 0.71/0.85 (e1 = op(e3, op(e3, e3))),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2489, 2499])).
% 0.71/0.85 tff(2501,plain,
% 0.71/0.85 (~(e0 = op(op(e3, op(e3, e3)), e3))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1352, 2500, 2496])).
% 0.71/0.85 tff(2502,plain,
% 0.71/0.85 (~(op(e1, e3) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2501, 2495])).
% 0.71/0.85 tff(2503,plain,
% 0.71/0.85 (op(e2, e3) = e0),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1797, 2502, 2488, 2487])).
% 0.71/0.85 tff(2504,plain,
% 0.71/0.85 (op(op(e2, e3), op(e2, e3)) = op(e0, e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2503, 2503])).
% 0.71/0.85 tff(2505,plain,
% 0.71/0.85 (op(e0, e0) = op(op(e2, e3), op(e2, e3))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2504])).
% 0.71/0.85 tff(2506,plain,
% 0.71/0.85 (~(op(e2, e3) = e3)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[914, 626, 16])).
% 0.71/0.85 tff(2507,plain,
% 0.71/0.85 ((e3 = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.85 inference(commutativity,[status(thm)],[])).
% 0.71/0.85 tff(2508,plain,
% 0.71/0.85 (op(e1, e2) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[520, 482, 6, 1396])).
% 0.71/0.85 tff(2509,plain,
% 0.71/0.85 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2508])).
% 0.71/0.85 tff(2510,plain,
% 0.71/0.85 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2509, 2507])).
% 0.71/0.85 tff(2511,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2510])).
% 0.71/0.85 tff(2512,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e1, e3)))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2513,plain,
% 0.71/0.85 (~(op(e1, e2) = op(e1, e3))),
% 0.71/0.85 inference(and_elim,[status(thm)],[73])).
% 0.71/0.85 tff(2514,plain,
% 0.71/0.85 (~(op(e1, e2) = op(e1, e3))),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 0.71/0.85 tff(2515,plain,
% 0.71/0.85 (~(op(e1, e3) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2514, 2511])).
% 0.71/0.85 tff(2516,plain,
% 0.71/0.85 (op(e0, e3) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1931, 2515, 2506, 817])).
% 0.71/0.85 tff(2517,plain,
% 0.71/0.85 ((op(e0, e3) = e1) <=> (e3 = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2516])).
% 0.71/0.85 tff(2518,plain,
% 0.71/0.85 ((op(e0, e3) = e1) <=> (e1 = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2517, 730])).
% 0.71/0.85 tff(2519,plain,
% 0.71/0.85 ((e1 = e3) <=> (op(e0, e3) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2518])).
% 0.71/0.85 tff(2520,plain,
% 0.71/0.85 ((~(e1 = e3)) <=> (~(op(e0, e3) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2519])).
% 0.71/0.85 tff(2521,plain,
% 0.71/0.85 (~(op(e0, e3) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[665, 2520])).
% 0.71/0.85 tff(2522,plain,
% 0.71/0.85 (op(e0, e0) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1191, 2521, 1398, 729])).
% 0.71/0.85 tff(2523,plain,
% 0.71/0.85 (e1 = op(e0, e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2522])).
% 0.71/0.85 tff(2524,plain,
% 0.71/0.85 (e1 = e3),
% 0.71/0.85 inference(transitivity,[status(thm)],[2523, 2505, 16])).
% 0.71/0.85 tff(2525,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[665, 2524])).
% 0.71/0.85 tff(2526,plain,((op(e3, e2) = e3) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e0, e2) = e1) | (op(e0, e1) = e1) | (op(e0, e3) = e0) | (~(op(e3, e3) = e2)) | (op(e3, e3) = e3) | (op(e3, e2) = e2) | (op(e3, e2) = e0) | (op(e2, e2) = e3) | (op(e0, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2527,plain,
% 0.71/0.85 (op(e3, e2) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2526, 15, 2482, 729, 2469, 2468, 731, 2459, 2478, 6, 2474])).
% 0.71/0.85 tff(2528,plain,
% 0.71/0.85 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2527])).
% 0.71/0.85 tff(2529,plain,
% 0.71/0.85 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2528])).
% 0.71/0.85 tff(2530,plain,
% 0.71/0.85 (~(op(e3, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1057, 2529])).
% 0.71/0.85 tff(2531,plain,
% 0.71/0.85 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2455])).
% 0.71/0.85 tff(2532,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2531])).
% 0.71/0.85 tff(2533,plain,
% 0.71/0.85 (~(op(e1, e2) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[331, 2532])).
% 0.71/0.85 tff(2534,plain,
% 0.71/0.85 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2468])).
% 0.71/0.85 tff(2535,plain,
% 0.71/0.85 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2534])).
% 0.71/0.85 tff(2536,plain,
% 0.71/0.85 (~(op(e1, e3) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1442, 2535])).
% 0.71/0.85 tff(2537,plain,
% 0.71/0.85 (op(e1, e0) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1239, 2536, 1124, 2533])).
% 0.71/0.85 tff(2538,plain,
% 0.71/0.85 ((op(e1, e0) = e3) <=> (e2 = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2537])).
% 0.71/0.85 tff(2539,plain,
% 0.71/0.85 ((e2 = e3) <=> (op(e1, e0) = e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2538])).
% 0.71/0.85 tff(2540,plain,
% 0.71/0.85 ((~(e2 = e3)) <=> (~(op(e1, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2539])).
% 0.71/0.85 tff(2541,plain,
% 0.71/0.85 (~(op(e1, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[195, 2540])).
% 0.71/0.85 tff(2542,plain,
% 0.71/0.85 (op(e0, e3) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1641, 1919, 1395, 2488])).
% 0.71/0.85 tff(2543,plain,
% 0.71/0.85 (op(e0, e0) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1025, 1919, 2454, 1396])).
% 0.71/0.85 tff(2544,plain,
% 0.71/0.85 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2543])).
% 0.71/0.85 tff(2545,plain,
% 0.71/0.85 (op(e0, op(e0, e0)) = e1),
% 0.71/0.85 inference(transitivity,[status(thm)],[2544, 2542])).
% 0.71/0.85 tff(2546,plain,
% 0.71/0.85 (op(op(e0, op(e0, e0)), e0) = op(e1, e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2545])).
% 0.71/0.85 tff(2547,plain,
% 0.71/0.85 (op(e1, e0) = op(op(e0, op(e0, e0)), e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2546])).
% 0.71/0.85 tff(2548,plain,
% 0.71/0.85 (e2 = op(e1, e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[1576])).
% 0.71/0.85 tff(2549,plain,
% 0.71/0.85 (e2 = op(op(e0, op(e0, e0)), e0)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2548, 2547])).
% 0.71/0.85 tff(2550,plain,
% 0.71/0.85 (e3 = op(e0, e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2543, 1652])).
% 0.71/0.85 tff(2551,plain,
% 0.71/0.85 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2544])).
% 0.71/0.85 tff(2552,plain,
% 0.71/0.85 (e1 = op(e0, e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2542])).
% 0.71/0.85 tff(2553,plain,
% 0.71/0.85 (e1 = op(e0, op(e0, e0))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2552, 2551])).
% 0.71/0.85 tff(2554,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1668, 2553, 2550, 2549])).
% 0.71/0.85 tff(2555,plain,((op(e0, e3) = e3) | (~(op(e1, e0) = e2)) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e2) | (op(e0, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2556,plain,
% 0.71/0.85 (op(e0, e3) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2555, 2537, 2454, 2474, 1395, 2469])).
% 0.71/0.85 tff(2557,plain,
% 0.71/0.85 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2556])).
% 0.71/0.85 tff(2558,plain,
% 0.71/0.85 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2557])).
% 0.71/0.85 tff(2559,plain,
% 0.71/0.85 (~(op(e0, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[727, 2558])).
% 0.71/0.85 tff(2560,plain,
% 0.71/0.85 (((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2561,plain,
% 0.71/0.85 ((((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2562,plain,
% 0.71/0.85 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2563,plain,
% 0.71/0.85 (((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)) <=> (((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2562])).
% 0.71/0.85 tff(2564,plain,
% 0.71/0.85 (((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2563, 2561])).
% 0.71/0.85 tff(2565,plain,
% 0.71/0.85 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)),
% 0.71/0.85 inference(and_elim,[status(thm)],[158])).
% 0.71/0.85 tff(2566,plain,
% 0.71/0.85 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 0.71/0.85 tff(2567,plain,
% 0.71/0.85 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2566, 2560])).
% 0.71/0.85 tff(2568,plain,
% 0.71/0.85 (op(e2, e0) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2567, 2559, 2541, 2530])).
% 0.71/0.85 tff(2569,plain,
% 0.71/0.85 (op(op(e2, e0), op(e2, e0)) = op(e3, e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2568, 2568])).
% 0.71/0.85 tff(2570,plain,
% 0.71/0.85 (e0 = e2),
% 0.71/0.85 inference(transitivity,[status(thm)],[48, 2569, 2468])).
% 0.71/0.85 tff(2571,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[272, 2570])).
% 0.71/0.85 tff(2572,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e0, e1) = e3) | (op(e0, e3) = e2) | (op(e0, e1) = e1) | (op(e2, e2) = e3) | (op(e1, e1) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e3, e1) = e2) | (op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e0) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2573,plain,
% 0.71/0.85 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2572, 6, 1395, 729, 2454, 1124, 1397, 2453, 168, 2452, 4, 13])).
% 0.71/0.85 tff(2574,plain,
% 0.71/0.85 (op(e3, e2) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1313, 2573, 1401, 1124, 6, 4, 231])).
% 0.71/0.85 tff(2575,plain,
% 0.71/0.85 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2574, 2574])).
% 0.71/0.85 tff(2576,plain,
% 0.71/0.85 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2575])).
% 0.71/0.85 tff(2577,plain,
% 0.71/0.85 ((op(e2, e2) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2576])).
% 0.71/0.85 tff(2578,plain,
% 0.71/0.85 ((~(op(e2, e2) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2577])).
% 0.71/0.85 tff(2579,plain,
% 0.71/0.85 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2574])).
% 0.71/0.85 tff(2580,plain,
% 0.71/0.85 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2579])).
% 0.71/0.85 tff(2581,plain,
% 0.71/0.85 (~(op(e2, e2) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[591, 2580])).
% 0.71/0.85 tff(2582,plain,
% 0.71/0.85 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2581, 2578])).
% 0.71/0.85 tff(2583,plain,
% 0.71/0.85 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[459, 2582])).
% 0.71/0.85 tff(2584,plain,
% 0.71/0.85 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[416, 2583, 1401, 2573])).
% 0.71/0.85 tff(2585,plain,
% 0.71/0.85 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[419, 2584])).
% 0.71/0.85 tff(2586,plain,
% 0.71/0.85 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2574])).
% 0.71/0.85 tff(2587,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2586])).
% 0.71/0.85 tff(2588,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e3, e2)))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2589,plain,
% 0.71/0.85 (~(op(e1, e2) = op(e3, e2))),
% 0.71/0.85 inference(and_elim,[status(thm)],[92])).
% 0.71/0.85 tff(2590,plain,
% 0.71/0.85 (~(op(e1, e2) = op(e3, e2))),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 0.71/0.85 tff(2591,plain,
% 0.71/0.85 (~(op(e1, e2) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2590, 2587])).
% 0.71/0.85 tff(2592,plain,
% 0.71/0.85 (op(op(e1, e3), op(e1, e3)) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[313, 2584])).
% 0.71/0.85 tff(2593,plain,
% 0.71/0.85 (~(op(e1, e3) = e2)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1230, 2592, 6])).
% 0.71/0.85 tff(2594,assumption,(~(op(e1, e3) = e2)), introduced(assumption)).
% 0.71/0.85 tff(2595,plain,
% 0.71/0.85 (op(e1, e0) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1239, 977, 2594, 1124])).
% 0.71/0.85 tff(2596,plain,
% 0.71/0.85 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2595, 2595])).
% 0.71/0.85 tff(2597,plain,
% 0.71/0.85 ((op(op(e1, e0), op(e1, e0)) = e0) <=> (op(e2, e2) = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2596])).
% 0.71/0.85 tff(2598,plain,
% 0.71/0.85 ((op(e2, e2) = e0) <=> (op(op(e1, e0), op(e1, e0)) = e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2597])).
% 0.71/0.86 tff(2599,plain,
% 0.71/0.86 ((~(op(e2, e2) = e0)) <=> (~(op(op(e1, e0), op(e1, e0)) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2598])).
% 0.71/0.86 tff(2600,plain,
% 0.71/0.86 (~(op(op(e1, e0), op(e1, e0)) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1064, 2599])).
% 0.71/0.86 tff(2601,plain,
% 0.71/0.86 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[333, 2600])).
% 0.71/0.86 tff(2602,plain,
% 0.71/0.86 (op(e3, e2) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[507, 977, 231, 3])).
% 0.71/0.86 tff(2603,plain,
% 0.71/0.86 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2602, 2602])).
% 0.71/0.86 tff(2604,plain,
% 0.71/0.86 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2603])).
% 0.71/0.86 tff(2605,plain,
% 0.71/0.86 ((op(e2, e2) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2604])).
% 0.71/0.86 tff(2606,plain,
% 0.71/0.86 ((~(op(e2, e2) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2605])).
% 0.71/0.86 tff(2607,plain,
% 0.71/0.86 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[3, 2606])).
% 0.71/0.86 tff(2608,plain,
% 0.71/0.86 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[459, 2607])).
% 0.71/0.86 tff(2609,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[416, 2608, 2601, 1289, 1288])).
% 0.71/0.86 tff(2610,plain,((op(e1, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e2, e2) = e2) | (op(e2, e2) = e0) | (op(e0, e2) = e2) | (op(e1, e3) = e2) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2611,plain,
% 0.71/0.86 (op(e2, e2) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2610, 2593, 1401, 231, 1124, 2573, 2591, 2581])).
% 0.71/0.86 tff(2612,plain,
% 0.71/0.86 (e0 = op(e2, e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2611])).
% 0.71/0.86 tff(2613,plain,
% 0.71/0.86 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2612, 2612])).
% 0.71/0.86 tff(2614,plain,
% 0.71/0.86 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2613])).
% 0.71/0.86 tff(2615,plain,
% 0.71/0.86 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e2, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2612])).
% 0.71/0.86 tff(2616,plain,
% 0.71/0.86 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2615])).
% 0.71/0.86 tff(2617,plain,
% 0.71/0.86 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2616])).
% 0.71/0.86 tff(2618,plain,
% 0.71/0.86 (~(op(e0, e2) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[126, 2617])).
% 0.71/0.86 tff(2619,plain,
% 0.71/0.86 (op(e0, e3) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[209, 2618, 168, 2452])).
% 0.71/0.86 tff(2620,plain,
% 0.71/0.86 ((op(e0, e3) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2619])).
% 0.71/0.86 tff(2621,plain,
% 0.71/0.86 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2620, 1287])).
% 0.71/0.86 tff(2622,plain,
% 0.71/0.86 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2621])).
% 0.71/0.86 tff(2623,plain,
% 0.71/0.86 (~(op(e1, e3) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1632, 2622])).
% 0.71/0.86 tff(2624,plain,
% 0.71/0.86 (op(e1, e1) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1481, 2623, 168, 2611, 2583, 4])).
% 0.71/0.86 tff(2625,plain,
% 0.71/0.86 (op(e1, e1) = op(e2, e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2624, 2612])).
% 0.71/0.86 tff(2626,plain,
% 0.71/0.86 (op(op(e1, e1), op(e1, e1)) = op(op(e2, e2), op(e2, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2625, 2625])).
% 0.71/0.86 tff(2627,plain,
% 0.71/0.86 (op(op(e1, e1), op(e1, e1)) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[316, 2584])).
% 0.71/0.86 tff(2628,plain,
% 0.71/0.86 (e1 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2627])).
% 0.71/0.86 tff(2629,plain,
% 0.71/0.86 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2612])).
% 0.71/0.86 tff(2630,plain,
% 0.71/0.86 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2629])).
% 0.71/0.86 tff(2631,plain,
% 0.71/0.86 (~(op(e2, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1182, 2630])).
% 0.71/0.86 tff(2632,plain,
% 0.71/0.86 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2574])).
% 0.71/0.86 tff(2633,plain,
% 0.71/0.86 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2632, 319])).
% 0.71/0.86 tff(2634,plain,
% 0.71/0.86 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2633])).
% 0.71/0.86 tff(2635,plain,
% 0.71/0.86 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2634])).
% 0.71/0.86 tff(2636,plain,
% 0.71/0.86 (~(op(e3, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[220, 2635])).
% 0.71/0.86 tff(2637,plain,
% 0.71/0.86 ((op(e0, e2) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e2))),
% 0.71/0.86 inference(commutativity,[status(thm)],[])).
% 0.71/0.86 tff(2638,plain,
% 0.71/0.86 (e1 = op(e0, e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2628, 2626, 2614])).
% 0.71/0.86 tff(2639,plain,
% 0.71/0.86 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2638])).
% 0.71/0.86 tff(2640,plain,
% 0.71/0.86 ((op(e0, e2) = e1) <=> (op(e0, e0) = op(e0, e2))),
% 0.71/0.86 inference(transitivity,[status(thm)],[2639, 2637])).
% 0.71/0.86 tff(2641,plain,
% 0.71/0.86 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2640])).
% 0.71/0.86 tff(2642,plain,
% 0.71/0.86 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2641])).
% 0.71/0.86 tff(2643,plain,
% 0.71/0.86 (~(op(e0, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[281, 2642])).
% 0.71/0.86 tff(2644,plain,
% 0.71/0.86 (op(e1, e2) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1331, 2643, 2636, 2631])).
% 0.71/0.86 tff(2645,plain,
% 0.71/0.86 (op(e1, e2) = op(e0, e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2644, 2628, 2626, 2614])).
% 0.71/0.86 tff(2646,plain,
% 0.71/0.86 (op(op(e1, e2), op(e1, e2)) = op(op(e0, e0), op(e0, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2645, 2645])).
% 0.71/0.86 tff(2647,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = op(op(e1, e2), op(e1, e2))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2646])).
% 0.71/0.86 tff(2648,plain,
% 0.71/0.86 (op(op(e2, e2), op(e2, e2)) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2626])).
% 0.71/0.86 tff(2649,plain,
% 0.71/0.86 (op(e0, e0) = e1),
% 0.71/0.86 inference(transitivity,[status(thm)],[2613, 2648, 2627])).
% 0.71/0.86 tff(2650,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2649, 2649])).
% 0.71/0.86 tff(2651,plain,
% 0.71/0.86 (op(e1, e1) = op(op(e0, e0), op(e0, e0))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2650])).
% 0.71/0.86 tff(2652,plain,
% 0.71/0.86 (e0 = op(e1, e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2624])).
% 0.71/0.86 tff(2653,plain,
% 0.71/0.86 (op(e2, e2) = e2),
% 0.71/0.86 inference(transitivity,[status(thm)],[2611, 2652, 2651, 2647, 2585])).
% 0.71/0.86 tff(2654,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2581, 2653])).
% 0.71/0.86 tff(2655,plain,((op(e2, e2) = e3) | (op(e0, e0) = e0) | (op(e0, e0) = e2) | (op(e0, e1) = e0) | (op(e0, e2) = e2) | (op(e1, e1) = e2) | (op(e0, e3) = e2) | (op(e0, e1) = e1) | (op(e0, e1) = e3) | (e2 = op(e3, op(e3, e3))) | (op(e3, e1) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2656,plain,
% 0.71/0.86 (op(e2, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2655, 2451, 4, 168, 2446, 2442, 2438, 2431, 2426, 1397, 2422, 2415])).
% 0.71/0.86 tff(2657,plain,
% 0.71/0.86 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2656])).
% 0.71/0.86 tff(2658,plain,
% 0.71/0.86 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2657, 937])).
% 0.71/0.86 tff(2659,plain,
% 0.71/0.86 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2658])).
% 0.71/0.86 tff(2660,plain,
% 0.71/0.86 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2659])).
% 0.71/0.86 tff(2661,plain,
% 0.71/0.86 (~(op(e2, e2) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[195, 2660])).
% 0.71/0.86 tff(2662,plain,
% 0.71/0.86 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[960, 2661, 2415, 2656])).
% 0.71/0.86 tff(2663,plain,
% 0.71/0.86 (e3 = op(e2, e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2656])).
% 0.71/0.86 tff(2664,plain,
% 0.71/0.86 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2663])).
% 0.71/0.86 tff(2665,plain,
% 0.71/0.86 ((op(e3, e2) = e3) <=> (op(e2, e2) = op(e3, e2))),
% 0.71/0.86 inference(transitivity,[status(thm)],[2664, 962])).
% 0.71/0.86 tff(2666,plain,
% 0.71/0.86 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2665])).
% 0.71/0.86 tff(2667,plain,
% 0.71/0.86 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2666])).
% 0.71/0.86 tff(2668,plain,
% 0.71/0.86 (~(op(e3, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[591, 2667])).
% 0.71/0.86 tff(2669,plain,
% 0.71/0.86 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1851, 483, 1124, 482, 4])).
% 0.71/0.86 tff(2670,plain,
% 0.71/0.86 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[459, 2669])).
% 0.71/0.86 tff(2671,plain,
% 0.71/0.86 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[416, 2670, 1289, 1288])).
% 0.71/0.86 tff(2672,plain,
% 0.71/0.86 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[419, 2671])).
% 0.71/0.86 tff(2673,plain,
% 0.71/0.86 (op(op(e1, e2), op(e1, e2)) = op(e2, e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1294, 1294])).
% 0.71/0.86 tff(2674,plain,
% 0.71/0.86 (op(e2, e2) = op(op(e1, e2), op(e1, e2))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2673])).
% 0.71/0.86 tff(2675,plain,
% 0.71/0.86 (op(e2, e2) = e2),
% 0.71/0.86 inference(transitivity,[status(thm)],[2674, 2672])).
% 0.71/0.86 tff(2676,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[3, 2675])).
% 0.71/0.86 tff(2677,plain,((op(e3, e2) = e2) | (op(e2, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e3, e2) = e3) | (op(e0, e0) = e2) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2678,plain,
% 0.71/0.86 (op(e3, e2) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2677, 2661, 1401, 2662, 2442, 2668, 4, 2446])).
% 0.71/0.86 tff(2679,plain,
% 0.71/0.86 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2678, 2678])).
% 0.71/0.86 tff(2680,plain,
% 0.71/0.86 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2679])).
% 0.71/0.86 tff(2681,plain,
% 0.71/0.86 ((op(e2, e2) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2680])).
% 0.71/0.86 tff(2682,plain,
% 0.71/0.86 ((~(op(e2, e2) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2681])).
% 0.71/0.86 tff(2683,plain,
% 0.71/0.86 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[2661, 2682])).
% 0.71/0.86 tff(2684,plain,
% 0.71/0.86 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[459, 2683])).
% 0.71/0.86 tff(2685,plain,
% 0.71/0.86 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[416, 2684, 1401, 2662])).
% 0.71/0.86 tff(2686,plain,
% 0.71/0.86 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[419, 2685])).
% 0.71/0.86 tff(2687,plain,
% 0.71/0.86 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2678])).
% 0.71/0.86 tff(2688,plain,
% 0.71/0.86 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2687])).
% 0.71/0.86 tff(2689,plain,
% 0.71/0.86 (~(op(e1, e2) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[2590, 2688])).
% 0.71/0.86 tff(2690,plain,
% 0.71/0.86 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2663])).
% 0.71/0.86 tff(2691,plain,
% 0.71/0.86 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2690])).
% 0.71/0.86 tff(2692,plain,
% 0.71/0.86 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2691])).
% 0.71/0.86 tff(2693,plain,
% 0.71/0.86 (~(op(e1, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[331, 2692])).
% 0.71/0.86 tff(2694,plain,
% 0.71/0.86 (~(op(e1, e2) = e0)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[435, 2686, 4])).
% 0.71/0.86 tff(2695,plain,
% 0.71/0.86 (op(e1, e2) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[449, 2694, 2693, 2689])).
% 0.71/0.86 tff(2696,plain,
% 0.71/0.86 (e1 = op(e1, e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2695])).
% 0.71/0.86 tff(2697,plain,
% 0.71/0.86 (op(e1, e1) = op(op(e1, e2), op(e1, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2696, 2696])).
% 0.71/0.86 tff(2698,plain,
% 0.71/0.86 (op(e1, e1) = e2),
% 0.71/0.86 inference(transitivity,[status(thm)],[2697, 2686])).
% 0.71/0.86 tff(2699,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2442, 2698])).
% 0.71/0.86 tff(2700,plain,((~(op(e0, e1) = e2)) | (op(e0, e0) = e2) | (op(e0, e0) = e0) | (e2 = op(e3, op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2701,plain,
% 0.71/0.86 (~(op(e0, e1) = e2)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2700, 4, 168, 1397])).
% 0.71/0.86 tff(2702,plain,
% 0.71/0.86 ((e0 = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.86 inference(commutativity,[status(thm)],[])).
% 0.71/0.86 tff(2703,plain,
% 0.71/0.86 ((e3 = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 0.71/0.86 inference(commutativity,[status(thm)],[])).
% 0.71/0.86 tff(2704,plain,
% 0.71/0.86 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.86 tff(2705,plain,
% 0.71/0.86 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2704, 421])).
% 0.71/0.86 tff(2706,plain,
% 0.71/0.86 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2705])).
% 0.71/0.86 tff(2707,plain,
% 0.71/0.86 (~(op(e1, e2) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[2277, 2706])).
% 0.71/0.86 tff(2708,plain,
% 0.71/0.86 ((op(e0, e2) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.86 tff(2709,plain,
% 0.71/0.86 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2708, 1362])).
% 0.71/0.86 tff(2710,plain,
% 0.71/0.86 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2709])).
% 0.71/0.86 tff(2711,plain,
% 0.71/0.86 (~(op(e0, e3) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1368, 2710])).
% 0.71/0.86 tff(2712,plain,
% 0.71/0.86 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.86 tff(2713,plain,
% 0.71/0.86 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2712, 378])).
% 0.71/0.86 tff(2714,plain,
% 0.71/0.86 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2713])).
% 0.71/0.86 tff(2715,plain,
% 0.71/0.86 (~(op(e3, e2) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1155, 2714])).
% 0.71/0.86 tff(2716,plain,
% 0.71/0.86 ((op(e0, e2) = e1) <=> (e2 = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.86 tff(2717,plain,
% 0.71/0.86 ((op(e0, e2) = e1) <=> (e1 = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2716, 319])).
% 0.71/0.86 tff(2718,plain,
% 0.71/0.86 ((e1 = e2) <=> (op(e0, e2) = e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2717])).
% 0.71/0.86 tff(2719,plain,
% 0.71/0.86 ((~(e1 = e2)) <=> (~(op(e0, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2718])).
% 0.71/0.86 tff(2720,plain,
% 0.71/0.86 (~(op(e0, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[220, 2719])).
% 0.71/0.86 tff(2721,plain,
% 0.71/0.86 ((op(e0, e2) = e0) <=> (e2 = e0)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.86 tff(2722,plain,
% 0.71/0.86 ((op(e0, e2) = e0) <=> (e0 = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2721, 263])).
% 0.71/0.86 tff(2723,plain,
% 0.71/0.86 ((e0 = e2) <=> (op(e0, e2) = e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2722])).
% 0.71/0.86 tff(2724,plain,
% 0.71/0.86 ((~(e0 = e2)) <=> (~(op(e0, e2) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2723])).
% 0.71/0.86 tff(2725,plain,
% 0.71/0.86 (~(op(e0, e2) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[272, 2724])).
% 0.71/0.87 tff(2726,plain,
% 0.71/0.87 ((op(e0, e2) = e3) <=> (e2 = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[117])).
% 0.71/0.87 tff(2727,plain,
% 0.71/0.87 ((e2 = e3) <=> (op(e0, e2) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2726])).
% 0.71/0.87 tff(2728,plain,
% 0.71/0.87 ((~(e2 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2727])).
% 0.71/0.87 tff(2729,plain,
% 0.71/0.87 (~(op(e0, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[195, 2728])).
% 0.71/0.87 tff(2730,plain,
% 0.71/0.87 (op(e2, e2) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1784, 2729, 2725, 168, 1397, 4, 127, 1677, 2720, 2715, 2711, 2707, 112])).
% 0.71/0.87 tff(2731,plain,
% 0.71/0.87 (e3 = op(e2, e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2730])).
% 0.71/0.87 tff(2732,plain,
% 0.71/0.87 ((e0 = e3) <=> (e0 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2731])).
% 0.71/0.87 tff(2733,plain,
% 0.71/0.87 ((e0 = e3) <=> (op(e2, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2732, 954])).
% 0.71/0.87 tff(2734,plain,
% 0.71/0.87 ((~(e0 = e3)) <=> (~(op(e2, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2733])).
% 0.71/0.87 tff(2735,plain,
% 0.71/0.87 (~(op(e2, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[684, 2734])).
% 0.71/0.87 tff(2736,plain,
% 0.71/0.87 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[944])).
% 0.71/0.87 tff(2737,plain,
% 0.71/0.87 ((op(e3, e2) = e3) <=> (op(e2, e2) = op(e3, e2))),
% 0.71/0.87 inference(transitivity,[status(thm)],[2736, 962])).
% 0.71/0.87 tff(2738,plain,
% 0.71/0.87 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2737])).
% 0.71/0.87 tff(2739,plain,
% 0.71/0.87 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2738])).
% 0.71/0.87 tff(2740,plain,
% 0.71/0.87 (~(op(e3, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[591, 2739])).
% 0.71/0.87 tff(2741,plain,
% 0.71/0.87 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1851, 1124, 483, 2740, 4])).
% 0.71/0.87 tff(2742,plain,
% 0.71/0.87 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[459, 2741])).
% 0.71/0.87 tff(2743,plain,
% 0.71/0.87 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2078, 1124, 112, 943])).
% 0.71/0.87 tff(2744,plain,
% 0.71/0.87 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[416, 2743, 1289, 2742])).
% 0.71/0.87 tff(2745,plain,
% 0.71/0.87 (op(op(e1, e2), op(e1, e2)) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[419, 2744])).
% 0.71/0.87 tff(2746,plain,
% 0.71/0.87 (~(op(e1, e2) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[435, 2745, 4])).
% 0.71/0.87 tff(2747,plain,
% 0.71/0.87 (op(e1, e2) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[449, 2746, 2100, 977])).
% 0.71/0.87 tff(2748,plain,
% 0.71/0.87 (e1 = op(e1, e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2747])).
% 0.71/0.87 tff(2749,plain,
% 0.71/0.87 (op(e1, e1) = op(op(e1, e2), op(e1, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2748, 2748])).
% 0.71/0.87 tff(2750,plain,
% 0.71/0.87 (op(e1, e1) = e2),
% 0.71/0.87 inference(transitivity,[status(thm)],[2749, 2745])).
% 0.71/0.87 tff(2751,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1124, 2750])).
% 0.71/0.87 tff(2752,plain,((op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e0, e0) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (op(e0, e1) = e2) | (~(op(e2, e2) = e3)) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(2753,plain,
% 0.71/0.87 (op(e1, e1) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2752, 2707, 4, 1401, 112, 2730, 2715])).
% 0.71/0.87 tff(2754,plain,
% 0.71/0.87 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1729, 2753, 2725, 4, 1677])).
% 0.71/0.87 tff(2755,plain,
% 0.71/0.87 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2753])).
% 0.71/0.87 tff(2756,plain,
% 0.71/0.87 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2755, 55])).
% 0.71/0.87 tff(2757,plain,
% 0.71/0.87 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2756])).
% 0.71/0.87 tff(2758,plain,
% 0.71/0.87 (~(op(e2, e1) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[101, 2757])).
% 0.71/0.87 tff(2759,plain,
% 0.71/0.87 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[960, 2758, 127, 2730])).
% 0.71/0.87 tff(2760,plain,
% 0.71/0.87 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[416, 2759, 1401, 2754])).
% 0.71/0.87 tff(2761,plain,
% 0.71/0.87 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[459, 2760])).
% 0.71/0.87 tff(2762,plain,
% 0.71/0.87 (~(op(e3, e2) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[474, 2761, 4])).
% 0.71/0.87 tff(2763,plain,
% 0.71/0.87 (op(e1, e2) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[997, 2762, 2725, 2735])).
% 0.71/0.87 tff(2764,plain,
% 0.71/0.87 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2753])).
% 0.71/0.87 tff(2765,plain,
% 0.71/0.87 (op(e1, op(e1, e1)) = e0),
% 0.71/0.87 inference(transitivity,[status(thm)],[2764, 2763])).
% 0.71/0.87 tff(2766,plain,
% 0.71/0.87 (op(op(e1, op(e1, e1)), e1) = op(e0, e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2765])).
% 0.71/0.87 tff(2767,plain,
% 0.71/0.87 ((e3 = op(op(e1, op(e1, e1)), e1)) <=> (e3 = op(e0, e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2766])).
% 0.71/0.87 tff(2768,plain,
% 0.71/0.87 ((e3 = op(op(e1, op(e1, e1)), e1)) <=> (op(e0, e1) = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2767, 2703])).
% 0.71/0.87 tff(2769,plain,
% 0.71/0.87 ((~(e3 = op(op(e1, op(e1, e1)), e1))) <=> (~(op(e0, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2768])).
% 0.71/0.87 tff(2770,plain,
% 0.71/0.87 (e2 = op(e1, e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2753, 529])).
% 0.71/0.87 tff(2771,plain,
% 0.71/0.87 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2764])).
% 0.71/0.87 tff(2772,plain,
% 0.71/0.87 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2771, 1])).
% 0.71/0.87 tff(2773,plain,
% 0.71/0.87 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[2772])).
% 0.71/0.87 tff(2774,plain,
% 0.71/0.87 (e0 = op(e1, op(e1, e1))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2763, 2773])).
% 0.71/0.87 tff(2775,plain,
% 0.71/0.87 (~(e3 = op(op(e1, op(e1, e1)), e1))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1038, 2774, 2770])).
% 0.71/0.87 tff(2776,plain,
% 0.71/0.87 (~(op(e0, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2775, 2769])).
% 0.71/0.87 tff(2777,plain,
% 0.71/0.87 ((op(e1, e1) = e3) <=> (e2 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2753, 2731])).
% 0.71/0.87 tff(2778,plain,
% 0.71/0.87 ((op(e1, e1) = e3) <=> (op(e2, e2) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2777, 7])).
% 0.71/0.87 tff(2779,plain,
% 0.71/0.87 ((op(e2, e2) = e2) <=> (op(e1, e1) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2778])).
% 0.71/0.87 tff(2780,plain,
% 0.71/0.87 ((~(op(e2, e2) = e2)) <=> (~(op(e1, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2779])).
% 0.71/0.87 tff(2781,plain,
% 0.71/0.87 (~(op(e1, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[127, 2780])).
% 0.71/0.87 tff(2782,plain,
% 0.71/0.87 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2731])).
% 0.71/0.87 tff(2783,plain,
% 0.71/0.87 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2782])).
% 0.71/0.87 tff(2784,plain,
% 0.71/0.87 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2783])).
% 0.71/0.87 tff(2785,plain,
% 0.71/0.87 (~(op(e2, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1695, 2784])).
% 0.71/0.87 tff(2786,plain,
% 0.71/0.87 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[476, 2760])).
% 0.71/0.87 tff(2787,plain,
% 0.71/0.87 (~(op(e3, e0) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1097, 2786, 168])).
% 0.71/0.87 tff(2788,plain,
% 0.71/0.87 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[633, 2760])).
% 0.71/0.87 tff(2789,plain,
% 0.71/0.87 (~(op(e3, e3) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1778, 2788, 2725, 168, 1397, 2786])).
% 0.71/0.87 tff(2790,plain,
% 0.71/0.87 (op(e3, e1) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[580, 2762, 2789, 2787])).
% 0.71/0.87 tff(2791,plain,
% 0.71/0.87 ((op(e3, e1) = e3) <=> (e0 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2790, 2731])).
% 0.71/0.87 tff(2792,plain,
% 0.71/0.87 ((op(e3, e1) = e3) <=> (op(e2, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2791, 954])).
% 0.71/0.87 tff(2793,plain,
% 0.71/0.87 ((op(e2, e2) = e0) <=> (op(e3, e1) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2792])).
% 0.71/0.87 tff(2794,plain,
% 0.71/0.87 ((~(op(e2, e2) = e0)) <=> (~(op(e3, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2793])).
% 0.71/0.87 tff(2795,plain,
% 0.71/0.87 (~(op(e3, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2735, 2794])).
% 0.71/0.87 tff(2796,plain,
% 0.71/0.87 (((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2797,plain,
% 0.71/0.87 ((((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2798,plain,
% 0.71/0.87 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2799,plain,
% 0.71/0.87 (((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)) <=> (((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2798])).
% 0.71/0.87 tff(2800,plain,
% 0.71/0.87 (((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3))),
% 0.71/0.87 inference(transitivity,[status(thm)],[2799, 2797])).
% 0.71/0.87 tff(2801,plain,
% 0.71/0.87 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)),
% 0.71/0.87 inference(and_elim,[status(thm)],[150])).
% 0.71/0.87 tff(2802,plain,
% 0.71/0.87 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 0.71/0.87 tff(2803,plain,
% 0.71/0.87 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2802, 2796])).
% 0.71/0.87 tff(2804,plain,
% 0.71/0.87 (op(e0, e1) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2803, 2795, 2785, 2781])).
% 0.71/0.87 tff(2805,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2804, 2776])).
% 0.71/0.87 tff(2806,plain,((~(op(e0, e2) = e2)) | (op(e0, e0) = e0) | (e2 = op(e3, op(e3, e3))) | (op(e0, e0) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(2807,plain,
% 0.71/0.87 (~(op(e0, e2) = e2)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2806, 112, 1397, 4, 1677, 168])).
% 0.71/0.87 tff(2808,plain,
% 0.71/0.87 (op(e0, e3) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[164, 2807, 4, 112])).
% 0.71/0.87 tff(2809,plain,
% 0.71/0.87 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[134])).
% 0.71/0.87 tff(2810,plain,
% 0.71/0.87 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2809, 263])).
% 0.71/0.87 tff(2811,plain,
% 0.71/0.87 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2810])).
% 0.71/0.87 tff(2812,plain,
% 0.71/0.87 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2811])).
% 0.71/0.87 tff(2813,plain,
% 0.71/0.87 (~(op(e0, e3) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[272, 2812])).
% 0.71/0.87 tff(2814,plain,
% 0.71/0.87 (op(e0, e2) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[209, 2452, 168, 2813])).
% 0.71/0.87 tff(2815,plain,
% 0.71/0.87 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2814])).
% 0.71/0.87 tff(2816,plain,
% 0.71/0.87 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2815, 1])).
% 0.71/0.87 tff(2817,plain,
% 0.71/0.87 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2816])).
% 0.71/0.87 tff(2818,plain,
% 0.71/0.87 (~(op(e1, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2277, 2817])).
% 0.71/0.87 tff(2819,plain,
% 0.71/0.87 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2814])).
% 0.71/0.87 tff(2820,plain,
% 0.71/0.87 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2819])).
% 0.71/0.87 tff(2821,plain,
% 0.71/0.87 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2820])).
% 0.71/0.87 tff(2822,plain,
% 0.71/0.87 (~(op(e0, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[684, 2821])).
% 0.71/0.87 tff(2823,plain,
% 0.71/0.87 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[134])).
% 0.71/0.87 tff(2824,plain,
% 0.71/0.87 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2823, 695])).
% 0.71/0.87 tff(2825,plain,
% 0.71/0.87 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2824])).
% 0.71/0.87 tff(2826,plain,
% 0.71/0.87 (~(op(e1, e3) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1632, 2825])).
% 0.71/0.87 tff(2827,plain,
% 0.71/0.87 ((op(e0, e2) = op(e2, e2)) <=> (e0 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2814])).
% 0.71/0.87 tff(2828,plain,
% 0.71/0.87 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2827, 954])).
% 0.71/0.87 tff(2829,plain,
% 0.71/0.87 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2828])).
% 0.71/0.87 tff(2830,plain,
% 0.71/0.87 (~(op(e2, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[126, 2829])).
% 0.71/0.87 tff(2831,plain,
% 0.71/0.87 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[134])).
% 0.71/0.87 tff(2832,plain,
% 0.71/0.87 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[2831, 703])).
% 0.71/0.87 tff(2833,plain,
% 0.71/0.87 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2832])).
% 0.71/0.87 tff(2834,plain,
% 0.71/0.87 (~(op(e2, e3) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1909, 2833])).
% 0.71/0.87 tff(2835,plain,
% 0.71/0.87 ((op(e0, e2) = e1) <=> (e0 = e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2814])).
% 0.71/0.87 tff(2836,plain,
% 0.71/0.87 ((e0 = e1) <=> (op(e0, e2) = e1)),
% 0.71/0.87 inference(symmetry,[status(thm)],[2835])).
% 0.71/0.87 tff(2837,plain,
% 0.71/0.87 ((~(e0 = e1)) <=> (~(op(e0, e2) = e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2836])).
% 0.71/0.87 tff(2838,plain,
% 0.71/0.87 (~(op(e0, e2) = e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1182, 2837])).
% 0.71/0.87 tff(2839,assumption,(~(op(e1, e2) = e0)), introduced(assumption)).
% 0.71/0.87 tff(2840,plain,
% 0.71/0.87 (((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2841,plain,
% 0.71/0.87 ((((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2842,plain,
% 0.71/0.87 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(2843,plain,
% 0.71/0.87 (((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)) <=> (((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2842])).
% 0.71/0.87 tff(2844,plain,
% 0.71/0.87 (((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3))),
% 0.71/0.87 inference(transitivity,[status(thm)],[2843, 2841])).
% 0.71/0.87 tff(2845,plain,
% 0.71/0.87 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)),
% 0.71/0.87 inference(and_elim,[status(thm)],[248])).
% 0.71/0.87 tff(2846,plain,
% 0.71/0.87 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 0.71/0.87 tff(2847,plain,
% 0.71/0.87 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2846, 2840])).
% 0.71/0.87 tff(2848,plain,
% 0.71/0.87 (op(e2, e2) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2847, 6, 3, 1064])).
% 0.71/0.88 tff(2849,plain,
% 0.71/0.88 (e1 = op(e2, e2)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2848])).
% 0.71/0.88 tff(2850,plain,
% 0.71/0.88 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2849, 2849])).
% 0.71/0.88 tff(2851,plain,
% 0.71/0.88 (op(op(e2, e2), op(e2, e2)) = op(e1, e1)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2850])).
% 0.71/0.88 tff(2852,plain,
% 0.71/0.88 ((op(op(e2, e2), op(e2, e2)) = e2) <=> (op(e1, e1) = e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2851])).
% 0.71/0.88 tff(2853,plain,
% 0.71/0.88 ((op(e1, e1) = e2) <=> (op(op(e2, e2), op(e2, e2)) = e2)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2852])).
% 0.71/0.88 tff(2854,plain,
% 0.71/0.88 ((~(op(e1, e1) = e2)) <=> (~(op(op(e2, e2), op(e2, e2)) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2853])).
% 0.71/0.88 tff(2855,plain,
% 0.71/0.88 (~(op(op(e2, e2), op(e2, e2)) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1124, 2854])).
% 0.71/0.88 tff(2856,plain,
% 0.71/0.88 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[9, 2855])).
% 0.71/0.88 tff(2857,plain,
% 0.71/0.88 (op(e1, e2) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[2610, 2856, 1289, 3, 1064, 231, 2594, 1124])).
% 0.71/0.88 tff(2858,plain,
% 0.71/0.88 ((op(e1, e2) = e3) <=> (e2 = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2857])).
% 0.71/0.88 tff(2859,plain,
% 0.71/0.88 ((e2 = e3) <=> (op(e1, e2) = e3)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2858])).
% 0.71/0.88 tff(2860,plain,
% 0.71/0.88 ((~(e2 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2859])).
% 0.71/0.88 tff(2861,plain,
% 0.71/0.88 (~(op(e1, e2) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[195, 2860])).
% 0.71/0.88 tff(2862,plain,
% 0.71/0.88 (op(e3, e2) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[520, 2861, 1396, 6])).
% 0.71/0.88 tff(2863,plain,
% 0.71/0.88 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[467, 2862, 418])).
% 0.71/0.88 tff(2864,plain,
% 0.71/0.88 (op(op(e1, e2), op(e1, e2)) = op(e2, e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2857, 2857])).
% 0.71/0.88 tff(2865,plain,
% 0.71/0.88 ((op(op(e1, e2), op(e1, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2864])).
% 0.71/0.88 tff(2866,plain,
% 0.71/0.88 ((op(e2, e2) = e2) <=> (op(op(e1, e2), op(e1, e2)) = e2)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2865])).
% 0.71/0.88 tff(2867,plain,
% 0.71/0.88 ((~(op(e2, e2) = e2)) <=> (~(op(op(e1, e2), op(e1, e2)) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2866])).
% 0.71/0.88 tff(2868,plain,
% 0.71/0.88 (~(op(op(e1, e2), op(e1, e2)) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3, 2867])).
% 0.71/0.88 tff(2869,plain,
% 0.71/0.88 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[419, 2868])).
% 0.71/0.88 tff(2870,plain,
% 0.71/0.88 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[416, 2869, 1289, 2856])).
% 0.71/0.88 tff(2871,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[459, 2870, 2863])).
% 0.71/0.88 tff(2872,plain,((op(e1, e1) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (op(e3, e3) = e2) | (op(e0, e2) = e3) | (op(e2, e2) = e3) | (op(e2, e2) = e2) | (op(e2, e2) = e0) | (op(e0, e2) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(2873,plain,
% 0.71/0.88 (op(e1, e1) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[2872, 6, 418, 1396, 1289, 3, 1064, 231, 2594])).
% 0.71/0.88 tff(2874,plain,
% 0.71/0.88 (e2 = op(e1, e1)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[2873, 529])).
% 0.71/0.88 tff(2875,plain,
% 0.71/0.88 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2873])).
% 0.71/0.88 tff(2876,plain,
% 0.71/0.88 ((e3 = op(e1, op(e1, e1))) <=> (e3 = op(e1, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2875])).
% 0.71/0.88 tff(2877,plain,
% 0.71/0.88 ((e3 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[2876, 531])).
% 0.71/0.88 tff(2878,plain,
% 0.71/0.88 ((op(e1, e2) = e3) <=> (e3 = op(e1, op(e1, e1)))),
% 0.71/0.88 inference(symmetry,[status(thm)],[2877])).
% 0.71/0.88 tff(2879,plain,
% 0.71/0.88 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e2, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2849])).
% 0.71/0.88 tff(2880,plain,
% 0.71/0.88 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2879])).
% 0.71/0.88 tff(2881,plain,
% 0.71/0.88 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2880])).
% 0.71/0.88 tff(2882,plain,
% 0.71/0.88 (~(op(e1, e2) = e1)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[331, 2881])).
% 0.71/0.88 tff(2883,plain,
% 0.71/0.88 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2873])).
% 0.71/0.88 tff(2884,plain,
% 0.71/0.88 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.88 inference(transitivity,[status(thm)],[2883, 421])).
% 0.71/0.88 tff(2885,plain,
% 0.71/0.88 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2884])).
% 0.71/0.88 tff(2886,plain,
% 0.71/0.88 (~(op(e1, e2) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[427, 2885])).
% 0.71/0.88 tff(2887,plain,
% 0.71/0.88 (op(e1, e2) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[449, 2886, 2839, 2882])).
% 0.71/0.88 tff(2888,plain,
% 0.71/0.88 (e3 = op(e1, op(e1, e1))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[2887, 2878])).
% 0.71/0.88 tff(2889,plain,
% 0.71/0.88 (op(e1, op(e1, e1)) = e3),
% 0.71/0.88 inference(transitivity,[status(thm)],[2875, 2887])).
% 0.71/0.88 tff(2890,plain,
% 0.71/0.88 (op(op(e1, op(e1, e1)), e1) = op(e3, e1)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2889])).
% 0.71/0.88 tff(2891,plain,
% 0.71/0.88 (op(e3, e1) = op(op(e1, op(e1, e1)), e1)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2890])).
% 0.71/0.88 tff(2892,plain,
% 0.71/0.88 (op(e2, e1) = op(e2, op(e2, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2849])).
% 0.71/0.88 tff(2893,plain,
% 0.71/0.88 ((op(e2, e1) = e0) <=> (op(e2, op(e2, e2)) = e0)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2892])).
% 0.71/0.88 tff(2894,plain,
% 0.71/0.88 ((op(e2, e1) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[2893, 1682])).
% 0.71/0.88 tff(2895,plain,
% 0.71/0.88 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e0)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2894])).
% 0.71/0.88 tff(2896,plain,
% 0.71/0.88 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e1) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2895])).
% 0.71/0.88 tff(2897,plain,
% 0.71/0.88 (~(op(e2, e1) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1677, 2896])).
% 0.71/0.88 tff(2898,plain,
% 0.71/0.88 ((op(e1, e1) = e0) <=> (e2 = e0)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2873])).
% 0.71/0.88 tff(2899,plain,
% 0.71/0.88 ((op(e1, e1) = e0) <=> (e0 = e2)),
% 0.71/0.88 inference(transitivity,[status(thm)],[2898, 263])).
% 0.71/0.88 tff(2900,plain,
% 0.71/0.88 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 0.71/0.88 inference(symmetry,[status(thm)],[2899])).
% 0.71/0.88 tff(2901,plain,
% 0.71/0.88 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.88 tff(2902,plain,
% 0.71/0.88 (~(op(e1, e1) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[272, 2901])).
% 0.71/0.88 tff(2903,plain,
% 0.71/0.88 (((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(2904,plain,
% 0.71/0.88 ((((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(2905,plain,
% 0.71/0.88 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(2906,plain,
% 0.71/0.88 (((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)) <=> (((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[2905])).
% 0.71/0.88 tff(2907,plain,
% 0.71/0.88 (((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0))),
% 0.71/0.88 inference(transitivity,[status(thm)],[2906, 2904])).
% 0.71/0.88 tff(2908,plain,
% 0.71/0.88 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)),
% 0.71/0.88 inference(and_elim,[status(thm)],[156])).
% 0.71/0.88 tff(2909,plain,
% 0.71/0.88 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 0.74/0.88 tff(2910,plain,
% 0.74/0.88 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[2909, 2903])).
% 0.74/0.88 tff(2911,plain,
% 0.74/0.88 (op(e3, e1) = e0),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[2910, 2902, 2452, 2897])).
% 0.74/0.88 tff(2912,plain,
% 0.74/0.88 (e0 = op(e3, e1)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2911])).
% 0.74/0.88 tff(2913,plain,
% 0.74/0.88 (e0 = op(op(e1, op(e1, e1)), e1)),
% 0.74/0.88 inference(transitivity,[status(thm)],[2912, 2891])).
% 0.74/0.88 tff(2914,plain,
% 0.74/0.88 ($false),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[545, 2913, 2888, 2874])).
% 0.74/0.88 tff(2915,plain,((op(e2, e2) = e3) | (op(e1, e2) = e0) | (op(e0, e1) = e0) | (op(e3, e3) = e2) | (op(e0, e2) = e3) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (op(e2, e2) = e2) | (op(e2, e2) = e0) | (op(e0, e2) = e2) | (op(e1, e3) = e2) | (e0 = op(e2, op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.88 tff(2916,plain,
% 0.74/0.88 (op(e2, e2) = e3),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[2915, 3, 2452, 418, 1396, 1289, 2839, 1064, 231, 2594, 1677])).
% 0.74/0.88 tff(2917,plain,
% 0.74/0.88 (e3 = op(e2, e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2916])).
% 0.74/0.88 tff(2918,plain,
% 0.74/0.88 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2917, 2917])).
% 0.74/0.88 tff(2919,plain,
% 0.74/0.88 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2918])).
% 0.74/0.88 tff(2920,plain,
% 0.74/0.88 ((op(op(e2, e2), op(e2, e2)) = e2) <=> (op(e3, e3) = e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2919])).
% 0.74/0.88 tff(2921,plain,
% 0.74/0.88 ((op(e3, e3) = e2) <=> (op(op(e2, e2), op(e2, e2)) = e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2920])).
% 0.74/0.88 tff(2922,plain,
% 0.74/0.88 ((~(op(e3, e3) = e2)) <=> (~(op(op(e2, e2), op(e2, e2)) = e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2921])).
% 0.74/0.88 tff(2923,plain,
% 0.74/0.88 (~(op(op(e2, e2), op(e2, e2)) = e2)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[418, 2922])).
% 0.74/0.88 tff(2924,plain,
% 0.74/0.88 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[9, 2923])).
% 0.74/0.88 tff(2925,plain,
% 0.74/0.88 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2917])).
% 0.74/0.88 tff(2926,plain,
% 0.74/0.88 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e2, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2917])).
% 0.74/0.88 tff(2927,plain,
% 0.74/0.88 ((op(e2, e3) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 0.74/0.88 inference(transitivity,[status(thm)],[2926, 1281])).
% 0.74/0.88 tff(2928,plain,
% 0.74/0.88 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2927])).
% 0.74/0.88 tff(2929,plain,
% 0.74/0.88 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2928])).
% 0.74/0.88 tff(2930,plain,
% 0.74/0.88 (~(op(e2, e3) = e3)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[709, 2929])).
% 0.74/0.88 tff(2931,plain,
% 0.74/0.88 ((op(e2, e3) = e0) <=> (op(e2, op(e2, e2)) = e0)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2925])).
% 0.74/0.88 tff(2932,plain,
% 0.74/0.88 ((op(e2, e3) = e0) <=> (e0 = op(e2, op(e2, e2)))),
% 0.74/0.88 inference(transitivity,[status(thm)],[2931, 1682])).
% 0.74/0.88 tff(2933,plain,
% 0.74/0.88 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e3) = e0)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2932])).
% 0.74/0.88 tff(2934,plain,
% 0.74/0.88 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e3) = e0))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2933])).
% 0.74/0.88 tff(2935,plain,
% 0.74/0.88 (~(op(e2, e3) = e0)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[1677, 2934])).
% 0.74/0.88 tff(2936,plain,
% 0.74/0.88 (op(e2, e3) = e1),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[903, 2935, 1896, 2930])).
% 0.74/0.88 tff(2937,plain,
% 0.74/0.88 (e1 = op(e2, e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2936])).
% 0.74/0.88 tff(2938,plain,
% 0.74/0.88 (e1 = op(e2, op(e2, e2))),
% 0.74/0.88 inference(transitivity,[status(thm)],[2937, 2925])).
% 0.74/0.88 tff(2939,plain,
% 0.74/0.88 (op(e1, e2) = e2),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[2610, 1124, 1289, 3, 1064, 231, 2594, 1288])).
% 0.74/0.88 tff(2940,plain,
% 0.74/0.88 (op(op(e1, e2), op(e1, e2)) = op(e2, e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2939, 2939])).
% 0.74/0.88 tff(2941,plain,
% 0.74/0.88 ((op(op(e1, e2), op(e1, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2940])).
% 0.74/0.88 tff(2942,plain,
% 0.74/0.88 ((op(e2, e2) = e2) <=> (op(op(e1, e2), op(e1, e2)) = e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2941])).
% 0.74/0.88 tff(2943,plain,
% 0.74/0.88 ((~(op(e2, e2) = e2)) <=> (~(op(op(e1, e2), op(e1, e2)) = e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2942])).
% 0.74/0.88 tff(2944,plain,
% 0.74/0.88 (~(op(op(e1, e2), op(e1, e2)) = e2)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[3, 2943])).
% 0.74/0.88 tff(2945,plain,
% 0.74/0.88 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[419, 2944])).
% 0.74/0.88 tff(2946,plain,
% 0.74/0.88 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[416, 2945, 1289, 1288])).
% 0.74/0.88 tff(2947,plain,
% 0.74/0.88 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[459, 2946])).
% 0.74/0.88 tff(2948,plain,
% 0.74/0.88 ((e1 = e3) <=> (e1 = op(e2, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[944])).
% 0.74/0.88 tff(2949,plain,
% 0.74/0.88 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 0.74/0.88 inference(transitivity,[status(thm)],[2948, 1703])).
% 0.74/0.88 tff(2950,plain,
% 0.74/0.88 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2949])).
% 0.74/0.88 tff(2951,plain,
% 0.74/0.88 (~(op(e2, e2) = e1)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[665, 2950])).
% 0.74/0.88 tff(2952,plain,
% 0.74/0.88 ((op(op(e2, op(e2, e2)), e2) = e1) <=> (e1 = op(op(e2, op(e2, e2)), e2))),
% 0.74/0.88 inference(commutativity,[status(thm)],[])).
% 0.74/0.88 tff(2953,assumption,(op(e2, e3) = e1), introduced(assumption)).
% 0.74/0.88 tff(2954,plain,
% 0.74/0.88 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[944])).
% 0.74/0.88 tff(2955,plain,
% 0.74/0.88 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2954])).
% 0.74/0.88 tff(2956,plain,
% 0.74/0.88 (op(e2, op(e2, e2)) = e1),
% 0.74/0.88 inference(transitivity,[status(thm)],[2955, 2953])).
% 0.74/0.88 tff(2957,plain,
% 0.74/0.88 (op(op(e2, op(e2, e2)), e2) = op(e1, e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2956])).
% 0.74/0.88 tff(2958,plain,
% 0.74/0.88 (op(e1, e2) = op(op(e2, op(e2, e2)), e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2957])).
% 0.74/0.88 tff(2959,plain,
% 0.74/0.88 ((op(e1, e2) = e1) <=> (op(op(e2, op(e2, e2)), e2) = e1)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2958])).
% 0.74/0.88 tff(2960,plain,
% 0.74/0.88 ((op(e1, e2) = e1) <=> (e1 = op(op(e2, op(e2, e2)), e2))),
% 0.74/0.88 inference(transitivity,[status(thm)],[2959, 2952])).
% 0.74/0.88 tff(2961,plain,
% 0.74/0.88 ((e1 = op(op(e2, op(e2, e2)), e2)) <=> (op(e1, e2) = e1)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2960])).
% 0.74/0.88 tff(2962,plain,
% 0.74/0.88 (op(op(e2, op(e2, e2)), e2) = e2),
% 0.74/0.88 inference(transitivity,[status(thm)],[2957, 2939])).
% 0.74/0.88 tff(2963,plain,
% 0.74/0.88 (e1 = op(e2, e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2953])).
% 0.74/0.88 tff(2964,plain,
% 0.74/0.88 ((e1 = op(op(e2, op(e2, e2)), e2)) <=> (op(e2, e3) = e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2963, 2962])).
% 0.74/0.88 tff(2965,plain,
% 0.74/0.88 ((op(e2, e3) = e2) <=> (e1 = op(op(e2, op(e2, e2)), e2))),
% 0.74/0.88 inference(symmetry,[status(thm)],[2964])).
% 0.74/0.88 tff(2966,plain,
% 0.74/0.88 ((op(e2, e3) = e2) <=> (op(e1, e2) = e1)),
% 0.74/0.88 inference(transitivity,[status(thm)],[2965, 2961])).
% 0.74/0.88 tff(2967,plain,
% 0.74/0.88 ((~(op(e2, e3) = e2)) <=> (~(op(e1, e2) = e1))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2966])).
% 0.74/0.88 tff(2968,plain,
% 0.74/0.88 (~(op(e1, e2) = e1)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[1896, 2967])).
% 0.74/0.88 tff(2969,plain,
% 0.74/0.88 (op(e3, e2) = e1),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[1331, 2968, 1398, 2951])).
% 0.74/0.88 tff(2970,plain,
% 0.74/0.88 (e1 = op(e3, e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2969])).
% 0.74/0.88 tff(2971,plain,
% 0.74/0.88 (op(e2, e3) = op(e3, e2)),
% 0.74/0.88 inference(transitivity,[status(thm)],[2953, 2970])).
% 0.74/0.88 tff(2972,plain,
% 0.74/0.88 (op(op(e2, e3), op(e2, e3)) = op(op(e3, e2), op(e3, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2971, 2971])).
% 0.74/0.88 tff(2973,plain,
% 0.74/0.88 (op(e1, e1) = op(op(e2, e3), op(e2, e3))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2963, 2963])).
% 0.74/0.88 tff(2974,plain,
% 0.74/0.88 (op(e1, e1) = e2),
% 0.74/0.88 inference(transitivity,[status(thm)],[2973, 2972, 2947])).
% 0.74/0.88 tff(2975,plain,
% 0.74/0.88 ($false),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[1124, 2974])).
% 0.74/0.88 tff(2976,plain,((op(e1, e1) = e2) | (~(op(e2, e3) = e1)) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e0, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e3) = e2) | (~(op(e2, e2) = e3)) | (op(e2, e2) = e0) | (op(e0, e2) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.88 tff(2977,plain,
% 0.74/0.88 (op(e1, e1) = e2),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[2976, 2936, 1289, 2924, 1398, 3, 1896, 2916, 1064, 231, 2594])).
% 0.74/0.88 tff(2978,plain,
% 0.74/0.88 (op(op(e1, e1), op(e1, e1)) = op(e2, e2)),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2977, 2977])).
% 0.74/0.88 tff(2979,plain,
% 0.74/0.88 (op(op(e1, e1), op(e1, e1)) = e3),
% 0.74/0.88 inference(transitivity,[status(thm)],[2978, 2916])).
% 0.74/0.88 tff(2980,plain,
% 0.74/0.88 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (e3 = op(e2, op(e2, e2)))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2979, 2938])).
% 0.74/0.88 tff(2981,plain,
% 0.74/0.88 ((e3 = op(e2, op(e2, e2))) <=> (op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2980])).
% 0.74/0.88 tff(2982,plain,
% 0.74/0.88 ((~(e3 = op(e2, op(e2, e2)))) <=> (~(op(op(e1, e1), op(e1, e1)) = e1))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2981])).
% 0.74/0.88 tff(2983,plain,
% 0.74/0.88 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2925])).
% 0.74/0.88 tff(2984,plain,
% 0.74/0.88 ((e3 = op(e2, op(e2, e2))) <=> (op(e2, e2) = op(e2, e3))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2917, 2983])).
% 0.74/0.88 tff(2985,plain,
% 0.74/0.88 ((op(e2, e2) = op(e2, e3)) <=> (e3 = op(e2, op(e2, e2)))),
% 0.74/0.88 inference(symmetry,[status(thm)],[2984])).
% 0.74/0.88 tff(2986,plain,
% 0.74/0.88 ((~(op(e2, e2) = op(e2, e3))) <=> (~(e3 = op(e2, op(e2, e2))))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2985])).
% 0.74/0.88 tff(2987,plain,
% 0.74/0.88 (~(e3 = op(e2, op(e2, e2)))),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[709, 2986])).
% 0.74/0.88 tff(2988,plain,
% 0.74/0.88 (~(op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[2987, 2982])).
% 0.74/0.88 tff(2989,plain,
% 0.74/0.88 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[316, 2988])).
% 0.74/0.88 tff(2990,plain,
% 0.74/0.88 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[416, 2989, 1289, 2924])).
% 0.74/0.88 tff(2991,plain,
% 0.74/0.88 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[459, 2990])).
% 0.74/0.88 tff(2992,plain,
% 0.74/0.88 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2977])).
% 0.74/0.88 tff(2993,plain,
% 0.74/0.88 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.74/0.88 inference(transitivity,[status(thm)],[2992, 421])).
% 0.74/0.88 tff(2994,plain,
% 0.74/0.88 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2993])).
% 0.74/0.88 tff(2995,plain,
% 0.74/0.88 (~(op(e1, e2) = e2)),
% 0.74/0.88 inference(modus_ponens,[status(thm)],[427, 2994])).
% 0.74/0.88 tff(2996,plain,
% 0.74/0.88 (op(e3, e2) = e2),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[507, 2995, 231, 3])).
% 0.74/0.88 tff(2997,plain,
% 0.74/0.88 (e2 = op(e3, e2)),
% 0.74/0.88 inference(symmetry,[status(thm)],[2996])).
% 0.74/0.88 tff(2998,plain,
% 0.74/0.88 (op(e2, e2) = op(op(e3, e2), op(e3, e2))),
% 0.74/0.88 inference(monotonicity,[status(thm)],[2997, 2997])).
% 0.74/0.88 tff(2999,plain,
% 0.74/0.88 (op(e2, e2) = e2),
% 0.74/0.88 inference(transitivity,[status(thm)],[2998, 2991])).
% 0.74/0.88 tff(3000,plain,
% 0.74/0.88 ($false),
% 0.74/0.88 inference(unit_resolution,[status(thm)],[3, 2999])).
% 0.74/0.88 tff(3001,plain,((op(e2, e2) = e2) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (op(e0, e2) = e2) | (op(e0, e2) = e1) | (op(e2, e3) = e2) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e3, e3) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e0, e1) = e0) | (op(e0, e2) = e3) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.89 tff(3002,plain,
% 0.74/0.89 (op(e2, e2) = e2),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3001, 2838, 231, 1401, 2834, 2830, 2826, 824, 1677, 2452, 2822, 2818])).
% 0.74/0.89 tff(3003,plain,
% 0.74/0.89 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[134])).
% 0.74/0.89 tff(3004,plain,
% 0.74/0.89 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3003, 319])).
% 0.74/0.89 tff(3005,plain,
% 0.74/0.89 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3004])).
% 0.74/0.89 tff(3006,plain,
% 0.74/0.89 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3005])).
% 0.74/0.89 tff(3007,plain,
% 0.74/0.89 (~(op(e0, e3) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[220, 3006])).
% 0.74/0.89 tff(3008,plain,
% 0.74/0.89 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[134])).
% 0.74/0.89 tff(3009,plain,
% 0.74/0.89 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3008])).
% 0.74/0.89 tff(3010,plain,
% 0.74/0.89 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3009])).
% 0.74/0.89 tff(3011,plain,
% 0.74/0.89 (~(op(e0, e3) = e3)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[195, 3010])).
% 0.74/0.89 tff(3012,plain,
% 0.74/0.89 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[1301])).
% 0.74/0.89 tff(3013,plain,
% 0.74/0.89 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3012])).
% 0.74/0.89 tff(3014,plain,
% 0.74/0.89 (~(op(e2, e1) = e2)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1695, 3013])).
% 0.74/0.89 tff(3015,plain,
% 0.74/0.89 (op(e3, e1) = e2),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1410, 1124, 112, 3014])).
% 0.74/0.89 tff(3016,plain,
% 0.74/0.89 (op(op(e3, e1), op(e3, e1)) = op(e2, e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3015, 3015])).
% 0.74/0.89 tff(3017,plain,
% 0.74/0.89 (op(op(e3, e1), op(e3, e1)) = e2),
% 0.74/0.89 inference(transitivity,[status(thm)],[3016, 1301])).
% 0.74/0.89 tff(3018,plain,
% 0.74/0.89 ((op(op(e3, e1), op(e3, e1)) = e1) <=> (e2 = e1)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3017])).
% 0.74/0.89 tff(3019,plain,
% 0.74/0.89 ((op(op(e3, e1), op(e3, e1)) = e1) <=> (e1 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3018, 319])).
% 0.74/0.89 tff(3020,plain,
% 0.74/0.89 ((e1 = e2) <=> (op(op(e3, e1), op(e3, e1)) = e1)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3019])).
% 0.74/0.89 tff(3021,plain,
% 0.74/0.89 ((~(e1 = e2)) <=> (~(op(op(e3, e1), op(e3, e1)) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3020])).
% 0.74/0.89 tff(3022,plain,
% 0.74/0.89 (~(op(op(e3, e1), op(e3, e1)) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[220, 3021])).
% 0.74/0.89 tff(3023,plain,
% 0.74/0.89 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[478, 3022])).
% 0.74/0.89 tff(3024,plain,
% 0.74/0.89 (op(e1, e0) = e2),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1239, 1124, 2594, 1304])).
% 0.74/0.89 tff(3025,plain,
% 0.74/0.89 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3024, 3024])).
% 0.74/0.89 tff(3026,plain,
% 0.74/0.89 (op(op(e1, e0), op(e1, e0)) = e2),
% 0.74/0.89 inference(transitivity,[status(thm)],[3025, 1301])).
% 0.74/0.89 tff(3027,plain,
% 0.74/0.89 ((op(op(e1, e0), op(e1, e0)) = e0) <=> (e2 = e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3026])).
% 0.74/0.89 tff(3028,plain,
% 0.74/0.89 ((op(op(e1, e0), op(e1, e0)) = e0) <=> (e0 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3027, 263])).
% 0.74/0.89 tff(3029,plain,
% 0.74/0.89 ((e0 = e2) <=> (op(op(e1, e0), op(e1, e0)) = e0)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3028])).
% 0.74/0.89 tff(3030,plain,
% 0.74/0.89 ((~(e0 = e2)) <=> (~(op(op(e1, e0), op(e1, e0)) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3029])).
% 0.74/0.89 tff(3031,plain,
% 0.74/0.89 (~(op(op(e1, e0), op(e1, e0)) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[272, 3030])).
% 0.74/0.89 tff(3032,plain,
% 0.74/0.89 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[333, 3031])).
% 0.74/0.89 tff(3033,plain,
% 0.74/0.89 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[416, 3032, 1289, 3023])).
% 0.74/0.89 tff(3034,plain,
% 0.74/0.89 (op(op(e2, e3), op(e2, e3)) = e3),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[14, 3033])).
% 0.74/0.89 tff(3035,plain,
% 0.74/0.89 (e2 = op(e2, e2)),
% 0.74/0.89 inference(symmetry,[status(thm)],[1301])).
% 0.74/0.89 tff(3036,plain,
% 0.74/0.89 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3035])).
% 0.74/0.89 tff(3037,plain,
% 0.74/0.89 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3036])).
% 0.74/0.89 tff(3038,plain,
% 0.74/0.89 (~(op(e2, e2) = e3)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[195, 3037])).
% 0.74/0.89 tff(3039,plain,
% 0.74/0.89 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[1301])).
% 0.74/0.89 tff(3040,plain,
% 0.74/0.89 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3039, 378])).
% 0.74/0.89 tff(3041,plain,
% 0.74/0.89 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3040])).
% 0.74/0.89 tff(3042,plain,
% 0.74/0.89 (~(op(e3, e2) = e2)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[591, 3041])).
% 0.74/0.89 tff(3043,plain,
% 0.74/0.89 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3015])).
% 0.74/0.89 tff(3044,plain,
% 0.74/0.89 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3043])).
% 0.74/0.89 tff(3045,plain,
% 0.74/0.89 (~(op(e3, e0) = e2)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1423, 3044])).
% 0.74/0.89 tff(3046,assumption,(~(op(e0, e3) = e1)), introduced(assumption)).
% 0.74/0.89 tff(3047,plain,
% 0.74/0.89 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3024])).
% 0.74/0.89 tff(3048,plain,
% 0.74/0.89 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3047, 263])).
% 0.74/0.89 tff(3049,plain,
% 0.74/0.89 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3048])).
% 0.74/0.89 tff(3050,plain,
% 0.74/0.89 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3049])).
% 0.74/0.89 tff(3051,plain,
% 0.74/0.89 (~(op(e1, e0) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[272, 3050])).
% 0.74/0.89 tff(3052,plain,
% 0.74/0.89 ((e1 = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.74/0.89 inference(commutativity,[status(thm)],[])).
% 0.74/0.89 tff(3053,assumption,(~(op(e1, e2) = e3)), introduced(assumption)).
% 0.74/0.89 tff(3054,plain,
% 0.74/0.89 (op(e1, e2) = e1),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[449, 3053, 2839, 977])).
% 0.74/0.89 tff(3055,plain,
% 0.74/0.89 ((op(e1, e2) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3054])).
% 0.74/0.89 tff(3056,plain,
% 0.74/0.89 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3055, 3052])).
% 0.74/0.89 tff(3057,plain,
% 0.74/0.89 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3056])).
% 0.74/0.89 tff(3058,plain,
% 0.74/0.89 (~(op(e1, e3) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[2514, 3057])).
% 0.74/0.89 tff(3059,plain,
% 0.74/0.89 ((e3 = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.74/0.89 inference(commutativity,[status(thm)],[])).
% 0.74/0.89 tff(3060,plain,
% 0.74/0.89 (op(e3, e2) = e3),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[520, 3053, 1396, 6])).
% 0.74/0.89 tff(3061,plain,
% 0.74/0.89 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3060])).
% 0.74/0.89 tff(3062,plain,
% 0.74/0.89 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3061, 3059])).
% 0.74/0.89 tff(3063,plain,
% 0.74/0.89 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3062])).
% 0.74/0.89 tff(3064,plain,
% 0.74/0.89 (~(op(e3, e3) = e3)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1166, 3063])).
% 0.74/0.89 tff(3065,plain,
% 0.74/0.89 (op(e3, e3) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1433, 3064, 418, 1428, 1397, 483])).
% 0.74/0.89 tff(3066,plain,
% 0.74/0.89 ((op(e3, e3) = e1) <=> (e0 = e1)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3065])).
% 0.74/0.89 tff(3067,plain,
% 0.74/0.89 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3066])).
% 0.74/0.89 tff(3068,plain,
% 0.74/0.89 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3067])).
% 0.74/0.89 tff(3069,plain,
% 0.74/0.89 (~(op(e3, e3) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1182, 3068])).
% 0.74/0.89 tff(3070,plain,
% 0.74/0.89 (((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.74/0.89 inference(rewrite,[status(thm)],[])).
% 0.74/0.89 tff(3071,plain,
% 0.74/0.89 ((((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.74/0.89 inference(rewrite,[status(thm)],[])).
% 0.74/0.89 tff(3072,plain,
% 0.74/0.89 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1))),
% 0.74/0.89 inference(rewrite,[status(thm)],[])).
% 0.74/0.89 tff(3073,plain,
% 0.74/0.89 (((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> (((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3072])).
% 0.74/0.89 tff(3074,plain,
% 0.74/0.89 (((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.74/0.89 inference(transitivity,[status(thm)],[3073, 3071])).
% 0.74/0.89 tff(3075,plain,
% 0.74/0.89 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)),
% 0.74/0.89 inference(and_elim,[status(thm)],[33])).
% 0.74/0.89 tff(3076,plain,
% 0.74/0.89 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 0.74/0.89 tff(3077,plain,
% 0.74/0.89 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[3076, 3070])).
% 0.74/0.89 tff(3078,plain,
% 0.74/0.89 (op(e2, e3) = e1),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3077, 3069, 3046, 3058])).
% 0.74/0.89 tff(3079,plain,
% 0.74/0.89 (op(op(e2, e3), op(e2, e3)) = op(e1, e1)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3078, 3078])).
% 0.74/0.89 tff(3080,plain,
% 0.74/0.89 (op(e1, e1) = op(op(e2, e3), op(e2, e3))),
% 0.74/0.89 inference(symmetry,[status(thm)],[3079])).
% 0.74/0.89 tff(3081,assumption,(~(op(e1, e0) = e0)), introduced(assumption)).
% 0.74/0.89 tff(3082,plain,
% 0.74/0.89 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3065])).
% 0.74/0.89 tff(3083,plain,
% 0.74/0.89 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3082])).
% 0.74/0.89 tff(3084,plain,
% 0.74/0.89 (~(op(e1, e3) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1442, 3083])).
% 0.74/0.89 tff(3085,plain,
% 0.74/0.89 (op(e1, e1) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1475, 3084, 2839, 3081])).
% 0.74/0.89 tff(3086,plain,
% 0.74/0.89 (e0 = op(e1, e1)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3085])).
% 0.74/0.89 tff(3087,plain,
% 0.74/0.89 (e0 = e3),
% 0.74/0.89 inference(transitivity,[status(thm)],[3086, 3080, 16])).
% 0.74/0.89 tff(3088,plain,
% 0.74/0.89 ($false),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[684, 3087])).
% 0.74/0.89 tff(3089,plain,((op(e1, e2) = e3) | (~(op(op(e2, e3), op(e2, e3)) = e3)) | (op(e1, e2) = e0) | (op(e1, e0) = e0) | (op(e0, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e3, e2) = e2) | (op(e1, e2) = e2) | (op(e0, e2) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.89 tff(3090,plain,
% 0.74/0.89 (op(e1, e2) = e3),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3089, 3034, 2839, 3051, 3046, 418, 3045, 1397, 3042, 1304, 1396, 3038])).
% 0.74/0.89 tff(3091,plain,
% 0.74/0.89 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3090])).
% 0.74/0.89 tff(3092,plain,
% 0.74/0.89 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3091, 2507])).
% 0.74/0.89 tff(3093,plain,
% 0.74/0.89 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3092])).
% 0.74/0.89 tff(3094,plain,
% 0.74/0.89 (~(op(e1, e3) = e3)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[2514, 3093])).
% 0.74/0.89 tff(3095,plain,
% 0.74/0.89 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[11, 3033])).
% 0.74/0.89 tff(3096,plain,
% 0.74/0.89 (op(op(e2, e0), op(e2, e0)) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[46, 3033])).
% 0.74/0.89 tff(3097,plain,
% 0.74/0.89 (~(op(e3, e3) = e3)),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[686, 3096, 3038, 3095])).
% 0.74/0.89 tff(3098,plain,
% 0.74/0.89 (op(e2, e3) = e3),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1931, 3097, 1919, 3094])).
% 0.74/0.89 tff(3099,plain,
% 0.74/0.89 (op(op(e2, e3), op(e2, e3)) = op(e3, e3)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3098, 3098])).
% 0.74/0.89 tff(3100,plain,
% 0.74/0.89 (op(e3, e3) = op(op(e2, e3), op(e2, e3))),
% 0.74/0.89 inference(symmetry,[status(thm)],[3099])).
% 0.74/0.89 tff(3101,plain,
% 0.74/0.89 (op(e3, e3) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1433, 3097, 418, 3045, 1397, 3042])).
% 0.74/0.89 tff(3102,plain,
% 0.74/0.89 (e0 = op(e3, e3)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3101])).
% 0.74/0.89 tff(3103,plain,
% 0.74/0.89 (e0 = e3),
% 0.74/0.89 inference(transitivity,[status(thm)],[3102, 3100, 3034])).
% 0.74/0.89 tff(3104,plain,
% 0.74/0.89 ($false),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[684, 3103])).
% 0.74/0.89 tff(3105,plain,((op(e1, e1) = e2) | (op(e0, e3) = e3) | (op(e3, e3) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e1, e2) = e0) | (op(e0, e3) = e1) | (op(e0, e2) = e3) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~(op(e2, e2) = e2)) | (op(e1, e3) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.89 tff(3106,plain,
% 0.74/0.89 (op(e1, e1) = e2),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3105, 2818, 824, 1397, 3011, 3007, 2822, 1401, 3002, 2826, 112])).
% 0.74/0.89 tff(3107,plain,
% 0.74/0.89 (op(op(e1, e1), op(e1, e1)) = op(e2, e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3106, 3106])).
% 0.74/0.89 tff(3108,plain,
% 0.74/0.89 (op(op(e1, e1), op(e1, e1)) = e2),
% 0.74/0.89 inference(transitivity,[status(thm)],[3107, 3002])).
% 0.74/0.89 tff(3109,plain,
% 0.74/0.89 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (e2 = e1)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3108])).
% 0.74/0.89 tff(3110,plain,
% 0.74/0.89 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (e1 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3109, 319])).
% 0.74/0.89 tff(3111,plain,
% 0.74/0.89 ((e1 = e2) <=> (op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3110])).
% 0.74/0.89 tff(3112,plain,
% 0.74/0.89 ((~(e1 = e2)) <=> (~(op(op(e1, e1), op(e1, e1)) = e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3111])).
% 0.74/0.89 tff(3113,plain,
% 0.74/0.89 (~(op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[220, 3112])).
% 0.74/0.89 tff(3114,plain,
% 0.74/0.89 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[316, 3113])).
% 0.74/0.89 tff(3115,plain,
% 0.74/0.89 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3002])).
% 0.74/0.89 tff(3116,plain,
% 0.74/0.89 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3115, 378])).
% 0.74/0.89 tff(3117,plain,
% 0.74/0.89 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3116])).
% 0.74/0.89 tff(3118,plain,
% 0.74/0.89 (~(op(e3, e2) = e2)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[591, 3117])).
% 0.74/0.89 tff(3119,plain,
% 0.74/0.89 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3106])).
% 0.74/0.89 tff(3120,plain,
% 0.74/0.89 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3119, 370])).
% 0.74/0.89 tff(3121,plain,
% 0.74/0.89 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3120])).
% 0.74/0.89 tff(3122,plain,
% 0.74/0.89 (~(op(e3, e1) = e2)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[376, 3121])).
% 0.74/0.89 tff(3123,plain,
% 0.74/0.89 (op(e3, e0) = e2),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[566, 3122, 824, 3118])).
% 0.74/0.89 tff(3124,plain,
% 0.74/0.89 (op(op(e3, e0), op(e3, e0)) = op(e2, e2)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3123, 3123])).
% 0.74/0.89 tff(3125,plain,
% 0.74/0.89 (op(op(e3, e0), op(e3, e0)) = e2),
% 0.74/0.89 inference(transitivity,[status(thm)],[3124, 3002])).
% 0.74/0.89 tff(3126,plain,
% 0.74/0.89 ((op(op(e3, e0), op(e3, e0)) = e0) <=> (e2 = e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3125])).
% 0.74/0.89 tff(3127,plain,
% 0.74/0.89 ((op(op(e3, e0), op(e3, e0)) = e0) <=> (e0 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3126, 263])).
% 0.74/0.89 tff(3128,plain,
% 0.74/0.89 ((e0 = e2) <=> (op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3127])).
% 0.74/0.89 tff(3129,plain,
% 0.74/0.89 ((~(e0 = e2)) <=> (~(op(op(e3, e0), op(e3, e0)) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3128])).
% 0.74/0.89 tff(3130,plain,
% 0.74/0.89 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[272, 3129])).
% 0.74/0.89 tff(3131,plain,
% 0.74/0.89 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[476, 3130])).
% 0.74/0.89 tff(3132,plain,
% 0.74/0.89 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[416, 3131, 1401, 3114])).
% 0.74/0.89 tff(3133,plain,
% 0.74/0.89 (op(op(e2, e1), op(e2, e1)) = e1),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[11, 3132])).
% 0.74/0.89 tff(3134,plain,
% 0.74/0.89 (e2 = op(e2, e2)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3002])).
% 0.74/0.89 tff(3135,plain,
% 0.74/0.89 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3134])).
% 0.74/0.89 tff(3136,plain,
% 0.74/0.89 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3135])).
% 0.74/0.89 tff(3137,plain,
% 0.74/0.89 (~(op(e2, e2) = e3)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[195, 3136])).
% 0.74/0.89 tff(3138,plain,
% 0.74/0.89 (op(op(e2, e0), op(e2, e0)) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[46, 3132])).
% 0.74/0.89 tff(3139,plain,
% 0.74/0.89 (~(op(e3, e3) = e3)),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[686, 3138, 3137, 3133])).
% 0.74/0.89 tff(3140,plain,
% 0.74/0.89 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3123])).
% 0.74/0.89 tff(3141,plain,
% 0.74/0.89 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3140, 263])).
% 0.74/0.89 tff(3142,plain,
% 0.74/0.89 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3141])).
% 0.74/0.89 tff(3143,plain,
% 0.74/0.89 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3142])).
% 0.74/0.89 tff(3144,plain,
% 0.74/0.89 (~(op(e3, e0) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[272, 3143])).
% 0.74/0.89 tff(3145,plain,
% 0.74/0.89 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[2814])).
% 0.74/0.89 tff(3146,plain,
% 0.74/0.89 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3145, 1144])).
% 0.74/0.89 tff(3147,plain,
% 0.74/0.89 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3146])).
% 0.74/0.89 tff(3148,plain,
% 0.74/0.89 (~(op(e3, e2) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1155, 3147])).
% 0.74/0.89 tff(3149,plain,
% 0.74/0.89 (op(e3, e3) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[857, 3148, 134, 3144, 3139])).
% 0.74/0.89 tff(3150,plain,
% 0.74/0.89 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3149])).
% 0.74/0.89 tff(3151,plain,
% 0.74/0.89 (op(e3, e0) = op(e3, op(e3, e3))),
% 0.74/0.89 inference(symmetry,[status(thm)],[3150])).
% 0.74/0.89 tff(3152,plain,
% 0.74/0.89 (e2 = op(e3, e0)),
% 0.74/0.89 inference(symmetry,[status(thm)],[3123])).
% 0.74/0.89 tff(3153,plain,
% 0.74/0.89 (e2 = op(e3, op(e3, e3))),
% 0.74/0.89 inference(transitivity,[status(thm)],[3152, 3151])).
% 0.74/0.89 tff(3154,plain,
% 0.74/0.89 ($false),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[1397, 3153])).
% 0.74/0.89 tff(3155,plain,((op(e0, e1) = e0) | (e2 = op(e3, op(e3, e3))) | (~(op(e0, e3) = e2)) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (e0 = op(e2, op(e2, e2))) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.89 tff(3156,plain,
% 0.74/0.89 (op(e0, e1) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3155, 2808, 1397, 112, 2807, 1677, 168])).
% 0.74/0.89 tff(3157,plain,
% 0.74/0.89 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3156])).
% 0.74/0.89 tff(3158,plain,
% 0.74/0.89 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.74/0.89 inference(transitivity,[status(thm)],[3157, 2702])).
% 0.74/0.89 tff(3159,plain,
% 0.74/0.89 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.74/0.89 inference(monotonicity,[status(thm)],[3158])).
% 0.74/0.89 tff(3160,plain,
% 0.74/0.89 (~(op(e0, e2) = e0)),
% 0.74/0.89 inference(modus_ponens,[status(thm)],[1360, 3159])).
% 0.74/0.89 tff(3161,assumption,(~(op(op(e0, e2), op(e0, e2)) = e2)), introduced(assumption)).
% 0.74/0.89 tff(3162,assumption,(~(op(op(e0, e1), op(e0, e1)) = e1)), introduced(assumption)).
% 0.74/0.89 tff(3163,plain,
% 0.74/0.89 (op(e0, e1) = e0),
% 0.74/0.89 inference(unit_resolution,[status(thm)],[3155, 233, 1397, 112, 231, 1677, 168])).
% 0.74/0.89 tff(3164,assumption,(op(e0, e1) = e0), introduced(assumption)).
% 0.74/0.90 tff(3165,plain,
% 0.74/0.90 (op(op(e0, e1), op(e0, e1)) = op(e0, e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3164, 3164])).
% 0.74/0.90 tff(3166,plain,
% 0.74/0.90 ((op(op(e0, e1), op(e0, e1)) = e1) <=> (op(e0, e0) = e1)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3165])).
% 0.74/0.90 tff(3167,plain,
% 0.74/0.90 ((~(op(op(e0, e1), op(e0, e1)) = e1)) <=> (~(op(e0, e0) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3166])).
% 0.74/0.90 tff(3168,plain,
% 0.74/0.90 (~(op(e0, e0) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3162, 3167])).
% 0.74/0.90 tff(3169,plain,
% 0.74/0.90 (((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3170,plain,
% 0.74/0.90 ((((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3171,plain,
% 0.74/0.90 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3172,plain,
% 0.74/0.90 (((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) <=> (((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2)) | (op(e0, e0) = e3))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3171])).
% 0.74/0.90 tff(3173,plain,
% 0.74/0.90 (((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3))),
% 0.74/0.90 inference(transitivity,[status(thm)],[3172, 3170])).
% 0.74/0.90 tff(3174,plain,
% 0.74/0.90 (((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))),
% 0.74/0.90 inference(and_elim,[status(thm)],[256])).
% 0.74/0.90 tff(3175,plain,
% 0.74/0.90 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)),
% 0.74/0.90 inference(and_elim,[status(thm)],[3174])).
% 0.74/0.90 tff(3176,plain,
% 0.74/0.90 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3175, 3173])).
% 0.74/0.90 tff(3177,plain,
% 0.74/0.90 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3176, 3169])).
% 0.74/0.90 tff(3178,plain,
% 0.74/0.90 (op(e0, e0) = e3),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[3177, 3168, 168, 4])).
% 0.74/0.90 tff(3179,plain,
% 0.74/0.90 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3178, 3178])).
% 0.74/0.90 tff(3180,plain,
% 0.74/0.90 (e3 = op(e0, e0)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3178])).
% 0.74/0.90 tff(3181,plain,
% 0.74/0.90 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.74/0.90 inference(symmetry,[status(thm)],[3179])).
% 0.74/0.90 tff(3182,plain,
% 0.74/0.90 ((op(e3, e3) = e0) <=> (op(op(e0, e0), op(e0, e0)) = e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3181])).
% 0.74/0.90 tff(3183,plain,
% 0.74/0.90 ((op(op(e0, e0), op(e0, e0)) = e0) <=> (op(e3, e3) = e0)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3182])).
% 0.74/0.90 tff(3184,plain,
% 0.74/0.90 ((~(op(op(e0, e0), op(e0, e0)) = e0)) <=> (~(op(e3, e3) = e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3183])).
% 0.74/0.90 tff(3185,assumption,(~(op(op(e0, e0), op(e0, e0)) = e0)), introduced(assumption)).
% 0.74/0.90 tff(3186,plain,
% 0.74/0.90 (~(op(e3, e3) = e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 0.74/0.90 tff(3187,plain,
% 0.74/0.90 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3164])).
% 0.74/0.90 tff(3188,plain,
% 0.74/0.90 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.74/0.90 inference(transitivity,[status(thm)],[3187, 499])).
% 0.74/0.90 tff(3189,plain,
% 0.74/0.90 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3188])).
% 0.74/0.90 tff(3190,plain,
% 0.74/0.90 (~(op(e3, e1) = e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[2421, 3189])).
% 0.74/0.90 tff(3191,plain,
% 0.74/0.90 ((e1 = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.74/0.90 inference(commutativity,[status(thm)],[])).
% 0.74/0.90 tff(3192,plain,
% 0.74/0.90 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3178])).
% 0.74/0.90 tff(3193,plain,
% 0.74/0.90 (op(e0, op(e0, e0)) = e2),
% 0.74/0.90 inference(transitivity,[status(thm)],[3192, 134])).
% 0.74/0.90 tff(3194,plain,
% 0.74/0.90 (op(op(e0, op(e0, e0)), e0) = op(e2, e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3193])).
% 0.74/0.90 tff(3195,plain,
% 0.74/0.90 ((e1 = op(op(e0, op(e0, e0)), e0)) <=> (e1 = op(e2, e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3194])).
% 0.74/0.90 tff(3196,plain,
% 0.74/0.90 ((e1 = op(op(e0, op(e0, e0)), e0)) <=> (op(e2, e0) = e1)),
% 0.74/0.90 inference(transitivity,[status(thm)],[3195, 3191])).
% 0.74/0.90 tff(3197,plain,
% 0.74/0.90 ((~(e1 = op(op(e0, op(e0, e0)), e0))) <=> (~(op(e2, e0) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3196])).
% 0.74/0.90 tff(3198,plain,
% 0.74/0.90 (e3 = op(e0, e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3178, 1652])).
% 0.74/0.90 tff(3199,plain,
% 0.74/0.90 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.74/0.90 inference(symmetry,[status(thm)],[3192])).
% 0.74/0.90 tff(3200,plain,
% 0.74/0.90 (e2 = op(e0, op(e0, e0))),
% 0.74/0.90 inference(transitivity,[status(thm)],[135, 3199])).
% 0.74/0.90 tff(3201,plain,
% 0.74/0.90 ((~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0)))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3202,plain,
% 0.74/0.90 (((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0))) <=> (~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0)))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3203,plain,
% 0.74/0.90 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0)))) <=> (~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3202])).
% 0.74/0.90 tff(3204,plain,
% 0.74/0.90 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0)))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[3203, 3201])).
% 0.74/0.90 tff(3205,plain,
% 0.74/0.90 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0)))) <=> (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3206,plain,
% 0.74/0.90 ((~(((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), e0)))) <=> (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3207,axiom,(~(((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), e0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax23')).
% 0.74/0.90 tff(3208,plain,
% 0.74/0.90 (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 0.74/0.90 tff(3209,plain,
% 0.74/0.90 (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(op(e0, op(e0, e0)), e0)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3208, 3205])).
% 0.74/0.90 tff(3210,plain,
% 0.74/0.90 ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), e0)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3209, 3204])).
% 0.74/0.90 tff(3211,plain,
% 0.74/0.90 (~(e1 = op(op(e0, op(e0, e0)), e0))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[3210, 3200, 3198])).
% 0.74/0.90 tff(3212,plain,
% 0.74/0.90 (~(op(e2, e0) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3211, 3197])).
% 0.74/0.90 tff(3213,plain,
% 0.74/0.90 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3164])).
% 0.74/0.90 tff(3214,plain,
% 0.74/0.90 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.74/0.90 inference(transitivity,[status(thm)],[3213, 1444])).
% 0.74/0.90 tff(3215,plain,
% 0.74/0.90 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3214])).
% 0.74/0.90 tff(3216,plain,
% 0.74/0.90 (~(op(e1, e1) = e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[110, 3215])).
% 0.74/0.90 tff(3217,assumption,(~(op(e3, e1) = e0)), introduced(assumption)).
% 0.74/0.90 tff(3218,plain,
% 0.74/0.90 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1454])).
% 0.74/0.90 tff(3219,plain,
% 0.74/0.90 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.74/0.90 inference(transitivity,[status(thm)],[3218, 1144])).
% 0.74/0.90 tff(3220,plain,
% 0.74/0.90 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3219])).
% 0.74/0.90 tff(3221,plain,
% 0.74/0.90 (~(op(e3, e2) = e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[591, 3220])).
% 0.74/0.90 tff(3222,plain,
% 0.74/0.90 (op(e3, e0) = e0),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[580, 3221, 3217, 825])).
% 0.74/0.90 tff(3223,plain,
% 0.74/0.90 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1097, 3222, 168])).
% 0.74/0.90 tff(3224,plain,
% 0.74/0.90 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[476, 3223])).
% 0.74/0.90 tff(3225,plain,
% 0.74/0.90 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[416, 3224, 1401, 1460])).
% 0.74/0.90 tff(3226,plain,
% 0.74/0.90 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[333, 3225])).
% 0.74/0.90 tff(3227,assumption,(~(op(e2, e0) = e1)), introduced(assumption)).
% 0.74/0.90 tff(3228,assumption,(~(op(e0, e0) = e1)), introduced(assumption)).
% 0.74/0.90 tff(3229,plain,
% 0.74/0.90 ((op(e3, e0) = e1) <=> (e0 = e1)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3222])).
% 0.74/0.90 tff(3230,plain,
% 0.74/0.90 ((e0 = e1) <=> (op(e3, e0) = e1)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3229])).
% 0.74/0.90 tff(3231,plain,
% 0.74/0.90 ((~(e0 = e1)) <=> (~(op(e3, e0) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3230])).
% 0.74/0.90 tff(3232,plain,
% 0.74/0.90 (~(op(e3, e0) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1182, 3231])).
% 0.74/0.90 tff(3233,plain,
% 0.74/0.90 (((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3234,plain,
% 0.74/0.90 ((((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3235,plain,
% 0.74/0.90 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(3236,plain,
% 0.74/0.90 (((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)) <=> (((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3235])).
% 0.74/0.90 tff(3237,plain,
% 0.74/0.90 (((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1))),
% 0.74/0.90 inference(transitivity,[status(thm)],[3236, 3234])).
% 0.74/0.90 tff(3238,plain,
% 0.74/0.90 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)),
% 0.74/0.90 inference(and_elim,[status(thm)],[204])).
% 0.74/0.90 tff(3239,plain,
% 0.74/0.90 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3238, 3237])).
% 0.74/0.90 tff(3240,plain,
% 0.74/0.90 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3239, 3233])).
% 0.74/0.90 tff(3241,plain,
% 0.74/0.90 (op(e1, e0) = e1),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[3240, 3232, 3228, 3227])).
% 0.74/0.90 tff(3242,plain,
% 0.74/0.90 (e1 = op(e1, e0)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3241])).
% 0.74/0.90 tff(3243,plain,
% 0.74/0.90 (op(e1, e1) = op(op(e1, e0), op(e1, e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3242, 3242])).
% 0.74/0.90 tff(3244,plain,
% 0.74/0.90 (op(e1, e1) = e0),
% 0.74/0.90 inference(transitivity,[status(thm)],[3243, 3226])).
% 0.74/0.90 tff(3245,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1463, 3244])).
% 0.74/0.90 tff(3246,plain,((~(op(e2, e2) = e0)) | (op(e1, e1) = e0) | (op(e0, e0) = e1) | (op(e2, e0) = e1) | (op(e0, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e3) = e0) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(3247,plain,
% 0.74/0.90 (~(op(e2, e2) = e0)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[3246, 3216, 3168, 3212, 168, 3190, 3186, 4])).
% 0.74/0.90 tff(3248,plain,
% 0.74/0.90 ((op(e0, e1) = e1) <=> (e0 = e1)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3164])).
% 0.74/0.90 tff(3249,plain,
% 0.74/0.90 ((e0 = e1) <=> (op(e0, e1) = e1)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3248])).
% 0.74/0.90 tff(3250,plain,
% 0.74/0.90 ((~(e0 = e1)) <=> (~(op(e0, e1) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3249])).
% 0.74/0.90 tff(3251,plain,
% 0.74/0.90 (~(op(e0, e1) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1182, 3250])).
% 0.74/0.90 tff(3252,plain,
% 0.74/0.90 (op(e0, e2) = e1),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1191, 3168, 3007, 3251])).
% 0.74/0.90 tff(3253,plain,
% 0.74/0.90 ((op(e0, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3252])).
% 0.74/0.90 tff(3254,plain,
% 0.74/0.90 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.74/0.90 inference(transitivity,[status(thm)],[3253, 1703])).
% 0.74/0.90 tff(3255,plain,
% 0.74/0.90 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3254])).
% 0.74/0.90 tff(3256,plain,
% 0.74/0.90 (~(op(e2, e2) = e1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[126, 3255])).
% 0.74/0.90 tff(3257,plain,
% 0.74/0.90 ((op(e2, e0) = op(e0, e0)) <=> (op(e0, e0) = op(e2, e0))),
% 0.74/0.90 inference(commutativity,[status(thm)],[])).
% 0.74/0.90 tff(3258,plain,
% 0.74/0.90 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3180])).
% 0.74/0.90 tff(3259,plain,
% 0.74/0.90 ((op(e2, e0) = e3) <=> (op(e0, e0) = op(e2, e0))),
% 0.74/0.90 inference(transitivity,[status(thm)],[3258, 3257])).
% 0.74/0.90 tff(3260,plain,
% 0.74/0.90 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3259])).
% 0.74/0.90 tff(3261,plain,
% 0.74/0.90 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3260])).
% 0.74/0.90 tff(3262,plain,
% 0.74/0.90 (~(op(e2, e0) = e3)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[392, 3261])).
% 0.74/0.90 tff(3263,plain,
% 0.74/0.90 (op(op(e0, e2), op(e0, e2)) = op(e1, e1)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3252, 3252])).
% 0.74/0.90 tff(3264,plain,
% 0.74/0.90 ((op(op(e0, e2), op(e0, e2)) = e2) <=> (op(e1, e1) = e2)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3263])).
% 0.74/0.90 tff(3265,plain,
% 0.74/0.90 ((~(op(op(e0, e2), op(e0, e2)) = e2)) <=> (~(op(e1, e1) = e2))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3264])).
% 0.74/0.90 tff(3266,plain,
% 0.74/0.90 (~(op(e1, e1) = e2)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[3161, 3265])).
% 0.74/0.90 tff(3267,assumption,(~(op(e2, e0) = e3)), introduced(assumption)).
% 0.74/0.90 tff(3268,plain,
% 0.74/0.90 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e2)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1301])).
% 0.74/0.90 tff(3269,plain,
% 0.74/0.90 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e2))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3268])).
% 0.74/0.90 tff(3270,plain,
% 0.74/0.90 (~(op(e2, e0) = e2)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1384, 3269])).
% 0.74/0.90 tff(3271,plain,
% 0.74/0.90 (op(e2, e0) = e0),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[2317, 3270, 3267, 3227])).
% 0.74/0.90 tff(3272,plain,
% 0.74/0.90 (op(op(e2, e0), op(e2, e0)) = op(e0, e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3271, 3271])).
% 0.74/0.90 tff(3273,plain,
% 0.74/0.90 ((op(op(e2, e0), op(e2, e0)) = e0) <=> (op(e0, e0) = e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3272])).
% 0.74/0.90 tff(3274,plain,
% 0.74/0.90 ((op(e0, e0) = e0) <=> (op(op(e2, e0), op(e2, e0)) = e0)),
% 0.74/0.90 inference(symmetry,[status(thm)],[3273])).
% 0.74/0.90 tff(3275,plain,
% 0.74/0.90 ((~(op(e0, e0) = e0)) <=> (~(op(op(e2, e0), op(e2, e0)) = e0))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3274])).
% 0.74/0.90 tff(3276,plain,
% 0.74/0.90 (~(op(op(e2, e0), op(e2, e0)) = e0)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[168, 3275])).
% 0.74/0.90 tff(3277,plain,
% 0.74/0.90 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[46, 3276])).
% 0.74/0.90 tff(3278,plain,
% 0.74/0.90 (op(e1, e0) = e2),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1239, 1304, 2594, 1124])).
% 0.74/0.90 tff(3279,plain,
% 0.74/0.90 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3278, 3278])).
% 0.74/0.90 tff(3280,plain,
% 0.74/0.90 (op(op(e1, e0), op(e1, e0)) = e2),
% 0.74/0.90 inference(transitivity,[status(thm)],[3279, 1301])).
% 0.74/0.90 tff(3281,plain,
% 0.74/0.90 ((op(op(e1, e0), op(e1, e0)) = e0) <=> (e2 = e0)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[3280])).
% 0.74/0.90 tff(3282,plain,
% 0.74/0.90 ((op(op(e1, e0), op(e1, e0)) = e0) <=> (e0 = e2)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3281, 263])).
% 0.74/0.91 tff(3283,plain,
% 0.74/0.91 ((e0 = e2) <=> (op(op(e1, e0), op(e1, e0)) = e0)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3282])).
% 0.74/0.91 tff(3284,plain,
% 0.74/0.91 ((~(e0 = e2)) <=> (~(op(op(e1, e0), op(e1, e0)) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3283])).
% 0.74/0.91 tff(3285,plain,
% 0.74/0.91 (~(op(op(e1, e0), op(e1, e0)) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[272, 3284])).
% 0.74/0.91 tff(3286,plain,
% 0.74/0.91 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[333, 3285])).
% 0.74/0.91 tff(3287,plain,
% 0.74/0.91 (op(e3, e1) = e2),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1410, 3014, 112, 1124])).
% 0.74/0.91 tff(3288,plain,
% 0.74/0.91 (op(op(e3, e1), op(e3, e1)) = op(e2, e2)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3287, 3287])).
% 0.74/0.91 tff(3289,plain,
% 0.74/0.91 (op(op(e3, e1), op(e3, e1)) = e2),
% 0.74/0.91 inference(transitivity,[status(thm)],[3288, 1301])).
% 0.74/0.91 tff(3290,plain,
% 0.74/0.91 ((op(op(e3, e1), op(e3, e1)) = e1) <=> (e2 = e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3289])).
% 0.74/0.91 tff(3291,plain,
% 0.74/0.91 ((op(op(e3, e1), op(e3, e1)) = e1) <=> (e1 = e2)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3290, 319])).
% 0.74/0.91 tff(3292,plain,
% 0.74/0.91 ((e1 = e2) <=> (op(op(e3, e1), op(e3, e1)) = e1)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3291])).
% 0.74/0.91 tff(3293,plain,
% 0.74/0.91 ((~(e1 = e2)) <=> (~(op(op(e3, e1), op(e3, e1)) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3292])).
% 0.74/0.91 tff(3294,plain,
% 0.74/0.91 (~(op(op(e3, e1), op(e3, e1)) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[220, 3293])).
% 0.74/0.91 tff(3295,plain,
% 0.74/0.91 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[478, 3294])).
% 0.74/0.91 tff(3296,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[416, 3295, 3286, 1401, 3277])).
% 0.74/0.91 tff(3297,plain,((~(op(e2, e2) = e2)) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e0) = e3) | (op(e2, e0) = e1) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(3298,plain,
% 0.74/0.91 (~(op(e2, e2) = e2)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[3297, 3266, 112, 168, 3262, 3212, 2826])).
% 0.74/0.91 tff(3299,plain,
% 0.74/0.91 (op(e2, e2) = e3),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[2847, 3298, 3256, 3247])).
% 0.74/0.91 tff(3300,plain,
% 0.74/0.91 (op(e2, e2) = op(e0, e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3299, 3180])).
% 0.74/0.91 tff(3301,plain,
% 0.74/0.91 (op(op(e2, e2), op(e2, e2)) = op(op(e0, e0), op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3300, 3300])).
% 0.74/0.91 tff(3302,plain,
% 0.74/0.91 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3301, 3179])).
% 0.74/0.91 tff(3303,plain,
% 0.74/0.91 ((op(op(e2, e2), op(e2, e2)) = e2) <=> (op(e3, e3) = e2)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3302])).
% 0.74/0.91 tff(3304,plain,
% 0.74/0.91 ((op(e3, e3) = e2) <=> (op(op(e2, e2), op(e2, e2)) = e2)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3303])).
% 0.74/0.91 tff(3305,plain,
% 0.74/0.91 ((~(op(e3, e3) = e2)) <=> (~(op(op(e2, e2), op(e2, e2)) = e2))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3304])).
% 0.74/0.91 tff(3306,plain,
% 0.74/0.91 (~(op(op(e2, e2), op(e2, e2)) = e2)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[824, 3305])).
% 0.74/0.91 tff(3307,plain,
% 0.74/0.91 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[9, 3306])).
% 0.74/0.91 tff(3308,plain,
% 0.74/0.91 ((e0 = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(3309,plain,
% 0.74/0.91 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3164])).
% 0.74/0.91 tff(3310,plain,
% 0.74/0.91 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3309, 1483])).
% 0.74/0.91 tff(3311,plain,
% 0.74/0.91 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3310])).
% 0.74/0.91 tff(3312,plain,
% 0.74/0.91 (~(op(e2, e1) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[776, 3311])).
% 0.74/0.91 tff(3313,plain,
% 0.74/0.91 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3299])).
% 0.74/0.91 tff(3314,plain,
% 0.74/0.91 ((e0 = op(e2, op(e2, e2))) <=> (e0 = op(e2, e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3313])).
% 0.74/0.91 tff(3315,plain,
% 0.74/0.91 ((e0 = op(e2, op(e2, e2))) <=> (op(e2, e3) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3314, 1903])).
% 0.74/0.91 tff(3316,plain,
% 0.74/0.91 ((~(e0 = op(e2, op(e2, e2)))) <=> (~(op(e2, e3) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3315])).
% 0.74/0.91 tff(3317,plain,
% 0.74/0.91 (~(op(e2, e3) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1677, 3316])).
% 0.74/0.91 tff(3318,plain,
% 0.74/0.91 (op(e2, e0) = e0),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1495, 3317, 3247, 3312])).
% 0.74/0.91 tff(3319,plain,
% 0.74/0.91 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3318])).
% 0.74/0.91 tff(3320,plain,
% 0.74/0.91 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3319, 3308])).
% 0.74/0.91 tff(3321,plain,
% 0.74/0.91 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3320])).
% 0.74/0.91 tff(3322,plain,
% 0.74/0.91 (~(op(e3, e0) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[2324, 3321])).
% 0.74/0.91 tff(3323,plain,
% 0.74/0.91 (op(e3, e2) = e0),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[580, 3322, 3190, 3186])).
% 0.74/0.91 tff(3324,plain,
% 0.74/0.91 (op(op(e3, e2), op(e3, e2)) = op(e0, e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3323, 3323])).
% 0.74/0.91 tff(3325,plain,
% 0.74/0.91 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e0, e0) = e2)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3324])).
% 0.74/0.91 tff(3326,plain,
% 0.74/0.91 ((op(e0, e0) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3325])).
% 0.74/0.91 tff(3327,plain,
% 0.74/0.91 ((~(op(e0, e0) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3326])).
% 0.74/0.91 tff(3328,plain,
% 0.74/0.91 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[4, 3327])).
% 0.74/0.91 tff(3329,plain,
% 0.74/0.91 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[459, 3328])).
% 0.74/0.91 tff(3330,plain,
% 0.74/0.91 ((e3 = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(3331,plain,
% 0.74/0.91 ((op(e2, e2) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3299])).
% 0.74/0.91 tff(3332,plain,
% 0.74/0.91 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3331, 3330])).
% 0.74/0.91 tff(3333,plain,
% 0.74/0.91 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3332])).
% 0.74/0.91 tff(3334,plain,
% 0.74/0.91 (~(op(e2, e3) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[709, 3333])).
% 0.74/0.91 tff(3335,plain,
% 0.74/0.91 (op(e2, e3) = e1),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[903, 3334, 2834, 3317])).
% 0.74/0.91 tff(3336,plain,
% 0.74/0.91 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3335])).
% 0.74/0.91 tff(3337,plain,
% 0.74/0.91 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3336, 815])).
% 0.74/0.91 tff(3338,plain,
% 0.74/0.91 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3337])).
% 0.74/0.91 tff(3339,plain,
% 0.74/0.91 (~(op(e3, e3) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[656, 3338])).
% 0.74/0.91 tff(3340,plain,
% 0.74/0.91 (op(e3, e3) = e3),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[833, 3339, 824, 3186])).
% 0.74/0.91 tff(3341,plain,
% 0.74/0.91 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3299])).
% 0.74/0.91 tff(3342,plain,
% 0.74/0.91 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3341])).
% 0.74/0.91 tff(3343,plain,
% 0.74/0.91 (~(op(e1, e2) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[331, 3342])).
% 0.74/0.91 tff(3344,plain,
% 0.74/0.91 ((op(e1, e0) = op(e0, e0)) <=> (op(e0, e0) = op(e1, e0))),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(3345,plain,
% 0.74/0.91 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3180])).
% 0.74/0.91 tff(3346,plain,
% 0.74/0.91 ((op(e1, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 0.74/0.91 inference(transitivity,[status(thm)],[3345, 3344])).
% 0.74/0.91 tff(3347,plain,
% 0.74/0.91 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3346])).
% 0.74/0.91 tff(3348,plain,
% 0.74/0.91 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3347])).
% 0.74/0.91 tff(3349,plain,
% 0.74/0.91 (~(op(e1, e0) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1880, 3348])).
% 0.74/0.91 tff(3350,plain,
% 0.74/0.91 ((e0 = op(e0, e0)) <=> (op(e0, e0) = e0)),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(3351,plain,
% 0.74/0.91 (op(e1, e3) = e0),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1797, 3317, 2813, 3186])).
% 0.74/0.91 tff(3352,plain,
% 0.74/0.91 ((op(e1, e3) = e3) <=> (e0 = op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3351, 3180])).
% 0.74/0.91 tff(3353,plain,
% 0.74/0.91 ((op(e1, e3) = e3) <=> (op(e0, e0) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3352, 3350])).
% 0.74/0.91 tff(3354,plain,
% 0.74/0.91 ((op(e0, e0) = e0) <=> (op(e1, e3) = e3)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3353])).
% 0.74/0.91 tff(3355,plain,
% 0.74/0.91 ((~(op(e0, e0) = e0)) <=> (~(op(e1, e3) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3354])).
% 0.74/0.91 tff(3356,plain,
% 0.74/0.91 (~(op(e1, e3) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[168, 3355])).
% 0.74/0.91 tff(3357,plain,
% 0.74/0.91 (((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(3358,plain,
% 0.74/0.91 ((((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(3359,plain,
% 0.74/0.91 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(3360,plain,
% 0.74/0.91 (((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)) <=> (((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3359])).
% 0.74/0.91 tff(3361,plain,
% 0.74/0.91 (((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3))),
% 0.74/0.91 inference(transitivity,[status(thm)],[3360, 3358])).
% 0.74/0.91 tff(3362,plain,
% 0.74/0.91 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)),
% 0.74/0.91 inference(and_elim,[status(thm)],[151])).
% 0.74/0.91 tff(3363,plain,
% 0.74/0.91 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 0.74/0.91 tff(3364,plain,
% 0.74/0.91 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3363, 3357])).
% 0.74/0.91 tff(3365,plain,
% 0.74/0.91 (op(e1, e1) = e3),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[3364, 3356, 3349, 3343])).
% 0.74/0.91 tff(3366,plain,
% 0.74/0.91 (op(e1, e1) = op(e0, e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3365, 3180])).
% 0.74/0.91 tff(3367,plain,
% 0.74/0.91 (op(op(e1, e1), op(e1, e1)) = op(op(e0, e0), op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3366, 3366])).
% 0.74/0.91 tff(3368,plain,
% 0.74/0.91 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3367, 3179, 3340, 3180])).
% 0.74/0.91 tff(3369,plain,
% 0.74/0.91 ((op(op(e1, e1), op(e1, e1)) = e1) <=> (op(e0, e0) = e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3368])).
% 0.74/0.91 tff(3370,plain,
% 0.74/0.91 ((op(e0, e0) = e1) <=> (op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3369])).
% 0.74/0.91 tff(3371,plain,
% 0.74/0.91 ((~(op(e0, e0) = e1)) <=> (~(op(op(e1, e1), op(e1, e1)) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3370])).
% 0.74/0.91 tff(3372,plain,
% 0.74/0.91 (~(op(op(e1, e1), op(e1, e1)) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3168, 3371])).
% 0.74/0.91 tff(3373,plain,
% 0.74/0.91 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[316, 3372])).
% 0.74/0.91 tff(3374,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[416, 3373, 3329, 1401, 3307])).
% 0.74/0.91 tff(3375,plain,((~(op(e0, e1) = e0)) | (op(e0, e0) = e2) | (op(e0, e0) = e0) | (e0 = op(e2, op(e2, e2))) | (op(e0, e1) = e2) | (~(op(e0, e3) = e2)) | (op(op(e0, e2), op(e0, e2)) = e2) | (op(op(e0, e0), op(e0, e0)) = e0) | (op(op(e0, e1), op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(3376,plain,
% 0.74/0.91 (op(op(e0, e0), op(e0, e0)) = e0),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[3375, 3163, 168, 1677, 112, 233, 3161, 4, 3162])).
% 0.74/0.91 tff(3377,plain,
% 0.74/0.91 (op(op(e0, e1), op(e0, e1)) = op(e0, e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3163, 3163])).
% 0.74/0.91 tff(3378,plain,
% 0.74/0.91 ((op(op(e0, e1), op(e0, e1)) = e1) <=> (op(e0, e0) = e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3377])).
% 0.74/0.91 tff(3379,plain,
% 0.74/0.91 ((~(op(op(e0, e1), op(e0, e1)) = e1)) <=> (~(op(e0, e0) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3378])).
% 0.74/0.91 tff(3380,plain,
% 0.74/0.91 (~(op(e0, e0) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3162, 3379])).
% 0.74/0.91 tff(3381,plain,
% 0.74/0.91 (op(e0, e0) = e3),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[3177, 3380, 168, 4])).
% 0.74/0.91 tff(3382,plain,
% 0.74/0.91 (e3 = op(e0, e0)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3381])).
% 0.74/0.91 tff(3383,plain,
% 0.74/0.91 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3382, 3382])).
% 0.74/0.91 tff(3384,plain,
% 0.74/0.91 (op(e3, e3) = e0),
% 0.74/0.91 inference(transitivity,[status(thm)],[3383, 3376])).
% 0.74/0.91 tff(3385,plain,
% 0.74/0.91 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3384])).
% 0.74/0.91 tff(3386,plain,
% 0.74/0.91 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3385])).
% 0.74/0.91 tff(3387,plain,
% 0.74/0.91 (~(op(e2, e3) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[656, 3386])).
% 0.74/0.91 tff(3388,plain,
% 0.74/0.91 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3163])).
% 0.74/0.91 tff(3389,plain,
% 0.74/0.91 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3388, 1483])).
% 0.74/0.91 tff(3390,plain,
% 0.74/0.91 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3389])).
% 0.74/0.91 tff(3391,plain,
% 0.74/0.91 (~(op(e2, e1) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[776, 3390])).
% 0.74/0.91 tff(3392,plain,
% 0.74/0.91 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3163])).
% 0.74/0.91 tff(3393,plain,
% 0.74/0.91 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3392, 1444])).
% 0.74/0.91 tff(3394,plain,
% 0.74/0.91 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3393])).
% 0.74/0.91 tff(3395,plain,
% 0.74/0.91 (~(op(e1, e1) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[110, 3394])).
% 0.74/0.91 tff(3396,plain,
% 0.74/0.91 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3384])).
% 0.74/0.91 tff(3397,plain,
% 0.74/0.91 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3396])).
% 0.74/0.91 tff(3398,plain,
% 0.74/0.91 (~(op(e1, e3) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1442, 3397])).
% 0.74/0.91 tff(3399,plain,
% 0.74/0.91 (op(op(e3, e3), op(e3, e3)) = op(e0, e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3384, 3384])).
% 0.74/0.91 tff(3400,plain,
% 0.74/0.91 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.74/0.91 inference(transitivity,[status(thm)],[3399, 3381])).
% 0.74/0.91 tff(3401,plain,
% 0.74/0.91 (op(e3, e0) = e1),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1769, 3400, 1397, 3384])).
% 0.74/0.91 tff(3402,plain,
% 0.74/0.91 (op(op(e3, e0), op(e3, e0)) = op(e1, e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3401, 3401])).
% 0.74/0.91 tff(3403,plain,
% 0.74/0.91 ((op(op(e3, e0), op(e3, e0)) = e0) <=> (op(e1, e1) = e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3402])).
% 0.74/0.91 tff(3404,plain,
% 0.74/0.91 ((op(e1, e1) = e0) <=> (op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3403])).
% 0.74/0.91 tff(3405,plain,
% 0.74/0.91 ((~(op(e1, e1) = e0)) <=> (~(op(op(e3, e0), op(e3, e0)) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3404])).
% 0.74/0.91 tff(3406,plain,
% 0.74/0.91 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3395, 3405])).
% 0.74/0.91 tff(3407,plain,
% 0.74/0.91 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[476, 3406])).
% 0.74/0.91 tff(3408,plain,
% 0.74/0.91 (~(op(e2, e2) = e0)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1481, 3407, 168, 3398, 3395, 4])).
% 0.74/0.91 tff(3409,plain,
% 0.74/0.91 (op(e2, e0) = e0),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1495, 3408, 3391, 3387])).
% 0.74/0.91 tff(3410,plain,
% 0.74/0.91 (op(op(e2, e0), op(e2, e0)) = op(e0, e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3409, 3409])).
% 0.74/0.91 tff(3411,plain,
% 0.74/0.91 ((op(op(e2, e0), op(e2, e0)) = e0) <=> (op(e0, e0) = e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3410])).
% 0.74/0.91 tff(3412,plain,
% 0.74/0.91 ((op(e0, e0) = e0) <=> (op(op(e2, e0), op(e2, e0)) = e0)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3411])).
% 0.74/0.91 tff(3413,plain,
% 0.74/0.91 ((~(op(e0, e0) = e0)) <=> (~(op(op(e2, e0), op(e2, e0)) = e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3412])).
% 0.74/0.91 tff(3414,plain,
% 0.74/0.91 (~(op(op(e2, e0), op(e2, e0)) = e0)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[168, 3413])).
% 0.74/0.91 tff(3415,plain,
% 0.74/0.91 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[233])).
% 0.74/0.91 tff(3416,plain,
% 0.74/0.91 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3415, 695])).
% 0.74/0.91 tff(3417,plain,
% 0.74/0.91 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3416])).
% 0.74/0.91 tff(3418,plain,
% 0.74/0.91 (~(op(e1, e3) = e2)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1632, 3417])).
% 0.74/0.91 tff(3419,plain,
% 0.74/0.91 ((op(e0, e1) = e1) <=> (e0 = e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3163])).
% 0.74/0.91 tff(3420,plain,
% 0.74/0.91 ((e0 = e1) <=> (op(e0, e1) = e1)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3419])).
% 0.74/0.91 tff(3421,plain,
% 0.74/0.91 ((~(e0 = e1)) <=> (~(op(e0, e1) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3420])).
% 0.74/0.91 tff(3422,plain,
% 0.74/0.91 (~(op(e0, e1) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1182, 3421])).
% 0.74/0.91 tff(3423,plain,
% 0.74/0.91 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[233])).
% 0.74/0.91 tff(3424,plain,
% 0.74/0.91 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.74/0.91 inference(transitivity,[status(thm)],[3423, 319])).
% 0.74/0.91 tff(3425,plain,
% 0.74/0.91 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3424])).
% 0.74/0.91 tff(3426,plain,
% 0.74/0.91 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3425])).
% 0.74/0.91 tff(3427,plain,
% 0.74/0.91 (~(op(e0, e3) = e1)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[220, 3426])).
% 0.74/0.91 tff(3428,plain,
% 0.74/0.91 (op(e0, e2) = e1),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1191, 3380, 3427, 3422])).
% 0.74/0.91 tff(3429,plain,
% 0.74/0.91 (op(op(e0, e2), op(e0, e2)) = op(e1, e1)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3428, 3428])).
% 0.74/0.91 tff(3430,plain,
% 0.74/0.91 ((op(op(e0, e2), op(e0, e2)) = e2) <=> (op(e1, e1) = e2)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3429])).
% 0.74/0.91 tff(3431,plain,
% 0.74/0.91 ((~(op(op(e0, e2), op(e0, e2)) = e2)) <=> (~(op(e1, e1) = e2))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3430])).
% 0.74/0.91 tff(3432,plain,
% 0.74/0.91 (~(op(e1, e1) = e2)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[3161, 3431])).
% 0.74/0.91 tff(3433,plain,
% 0.74/0.91 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3382])).
% 0.74/0.91 tff(3434,plain,
% 0.74/0.91 ((op(e2, e0) = e3) <=> (op(e0, e0) = op(e2, e0))),
% 0.74/0.91 inference(transitivity,[status(thm)],[3433, 3257])).
% 0.74/0.91 tff(3435,plain,
% 0.74/0.91 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.74/0.91 inference(symmetry,[status(thm)],[3434])).
% 0.74/0.91 tff(3436,plain,
% 0.74/0.91 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3435])).
% 0.74/0.91 tff(3437,plain,
% 0.74/0.91 (~(op(e2, e0) = e3)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[392, 3436])).
% 0.74/0.91 tff(3438,plain,
% 0.74/0.91 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3381])).
% 0.74/0.91 tff(3439,plain,
% 0.74/0.91 (op(e0, op(e0, e0)) = e2),
% 0.74/0.91 inference(transitivity,[status(thm)],[3438, 233])).
% 0.74/0.91 tff(3440,plain,
% 0.74/0.91 (op(op(e0, op(e0, e0)), e0) = op(e2, e0)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3439])).
% 0.74/0.91 tff(3441,plain,
% 0.74/0.91 ((e1 = op(op(e0, op(e0, e0)), e0)) <=> (e1 = op(e2, e0))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[3440])).
% 0.74/0.91 tff(3442,plain,
% 0.74/0.91 ((e1 = op(op(e0, op(e0, e0)), e0)) <=> (op(e2, e0) = e1)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3441, 3191])).
% 0.74/0.92 tff(3443,plain,
% 0.74/0.92 ((~(e1 = op(op(e0, op(e0, e0)), e0))) <=> (~(op(e2, e0) = e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3442])).
% 0.74/0.92 tff(3444,plain,
% 0.74/0.92 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.74/0.92 inference(symmetry,[status(thm)],[3438])).
% 0.74/0.92 tff(3445,plain,
% 0.74/0.92 (e2 = op(e0, e3)),
% 0.74/0.92 inference(symmetry,[status(thm)],[233])).
% 0.74/0.92 tff(3446,plain,
% 0.74/0.92 (e2 = op(e0, op(e0, e0))),
% 0.74/0.92 inference(transitivity,[status(thm)],[3445, 3444])).
% 0.74/0.92 tff(3447,plain,
% 0.74/0.92 (e3 = op(e0, e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3381, 1652])).
% 0.74/0.92 tff(3448,plain,
% 0.74/0.92 (~(e1 = op(op(e0, op(e0, e0)), e0))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3210, 3447, 3446])).
% 0.74/0.92 tff(3449,plain,
% 0.74/0.92 (~(op(e2, e0) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3448, 3443])).
% 0.74/0.92 tff(3450,plain,
% 0.74/0.92 (~(op(e2, e2) = e2)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3297, 3449, 112, 168, 3437, 3432, 3418])).
% 0.74/0.92 tff(3451,plain,
% 0.74/0.92 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3384])).
% 0.74/0.92 tff(3452,plain,
% 0.74/0.92 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3451])).
% 0.74/0.92 tff(3453,plain,
% 0.74/0.92 (~(op(e3, e2) = e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1166, 3452])).
% 0.74/0.92 tff(3454,plain,
% 0.74/0.92 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3163])).
% 0.74/0.92 tff(3455,plain,
% 0.74/0.92 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3454, 2702])).
% 0.74/0.92 tff(3456,plain,
% 0.74/0.92 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3455])).
% 0.74/0.92 tff(3457,plain,
% 0.74/0.92 (~(op(e0, e2) = e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1360, 3456])).
% 0.74/0.92 tff(3458,plain,
% 0.74/0.92 (op(e1, e2) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[997, 3408, 3457, 3453])).
% 0.74/0.92 tff(3459,plain,
% 0.74/0.92 ((op(e1, e2) = e2) <=> (e0 = e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3458])).
% 0.74/0.92 tff(3460,plain,
% 0.74/0.92 ((e0 = e2) <=> (op(e1, e2) = e2)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3459])).
% 0.74/0.92 tff(3461,plain,
% 0.74/0.92 ((~(e0 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3460])).
% 0.74/0.92 tff(3462,plain,
% 0.74/0.92 (~(op(e1, e2) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[272, 3461])).
% 0.74/0.92 tff(3463,plain,
% 0.74/0.92 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2610, 3462, 1401, 3432, 3450, 231, 3418, 3408])).
% 0.74/0.92 tff(3464,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[46, 3463, 3414])).
% 0.74/0.92 tff(3465,plain,((op(e0, e2) = e2) | (op(e0, e0) = e0) | (op(e0, e0) = e2) | (op(e0, e1) = e2) | (e2 = op(e3, op(e3, e3))) | (op(op(e0, e2), op(e0, e2)) = e2) | (op(op(e0, e1), op(e0, e1)) = e1) | (e0 = op(e2, op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3466,plain,
% 0.74/0.92 (op(op(e0, e1), op(e0, e1)) = e1),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3465, 2807, 4, 112, 1397, 3161, 168, 1677])).
% 0.74/0.92 tff(3467,plain,
% 0.74/0.92 (op(op(e0, e3), op(e0, e3)) = op(e2, e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[233, 233])).
% 0.74/0.92 tff(3468,plain,
% 0.74/0.92 ((op(op(e0, e3), op(e0, e3)) = e3) <=> (op(e2, e2) = e3)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3467])).
% 0.74/0.92 tff(3469,plain,
% 0.74/0.92 ((~(op(op(e0, e3), op(e0, e3)) = e3)) <=> (~(op(e2, e2) = e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3468])).
% 0.74/0.92 tff(3470,plain,
% 0.74/0.92 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3164])).
% 0.74/0.92 tff(3471,plain,
% 0.74/0.92 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3470, 2702])).
% 0.74/0.92 tff(3472,plain,
% 0.74/0.92 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3471])).
% 0.74/0.92 tff(3473,plain,
% 0.74/0.92 (~(op(e0, e2) = e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1360, 3472])).
% 0.74/0.92 tff(3474,plain,
% 0.74/0.92 (~(op(op(e0, e3), op(e0, e3)) = e3)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[283, 3473, 112, 168, 231, 4, 213])).
% 0.74/0.92 tff(3475,plain,
% 0.74/0.92 (~(op(e2, e2) = e3)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3474, 3469])).
% 0.74/0.92 tff(3476,plain,
% 0.74/0.92 (op(e3, e2) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1501, 8, 4, 232, 1397, 6, 112, 168, 1124])).
% 0.74/0.92 tff(3477,plain,
% 0.74/0.92 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3476])).
% 0.74/0.92 tff(3478,plain,
% 0.74/0.92 ((op(e2, e2) = e2) <=> (op(e2, e2) = op(e3, e2))),
% 0.74/0.92 inference(symmetry,[status(thm)],[3477])).
% 0.74/0.92 tff(3479,plain,
% 0.74/0.92 (op(e2, e2) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[53, 1402, 4, 6, 8])).
% 0.74/0.92 tff(3480,plain,
% 0.74/0.92 (op(e2, e2) = op(e3, e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 0.74/0.92 tff(3481,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[591, 3480])).
% 0.74/0.92 tff(3482,plain,(((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))) | (op(e0, e0) = e2) | (op(e2, e2) = e3) | (op(e1, e1) = e2) | (op(e0, e2) = e0) | (e2 = op(e3, op(e3, e3))) | (op(e0, e1) = e2) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3483,plain,
% 0.74/0.92 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3482, 1124, 3475, 4, 3473, 1397, 112, 168])).
% 0.74/0.92 tff(3484,plain,
% 0.74/0.92 (op(e3, e2) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1299, 3, 1401, 1288, 6, 4, 1124, 231])).
% 0.74/0.92 tff(3485,plain,
% 0.74/0.92 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3484, 3484])).
% 0.74/0.92 tff(3486,plain,
% 0.74/0.92 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3485])).
% 0.74/0.92 tff(3487,plain,
% 0.74/0.92 ((op(e2, e2) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3486])).
% 0.74/0.92 tff(3488,plain,
% 0.74/0.92 ((~(op(e2, e2) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3487])).
% 0.74/0.92 tff(3489,plain,
% 0.74/0.92 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3, 3488])).
% 0.74/0.92 tff(3490,plain,
% 0.74/0.92 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[459, 3489])).
% 0.74/0.92 tff(3491,plain,
% 0.74/0.92 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[416, 3490, 1401, 1288])).
% 0.74/0.92 tff(3492,plain,
% 0.74/0.92 (op(op(e1, e3), op(e1, e3)) = e3),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[313, 3491])).
% 0.74/0.92 tff(3493,plain,
% 0.74/0.92 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3484])).
% 0.74/0.92 tff(3494,plain,
% 0.74/0.92 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3493])).
% 0.74/0.92 tff(3495,plain,
% 0.74/0.92 (~(op(e1, e2) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2590, 3494])).
% 0.74/0.92 tff(3496,plain,
% 0.74/0.92 (op(e2, e2) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2610, 3495, 1401, 231, 1288, 1124, 2594, 3])).
% 0.74/0.92 tff(3497,plain,
% 0.74/0.92 (op(e1, e3) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1481, 3496, 168, 3216, 3490, 4])).
% 0.74/0.92 tff(3498,plain,
% 0.74/0.92 (op(op(e1, e3), op(e1, e3)) = op(e0, e0)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3497, 3497])).
% 0.74/0.92 tff(3499,plain,
% 0.74/0.92 (op(e0, e0) = op(op(e1, e3), op(e1, e3))),
% 0.74/0.92 inference(symmetry,[status(thm)],[3498])).
% 0.74/0.92 tff(3500,plain,
% 0.74/0.92 (e0 = op(e0, e1)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3164])).
% 0.74/0.92 tff(3501,plain,
% 0.74/0.92 (op(e0, e0) = op(op(e0, e1), op(e0, e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3500, 3500])).
% 0.74/0.92 tff(3502,plain,
% 0.74/0.92 (op(op(e0, e1), op(e0, e1)) = op(e0, e0)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3501])).
% 0.74/0.92 tff(3503,plain,
% 0.74/0.92 (e1 = e3),
% 0.74/0.92 inference(transitivity,[status(thm)],[214, 3502, 3499, 3492])).
% 0.74/0.92 tff(3504,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[665, 3503])).
% 0.74/0.92 tff(3505,plain,((op(e2, e2) = e2) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(e0, e1) = e0)) | (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))) | (op(e0, e0) = e0) | (op(e0, e0) = e2) | (op(e0, e2) = e2) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3506,plain,
% 0.74/0.92 (op(e2, e2) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3505, 3483, 3164, 213, 168, 4, 231, 1124, 3418, 3475])).
% 0.74/0.92 tff(3507,plain,
% 0.74/0.92 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3506])).
% 0.74/0.92 tff(3508,plain,
% 0.74/0.92 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3507])).
% 0.74/0.92 tff(3509,plain,
% 0.74/0.92 (~(op(e1, e2) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[331, 3508])).
% 0.74/0.92 tff(3510,plain,
% 0.74/0.92 (op(e1, e0) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1239, 3509, 3418, 1124])).
% 0.74/0.92 tff(3511,plain,
% 0.74/0.92 (op(op(e1, e0), op(e1, e0)) = op(e2, e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3510, 3510])).
% 0.74/0.92 tff(3512,plain,
% 0.74/0.92 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3506])).
% 0.74/0.92 tff(3513,plain,
% 0.74/0.92 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3512, 378])).
% 0.74/0.92 tff(3514,plain,
% 0.74/0.92 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3513])).
% 0.74/0.92 tff(3515,plain,
% 0.74/0.92 (~(op(e3, e2) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[591, 3514])).
% 0.74/0.92 tff(3516,plain,
% 0.74/0.92 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1219, 3515, 3475, 4, 1124])).
% 0.74/0.92 tff(3517,plain,
% 0.74/0.92 (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[416, 3516, 1401, 3483])).
% 0.74/0.92 tff(3518,plain,
% 0.74/0.92 (op(op(e1, e0), op(e1, e0)) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[333, 3517])).
% 0.74/0.92 tff(3519,plain,
% 0.74/0.92 (e0 = op(op(e1, e0), op(e1, e0))),
% 0.74/0.92 inference(symmetry,[status(thm)],[3518])).
% 0.74/0.92 tff(3520,plain,
% 0.74/0.92 (e0 = e2),
% 0.74/0.92 inference(transitivity,[status(thm)],[3519, 3511, 3506])).
% 0.74/0.92 tff(3521,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[272, 3520])).
% 0.74/0.92 tff(3522,plain,((op(e1, e1) = e2) | (op(e0, e0) = e2) | (~(op(e0, e1) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (op(e0, e0) = e0) | (op(e0, e2) = e2) | (e2 = op(e3, op(e3, e3))) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3523,plain,
% 0.74/0.92 (op(e1, e1) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3522, 3156, 4, 3466, 168, 2807, 1397, 112])).
% 0.74/0.92 tff(3524,plain,
% 0.74/0.92 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1729, 3523, 3160, 4, 1677])).
% 0.74/0.92 tff(3525,plain,
% 0.74/0.92 (op(op(e0, e3), op(e0, e3)) = op(e2, e2)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2808, 2808])).
% 0.74/0.92 tff(3526,plain,
% 0.74/0.92 ((op(op(e0, e3), op(e0, e3)) = e3) <=> (op(e2, e2) = e3)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3525])).
% 0.74/0.92 tff(3527,plain,
% 0.74/0.92 ((~(op(op(e0, e3), op(e0, e3)) = e3)) <=> (~(op(e2, e2) = e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3526])).
% 0.74/0.92 tff(3528,plain,
% 0.74/0.92 (~(op(op(e0, e3), op(e0, e3)) = e3)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[283, 3160, 112, 168, 2807, 4, 3466])).
% 0.74/0.92 tff(3529,plain,
% 0.74/0.92 (~(op(e2, e2) = e3)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3528, 3527])).
% 0.74/0.92 tff(3530,plain,
% 0.74/0.92 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2808])).
% 0.74/0.92 tff(3531,plain,
% 0.74/0.92 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3530, 5])).
% 0.74/0.92 tff(3532,plain,
% 0.74/0.92 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3531])).
% 0.74/0.92 tff(3533,plain,
% 0.74/0.92 (~(op(e3, e3) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[823, 3532])).
% 0.74/0.92 tff(3534,plain,
% 0.74/0.92 (e0 = op(e0, e1)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3156])).
% 0.74/0.92 tff(3535,plain,
% 0.74/0.92 (op(e0, e0) = op(op(e0, e1), op(e0, e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3534, 3534])).
% 0.74/0.92 tff(3536,plain,
% 0.74/0.92 (op(e0, e0) = e1),
% 0.74/0.92 inference(transitivity,[status(thm)],[3535, 3466])).
% 0.74/0.92 tff(3537,plain,
% 0.74/0.92 ((op(e0, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3536])).
% 0.74/0.92 tff(3538,plain,
% 0.74/0.92 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3537, 2254])).
% 0.74/0.92 tff(3539,plain,
% 0.74/0.92 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3538])).
% 0.74/0.92 tff(3540,plain,
% 0.74/0.92 (~(op(e0, e2) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[281, 3539])).
% 0.74/0.92 tff(3541,plain,
% 0.74/0.92 (op(e0, e2) = e3),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[259, 3160, 2807, 3540])).
% 0.74/0.92 tff(3542,plain,
% 0.74/0.92 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3541])).
% 0.74/0.92 tff(3543,plain,
% 0.74/0.92 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3542, 1149])).
% 0.74/0.92 tff(3544,plain,
% 0.74/0.92 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3543])).
% 0.74/0.92 tff(3545,plain,
% 0.74/0.92 (~(op(e3, e2) = e3)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1155, 3544])).
% 0.74/0.92 tff(3546,plain,
% 0.74/0.92 ((op(e0, e1) = e1) <=> (e0 = e1)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3156])).
% 0.74/0.92 tff(3547,plain,
% 0.74/0.92 ((e0 = e1) <=> (op(e0, e1) = e1)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3546])).
% 0.74/0.92 tff(3548,plain,
% 0.74/0.92 ((~(e0 = e1)) <=> (~(op(e0, e1) = e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3547])).
% 0.74/0.92 tff(3549,plain,
% 0.74/0.92 (~(op(e0, e1) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1182, 3548])).
% 0.74/0.92 tff(3550,plain,
% 0.74/0.92 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[769, 3523, 3549, 3545, 3533, 4, 3529])).
% 0.74/0.92 tff(3551,plain,
% 0.74/0.92 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[416, 3550, 1401, 3524])).
% 0.74/0.92 tff(3552,plain,
% 0.74/0.92 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[476, 3551])).
% 0.74/0.92 tff(3553,plain,
% 0.74/0.92 (~(op(e3, e0) = e0)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1097, 3552, 168])).
% 0.74/0.92 tff(3554,plain,
% 0.74/0.92 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3156])).
% 0.74/0.92 tff(3555,plain,
% 0.74/0.92 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3554, 499])).
% 0.74/0.92 tff(3556,plain,
% 0.74/0.92 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3555])).
% 0.74/0.92 tff(3557,plain,
% 0.74/0.92 (~(op(e3, e1) = e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2421, 3556])).
% 0.74/0.92 tff(3558,plain,
% 0.74/0.92 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[459, 3551])).
% 0.74/0.92 tff(3559,plain,
% 0.74/0.92 (~(op(e3, e2) = e0)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[474, 3558, 4])).
% 0.74/0.92 tff(3560,plain,
% 0.74/0.92 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[633, 3551])).
% 0.74/0.92 tff(3561,plain,
% 0.74/0.92 (~(op(e3, e3) = e0)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1778, 3560, 3160, 168, 1397, 3552])).
% 0.74/0.92 tff(3562,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[580, 3561, 3559, 3557, 3553])).
% 0.74/0.92 tff(3563,plain,((op(e0, e1) = e2) | (op(e0, e0) = e0) | (e2 = op(e3, op(e3, e3))) | (op(e0, e0) = e2) | (e0 = op(e2, op(e2, e2))) | (op(op(e0, e2), op(e0, e2)) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3564,plain,
% 0.74/0.92 (op(op(e0, e2), op(e0, e2)) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3563, 2701, 1397, 4, 1677, 168])).
% 0.74/0.92 tff(3565,plain,
% 0.74/0.92 (~(op(e0, e2) = e0)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[229, 3564, 4])).
% 0.74/0.92 tff(3566,plain,
% 0.74/0.92 (~(op(e0, e2) = e2)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2806, 2701, 1397, 4, 1677, 168])).
% 0.74/0.92 tff(3567,plain,
% 0.74/0.92 (op(e0, e3) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[164, 2701, 4, 3566])).
% 0.74/0.92 tff(3568,plain,
% 0.74/0.92 (op(e0, e1) = e0),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3155, 3567, 1397, 2701, 3566, 1677, 168])).
% 0.74/0.92 tff(3569,plain,
% 0.74/0.92 (op(e0, e3) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[164, 2701, 4, 231])).
% 0.74/0.92 tff(3570,plain,
% 0.74/0.92 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3569])).
% 0.74/0.92 tff(3571,plain,
% 0.74/0.92 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3570, 319])).
% 0.74/0.92 tff(3572,plain,
% 0.74/0.92 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3571])).
% 0.74/0.92 tff(3573,plain,
% 0.74/0.92 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3572])).
% 0.74/0.92 tff(3574,plain,
% 0.74/0.92 (~(op(e0, e3) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[220, 3573])).
% 0.74/0.92 tff(3575,plain,
% 0.74/0.92 (~(op(op(e0, e1), op(e0, e1)) = e1)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3522, 1124, 4, 3164, 168, 231, 1397, 2701])).
% 0.74/0.92 tff(3576,plain,
% 0.74/0.92 (~(op(e0, e0) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[3575, 3167])).
% 0.74/0.92 tff(3577,plain,
% 0.74/0.92 (op(e0, e2) = e1),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1191, 3576, 3574, 3251])).
% 0.74/0.92 tff(3578,plain,
% 0.74/0.92 (e1 = op(e0, e2)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3577])).
% 0.74/0.92 tff(3579,plain,
% 0.74/0.92 (op(e1, e1) = op(op(e0, e2), op(e0, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3578, 3578])).
% 0.74/0.92 tff(3580,plain,
% 0.74/0.92 (op(e1, e1) = e2),
% 0.74/0.92 inference(transitivity,[status(thm)],[3579, 116])).
% 0.74/0.92 tff(3581,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1124, 3580])).
% 0.74/0.92 tff(3582,plain,((op(e1, e1) = e2) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(e0, e1) = e0)) | (op(e0, e0) = e2) | (op(e0, e0) = e0) | (op(e0, e2) = e2) | (e2 = op(e3, op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(3583,plain,
% 0.74/0.92 (op(e1, e1) = e2),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[3582, 3564, 3568, 4, 168, 3566, 1397])).
% 0.74/0.92 tff(3584,plain,
% 0.74/0.92 ((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1729, 3583, 3565, 4, 1677])).
% 0.74/0.92 tff(3585,plain,
% 0.74/0.92 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3568])).
% 0.74/0.92 tff(3586,plain,
% 0.74/0.92 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3585, 499])).
% 0.74/0.92 tff(3587,plain,
% 0.74/0.92 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3586])).
% 0.74/0.92 tff(3588,plain,
% 0.74/0.92 (~(op(e3, e1) = e0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2421, 3587])).
% 0.74/0.92 tff(3589,plain,
% 0.74/0.92 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3567])).
% 0.74/0.92 tff(3590,plain,
% 0.74/0.92 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3589])).
% 0.74/0.92 tff(3591,plain,
% 0.74/0.92 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3590])).
% 0.74/0.92 tff(3592,plain,
% 0.74/0.92 (~(op(e0, e3) = e3)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[195, 3591])).
% 0.74/0.92 tff(3593,plain,
% 0.74/0.92 ((op(e0, e1) = e3) <=> (e0 = e3)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3568])).
% 0.74/0.92 tff(3594,plain,
% 0.74/0.92 ((e0 = e3) <=> (op(e0, e1) = e3)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3593])).
% 0.74/0.92 tff(3595,plain,
% 0.74/0.92 ((~(e0 = e3)) <=> (~(op(e0, e1) = e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3594])).
% 0.74/0.92 tff(3596,plain,
% 0.74/0.92 (~(op(e0, e1) = e3)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[684, 3595])).
% 0.74/0.92 tff(3597,plain,
% 0.74/0.92 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3567])).
% 0.74/0.92 tff(3598,plain,
% 0.74/0.92 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3597, 5])).
% 0.74/0.92 tff(3599,plain,
% 0.74/0.92 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3598])).
% 0.74/0.92 tff(3600,plain,
% 0.74/0.92 (~(op(e3, e3) = e2)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[823, 3599])).
% 0.74/0.92 tff(3601,plain,
% 0.74/0.92 ((op(e0, e1) = e1) <=> (e0 = e1)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3568])).
% 0.74/0.92 tff(3602,plain,
% 0.74/0.92 ((e0 = e1) <=> (op(e0, e1) = e1)),
% 0.74/0.92 inference(symmetry,[status(thm)],[3601])).
% 0.74/0.92 tff(3603,plain,
% 0.74/0.92 ((~(e0 = e1)) <=> (~(op(e0, e1) = e1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[3602])).
% 0.74/0.92 tff(3604,plain,
% 0.74/0.92 (~(op(e0, e1) = e1)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1182, 3603])).
% 0.74/0.92 tff(3605,assumption,((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3))), introduced(assumption)).
% 0.74/0.92 tff(3606,plain,
% 0.74/0.92 ((op(e3, e0) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1060])).
% 0.74/0.92 tff(3607,plain,
% 0.74/0.92 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.74/0.92 inference(transitivity,[status(thm)],[3606, 378])).
% 0.74/0.92 tff(3608,plain,
% 0.74/0.92 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3607])).
% 0.74/0.93 tff(3609,plain,
% 0.74/0.93 (~(op(e3, e2) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1057, 3608])).
% 0.74/0.93 tff(3610,plain,
% 0.74/0.93 (e2 = op(e3, e0)),
% 0.74/0.93 inference(symmetry,[status(thm)],[1060])).
% 0.74/0.93 tff(3611,plain,
% 0.74/0.93 (op(e2, e2) = op(op(e3, e0), op(e3, e0))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3610, 3610])).
% 0.74/0.93 tff(3612,plain,
% 0.74/0.93 (op(e2, e2) = e0),
% 0.74/0.93 inference(transitivity,[status(thm)],[3611, 583])).
% 0.74/0.93 tff(3613,plain,
% 0.74/0.93 ((op(e2, e2) = e2) <=> (e0 = e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3612])).
% 0.74/0.93 tff(3614,plain,
% 0.74/0.93 ((e0 = e2) <=> (op(e2, e2) = e2)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3613])).
% 0.74/0.93 tff(3615,plain,
% 0.74/0.93 ((~(e0 = e2)) <=> (~(op(e2, e2) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3614])).
% 0.74/0.93 tff(3616,plain,
% 0.74/0.93 (~(op(e2, e2) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[272, 3615])).
% 0.74/0.93 tff(3617,plain,
% 0.74/0.93 (op(e0, e2) = e2),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[507, 3616, 977, 3609])).
% 0.74/0.93 tff(3618,plain,
% 0.74/0.93 (op(op(e0, e2), op(e0, e2)) = op(e2, e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3617, 3617])).
% 0.74/0.93 tff(3619,plain,
% 0.74/0.93 (op(e2, e2) = op(op(e0, e2), op(e0, e2))),
% 0.74/0.93 inference(symmetry,[status(thm)],[3618])).
% 0.74/0.93 tff(3620,plain,
% 0.74/0.93 (op(op(e3, e0), op(e3, e0)) = op(e2, e2)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3611])).
% 0.74/0.93 tff(3621,plain,
% 0.74/0.93 (e0 = op(op(e3, e0), op(e3, e0))),
% 0.74/0.93 inference(symmetry,[status(thm)],[583])).
% 0.74/0.93 tff(3622,plain,
% 0.74/0.93 (e0 = e2),
% 0.74/0.93 inference(transitivity,[status(thm)],[3621, 3620, 3619, 116])).
% 0.74/0.93 tff(3623,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[272, 3622])).
% 0.74/0.93 tff(3624,plain,((~(op(e3, e0) = e2)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e3, e0), op(e3, e0)) = e0)) | (op(e1, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(3625,plain,
% 0.74/0.93 (~(op(op(e3, e0), op(e3, e0)) = e0)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[3624, 1060, 116, 428])).
% 0.74/0.93 tff(3626,plain,
% 0.74/0.93 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[476, 3625])).
% 0.74/0.93 tff(3627,plain,
% 0.74/0.93 (~((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[416, 3626, 1289, 3605])).
% 0.74/0.93 tff(3628,plain,
% 0.74/0.93 (op(e3, e2) = e3),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[769, 3627, 729, 56, 418, 4, 6])).
% 0.74/0.93 tff(3629,plain,
% 0.74/0.93 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3628])).
% 0.74/0.93 tff(3630,plain,
% 0.74/0.93 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3629])).
% 0.74/0.93 tff(3631,plain,
% 0.74/0.93 (~(op(e0, e2) = e3)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1155, 3630])).
% 0.74/0.93 tff(3632,plain,
% 0.74/0.93 (op(e0, e0) = e3),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1025, 3631, 2454, 1919])).
% 0.74/0.93 tff(3633,plain,
% 0.74/0.93 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3628])).
% 0.74/0.93 tff(3634,plain,
% 0.74/0.93 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.74/0.93 inference(transitivity,[status(thm)],[3633, 720])).
% 0.74/0.93 tff(3635,plain,
% 0.74/0.93 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3634])).
% 0.74/0.93 tff(3636,plain,
% 0.74/0.93 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3635])).
% 0.74/0.93 tff(3637,plain,
% 0.74/0.93 (~(op(e3, e2) = e0)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[684, 3636])).
% 0.74/0.93 tff(3638,plain,
% 0.74/0.93 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1060])).
% 0.74/0.93 tff(3639,plain,
% 0.74/0.93 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.74/0.93 inference(transitivity,[status(thm)],[3638, 263])).
% 0.74/0.93 tff(3640,plain,
% 0.74/0.93 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3639])).
% 0.74/0.93 tff(3641,plain,
% 0.74/0.93 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3640])).
% 0.74/0.93 tff(3642,plain,
% 0.74/0.93 (~(op(e3, e0) = e0)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[272, 3641])).
% 0.74/0.93 tff(3643,plain,
% 0.74/0.93 (op(e3, e3) = e0),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[580, 3642, 3217, 3637])).
% 0.74/0.93 tff(3644,plain,
% 0.74/0.93 (op(op(e3, e3), op(e3, e3)) = op(e0, e0)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3643, 3643])).
% 0.74/0.93 tff(3645,plain,
% 0.74/0.93 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.74/0.93 inference(transitivity,[status(thm)],[3644, 3632])).
% 0.74/0.93 tff(3646,plain,
% 0.74/0.93 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1060])).
% 0.74/0.93 tff(3647,plain,
% 0.74/0.93 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.74/0.93 inference(transitivity,[status(thm)],[3646, 319])).
% 0.74/0.93 tff(3648,plain,
% 0.74/0.93 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3647])).
% 0.74/0.93 tff(3649,plain,
% 0.74/0.93 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3648])).
% 0.74/0.93 tff(3650,plain,
% 0.74/0.93 (~(op(e3, e0) = e1)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[220, 3649])).
% 0.74/0.93 tff(3651,plain,
% 0.74/0.93 (~(op(op(e3, e3), op(e3, e3)) = e3)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1769, 3643, 1397, 3650])).
% 0.74/0.93 tff(3652,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[3651, 3645])).
% 0.74/0.93 tff(3653,plain,((~(op(e3, e0) = e2)) | (e2 = op(e3, op(e3, e3))) | (op(e0, e1) = e3) | (op(e0, e3) = e3) | (op(e3, e1) = e0) | (op(e0, e1) = e1) | (~(op(e1, e1) = e2)) | (op(e3, e3) = e2) | (op(e0, e0) = e2) | (op(e2, e2) = e3) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))) | (~(op(op(e0, e2), op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(3654,plain,
% 0.74/0.93 (~(op(e3, e0) = e2)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[3653, 6, 2454, 1919, 3217, 729, 56, 418, 4, 1397, 1289, 3605, 116])).
% 0.74/0.93 tff(3655,plain,
% 0.74/0.93 (op(e3, e2) = e2),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[566, 3654, 418, 377])).
% 0.74/0.93 tff(3656,plain,
% 0.74/0.93 ((op(e3, e2) = e3) <=> (e2 = e3)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3655])).
% 0.74/0.93 tff(3657,plain,
% 0.74/0.93 ((e2 = e3) <=> (op(e3, e2) = e3)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3656])).
% 0.74/0.93 tff(3658,plain,
% 0.74/0.93 ((~(e2 = e3)) <=> (~(op(e3, e2) = e3))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3657])).
% 0.74/0.93 tff(3659,plain,
% 0.74/0.93 (~(op(e3, e2) = e3)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[195, 3658])).
% 0.74/0.93 tff(3660,plain,
% 0.74/0.93 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[769, 3659, 729, 56, 418, 4, 6])).
% 0.74/0.93 tff(3661,plain,
% 0.74/0.93 (op(op(e3, e2), op(e3, e2)) = op(e2, e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3655, 3655])).
% 0.74/0.93 tff(3662,plain,
% 0.74/0.93 ((op(op(e3, e2), op(e3, e2)) = e2) <=> (op(e2, e2) = e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3661])).
% 0.74/0.93 tff(3663,plain,
% 0.74/0.93 ((op(e2, e2) = e2) <=> (op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3662])).
% 0.74/0.93 tff(3664,plain,
% 0.74/0.93 ((~(op(e2, e2) = e2)) <=> (~(op(op(e3, e2), op(e3, e2)) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3663])).
% 0.74/0.93 tff(3665,plain,
% 0.74/0.93 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3655])).
% 0.74/0.93 tff(3666,plain,
% 0.74/0.93 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3665])).
% 0.74/0.93 tff(3667,plain,
% 0.74/0.93 (~(op(e2, e2) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[591, 3666])).
% 0.74/0.93 tff(3668,plain,
% 0.74/0.93 (~(op(op(e3, e2), op(e3, e2)) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[3667, 3664])).
% 0.74/0.93 tff(3669,plain,
% 0.74/0.93 ((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[459, 3668])).
% 0.74/0.93 tff(3670,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[416, 3669, 3660, 1289, 3605])).
% 0.74/0.93 tff(3671,plain,((op(e2, e2) = e3) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (~((~(op(op(e1, e0), op(e1, e0)) = e0)) | (~(op(op(e1, e1), op(e1, e1)) = e1)) | (~(op(op(e1, e2), op(e1, e2)) = e2)) | (~(op(op(e1, e3), op(e1, e3)) = e3)))) | (op(e0, e1) = e1) | (~(op(e1, e1) = e2)) | (op(e3, e3) = e2) | (op(e0, e0) = e2) | (op(e0, e1) = e3) | (op(e0, e3) = e3) | (op(e3, e1) = e0) | (e2 = op(e3, op(e3, e3))) | (~(op(op(e0, e2), op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(3672,plain,
% 0.74/0.93 (op(e2, e2) = e3),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[3671, 3584, 1401, 3604, 3583, 3600, 4, 3596, 3592, 3588, 1397, 3564])).
% 0.74/0.93 tff(3673,plain,
% 0.74/0.93 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3583])).
% 0.74/0.93 tff(3674,plain,
% 0.74/0.93 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.74/0.93 inference(transitivity,[status(thm)],[3673, 55])).
% 0.74/0.93 tff(3675,plain,
% 0.74/0.93 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3674])).
% 0.74/0.93 tff(3676,plain,
% 0.74/0.93 (~(op(e2, e1) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[101, 3675])).
% 0.74/0.93 tff(3677,plain,
% 0.74/0.93 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3672])).
% 0.74/0.93 tff(3678,plain,
% 0.74/0.93 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.74/0.93 inference(transitivity,[status(thm)],[3677, 937])).
% 0.74/0.93 tff(3679,plain,
% 0.74/0.93 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.74/0.93 inference(symmetry,[status(thm)],[3678])).
% 0.74/0.93 tff(3680,plain,
% 0.74/0.93 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[3679])).
% 0.74/0.93 tff(3681,plain,
% 0.74/0.93 (~(op(e2, e2) = e2)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[195, 3680])).
% 0.74/0.93 tff(3682,plain,
% 0.74/0.93 ((~(op(op(e2, e0), op(e2, e0)) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(op(e2, e2), op(e2, e2)) = e2)) | (~(op(op(e2, e3), op(e2, e3)) = e3))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[960, 3681, 3676, 3672])).
% 0.74/0.93 tff(3683,plain,
% 0.74/0.93 (~((~(op(op(e3, e0), op(e3, e0)) = e0)) | (~(op(op(e3, e1), op(e3, e1)) = e1)) | (~(op(op(e3, e2), op(e3, e2)) = e2)) | (~(op(op(e3, e3), op(e3, e3)) = e3)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[416, 3682, 1401, 3584])).
% 0.74/0.93 tff(3684,plain,
% 0.74/0.93 (op(op(e3, e2), op(e3, e2)) = e2),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[459, 3683])).
% 0.74/0.93 tff(3685,plain,
% 0.74/0.93 (~(op(e3, e2) = e0)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[474, 3684, 4])).
% 0.74/0.93 tff(3686,plain,
% 0.74/0.93 (op(op(e3, e0), op(e3, e0)) = e0),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[476, 3683])).
% 0.74/0.93 tff(3687,plain,
% 0.74/0.93 (~(op(e3, e0) = e0)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1097, 3686, 168])).
% 0.74/0.93 tff(3688,plain,
% 0.74/0.93 (op(op(e3, e3), op(e3, e3)) = e3),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[633, 3683])).
% 0.74/0.93 tff(3689,plain,
% 0.74/0.93 (~(op(e3, e3) = e0)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1778, 3688, 3565, 168, 1397, 3686])).
% 0.74/0.93 tff(3690,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[580, 3689, 3687, 3588, 3685])).
% 0.74/0.93 tff(3691,plain,((op(e0, e0) = e2) | (op(e0, e0) = e0) | (e2 = op(e3, op(e3, e3))) | (e0 = op(e2, op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(3692,plain,
% 0.74/0.93 (op(e0, e0) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3691, 2410, 4, 2343])).
% 0.79/0.93 tff(3693,plain,
% 0.79/0.93 ((op(e0, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3692])).
% 0.79/0.93 tff(3694,plain,
% 0.79/0.93 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 0.79/0.93 inference(transitivity,[status(thm)],[3693, 2358])).
% 0.79/0.93 tff(3695,plain,
% 0.79/0.93 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3694])).
% 0.79/0.93 tff(3696,plain,
% 0.79/0.93 (~(op(e2, e0) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[392, 3695])).
% 0.79/0.93 tff(3697,plain,
% 0.79/0.93 ((e0 = e2) <=> (e0 = op(e2, e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[2344])).
% 0.79/0.93 tff(3698,plain,
% 0.79/0.93 ((e0 = e2) <=> (op(e2, e2) = e0)),
% 0.79/0.93 inference(transitivity,[status(thm)],[3697, 954])).
% 0.79/0.93 tff(3699,plain,
% 0.79/0.93 ((~(e0 = e2)) <=> (~(op(e2, e2) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3698])).
% 0.79/0.93 tff(3700,plain,
% 0.79/0.93 (~(op(e2, e2) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[272, 3699])).
% 0.79/0.93 tff(3701,plain,
% 0.79/0.93 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[2337])).
% 0.79/0.93 tff(3702,plain,
% 0.79/0.93 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3701])).
% 0.79/0.93 tff(3703,plain,
% 0.79/0.93 (~(op(e1, e2) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[331, 3702])).
% 0.79/0.93 tff(3704,plain,
% 0.79/0.93 (op(e0, e3) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1962, 825, 16, 418, 817, 2374])).
% 0.79/0.93 tff(3705,plain,
% 0.79/0.93 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3704])).
% 0.79/0.93 tff(3706,plain,
% 0.79/0.93 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.79/0.93 inference(transitivity,[status(thm)],[3705, 695])).
% 0.79/0.93 tff(3707,plain,
% 0.79/0.93 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3706])).
% 0.79/0.93 tff(3708,plain,
% 0.79/0.93 (~(op(e1, e3) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1632, 3707])).
% 0.79/0.93 tff(3709,plain,
% 0.79/0.93 (~(e2 = op(e3, op(e3, e3)))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[2409, 418, 16, 817])).
% 0.79/0.93 tff(3710,plain,
% 0.79/0.93 (op(e3, e0) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1433, 825, 817, 2351, 418, 3709])).
% 0.79/0.93 tff(3711,plain,
% 0.79/0.93 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3710])).
% 0.79/0.93 tff(3712,plain,
% 0.79/0.93 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3711])).
% 0.79/0.93 tff(3713,plain,
% 0.79/0.93 (~(op(e1, e0) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1552, 3712])).
% 0.79/0.93 tff(3714,plain,
% 0.79/0.93 ((op(e1, e0) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1239, 1117])).
% 0.79/0.93 tff(3715,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3714, 3713, 3708, 3703])).
% 0.79/0.93 tff(3716,plain,((op(e3, e3) = e0) | (op(e3, e3) = e3) | (op(e3, e3) = e2) | (~(op(op(e2, e3), op(e2, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(3717,plain,
% 0.79/0.93 (op(e3, e3) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3716, 418, 2360, 2357])).
% 0.79/0.93 tff(3718,plain,
% 0.79/0.93 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3717])).
% 0.79/0.93 tff(3719,plain,
% 0.79/0.93 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3718])).
% 0.79/0.93 tff(3720,plain,
% 0.79/0.93 (~(op(e2, e3) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[656, 3719])).
% 0.79/0.93 tff(3721,plain,
% 0.79/0.93 (op(e2, e1) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1495, 3720, 3700, 3696])).
% 0.79/0.93 tff(3722,plain,
% 0.79/0.93 (op(op(e2, e1), op(e2, e1)) = op(e0, e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3721, 3721])).
% 0.79/0.93 tff(3723,plain,
% 0.79/0.93 (op(e0, e0) = op(op(e2, e1), op(e2, e1))),
% 0.79/0.93 inference(symmetry,[status(thm)],[3722])).
% 0.79/0.93 tff(3724,plain,
% 0.79/0.93 (e0 = op(e0, e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[3692])).
% 0.79/0.93 tff(3725,plain,
% 0.79/0.93 (e0 = e1),
% 0.79/0.93 inference(transitivity,[status(thm)],[3724, 3723, 2359])).
% 0.79/0.93 tff(3726,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1182, 3725])).
% 0.79/0.93 tff(3727,plain,((op(e3, e3) = e2) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(3728,plain,
% 0.79/0.93 (op(e3, e3) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3727, 4])).
% 0.79/0.93 tff(3729,plain,
% 0.79/0.93 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3728])).
% 0.79/0.93 tff(3730,plain,
% 0.79/0.93 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3729])).
% 0.79/0.93 tff(3731,plain,
% 0.79/0.93 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e2)),
% 0.79/0.93 inference(transitivity,[status(thm)],[3730, 378])).
% 0.79/0.93 tff(3732,plain,
% 0.79/0.93 ((op(e3, e2) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.79/0.93 inference(symmetry,[status(thm)],[3731])).
% 0.79/0.93 tff(3733,plain,
% 0.79/0.93 ((~(op(e3, e2) = e2)) <=> (~(e2 = op(e3, op(e3, e3))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3732])).
% 0.79/0.93 tff(3734,plain,
% 0.79/0.93 (~(e2 = op(e3, op(e3, e3)))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[2351, 3733])).
% 0.79/0.93 tff(3735,plain,
% 0.79/0.93 (op(e0, e0) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3691, 3734, 4, 2343])).
% 0.79/0.93 tff(3736,plain,
% 0.79/0.93 ((op(e0, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3735])).
% 0.79/0.93 tff(3737,plain,
% 0.79/0.93 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 0.79/0.93 inference(transitivity,[status(thm)],[3736, 2358])).
% 0.79/0.93 tff(3738,plain,
% 0.79/0.93 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3737])).
% 0.79/0.93 tff(3739,plain,
% 0.79/0.93 (~(op(e2, e0) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[392, 3738])).
% 0.79/0.93 tff(3740,assumption,(op(e2, e1) = e0), introduced(assumption)).
% 0.79/0.93 tff(3741,plain,
% 0.79/0.93 (op(op(e2, e1), op(e2, e1)) = op(e0, e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3740, 3740])).
% 0.79/0.93 tff(3742,plain,
% 0.79/0.93 (op(e0, e0) = op(op(e2, e1), op(e2, e1))),
% 0.79/0.93 inference(symmetry,[status(thm)],[3741])).
% 0.79/0.93 tff(3743,assumption,(op(e0, e0) = e0), introduced(assumption)).
% 0.79/0.93 tff(3744,plain,
% 0.79/0.93 (e0 = op(e0, e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[3743])).
% 0.79/0.93 tff(3745,plain,
% 0.79/0.93 (e0 = e1),
% 0.79/0.93 inference(transitivity,[status(thm)],[3744, 3742, 658])).
% 0.79/0.93 tff(3746,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1182, 3745])).
% 0.79/0.93 tff(3747,plain,((~(op(e2, e1) = e0)) | (~(op(op(e2, e1), op(e2, e1)) = e1)) | (~(op(e0, e0) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(3748,plain,
% 0.79/0.93 (~(op(e2, e1) = e0)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3747, 2359, 3735])).
% 0.79/0.93 tff(3749,plain,
% 0.79/0.93 (op(e2, e3) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1495, 3748, 3700, 3739])).
% 0.79/0.93 tff(3750,plain,
% 0.79/0.93 (op(op(e2, e3), op(e2, e3)) = op(e0, e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[3749, 3749])).
% 0.79/0.93 tff(3751,plain,
% 0.79/0.93 (op(e0, e0) = op(op(e2, e3), op(e2, e3))),
% 0.79/0.93 inference(symmetry,[status(thm)],[3750])).
% 0.79/0.93 tff(3752,plain,
% 0.79/0.93 (e0 = op(e0, e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[3735])).
% 0.79/0.93 tff(3753,plain,
% 0.79/0.93 (e0 = e3),
% 0.79/0.93 inference(transitivity,[status(thm)],[3752, 3751, 2357])).
% 0.79/0.93 tff(3754,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[684, 3753])).
% 0.79/0.93 tff(3755,plain,(op(e0, e0) = e2), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(3756,plain,
% 0.79/0.93 ((op(e2, e2) = e3) | (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))) | (e0 = op(e2, op(e2, e2))) | (~(op(e0, e0) = e2))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[2061, 1117])).
% 0.79/0.93 tff(3757,plain,
% 0.79/0.93 (~((~(op(op(e0, e0), op(e0, e0)) = e0)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(op(e0, e2), op(e0, e2)) = e2)) | (~(op(op(e0, e3), op(e0, e3)) = e3)))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[3756, 3755, 2347, 2343])).
% 0.79/0.93 tff(3758,plain,
% 0.79/0.93 (op(op(e0, e1), op(e0, e1)) = e1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[171, 3757])).
% 0.79/0.93 tff(3759,plain,
% 0.79/0.93 (op(e0, e1) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[310, 3757, 2347])).
% 0.79/0.93 tff(3760,plain,
% 0.79/0.93 (op(op(e0, e1), op(e0, e1)) = op(e2, e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[2411, 2411])).
% 0.79/0.93 tff(3761,plain,
% 0.79/0.93 (e1 = e2),
% 0.79/0.93 inference(transitivity,[status(thm)],[214, 3760, 1301])).
% 0.79/0.93 tff(3762,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[220, 3761])).
% 0.79/0.93 tff(3763,plain,((~(op(e0, e1) = e2)) | (~(op(op(e0, e1), op(e0, e1)) = e1)) | (~(op(e2, e2) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(3764,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[3763, 3759, 3758, 2337])).
% 0.79/0.94 % SZS output end Proof
%------------------------------------------------------------------------------