TSTP Solution File: ALG150+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG150+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 16:08:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG150+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 13:31:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(e0_type, type, (
% 0.19/0.44 e0: $i)).
% 0.19/0.44 tff(op_type, type, (
% 0.19/0.44 op: ( $i * $i ) > $i)).
% 0.19/0.44 tff(e1_type, type, (
% 0.19/0.44 e1: $i)).
% 0.19/0.44 tff(e3_type, type, (
% 0.19/0.44 e3: $i)).
% 0.19/0.44 tff(e2_type, type, (
% 0.19/0.44 e2: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((e3 = e0) <=> (e0 = e3)),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((e0 = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(3,assumption,(e0 = op(op(e2, e2), op(e2, e2))), introduced(assumption)).
% 0.19/0.44 tff(4,assumption,(op(e2, e2) = e2), introduced(assumption)).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (e2 = op(e2, e2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[4])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (op(e2, e2) = op(op(e2, e2), op(e2, e2))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[5, 5])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (op(op(e2, e2), op(e2, e2)) = op(e2, e2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[6])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (e0 = e2),
% 0.19/0.44 inference(transitivity,[status(thm)],[3, 7, 4])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 ((~(e0 = e2)) <=> (~(e0 = e2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(10,axiom,((((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))) & (~(e2 = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))),
% 0.19/0.44 inference(and_elim,[status(thm)],[10])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 ((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))),
% 0.19/0.44 inference(and_elim,[status(thm)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))),
% 0.19/0.44 inference(and_elim,[status(thm)],[12])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 ((~(e0 = e1)) & (~(e0 = e2))),
% 0.19/0.44 inference(and_elim,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (~(e0 = e2)),
% 0.19/0.44 inference(and_elim,[status(thm)],[14])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (~(e0 = e2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[16, 8])).
% 0.19/0.44 tff(18,plain,((~(op(e2, e2) = e2)) | (~(e0 = op(op(e2, e2), op(e2, e2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (~(op(e2, e2) = e2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[18, 3])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 ((op(op(e2, e2), op(e2, e2)) = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 ((op(e2, op(op(e2, e2), op(e2, e2))) = e3) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (op(e2, e0) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((op(e2, e0) = e3) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e3)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((op(e2, e0) = e3) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ((e3 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e0) = e3)),
% 0.19/0.44 inference(symmetry,[status(thm)],[24])).
% 0.19/0.44 tff(26,assumption,(~(op(e2, e2) = e3)), introduced(assumption)).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((op(op(e2, e2), op(e2, e2)) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(28,assumption,(op(e2, e2) = e1), introduced(assumption)).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (e1 = op(e2, e2)),
% 0.19/0.44 inference(symmetry,[status(thm)],[28])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[29, 29])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 ((op(e1, e1) = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 ((op(e1, e1) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[31, 27])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e1, e1) = e1)),
% 0.19/0.44 inference(symmetry,[status(thm)],[32])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e1, e1) = e1))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((e0 = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((e0 = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[35, 27])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 ((~(e0 = e1)) <=> (~(e1 = op(op(e2, e2), op(e2, e2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 ((~(e0 = e1)) <=> (~(e0 = e1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (~(e0 = e1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[14])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (~(e0 = e1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (~(e1 = op(op(e2, e2), op(e2, e2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (~(op(e1, e1) = e1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (((~(op(e2, e2) = e1)) | (op(e2, e1) = e2)) <=> ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(44,axiom,((((((((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))) & ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))) & ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3))) & ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3))) & ((~(op(e3, e3) = e2)) | (op(e3, e2) = e3))) & ((~(op(e3, e3) = e3)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax5')).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (((((((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))) & ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))) & ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3))) & ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3))) & ((~(op(e3, e3) = e2)) | (op(e3, e2) = e3))),
% 0.19/0.45 inference(and_elim,[status(thm)],[44])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((((((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))) & ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))) & ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3))) & ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3))),
% 0.19/0.45 inference(and_elim,[status(thm)],[45])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (((((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))) & ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))) & ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3))),
% 0.19/0.45 inference(and_elim,[status(thm)],[46])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))) & ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))),
% 0.19/0.45 inference(and_elim,[status(thm)],[47])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))) & ((~(op(e2, e2) = e2)) | (op(e2, e2) = e2))),
% 0.19/0.46 inference(and_elim,[status(thm)],[48])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 ((((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))) & ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2))),
% 0.19/0.46 inference(and_elim,[status(thm)],[49])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2)),
% 0.19/0.46 inference(and_elim,[status(thm)],[50])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 ((~(op(e2, e2) = e1)) | (op(e2, e1) = e2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[51, 43])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (op(e2, e1) = e2),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[52, 28])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = op(e2, e1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(57,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/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (((((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[57])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 ((((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[58])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[59])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[60])).
% 0.19/0.47 tff(62,plain,
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% 0.19/0.47 inference(and_elim,[status(thm)],[61])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[62])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[64])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 (((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[65])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 ((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[66])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 (((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[67])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (~(op(e2, e0) = op(e2, e1))),
% 0.19/0.48 inference(and_elim,[status(thm)],[68])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (~(op(e2, e0) = op(e2, e1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (~(op(e2, e0) = e2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[70, 55])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((op(e2, op(op(e2, e2), op(e2, e2))) = e1) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 (op(op(e2, e2), op(e2, e2)) = e0),
% 0.19/0.48 inference(symmetry,[status(thm)],[3])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 (op(e2, op(op(e2, e2), op(e2, e2))) = op(e2, e0)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (op(e2, e0) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.19/0.48 inference(symmetry,[status(thm)],[74])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 ((op(e2, e0) = e1) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e1)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[76, 72])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 ((e1 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 0.19/0.48 inference(symmetry,[status(thm)],[77])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e1)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[75, 28])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 ((op(e2, e0) = op(e2, e2)) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[79, 72])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e1)),
% 0.19/0.48 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e1))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = op(e2, e2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (~(op(e2, e0) = op(e2, e2))),
% 0.19/0.48 inference(and_elim,[status(thm)],[67])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 (~(op(e2, e0) = op(e2, e2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (~(op(e2, e0) = e1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 ((op(e2, e0) = e3) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e3)),
% 0.19/0.48 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((op(e2, e0) = e3) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[87, 21])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 ((e3 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e0) = e3)),
% 0.19/0.48 inference(symmetry,[status(thm)],[88])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 ((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e2, e0) = e3))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 ((e1 = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 ((op(e2, e2) = e1) <=> (e1 = op(e2, e2))),
% 0.19/0.48 inference(symmetry,[status(thm)],[91])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (e1 = op(e2, e2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[28, 92])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ((~(~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2)))))))) <=> ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2)))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 ((~(((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(100,axiom,(~(((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax7')).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (~((e0 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[103, 93, 3])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (~(op(e2, e0) = e3)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[104, 90])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (((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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 ((((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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (((((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))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (((((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))),
% 0.19/0.49 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.49 tff(111,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/sandbox2/benchmark/theBenchmark.p','ax1')).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 ((((((((((((((((((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))),
% 0.19/0.49 inference(and_elim,[status(thm)],[111])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (((((((((((((((((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))),
% 0.19/0.49 inference(and_elim,[status(thm)],[112])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 ((((((((((((((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[113])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (((((((((((((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[114])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 ((((((((((((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[115])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (((((((((((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[116])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 ((((((((((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[117])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)),
% 0.19/0.50 inference(and_elim,[status(thm)],[118])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[119, 110])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[120, 106])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 (op(e2, e0) = e0),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[121, 105, 86, 71])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = op(e2, e0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 ((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[68])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[126])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 ((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[127])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[128])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 ((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[129])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 (((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[130])).
% 0.19/0.51 tff(132,plain,
% 0.19/0.51 ((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[131])).
% 0.19/0.51 tff(133,plain,
% 0.19/0.51 (((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[132])).
% 0.19/0.51 tff(134,plain,
% 0.19/0.51 ((((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[133])).
% 0.19/0.51 tff(135,plain,
% 0.19/0.51 (((((((((((((((((((((((((((~(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)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[134])).
% 0.19/0.51 tff(136,plain,
% 0.19/0.51 ((((((((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[135])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (((((((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[136])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 ((((((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[137])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (((((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[138])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 ((((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[139])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 (((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[140])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.52 ((((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[141])).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 (((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[142])).
% 0.19/0.52 tff(144,plain,
% 0.19/0.52 ((((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[143])).
% 0.19/0.52 tff(145,plain,
% 0.19/0.52 (((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[144])).
% 0.19/0.52 tff(146,plain,
% 0.19/0.52 ((((((((((((((((~(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)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[145])).
% 0.19/0.52 tff(147,plain,
% 0.19/0.52 (((((((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[146])).
% 0.39/0.52 tff(148,plain,
% 0.39/0.52 ((((((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[147])).
% 0.39/0.52 tff(149,plain,
% 0.39/0.52 (((((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[148])).
% 0.39/0.52 tff(150,plain,
% 0.39/0.52 ((((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[149])).
% 0.39/0.52 tff(151,plain,
% 0.39/0.52 (((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[150])).
% 0.39/0.52 tff(152,plain,
% 0.39/0.52 ((((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[151])).
% 0.39/0.52 tff(153,plain,
% 0.39/0.52 (((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[152])).
% 0.39/0.52 tff(154,plain,
% 0.39/0.52 ((((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[153])).
% 0.39/0.52 tff(155,plain,
% 0.39/0.52 (((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[154])).
% 0.39/0.52 tff(156,plain,
% 0.39/0.52 ((((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[155])).
% 0.39/0.52 tff(157,plain,
% 0.39/0.52 (((((~(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)))),
% 0.39/0.52 inference(and_elim,[status(thm)],[156])).
% 0.39/0.52 tff(158,plain,
% 0.39/0.53 ((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))),
% 0.39/0.53 inference(and_elim,[status(thm)],[157])).
% 0.39/0.53 tff(159,plain,
% 0.39/0.53 (((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))),
% 0.39/0.53 inference(and_elim,[status(thm)],[158])).
% 0.39/0.53 tff(160,plain,
% 0.39/0.53 ((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))),
% 0.39/0.53 inference(and_elim,[status(thm)],[159])).
% 0.39/0.53 tff(161,plain,
% 0.39/0.53 (~(op(e0, e0) = op(e2, e0))),
% 0.39/0.53 inference(and_elim,[status(thm)],[160])).
% 0.39/0.53 tff(162,plain,
% 0.39/0.53 (~(op(e0, e0) = op(e2, e0))),
% 0.39/0.53 inference(modus_ponens,[status(thm)],[161, 125])).
% 0.39/0.53 tff(163,plain,
% 0.39/0.53 (~(op(e0, e0) = e0)),
% 0.39/0.53 inference(modus_ponens,[status(thm)],[162, 124])).
% 0.39/0.53 tff(164,plain,
% 0.39/0.53 ((e3 = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.39/0.53 inference(commutativity,[status(thm)],[])).
% 0.39/0.53 tff(165,plain,
% 0.39/0.53 ((op(e2, e1) = e3) <=> (e2 = e3)),
% 0.39/0.53 inference(monotonicity,[status(thm)],[53])).
% 0.39/0.53 tff(166,plain,
% 0.39/0.53 ((e2 = e3) <=> (op(e2, e1) = e3)),
% 0.39/0.53 inference(symmetry,[status(thm)],[165])).
% 0.39/0.53 tff(167,plain,
% 0.39/0.53 ((~(e2 = e3)) <=> (~(op(e2, e1) = e3))),
% 0.39/0.53 inference(monotonicity,[status(thm)],[166])).
% 0.39/0.53 tff(168,plain,
% 0.39/0.53 ((~(e2 = e3)) <=> (~(e2 = e3))),
% 0.39/0.53 inference(rewrite,[status(thm)],[])).
% 0.39/0.53 tff(169,plain,
% 0.39/0.53 (~(e2 = e3)),
% 0.39/0.53 inference(and_elim,[status(thm)],[10])).
% 0.39/0.53 tff(170,plain,
% 0.39/0.53 (~(e2 = e3)),
% 0.39/0.53 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.39/0.53 tff(171,plain,
% 0.39/0.53 (~(op(e2, e1) = e3)),
% 0.39/0.53 inference(modus_ponens,[status(thm)],[170, 167])).
% 0.39/0.53 tff(172,plain,
% 0.39/0.53 (((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))),
% 0.39/0.53 inference(rewrite,[status(thm)],[])).
% 0.39/0.53 tff(173,plain,
% 0.39/0.53 ((((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))),
% 0.39/0.53 inference(rewrite,[status(thm)],[])).
% 0.39/0.53 tff(174,plain,
% 0.39/0.53 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3))),
% 0.39/0.53 inference(rewrite,[status(thm)],[])).
% 0.39/0.53 tff(175,plain,
% 0.39/0.53 (((((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))),
% 0.39/0.53 inference(monotonicity,[status(thm)],[174])).
% 0.39/0.53 tff(176,plain,
% 0.39/0.53 (((((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))),
% 0.39/0.53 inference(transitivity,[status(thm)],[175, 173])).
% 0.39/0.53 tff(177,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/sandbox2/benchmark/theBenchmark.p','ax2')).
% 0.39/0.53 tff(178,plain,
% 0.39/0.53 ((((((((((((((((((((((((((((((((((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))),
% 0.41/0.54 inference(and_elim,[status(thm)],[177])).
% 0.41/0.54 tff(179,plain,
% 0.41/0.54 (((((((((((((((((((((((((((((((((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))),
% 0.41/0.54 inference(and_elim,[status(thm)],[178])).
% 0.41/0.54 tff(180,plain,
% 0.41/0.54 ((((((((((((((((((((((((((((((((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))),
% 0.41/0.54 inference(and_elim,[status(thm)],[179])).
% 0.41/0.54 tff(181,plain,
% 0.41/0.54 (((((((((((((((((((((((((((((((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))),
% 0.41/0.54 inference(and_elim,[status(thm)],[180])).
% 0.41/0.54 tff(182,plain,
% 0.41/0.54 ((((((((((((((((((((((((((((((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))),
% 0.41/0.55 inference(and_elim,[status(thm)],[181])).
% 0.41/0.55 tff(183,plain,
% 0.41/0.55 (((((((((((((((((((((((((((((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))),
% 0.41/0.56 inference(and_elim,[status(thm)],[182])).
% 0.41/0.56 tff(184,plain,
% 0.41/0.56 ((((((((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.56 inference(and_elim,[status(thm)],[183])).
% 0.41/0.56 tff(185,plain,
% 0.41/0.56 (((((((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.56 inference(and_elim,[status(thm)],[184])).
% 0.41/0.56 tff(186,plain,
% 0.41/0.56 ((((((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.56 inference(and_elim,[status(thm)],[185])).
% 0.41/0.56 tff(187,plain,
% 0.41/0.56 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)),
% 0.41/0.56 inference(and_elim,[status(thm)],[186])).
% 0.41/0.56 tff(188,plain,
% 0.41/0.56 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[187, 176])).
% 0.41/0.56 tff(189,plain,
% 0.41/0.56 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[188, 172])).
% 0.41/0.56 tff(190,plain,
% 0.41/0.56 (op(e2, e3) = e3),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[189, 105, 26, 171])).
% 0.41/0.56 tff(191,plain,
% 0.41/0.56 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[190])).
% 0.41/0.56 tff(192,plain,
% 0.41/0.56 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.41/0.56 inference(transitivity,[status(thm)],[191, 164])).
% 0.41/0.56 tff(193,plain,
% 0.41/0.56 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[192])).
% 0.41/0.56 tff(194,plain,
% 0.41/0.56 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = op(e3, e3)))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(195,plain,
% 0.41/0.56 (~(op(e2, e3) = op(e3, e3))),
% 0.41/0.56 inference(and_elim,[status(thm)],[138])).
% 0.41/0.57 tff(196,plain,
% 0.41/0.57 (~(op(e2, e3) = op(e3, e3))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.41/0.57 tff(197,plain,
% 0.41/0.57 (~(op(e3, e3) = e3)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.41/0.57 tff(198,plain,
% 0.41/0.57 (((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3)) <=> ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(199,plain,
% 0.41/0.57 ((((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2)) | (op(e3, e3) = e3)) <=> ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(200,plain,
% 0.41/0.57 ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) <=> ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(201,plain,
% 0.41/0.57 (((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3)) <=> (((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[200])).
% 0.41/0.57 tff(202,plain,
% 0.41/0.57 (((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3)) <=> ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3))),
% 0.41/0.57 inference(transitivity,[status(thm)],[201, 199])).
% 0.41/0.57 tff(203,plain,
% 0.41/0.57 (((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))) & ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))),
% 0.41/0.57 inference(and_elim,[status(thm)],[50])).
% 0.41/0.57 tff(204,plain,
% 0.41/0.57 ((((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))) & ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[203])).
% 0.41/0.57 tff(205,plain,
% 0.41/0.57 (((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))) & ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[204])).
% 0.41/0.57 tff(206,plain,
% 0.41/0.57 ((((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))) & ((~(op(e1, e1) = e1)) | (op(e1, e1) = e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[205])).
% 0.41/0.57 tff(207,plain,
% 0.41/0.57 (((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))) & ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[206])).
% 0.41/0.57 tff(208,plain,
% 0.41/0.57 ((((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))) & ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))),
% 0.41/0.57 inference(and_elim,[status(thm)],[207])).
% 0.41/0.57 tff(209,plain,
% 0.41/0.57 (((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))) & ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))),
% 0.41/0.57 inference(and_elim,[status(thm)],[208])).
% 0.41/0.57 tff(210,plain,
% 0.41/0.57 ((((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))) & ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))),
% 0.41/0.57 inference(and_elim,[status(thm)],[209])).
% 0.41/0.57 tff(211,plain,
% 0.41/0.57 (((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))) & ((~(op(e0, e0) = e0)) | (op(e0, e0) = e0))),
% 0.41/0.57 inference(and_elim,[status(thm)],[210])).
% 0.41/0.57 tff(212,plain,
% 0.41/0.57 ((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) & ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3))),
% 0.41/0.57 inference(and_elim,[status(thm)],[211])).
% 0.41/0.57 tff(213,plain,
% 0.41/0.57 ((((op(e0, e0) = e0) | (op(e1, e1) = e1)) | (op(e2, e2) = e2)) | (op(e3, e3) = e3)),
% 0.41/0.57 inference(and_elim,[status(thm)],[212])).
% 0.41/0.57 tff(214,plain,
% 0.41/0.57 ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[213, 202])).
% 0.41/0.57 tff(215,plain,
% 0.41/0.57 ((op(e0, e0) = e0) | (op(e1, e1) = e1) | (op(e2, e2) = e2) | (op(e3, e3) = e3)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[214, 198])).
% 0.41/0.57 tff(216,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[215, 197, 163, 42, 19])).
% 0.41/0.57 tff(217,plain,((~(op(e2, e2) = e1)) | (op(e2, e2) = e3) | (~(e0 = op(op(e2, e2), op(e2, e2))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(218,plain,
% 0.41/0.57 (~(op(e2, e2) = e1)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[217, 26, 3])).
% 0.41/0.58 tff(219,plain,
% 0.41/0.58 (((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(220,plain,
% 0.41/0.58 ((((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(221,plain,
% 0.41/0.58 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(222,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[221])).
% 0.41/0.58 tff(223,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(transitivity,[status(thm)],[222, 220])).
% 0.41/0.58 tff(224,plain,
% 0.41/0.58 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)),
% 0.41/0.58 inference(and_elim,[status(thm)],[116])).
% 0.41/0.58 tff(225,plain,
% 0.41/0.58 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.41/0.58 tff(226,plain,
% 0.41/0.58 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[225, 219])).
% 0.41/0.58 tff(227,plain,
% 0.41/0.58 (op(e2, e2) = e0),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[226, 218, 19, 26])).
% 0.41/0.58 tff(228,plain,
% 0.41/0.58 (((~(op(e2, e2) = e0)) | (op(e2, e0) = e2)) <=> ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(229,plain,
% 0.41/0.58 ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2)),
% 0.41/0.58 inference(and_elim,[status(thm)],[203])).
% 0.41/0.58 tff(230,plain,
% 0.41/0.58 ((~(op(e2, e2) = e0)) | (op(e2, e0) = e2)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.41/0.58 tff(231,plain,
% 0.41/0.58 (op(e2, e0) = e2),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.41/0.58 tff(232,plain,
% 0.41/0.58 (e2 = op(e2, e0)),
% 0.41/0.58 inference(symmetry,[status(thm)],[231])).
% 0.41/0.58 tff(233,plain,
% 0.41/0.58 (e2 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.41/0.58 inference(transitivity,[status(thm)],[232, 22])).
% 0.41/0.58 tff(234,plain,
% 0.41/0.58 ((e2 = e3) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e3)),
% 0.41/0.58 inference(monotonicity,[status(thm)],[233])).
% 0.41/0.58 tff(235,plain,
% 0.41/0.58 ((e2 = e3) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[234, 21])).
% 0.41/0.58 tff(236,plain,
% 0.41/0.58 ((e2 = e3) <=> (op(e2, e0) = e3)),
% 0.41/0.58 inference(transitivity,[status(thm)],[235, 25])).
% 0.41/0.58 tff(237,plain,
% 0.41/0.58 ((~(e2 = e3)) <=> (~(op(e2, e0) = e3))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[236])).
% 0.41/0.58 tff(238,plain,
% 0.41/0.58 (~(op(e2, e0) = e3)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[170, 237])).
% 0.41/0.58 tff(239,plain,
% 0.41/0.58 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e0)),
% 0.41/0.58 inference(monotonicity,[status(thm)],[227])).
% 0.41/0.58 tff(240,plain,
% 0.41/0.58 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[239])).
% 0.41/0.58 tff(241,plain,
% 0.41/0.58 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = op(e2, e2)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(242,plain,
% 0.41/0.58 (~(op(e1, e2) = op(e2, e2))),
% 0.41/0.58 inference(and_elim,[status(thm)],[146])).
% 0.41/0.58 tff(243,plain,
% 0.41/0.58 (~(op(e1, e2) = op(e2, e2))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.41/0.58 tff(244,plain,
% 0.41/0.58 (~(op(e1, e2) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.41/0.58 tff(245,plain,
% 0.41/0.58 ((e0 = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(246,plain,
% 0.41/0.58 (e0 = op(e2, e2)),
% 0.41/0.58 inference(symmetry,[status(thm)],[227])).
% 0.41/0.58 tff(247,plain,
% 0.41/0.58 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[246, 246])).
% 0.41/0.58 tff(248,plain,
% 0.41/0.58 (op(e0, e0) = e0),
% 0.41/0.58 inference(transitivity,[status(thm)],[247, 73])).
% 0.41/0.58 tff(249,plain,
% 0.41/0.58 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[248])).
% 0.41/0.58 tff(250,plain,
% 0.41/0.58 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.41/0.58 inference(transitivity,[status(thm)],[249, 245])).
% 0.41/0.58 tff(251,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[250])).
% 0.41/0.58 tff(252,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = op(e1, e0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(253,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e1, e0))),
% 0.41/0.58 inference(and_elim,[status(thm)],[160])).
% 0.41/0.58 tff(254,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e1, e0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.41/0.58 tff(255,plain,
% 0.41/0.58 (~(op(e1, e0) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[254, 251])).
% 0.41/0.58 tff(256,plain,
% 0.41/0.58 ((e3 = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(257,assumption,(op(e2, e2) = e0), introduced(assumption)).
% 0.41/0.58 tff(258,plain,
% 0.41/0.58 (op(e2, e0) = e2),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[230, 257])).
% 0.41/0.58 tff(259,plain,
% 0.41/0.58 (e2 = op(e2, e0)),
% 0.41/0.58 inference(symmetry,[status(thm)],[258])).
% 0.41/0.58 tff(260,plain,
% 0.41/0.58 (e2 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.41/0.58 inference(transitivity,[status(thm)],[259, 22])).
% 0.41/0.58 tff(261,plain,
% 0.41/0.58 ((e0 = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(262,plain,
% 0.41/0.58 (e0 = op(e2, e2)),
% 0.41/0.58 inference(symmetry,[status(thm)],[257])).
% 0.41/0.58 tff(263,plain,
% 0.41/0.58 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[262, 262])).
% 0.41/0.58 tff(264,plain,
% 0.41/0.58 (op(e0, e0) = e0),
% 0.41/0.58 inference(transitivity,[status(thm)],[263, 73])).
% 0.41/0.58 tff(265,plain,
% 0.41/0.58 ((op(e0, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[264])).
% 0.41/0.58 tff(266,plain,
% 0.41/0.58 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.41/0.58 inference(transitivity,[status(thm)],[265, 261])).
% 0.41/0.58 tff(267,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[266])).
% 0.41/0.58 tff(268,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = op(e3, e0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(269,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e3, e0))),
% 0.41/0.58 inference(and_elim,[status(thm)],[159])).
% 0.41/0.58 tff(270,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e3, e0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.41/0.58 tff(271,plain,
% 0.41/0.58 (~(op(e3, e0) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[270, 267])).
% 0.41/0.58 tff(272,plain,
% 0.41/0.58 ((e0 = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(273,plain,
% 0.41/0.58 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[257])).
% 0.41/0.58 tff(274,plain,
% 0.41/0.58 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.41/0.58 inference(transitivity,[status(thm)],[273, 272])).
% 0.41/0.58 tff(275,plain,
% 0.41/0.58 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[274])).
% 0.41/0.58 tff(276,plain,
% 0.41/0.58 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = op(e3, e2)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(277,plain,
% 0.41/0.58 (~(op(e2, e2) = op(e3, e2))),
% 0.41/0.58 inference(and_elim,[status(thm)],[144])).
% 0.41/0.58 tff(278,plain,
% 0.41/0.58 (~(op(e2, e2) = op(e3, e2))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.41/0.58 tff(279,plain,
% 0.41/0.58 (~(op(e3, e2) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.41/0.58 tff(280,assumption,(~(op(e3, e3) = e0)), introduced(assumption)).
% 0.41/0.58 tff(281,plain,
% 0.41/0.58 (((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(282,plain,
% 0.41/0.58 ((((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(283,plain,
% 0.41/0.58 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(284,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[283])).
% 0.41/0.58 tff(285,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(transitivity,[status(thm)],[284, 282])).
% 0.41/0.58 tff(286,plain,
% 0.41/0.58 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)),
% 0.41/0.58 inference(and_elim,[status(thm)],[184])).
% 0.41/0.58 tff(287,plain,
% 0.41/0.58 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.41/0.58 tff(288,plain,
% 0.41/0.58 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[287, 281])).
% 0.41/0.58 tff(289,plain,
% 0.41/0.58 (op(e3, e1) = e0),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[288, 280, 279, 271])).
% 0.41/0.58 tff(290,plain,
% 0.41/0.58 ((op(e3, e1) = e2) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[289, 260])).
% 0.41/0.58 tff(291,plain,
% 0.41/0.58 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e3, e1) = e2)),
% 0.41/0.58 inference(symmetry,[status(thm)],[290])).
% 0.41/0.58 tff(292,plain,
% 0.41/0.58 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e3, e1) = e2))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[291])).
% 0.41/0.58 tff(293,plain,
% 0.41/0.58 ((op(e2, op(op(e2, e2), op(e2, e2))) = e0) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(294,plain,
% 0.41/0.58 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e0)),
% 0.41/0.58 inference(monotonicity,[status(thm)],[22, 257])).
% 0.41/0.58 tff(295,plain,
% 0.41/0.58 ((op(e2, e0) = op(e2, e2)) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[294, 293])).
% 0.41/0.58 tff(296,plain,
% 0.41/0.58 ((~(op(e2, e0) = op(e2, e2))) <=> (~(e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[295])).
% 0.41/0.58 tff(297,plain,
% 0.41/0.58 (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[85, 296])).
% 0.41/0.58 tff(298,plain,
% 0.41/0.58 (~(op(e3, e1) = e2)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[297, 292])).
% 0.41/0.58 tff(299,plain,
% 0.41/0.58 ((e0 = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(300,plain,
% 0.41/0.58 ((op(e0, e0) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[264])).
% 0.41/0.58 tff(301,plain,
% 0.41/0.58 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.41/0.58 inference(transitivity,[status(thm)],[300, 299])).
% 0.41/0.58 tff(302,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[301])).
% 0.41/0.58 tff(303,plain,
% 0.41/0.58 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = op(e0, e3)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(304,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e0, e3))),
% 0.41/0.58 inference(and_elim,[status(thm)],[135])).
% 0.41/0.58 tff(305,plain,
% 0.41/0.58 (~(op(e0, e0) = op(e0, e3))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.41/0.58 tff(306,plain,
% 0.41/0.58 (~(op(e0, e3) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[305, 302])).
% 0.41/0.58 tff(307,plain,
% 0.41/0.58 ((e0 = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(308,plain,
% 0.41/0.58 ((op(e2, e2) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[257])).
% 0.41/0.58 tff(309,plain,
% 0.41/0.58 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.41/0.58 inference(transitivity,[status(thm)],[308, 307])).
% 0.41/0.58 tff(310,plain,
% 0.41/0.58 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[309])).
% 0.41/0.58 tff(311,plain,
% 0.41/0.58 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = op(e2, e3)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(312,plain,
% 0.41/0.58 (~(op(e2, e2) = op(e2, e3))),
% 0.41/0.58 inference(and_elim,[status(thm)],[63])).
% 0.41/0.58 tff(313,plain,
% 0.41/0.58 (~(op(e2, e2) = op(e2, e3))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.41/0.58 tff(314,plain,
% 0.41/0.58 (~(op(e2, e3) = e0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.41/0.58 tff(315,plain,
% 0.41/0.58 (((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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(316,plain,
% 0.41/0.59 ((((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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(317,plain,
% 0.41/0.59 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(318,plain,
% 0.41/0.59 (((((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))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[317])).
% 0.41/0.59 tff(319,plain,
% 0.41/0.59 (((((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))),
% 0.41/0.59 inference(transitivity,[status(thm)],[318, 316])).
% 0.41/0.59 tff(320,plain,
% 0.41/0.59 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)),
% 0.41/0.59 inference(and_elim,[status(thm)],[183])).
% 0.41/0.59 tff(321,plain,
% 0.41/0.59 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.41/0.59 tff(322,plain,
% 0.41/0.59 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[321, 315])).
% 0.41/0.59 tff(323,plain,
% 0.41/0.59 (op(e1, e3) = e0),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[322, 280, 314, 306])).
% 0.41/0.59 tff(324,plain,
% 0.41/0.59 (op(e1, e3) = op(op(e2, e2), op(e2, e2))),
% 0.41/0.59 inference(transitivity,[status(thm)],[323, 3])).
% 0.41/0.59 tff(325,plain,
% 0.41/0.59 ((op(e1, e3) = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.41/0.59 inference(monotonicity,[status(thm)],[324])).
% 0.41/0.59 tff(326,plain,
% 0.41/0.59 ((op(e1, e3) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.41/0.59 inference(transitivity,[status(thm)],[325, 27])).
% 0.41/0.59 tff(327,plain,
% 0.41/0.59 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e1, e3) = e1)),
% 0.41/0.59 inference(symmetry,[status(thm)],[326])).
% 0.41/0.59 tff(328,plain,
% 0.41/0.59 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e1, e3) = e1))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[327])).
% 0.41/0.59 tff(329,plain,
% 0.41/0.59 (~(op(e1, e3) = e1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[41, 328])).
% 0.41/0.59 tff(330,plain,
% 0.41/0.59 (((~(op(e1, e1) = e3)) | (op(e1, e3) = e1)) <=> ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(331,plain,
% 0.41/0.59 ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1)),
% 0.41/0.59 inference(and_elim,[status(thm)],[204])).
% 0.41/0.59 tff(332,plain,
% 0.41/0.59 ((~(op(e1, e1) = e3)) | (op(e1, e3) = e1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.41/0.59 tff(333,plain,
% 0.41/0.59 (~(op(e1, e1) = e3)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[332, 329])).
% 0.41/0.59 tff(334,plain,
% 0.41/0.59 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e0)),
% 0.41/0.59 inference(monotonicity,[status(thm)],[289])).
% 0.41/0.59 tff(335,plain,
% 0.41/0.59 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e0))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[334])).
% 0.41/0.59 tff(336,plain,
% 0.41/0.59 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = op(e3, e1)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(337,plain,
% 0.41/0.59 (~(op(e1, e1) = op(e3, e1))),
% 0.41/0.59 inference(and_elim,[status(thm)],[151])).
% 0.41/0.59 tff(338,plain,
% 0.41/0.59 (~(op(e1, e1) = op(e3, e1))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.41/0.59 tff(339,plain,
% 0.41/0.59 (~(op(e1, e1) = e0)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[338, 335])).
% 0.41/0.59 tff(340,plain,
% 0.41/0.59 ((op(e0, e0) = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.41/0.59 inference(monotonicity,[status(thm)],[263])).
% 0.41/0.59 tff(341,plain,
% 0.41/0.59 ((op(e0, e0) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.41/0.59 inference(transitivity,[status(thm)],[340, 27])).
% 0.41/0.59 tff(342,plain,
% 0.41/0.59 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e0, e0) = e1)),
% 0.41/0.59 inference(symmetry,[status(thm)],[341])).
% 0.41/0.59 tff(343,plain,
% 0.41/0.59 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e0, e0) = e1))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[342])).
% 0.41/0.59 tff(344,plain,
% 0.41/0.59 (~(op(e0, e0) = e1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[41, 343])).
% 0.41/0.59 tff(345,plain,
% 0.41/0.59 ((op(e2, e0) = e1) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e1)),
% 0.41/0.59 inference(monotonicity,[status(thm)],[22])).
% 0.41/0.59 tff(346,plain,
% 0.41/0.59 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[345, 72])).
% 0.41/0.59 tff(347,plain,
% 0.41/0.59 ((e1 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 0.41/0.59 inference(symmetry,[status(thm)],[346])).
% 0.41/0.59 tff(348,plain,
% 0.41/0.59 ((e1 = e2) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[260])).
% 0.41/0.59 tff(349,plain,
% 0.41/0.59 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 0.41/0.59 inference(transitivity,[status(thm)],[348, 347])).
% 0.41/0.59 tff(350,plain,
% 0.41/0.59 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[349])).
% 0.41/0.59 tff(351,plain,
% 0.41/0.59 ((~(e1 = e2)) <=> (~(e1 = e2))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(352,plain,
% 0.41/0.59 (~(e1 = e2)),
% 0.41/0.59 inference(and_elim,[status(thm)],[12])).
% 0.41/0.59 tff(353,plain,
% 0.41/0.59 (~(e1 = e2)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.41/0.59 tff(354,plain,
% 0.41/0.59 (~(op(e2, e0) = e1)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.41/0.59 tff(355,plain,
% 0.41/0.59 ((op(e1, e3) = e2) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[323, 260])).
% 0.41/0.59 tff(356,plain,
% 0.41/0.59 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e1, e3) = e2)),
% 0.41/0.59 inference(symmetry,[status(thm)],[355])).
% 0.41/0.59 tff(357,plain,
% 0.41/0.59 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e1, e3) = e2))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[356])).
% 0.41/0.59 tff(358,plain,
% 0.41/0.59 (~(op(e1, e3) = e2)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[297, 357])).
% 0.41/0.59 tff(359,plain,
% 0.41/0.59 ((e2 = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.41/0.59 inference(commutativity,[status(thm)],[])).
% 0.41/0.59 tff(360,plain,
% 0.41/0.59 ((op(e3, e3) = e2) <=> (e2 = op(e3, e3))),
% 0.41/0.59 inference(symmetry,[status(thm)],[359])).
% 0.41/0.59 tff(361,assumption,(~(op(e1, e3) = e2)), introduced(assumption)).
% 0.41/0.59 tff(362,plain,
% 0.41/0.59 ((op(e2, e3) = op(e2, e0)) <=> (op(e2, e0) = op(e2, e3))),
% 0.41/0.59 inference(commutativity,[status(thm)],[])).
% 0.41/0.59 tff(363,plain,
% 0.41/0.59 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e2, e0))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[259])).
% 0.41/0.59 tff(364,plain,
% 0.41/0.59 ((op(e2, e3) = e2) <=> (op(e2, e0) = op(e2, e3))),
% 0.41/0.59 inference(transitivity,[status(thm)],[363, 362])).
% 0.41/0.59 tff(365,plain,
% 0.41/0.59 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.41/0.59 inference(symmetry,[status(thm)],[364])).
% 0.41/0.59 tff(366,plain,
% 0.41/0.59 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[365])).
% 0.41/0.59 tff(367,plain,
% 0.41/0.59 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = op(e2, e3)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(368,plain,
% 0.41/0.59 (~(op(e2, e0) = op(e2, e3))),
% 0.41/0.59 inference(and_elim,[status(thm)],[66])).
% 0.41/0.59 tff(369,plain,
% 0.41/0.59 (~(op(e2, e0) = op(e2, e3))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.41/0.59 tff(370,plain,
% 0.41/0.59 (~(op(e2, e3) = e2)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[369, 366])).
% 0.41/0.59 tff(371,plain,
% 0.41/0.59 ((e2 = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.41/0.59 inference(commutativity,[status(thm)],[])).
% 0.41/0.59 tff(372,assumption,(~(op(e3, e1) = e2)), introduced(assumption)).
% 0.41/0.59 tff(373,plain,
% 0.41/0.59 ((op(e2, e1) = op(e2, e0)) <=> (op(e2, e0) = op(e2, e1))),
% 0.41/0.59 inference(commutativity,[status(thm)],[])).
% 0.41/0.59 tff(374,plain,
% 0.41/0.59 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e2, e0))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[259])).
% 0.41/0.59 tff(375,plain,
% 0.41/0.59 ((op(e2, e1) = e2) <=> (op(e2, e0) = op(e2, e1))),
% 0.41/0.59 inference(transitivity,[status(thm)],[374, 373])).
% 0.41/0.59 tff(376,plain,
% 0.41/0.59 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.41/0.59 inference(symmetry,[status(thm)],[375])).
% 0.41/0.59 tff(377,plain,
% 0.41/0.59 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[376])).
% 0.41/0.59 tff(378,plain,
% 0.41/0.59 (~(op(e2, e1) = e2)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[70, 377])).
% 0.41/0.59 tff(379,assumption,(~(op(e1, e1) = e2)), introduced(assumption)).
% 0.41/0.59 tff(380,plain,
% 0.41/0.59 (((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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(381,plain,
% 0.41/0.59 ((((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))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(382,plain,
% 0.41/0.59 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(383,plain,
% 0.41/0.59 (((((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))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[382])).
% 0.41/0.59 tff(384,plain,
% 0.41/0.59 (((((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))),
% 0.41/0.59 inference(transitivity,[status(thm)],[383, 381])).
% 0.41/0.59 tff(385,plain,
% 0.41/0.59 (((((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.59 inference(and_elim,[status(thm)],[186])).
% 0.41/0.59 tff(386,plain,
% 0.41/0.59 ((((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.60 inference(and_elim,[status(thm)],[385])).
% 0.41/0.60 tff(387,plain,
% 0.41/0.60 (((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.60 inference(and_elim,[status(thm)],[386])).
% 0.41/0.60 tff(388,plain,
% 0.41/0.60 ((((((((((((((((((((((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))) & ((((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))),
% 0.41/0.60 inference(and_elim,[status(thm)],[387])).
% 0.41/0.60 tff(389,plain,
% 0.41/0.60 (((((((((((((((((((((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))) & ((((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))),
% 0.41/0.60 inference(and_elim,[status(thm)],[388])).
% 0.41/0.60 tff(390,plain,
% 0.41/0.60 ((((((((((((((((((((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))) & ((((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))),
% 0.41/0.60 inference(and_elim,[status(thm)],[389])).
% 0.41/0.60 tff(391,plain,
% 0.41/0.60 (((((((((((((((((((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))) & ((((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))),
% 0.41/0.61 inference(and_elim,[status(thm)],[390])).
% 0.41/0.61 tff(392,plain,
% 0.41/0.61 ((((((((((((((((((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))),
% 0.41/0.61 inference(and_elim,[status(thm)],[391])).
% 0.41/0.61 tff(393,plain,
% 0.41/0.61 (((((((((((((((((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))),
% 0.41/0.61 inference(and_elim,[status(thm)],[392])).
% 0.41/0.61 tff(394,plain,
% 0.41/0.61 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)),
% 0.41/0.61 inference(and_elim,[status(thm)],[393])).
% 0.41/0.61 tff(395,plain,
% 0.41/0.61 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[394, 384])).
% 0.41/0.61 tff(396,plain,
% 0.41/0.61 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[395, 380])).
% 0.41/0.61 tff(397,plain,
% 0.41/0.61 (op(e0, e1) = e2),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[396, 379, 378, 372])).
% 0.41/0.61 tff(398,plain,
% 0.41/0.61 ((op(e0, e1) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[397])).
% 0.41/0.61 tff(399,plain,
% 0.41/0.61 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.41/0.61 inference(transitivity,[status(thm)],[398, 371])).
% 0.41/0.61 tff(400,plain,
% 0.41/0.61 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[399])).
% 0.41/0.61 tff(401,plain,
% 0.41/0.61 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e0, e3)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(402,plain,
% 0.41/0.61 (~(op(e0, e1) = op(e0, e3))),
% 0.41/0.61 inference(and_elim,[status(thm)],[133])).
% 0.41/0.61 tff(403,plain,
% 0.41/0.61 (~(op(e0, e1) = op(e0, e3))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.41/0.61 tff(404,plain,
% 0.41/0.61 (~(op(e0, e3) = e2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[403, 400])).
% 0.41/0.61 tff(405,plain,
% 0.41/0.61 (((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))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(406,plain,
% 0.41/0.61 ((((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))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(407,plain,
% 0.41/0.61 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(408,plain,
% 0.41/0.61 (((((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))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[407])).
% 0.41/0.61 tff(409,plain,
% 0.41/0.61 (((((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))),
% 0.41/0.61 inference(transitivity,[status(thm)],[408, 406])).
% 0.41/0.61 tff(410,plain,
% 0.41/0.61 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)),
% 0.41/0.61 inference(and_elim,[status(thm)],[179])).
% 0.41/0.61 tff(411,plain,
% 0.41/0.61 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.41/0.61 tff(412,plain,
% 0.41/0.61 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[411, 405])).
% 0.41/0.61 tff(413,plain,
% 0.41/0.61 (op(e3, e3) = e2),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[412, 404, 370, 361])).
% 0.41/0.61 tff(414,plain,
% 0.41/0.61 (e2 = op(e3, e3)),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[413, 360])).
% 0.41/0.61 tff(415,plain,
% 0.41/0.61 (op(op(e3, e3), op(e3, e3)) = op(e2, e2)),
% 0.41/0.61 inference(monotonicity,[status(thm)],[413, 413])).
% 0.41/0.61 tff(416,plain,
% 0.41/0.61 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.41/0.61 inference(symmetry,[status(thm)],[415])).
% 0.41/0.61 tff(417,plain,
% 0.41/0.61 (e0 = op(op(e3, e3), op(e3, e3))),
% 0.41/0.61 inference(transitivity,[status(thm)],[262, 416])).
% 0.41/0.61 tff(418,plain,
% 0.41/0.61 (op(op(e3, e3), op(e3, e3)) = e0),
% 0.41/0.61 inference(transitivity,[status(thm)],[415, 257])).
% 0.41/0.61 tff(419,plain,
% 0.41/0.61 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e0)),
% 0.41/0.61 inference(monotonicity,[status(thm)],[418])).
% 0.41/0.61 tff(420,plain,
% 0.41/0.61 (op(e3, e0) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.41/0.61 inference(symmetry,[status(thm)],[419])).
% 0.41/0.61 tff(421,assumption,(~(op(e0, e0) = e1)), introduced(assumption)).
% 0.41/0.61 tff(422,assumption,(~(op(e2, e0) = e1)), introduced(assumption)).
% 0.41/0.61 tff(423,assumption,(~(op(e1, e1) = e3)), introduced(assumption)).
% 0.41/0.61 tff(424,assumption,(~(op(e1, e1) = e0)), introduced(assumption)).
% 0.41/0.61 tff(425,plain,
% 0.41/0.61 (((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(426,plain,
% 0.41/0.61 ((((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(427,plain,
% 0.41/0.61 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(428,plain,
% 0.41/0.62 (((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)) <=> (((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[427])).
% 0.41/0.62 tff(429,plain,
% 0.41/0.62 (((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3))),
% 0.41/0.62 inference(transitivity,[status(thm)],[428, 426])).
% 0.41/0.62 tff(430,plain,
% 0.41/0.62 (((((((((((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))),
% 0.41/0.62 inference(and_elim,[status(thm)],[118])).
% 0.41/0.62 tff(431,plain,
% 0.41/0.62 ((((((((((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))),
% 0.41/0.62 inference(and_elim,[status(thm)],[430])).
% 0.41/0.62 tff(432,plain,
% 0.41/0.62 (((((((((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))),
% 0.41/0.62 inference(and_elim,[status(thm)],[431])).
% 0.41/0.62 tff(433,plain,
% 0.41/0.62 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)),
% 0.41/0.62 inference(and_elim,[status(thm)],[432])).
% 0.41/0.62 tff(434,plain,
% 0.41/0.62 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.41/0.62 tff(435,plain,
% 0.41/0.62 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[434, 425])).
% 0.41/0.62 tff(436,plain,
% 0.41/0.62 (op(e1, e1) = e1),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[435, 379, 424, 423])).
% 0.41/0.62 tff(437,plain,
% 0.41/0.62 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 0.41/0.62 inference(monotonicity,[status(thm)],[436])).
% 0.41/0.62 tff(438,plain,
% 0.41/0.62 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[437])).
% 0.41/0.62 tff(439,plain,
% 0.41/0.62 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = op(e1, e1)))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(440,plain,
% 0.41/0.62 (~(op(e1, e0) = op(e1, e1))),
% 0.41/0.62 inference(and_elim,[status(thm)],[131])).
% 0.41/0.62 tff(441,plain,
% 0.41/0.62 (~(op(e1, e0) = op(e1, e1))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.41/0.62 tff(442,plain,
% 0.41/0.62 (~(op(e1, e0) = e1)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[441, 438])).
% 0.41/0.62 tff(443,plain,
% 0.41/0.62 (((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))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(444,plain,
% 0.41/0.62 ((((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))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(445,plain,
% 0.41/0.62 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(446,plain,
% 0.41/0.62 (((((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))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[445])).
% 0.41/0.62 tff(447,plain,
% 0.41/0.62 (((((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))),
% 0.41/0.62 inference(transitivity,[status(thm)],[446, 444])).
% 0.41/0.62 tff(448,plain,
% 0.41/0.62 ((((((((((((((((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))),
% 0.41/0.62 inference(and_elim,[status(thm)],[393])).
% 0.41/0.62 tff(449,plain,
% 0.41/0.62 (((((((((((((((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))),
% 0.41/0.62 inference(and_elim,[status(thm)],[448])).
% 0.41/0.62 tff(450,plain,
% 0.41/0.62 ((((((((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[449])).
% 0.49/0.63 tff(451,plain,
% 0.49/0.63 (((((((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[450])).
% 0.49/0.63 tff(452,plain,
% 0.49/0.63 ((((((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[451])).
% 0.49/0.63 tff(453,plain,
% 0.49/0.63 (((((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[452])).
% 0.49/0.63 tff(454,plain,
% 0.49/0.63 ((((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[453])).
% 0.49/0.63 tff(455,plain,
% 0.49/0.63 (((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[454])).
% 0.49/0.63 tff(456,plain,
% 0.49/0.63 ((((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[455])).
% 0.49/0.63 tff(457,plain,
% 0.49/0.63 (((((((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))),
% 0.49/0.63 inference(and_elim,[status(thm)],[456])).
% 0.49/0.63 tff(458,plain,
% 0.49/0.63 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)),
% 0.49/0.63 inference(and_elim,[status(thm)],[457])).
% 0.49/0.63 tff(459,plain,
% 0.49/0.63 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[458, 447])).
% 0.49/0.63 tff(460,plain,
% 0.49/0.63 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[459, 443])).
% 0.49/0.63 tff(461,plain,
% 0.49/0.63 (op(e3, e0) = e1),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[460, 442, 422, 421])).
% 0.49/0.63 tff(462,plain,
% 0.49/0.63 (e1 = op(e3, e0)),
% 0.49/0.63 inference(symmetry,[status(thm)],[461])).
% 0.49/0.63 tff(463,plain,
% 0.49/0.63 (e1 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[462, 420])).
% 0.49/0.63 tff(464,plain,
% 0.49/0.63 ((~(~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))))) <=> ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(465,plain,
% 0.49/0.63 (((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(466,plain,
% 0.49/0.63 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[465])).
% 0.49/0.63 tff(467,plain,
% 0.49/0.63 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[466, 464])).
% 0.49/0.63 tff(468,plain,
% 0.49/0.63 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(469,plain,
% 0.49/0.63 ((~(((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(470,axiom,(~(((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax8')).
% 0.49/0.63 tff(471,plain,
% 0.49/0.63 (~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.49/0.63 tff(472,plain,
% 0.49/0.63 (~((e0 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[471, 468])).
% 0.49/0.63 tff(473,plain,
% 0.49/0.63 ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[472, 467])).
% 0.49/0.63 tff(474,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[473, 463, 417, 414])).
% 0.49/0.63 tff(475,plain,((op(e1, e1) = e2) | (~(op(e2, e2) = e0)) | (op(e2, e0) = e1) | (op(e0, e0) = e1) | (op(e1, e3) = e2) | (op(e1, e1) = e0) | (op(e1, e1) = e3) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(476,plain,
% 0.49/0.63 (op(e1, e1) = e2),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[475, 358, 354, 344, 257, 339, 333, 298])).
% 0.49/0.63 tff(477,plain,
% 0.49/0.63 (op(op(e1, e1), op(e1, e1)) = op(e2, e2)),
% 0.49/0.63 inference(monotonicity,[status(thm)],[476, 476])).
% 0.49/0.63 tff(478,plain,
% 0.49/0.63 (op(op(e1, e1), op(e1, e1)) = e0),
% 0.49/0.63 inference(transitivity,[status(thm)],[477, 257])).
% 0.49/0.63 tff(479,plain,
% 0.49/0.63 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e0)),
% 0.49/0.63 inference(monotonicity,[status(thm)],[478])).
% 0.49/0.63 tff(480,plain,
% 0.49/0.63 ((e3 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (e3 = op(e1, e0))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[479])).
% 0.49/0.63 tff(481,plain,
% 0.49/0.63 ((e3 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e0) = e3)),
% 0.49/0.63 inference(transitivity,[status(thm)],[480, 256])).
% 0.49/0.63 tff(482,plain,
% 0.49/0.63 ((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e0) = e3))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[481])).
% 0.49/0.63 tff(483,plain,
% 0.49/0.63 ((e2 = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.49/0.63 inference(commutativity,[status(thm)],[])).
% 0.49/0.63 tff(484,plain,
% 0.49/0.63 ((op(e1, e1) = e2) <=> (e2 = op(e1, e1))),
% 0.49/0.63 inference(symmetry,[status(thm)],[483])).
% 0.49/0.63 tff(485,plain,
% 0.49/0.63 (e2 = op(e1, e1)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[476, 484])).
% 0.49/0.63 tff(486,plain,
% 0.49/0.63 (op(e2, e2) = op(op(e1, e1), op(e1, e1))),
% 0.49/0.63 inference(symmetry,[status(thm)],[477])).
% 0.49/0.63 tff(487,plain,
% 0.49/0.63 (e0 = op(op(e1, e1), op(e1, e1))),
% 0.49/0.63 inference(transitivity,[status(thm)],[262, 486])).
% 0.49/0.63 tff(488,plain,
% 0.49/0.63 ((~(~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1)))))))) <=> ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(489,plain,
% 0.49/0.63 (((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1)))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(490,plain,
% 0.49/0.63 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[489])).
% 0.49/0.63 tff(491,plain,
% 0.49/0.63 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[490, 488])).
% 0.49/0.63 tff(492,plain,
% 0.49/0.63 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(493,plain,
% 0.49/0.63 ((~(((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(494,axiom,(~(((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax9')).
% 0.49/0.63 tff(495,plain,
% 0.49/0.63 (~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.49/0.63 tff(496,plain,
% 0.49/0.63 (~((e0 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[495, 492])).
% 0.49/0.63 tff(497,plain,
% 0.49/0.63 ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[496, 491])).
% 0.49/0.63 tff(498,plain,
% 0.49/0.63 (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[497, 487, 485])).
% 0.49/0.64 tff(499,plain,
% 0.49/0.64 (~(op(e1, e0) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[498, 482])).
% 0.49/0.64 tff(500,plain,
% 0.49/0.64 ((op(e1, e3) = e3) <=> (op(op(e2, e2), op(e2, e2)) = e3)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[324])).
% 0.49/0.64 tff(501,plain,
% 0.49/0.64 ((op(e1, e3) = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[500, 20])).
% 0.49/0.64 tff(502,plain,
% 0.49/0.64 ((e3 = op(op(e2, e2), op(e2, e2))) <=> (op(e1, e3) = e3)),
% 0.49/0.64 inference(symmetry,[status(thm)],[501])).
% 0.49/0.64 tff(503,plain,
% 0.49/0.64 ((~(e3 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e1, e3) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[502])).
% 0.49/0.64 tff(504,plain,
% 0.49/0.64 ((e0 = e3) <=> (op(op(e2, e2), op(e2, e2)) = e3)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[3])).
% 0.49/0.64 tff(505,plain,
% 0.49/0.64 ((e0 = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[504, 20])).
% 0.49/0.64 tff(506,plain,
% 0.49/0.64 ((~(e0 = e3)) <=> (~(e3 = op(op(e2, e2), op(e2, e2))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[505])).
% 0.49/0.64 tff(507,plain,
% 0.49/0.64 ((~(e0 = e3)) <=> (~(e0 = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(508,plain,
% 0.49/0.64 (~(e0 = e3)),
% 0.49/0.64 inference(and_elim,[status(thm)],[13])).
% 0.49/0.64 tff(509,plain,
% 0.49/0.64 (~(e0 = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.49/0.64 tff(510,plain,
% 0.49/0.64 (~(e3 = op(op(e2, e2), op(e2, e2)))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[509, 506])).
% 0.49/0.64 tff(511,plain,
% 0.49/0.64 (~(op(e1, e3) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[510, 503])).
% 0.49/0.64 tff(512,plain,
% 0.49/0.64 (((~(op(e1, e1) = e2)) | (op(e1, e2) = e1)) <=> ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(513,plain,
% 0.49/0.64 ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1)),
% 0.49/0.64 inference(and_elim,[status(thm)],[205])).
% 0.49/0.64 tff(514,plain,
% 0.49/0.64 ((~(op(e1, e1) = e2)) | (op(e1, e2) = e1)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.49/0.64 tff(515,plain,
% 0.49/0.64 (op(e1, e2) = e1),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[514, 476])).
% 0.49/0.64 tff(516,plain,
% 0.49/0.64 ((op(e1, e2) = e3) <=> (e1 = e3)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[515])).
% 0.49/0.64 tff(517,plain,
% 0.49/0.64 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.49/0.64 inference(symmetry,[status(thm)],[516])).
% 0.49/0.64 tff(518,plain,
% 0.49/0.64 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[517])).
% 0.49/0.64 tff(519,plain,
% 0.49/0.64 ((~(e1 = e3)) <=> (~(e1 = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(520,plain,
% 0.49/0.64 (~(e1 = e3)),
% 0.49/0.64 inference(and_elim,[status(thm)],[11])).
% 0.49/0.64 tff(521,plain,
% 0.49/0.64 (~(e1 = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.49/0.64 tff(522,plain,
% 0.49/0.64 (~(op(e1, e2) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[521, 518])).
% 0.49/0.64 tff(523,plain,
% 0.49/0.64 (((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(524,plain,
% 0.49/0.64 ((((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(525,plain,
% 0.49/0.64 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(526,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[525])).
% 0.49/0.64 tff(527,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(transitivity,[status(thm)],[526, 524])).
% 0.49/0.64 tff(528,plain,
% 0.49/0.64 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)),
% 0.49/0.64 inference(and_elim,[status(thm)],[392])).
% 0.49/0.64 tff(529,plain,
% 0.49/0.64 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.49/0.64 tff(530,plain,
% 0.49/0.64 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[529, 523])).
% 0.49/0.64 tff(531,plain,
% 0.49/0.64 (op(e1, e0) = e3),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[530, 522, 511, 333])).
% 0.49/0.64 tff(532,plain,
% 0.49/0.64 ($false),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[531, 499])).
% 0.49/0.64 tff(533,plain,((op(e3, e3) = e0) | (~(op(e2, e2) = e0)) | (~(e0 = op(op(e2, e2), op(e2, e2))))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.64 tff(534,plain,
% 0.49/0.64 (op(e3, e3) = e0),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[533, 227, 3])).
% 0.49/0.64 tff(535,plain,
% 0.49/0.64 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[534])).
% 0.49/0.64 tff(536,plain,
% 0.49/0.64 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[535])).
% 0.49/0.64 tff(537,plain,
% 0.49/0.64 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = op(e3, e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(538,plain,
% 0.49/0.64 (~(op(e1, e3) = op(e3, e3))),
% 0.49/0.64 inference(and_elim,[status(thm)],[139])).
% 0.49/0.64 tff(539,plain,
% 0.49/0.64 (~(op(e1, e3) = op(e3, e3))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.49/0.64 tff(540,plain,
% 0.49/0.64 (~(op(e1, e3) = e0)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.49/0.64 tff(541,plain,
% 0.49/0.64 (((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(542,plain,
% 0.49/0.64 ((((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(543,plain,
% 0.49/0.64 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(544,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[543])).
% 0.49/0.64 tff(545,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(transitivity,[status(thm)],[544, 542])).
% 0.49/0.64 tff(546,plain,
% 0.49/0.64 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)),
% 0.49/0.64 inference(and_elim,[status(thm)],[452])).
% 0.49/0.64 tff(547,plain,
% 0.49/0.64 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.49/0.64 tff(548,plain,
% 0.49/0.64 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[547, 541])).
% 0.49/0.64 tff(549,plain,
% 0.49/0.64 (op(e1, e1) = e0),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[548, 540, 255, 244])).
% 0.49/0.64 tff(550,plain,
% 0.49/0.64 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.49/0.64 inference(transitivity,[status(thm)],[549, 3])).
% 0.49/0.64 tff(551,plain,
% 0.49/0.64 ((op(e1, e1) = e3) <=> (op(op(e2, e2), op(e2, e2)) = e3)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[550])).
% 0.49/0.64 tff(552,plain,
% 0.49/0.64 ((op(e1, e1) = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
% 0.49/0.64 inference(transitivity,[status(thm)],[551, 20])).
% 0.49/0.64 tff(553,plain,
% 0.49/0.64 ((e3 = op(op(e2, e2), op(e2, e2))) <=> (op(e1, e1) = e3)),
% 0.49/0.64 inference(symmetry,[status(thm)],[552])).
% 0.49/0.64 tff(554,plain,
% 0.49/0.64 ((~(e3 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e1, e1) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[553])).
% 0.49/0.64 tff(555,plain,
% 0.49/0.64 (~(op(e1, e1) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[510, 554])).
% 0.49/0.64 tff(556,plain,
% 0.49/0.64 (((~(op(e3, e3) = e0)) | (op(e3, e0) = e3)) <=> ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(557,plain,
% 0.49/0.64 ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3)),
% 0.49/0.64 inference(and_elim,[status(thm)],[47])).
% 0.49/0.64 tff(558,plain,
% 0.49/0.64 ((~(op(e3, e3) = e0)) | (op(e3, e0) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.49/0.64 tff(559,plain,
% 0.49/0.64 (op(e3, e0) = e3),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[558, 534])).
% 0.49/0.64 tff(560,plain,
% 0.49/0.64 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[559])).
% 0.49/0.64 tff(561,plain,
% 0.49/0.64 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[560])).
% 0.49/0.64 tff(562,plain,
% 0.49/0.64 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e3, e0)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(563,plain,
% 0.49/0.64 (~(op(e1, e0) = op(e3, e0))),
% 0.49/0.64 inference(and_elim,[status(thm)],[157])).
% 0.49/0.64 tff(564,plain,
% 0.49/0.64 (~(op(e1, e0) = op(e3, e0))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.49/0.64 tff(565,plain,
% 0.49/0.64 (~(op(e1, e0) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[564, 561])).
% 0.49/0.64 tff(566,plain,
% 0.49/0.64 ((e3 = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(567,plain,
% 0.49/0.64 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[559])).
% 0.49/0.64 tff(568,plain,
% 0.49/0.64 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.49/0.64 inference(transitivity,[status(thm)],[567, 566])).
% 0.49/0.64 tff(569,plain,
% 0.49/0.64 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[568])).
% 0.49/0.64 tff(570,plain,
% 0.49/0.64 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = op(e3, e2)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(571,plain,
% 0.49/0.64 (~(op(e3, e0) = op(e3, e2))),
% 0.49/0.64 inference(and_elim,[status(thm)],[61])).
% 0.49/0.64 tff(572,plain,
% 0.49/0.64 (~(op(e3, e0) = op(e3, e2))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.49/0.64 tff(573,plain,
% 0.49/0.64 (~(op(e3, e2) = e3)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.49/0.64 tff(574,plain,
% 0.49/0.64 ((op(e3, e3) = e2) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[534, 233])).
% 0.49/0.64 tff(575,plain,
% 0.49/0.64 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e3, e3) = e2)),
% 0.49/0.64 inference(symmetry,[status(thm)],[574])).
% 0.49/0.64 tff(576,plain,
% 0.49/0.64 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e3, e3) = e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[575])).
% 0.49/0.64 tff(577,plain,
% 0.49/0.64 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e0)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[22, 227])).
% 0.49/0.64 tff(578,plain,
% 0.49/0.64 ((op(e2, e0) = op(e2, e2)) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[577, 293])).
% 0.49/0.64 tff(579,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e2, e2))) <=> (~(e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[578])).
% 0.49/0.64 tff(580,plain,
% 0.49/0.64 (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[85, 579])).
% 0.49/0.64 tff(581,plain,
% 0.49/0.64 (~(op(e3, e3) = e2)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[580, 576])).
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% 0.49/0.64 ((op(e3, e0) = op(e2, e0)) <=> (op(e2, e0) = op(e3, e0))),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(583,plain,
% 0.49/0.64 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e2, e0))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[232])).
% 0.49/0.64 tff(584,plain,
% 0.49/0.64 ((op(e3, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 0.49/0.64 inference(transitivity,[status(thm)],[583, 582])).
% 0.49/0.64 tff(585,plain,
% 0.49/0.64 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.49/0.64 inference(symmetry,[status(thm)],[584])).
% 0.49/0.64 tff(586,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[585])).
% 0.49/0.64 tff(587,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = op(e3, e0)))),
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% 0.49/0.64 tff(588,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e3, e0))),
% 0.49/0.64 inference(and_elim,[status(thm)],[156])).
% 0.49/0.64 tff(589,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e3, e0))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.49/0.64 tff(590,plain,
% 0.49/0.64 (~(op(e3, e0) = e2)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[589, 586])).
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% 0.49/0.64 ((e1 = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(592,plain,
% 0.49/0.64 ((op(e0, e0) = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[247])).
% 0.49/0.64 tff(593,plain,
% 0.49/0.64 ((op(e0, e0) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
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% 0.49/0.64 tff(594,plain,
% 0.49/0.64 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e0, e0) = e1)),
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% 0.49/0.64 tff(595,plain,
% 0.49/0.64 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e0, e0) = e1))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[594])).
% 0.49/0.64 tff(596,plain,
% 0.49/0.64 (~(op(e0, e0) = e1)),
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% 0.49/0.64 ((e1 = e2) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
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% 0.49/0.64 tff(598,plain,
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% 0.49/0.64 inference(transitivity,[status(thm)],[597, 347])).
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% 0.49/0.64 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[598])).
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% 0.49/0.64 inference(commutativity,[status(thm)],[])).
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% 0.49/0.64 ((op(e3, e0) = e1) <=> (e3 = e1)),
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% 0.49/0.64 ((op(e3, e0) = e1) <=> (e1 = e3)),
% 0.49/0.64 inference(transitivity,[status(thm)],[602, 601])).
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% 0.49/0.64 ((e1 = e3) <=> (op(e3, e0) = e1)),
% 0.49/0.64 inference(symmetry,[status(thm)],[603])).
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% 0.49/0.64 ((~(e1 = e3)) <=> (~(op(e3, e0) = e1))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[604])).
% 0.49/0.64 tff(606,plain,
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% 0.49/0.64 inference(modus_ponens,[status(thm)],[521, 605])).
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% 0.49/0.64 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[607])).
% 0.49/0.64 tff(609,plain,
% 0.49/0.64 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.49/0.64 inference(transitivity,[status(thm)],[608, 591])).
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% 0.49/0.64 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
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% 0.49/0.64 tff(611,plain,
% 0.49/0.64 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = op(e1, e2)))),
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% 0.49/0.64 tff(612,plain,
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% 0.49/0.64 (~(op(e1, e0) = op(e1, e2))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[612, 611])).
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% 0.49/0.64 inference(modus_ponens,[status(thm)],[613, 610])).
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% 0.49/0.64 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
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% 0.49/0.64 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
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% 0.49/0.64 ((e1 = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(620,plain,
% 0.49/0.64 ((op(e1, e0) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[607])).
% 0.49/0.64 tff(621,plain,
% 0.49/0.64 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e1)),
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% 0.49/0.64 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
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% 0.49/0.64 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e1, e3)))),
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% 0.49/0.64 tff(624,plain,
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% 0.49/0.64 ((op(e3, e3) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
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% 0.49/0.65 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e1))),
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% 0.49/0.65 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e2, e0))),
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% 0.49/0.65 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
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% 0.49/0.65 (~(op(e1, e0) = op(e2, e0))),
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% 0.49/0.65 (~(op(e1, e0) = op(e2, e0))),
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% 0.49/0.65 ((op(e1, e1) = e2) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
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% 0.49/0.65 tff(641,plain,
% 0.49/0.65 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e1, e1) = e2)),
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% 0.49/0.65 tff(642,plain,
% 0.49/0.65 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e1, e1) = e2))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[641])).
% 0.49/0.65 tff(643,plain,
% 0.49/0.65 (~(op(e1, e1) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[580, 642])).
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% 0.49/0.65 ((op(e3, e3) = e3) <=> (op(op(e2, e2), op(e2, e2)) = e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[627])).
% 0.49/0.65 tff(645,plain,
% 0.49/0.65 ((op(e3, e3) = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
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% 0.49/0.65 ((e3 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e3)),
% 0.49/0.65 inference(symmetry,[status(thm)],[645])).
% 0.49/0.65 tff(647,plain,
% 0.49/0.65 ((~(e3 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[646])).
% 0.49/0.65 tff(648,plain,
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% 0.49/0.65 inference(modus_ponens,[status(thm)],[510, 647])).
% 0.49/0.65 tff(649,plain,
% 0.49/0.65 (op(e0, op(e0, e0)) = op(e0, e0)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[248])).
% 0.49/0.65 tff(650,plain,
% 0.49/0.65 (((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (~(op(e0, op(e0, e0)) = op(e0, e0)))),
% 0.49/0.65 inference(tautology,[status(thm)],[])).
% 0.49/0.65 tff(651,plain,
% 0.49/0.65 ((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[650, 649])).
% 0.49/0.65 tff(652,assumption,(op(e3, e0) = e3), introduced(assumption)).
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% 0.49/0.65 inference(monotonicity,[status(thm)],[652])).
% 0.49/0.65 tff(654,plain,
% 0.49/0.65 ((op(e0, op(e3, e0)) = op(e3, e0)) <=> (op(e0, e3) = e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[653, 652])).
% 0.49/0.65 tff(655,plain,
% 0.49/0.65 ((op(e0, e3) = e3) <=> (op(e0, op(e3, e0)) = op(e3, e0))),
% 0.49/0.65 inference(symmetry,[status(thm)],[654])).
% 0.49/0.65 tff(656,plain,
% 0.49/0.65 ((e3 = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.49/0.65 inference(commutativity,[status(thm)],[])).
% 0.49/0.65 tff(657,plain,
% 0.49/0.65 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[652])).
% 0.49/0.65 tff(658,plain,
% 0.49/0.65 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.49/0.65 inference(transitivity,[status(thm)],[657, 566])).
% 0.49/0.65 tff(659,plain,
% 0.49/0.65 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[658])).
% 0.49/0.65 tff(660,plain,
% 0.49/0.65 (~(op(e3, e2) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[572, 659])).
% 0.49/0.65 tff(661,assumption,(~(op(e1, e2) = e1)), introduced(assumption)).
% 0.49/0.65 tff(662,assumption,(~(op(e2, e2) = e1)), introduced(assumption)).
% 0.49/0.65 tff(663,assumption,(~(op(e3, e2) = e1)), introduced(assumption)).
% 0.49/0.65 tff(664,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(665,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(666,plain,
% 0.49/0.65 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(667,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[666])).
% 0.49/0.65 tff(668,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[667, 665])).
% 0.49/0.65 tff(669,plain,
% 0.49/0.65 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)),
% 0.49/0.65 inference(and_elim,[status(thm)],[387])).
% 0.49/0.65 tff(670,plain,
% 0.49/0.65 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.49/0.65 tff(671,plain,
% 0.49/0.65 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[670, 664])).
% 0.49/0.65 tff(672,plain,
% 0.49/0.65 (op(e0, e2) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[671, 663, 662, 661])).
% 0.49/0.65 tff(673,plain,
% 0.49/0.65 ((op(e0, e2) = e3) <=> (e1 = e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[672])).
% 0.49/0.65 tff(674,plain,
% 0.49/0.65 ((e1 = e3) <=> (op(e0, e2) = e3)),
% 0.49/0.65 inference(symmetry,[status(thm)],[673])).
% 0.49/0.65 tff(675,plain,
% 0.49/0.65 ((~(e1 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[674])).
% 0.49/0.65 tff(676,plain,
% 0.49/0.65 (~(op(e0, e2) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[521, 675])).
% 0.49/0.65 tff(677,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(678,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(679,plain,
% 0.49/0.65 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(680,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[679])).
% 0.49/0.65 tff(681,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[680, 678])).
% 0.49/0.65 tff(682,plain,
% 0.49/0.65 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)),
% 0.49/0.65 inference(and_elim,[status(thm)],[185])).
% 0.49/0.65 tff(683,plain,
% 0.49/0.65 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.49/0.65 tff(684,plain,
% 0.49/0.65 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[683, 677])).
% 0.49/0.65 tff(685,plain,
% 0.49/0.65 (op(e1, e2) = e3),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[684, 676, 26, 660])).
% 0.49/0.65 tff(686,plain,
% 0.49/0.65 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[685])).
% 0.49/0.65 tff(687,plain,
% 0.49/0.65 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.49/0.65 inference(transitivity,[status(thm)],[686, 656])).
% 0.49/0.65 tff(688,plain,
% 0.49/0.65 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[687])).
% 0.49/0.65 tff(689,plain,
% 0.49/0.65 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e1, e3)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(690,plain,
% 0.49/0.65 (~(op(e1, e2) = op(e1, e3))),
% 0.49/0.65 inference(and_elim,[status(thm)],[126])).
% 0.49/0.65 tff(691,plain,
% 0.49/0.65 (~(op(e1, e2) = op(e1, e3))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.49/0.65 tff(692,plain,
% 0.49/0.65 (~(op(e1, e3) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[691, 688])).
% 0.49/0.65 tff(693,assumption,(~(op(e3, e3) = e3)), introduced(assumption)).
% 0.49/0.65 tff(694,assumption,(~(op(e1, e3) = e1)), introduced(assumption)).
% 0.49/0.65 tff(695,assumption,(~(op(e3, e3) = e1)), introduced(assumption)).
% 0.49/0.65 tff(696,plain,
% 0.49/0.65 ((e1 = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.49/0.65 inference(commutativity,[status(thm)],[])).
% 0.49/0.65 tff(697,plain,
% 0.49/0.65 ((op(e0, e2) = op(e0, e3)) <=> (e1 = op(e0, e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[672])).
% 0.49/0.65 tff(698,plain,
% 0.49/0.65 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.49/0.65 inference(transitivity,[status(thm)],[697, 696])).
% 0.49/0.65 tff(699,plain,
% 0.49/0.65 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[698])).
% 0.49/0.65 tff(700,plain,
% 0.49/0.65 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e0, e3)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(701,plain,
% 0.49/0.65 (~(op(e0, e2) = op(e0, e3))),
% 0.49/0.65 inference(and_elim,[status(thm)],[132])).
% 0.49/0.65 tff(702,plain,
% 0.49/0.65 (~(op(e0, e2) = op(e0, e3))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.49/0.65 tff(703,plain,
% 0.49/0.65 (~(op(e0, e3) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[702, 699])).
% 0.49/0.65 tff(704,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(705,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(706,plain,
% 0.49/0.65 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(707,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[706])).
% 0.49/0.65 tff(708,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[707, 705])).
% 0.49/0.65 tff(709,plain,
% 0.49/0.65 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)),
% 0.49/0.65 inference(and_elim,[status(thm)],[181])).
% 0.49/0.65 tff(710,plain,
% 0.49/0.65 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.49/0.65 tff(711,plain,
% 0.49/0.65 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[710, 704])).
% 0.49/0.65 tff(712,plain,
% 0.49/0.65 (op(e2, e3) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[711, 703, 695, 694])).
% 0.49/0.65 tff(713,plain,
% 0.49/0.65 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[712])).
% 0.49/0.65 tff(714,plain,
% 0.49/0.65 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 0.49/0.65 inference(symmetry,[status(thm)],[713])).
% 0.49/0.65 tff(715,plain,
% 0.49/0.65 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[714])).
% 0.49/0.65 tff(716,plain,
% 0.49/0.65 (~(op(e2, e3) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[521, 715])).
% 0.49/0.65 tff(717,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(718,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(719,plain,
% 0.49/0.65 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(720,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[719])).
% 0.49/0.66 tff(721,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(transitivity,[status(thm)],[720, 718])).
% 0.49/0.66 tff(722,plain,
% 0.49/0.66 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)),
% 0.49/0.66 inference(and_elim,[status(thm)],[177])).
% 0.49/0.66 tff(723,plain,
% 0.49/0.66 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.49/0.66 tff(724,plain,
% 0.49/0.66 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[723, 717])).
% 0.49/0.66 tff(725,plain,
% 0.49/0.66 (op(e0, e3) = e3),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[724, 716, 693, 692])).
% 0.49/0.66 tff(726,plain,
% 0.49/0.66 (op(e0, op(e3, e0)) = op(e3, e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[725, 655])).
% 0.49/0.66 tff(727,assumption,(~(op(e1, e0) = e2)), introduced(assumption)).
% 0.49/0.66 tff(728,assumption,(~(op(e3, e2) = e0)), introduced(assumption)).
% 0.49/0.66 tff(729,plain,
% 0.49/0.66 (((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))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(730,plain,
% 0.49/0.66 ((((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))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(731,plain,
% 0.49/0.66 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(732,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[731])).
% 0.49/0.66 tff(733,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(transitivity,[status(thm)],[732, 730])).
% 0.49/0.66 tff(734,plain,
% 0.49/0.66 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)),
% 0.49/0.66 inference(and_elim,[status(thm)],[112])).
% 0.49/0.66 tff(735,plain,
% 0.49/0.66 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.49/0.66 tff(736,plain,
% 0.49/0.66 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[735, 729])).
% 0.49/0.66 tff(737,plain,
% 0.49/0.66 (op(e3, e2) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[736, 663, 728, 660])).
% 0.49/0.66 tff(738,plain,
% 0.49/0.66 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[737])).
% 0.49/0.66 tff(739,plain,
% 0.49/0.66 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[738])).
% 0.49/0.66 tff(740,plain,
% 0.49/0.66 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e3, e2)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(741,plain,
% 0.49/0.66 (~(op(e1, e2) = op(e3, e2))),
% 0.49/0.66 inference(and_elim,[status(thm)],[145])).
% 0.49/0.66 tff(742,plain,
% 0.49/0.66 (~(op(e1, e2) = op(e3, e2))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.49/0.66 tff(743,plain,
% 0.49/0.66 (~(op(e1, e2) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[742, 739])).
% 0.49/0.66 tff(744,plain,
% 0.49/0.66 (((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))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(745,plain,
% 0.49/0.66 ((((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))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(746,plain,
% 0.49/0.66 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(747,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[746])).
% 0.49/0.66 tff(748,plain,
% 0.49/0.66 (((((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))),
% 0.49/0.66 inference(transitivity,[status(thm)],[747, 745])).
% 0.49/0.66 tff(749,plain,
% 0.49/0.66 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)),
% 0.49/0.66 inference(and_elim,[status(thm)],[448])).
% 0.49/0.66 tff(750,plain,
% 0.49/0.66 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.49/0.66 tff(751,plain,
% 0.49/0.66 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[750, 744])).
% 0.49/0.66 tff(752,plain,
% 0.49/0.66 (op(e1, e3) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[751, 743, 379, 727])).
% 0.49/0.66 tff(753,plain,
% 0.49/0.66 (e2 = op(e1, e3)),
% 0.49/0.66 inference(symmetry,[status(thm)],[752])).
% 0.49/0.66 tff(754,plain,
% 0.49/0.66 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[752])).
% 0.49/0.66 tff(755,plain,
% 0.49/0.66 (op(e3, op(e1, e3)) = op(e1, e3)),
% 0.49/0.66 inference(transitivity,[status(thm)],[754, 737, 753])).
% 0.49/0.66 tff(756,plain,
% 0.49/0.66 (((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))) | (~(op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(757,plain,
% 0.49/0.66 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[756, 755])).
% 0.49/0.66 tff(758,assumption,((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))), introduced(assumption)).
% 0.49/0.66 tff(759,plain,
% 0.49/0.66 (e1 = op(e2, e3)),
% 0.49/0.66 inference(symmetry,[status(thm)],[712])).
% 0.49/0.66 tff(760,plain,
% 0.49/0.66 ((op(e3, e0) = e1) <=> (e3 = e1)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[652])).
% 0.49/0.66 tff(761,plain,
% 0.49/0.66 ((op(e3, e0) = e1) <=> (e1 = e3)),
% 0.49/0.66 inference(transitivity,[status(thm)],[760, 601])).
% 0.49/0.66 tff(762,plain,
% 0.49/0.66 ((e1 = e3) <=> (op(e3, e0) = e1)),
% 0.49/0.66 inference(symmetry,[status(thm)],[761])).
% 0.49/0.66 tff(763,plain,
% 0.49/0.66 ((~(e1 = e3)) <=> (~(op(e3, e0) = e1))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[762])).
% 0.49/0.66 tff(764,plain,
% 0.49/0.66 (~(op(e3, e0) = e1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[521, 763])).
% 0.49/0.66 tff(765,plain,
% 0.49/0.66 (((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(766,plain,
% 0.49/0.66 ((((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(767,plain,
% 0.49/0.66 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(768,plain,
% 0.49/0.66 (((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)) <=> (((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[767])).
% 0.49/0.66 tff(769,plain,
% 0.49/0.66 (((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1))),
% 0.49/0.66 inference(transitivity,[status(thm)],[768, 766])).
% 0.49/0.66 tff(770,plain,
% 0.49/0.66 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)),
% 0.49/0.66 inference(and_elim,[status(thm)],[182])).
% 0.49/0.66 tff(771,plain,
% 0.49/0.66 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.49/0.66 tff(772,plain,
% 0.49/0.66 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[771, 765])).
% 0.49/0.66 tff(773,plain,
% 0.49/0.66 (op(e3, e1) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[772, 663, 764, 695])).
% 0.49/0.66 tff(774,plain,
% 0.49/0.66 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[712])).
% 0.49/0.66 tff(775,plain,
% 0.49/0.66 (op(e3, op(e2, e3)) = op(e2, e3)),
% 0.49/0.66 inference(transitivity,[status(thm)],[774, 773, 759])).
% 0.49/0.66 tff(776,plain,
% 0.49/0.66 (((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))) | (~(op(e3, op(e2, e3)) = op(e2, e3)))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(777,plain,
% 0.49/0.66 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[776, 775])).
% 0.49/0.66 tff(778,plain,
% 0.49/0.66 ((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) <=> ((~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))) | (~((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(779,plain,
% 0.49/0.66 ((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(780,plain,
% 0.49/0.66 (((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(781,plain,
% 0.49/0.67 ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))) <=> ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(782,plain,
% 0.49/0.67 ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) <=> ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(783,plain,
% 0.49/0.67 (((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))) <=> (((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[782])).
% 0.49/0.67 tff(784,plain,
% 0.49/0.67 (((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))) <=> ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.67 inference(transitivity,[status(thm)],[783, 781])).
% 0.49/0.67 tff(785,plain,
% 0.49/0.67 (((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(786,plain,
% 0.49/0.67 ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) <=> ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(787,plain,
% 0.49/0.67 ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) <=> ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(788,plain,
% 0.49/0.67 (((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) <=> (((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[787])).
% 0.49/0.67 tff(789,plain,
% 0.49/0.67 (((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) <=> ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))),
% 0.49/0.67 inference(transitivity,[status(thm)],[788, 786])).
% 0.49/0.67 tff(790,plain,
% 0.49/0.67 ((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(791,plain,
% 0.49/0.67 (((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) <=> ((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[790, 789])).
% 0.49/0.67 tff(792,plain,
% 0.49/0.67 (((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))))),
% 0.49/0.67 inference(transitivity,[status(thm)],[791, 785])).
% 0.49/0.67 tff(793,plain,
% 0.49/0.67 ((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) <=> ((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[792, 784])).
% 0.49/0.68 tff(794,plain,
% 0.49/0.68 ((((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))) <=> (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3)))))),
% 0.49/0.68 inference(transitivity,[status(thm)],[793, 780])).
% 0.49/0.68 tff(795,plain,
% 0.49/0.68 (((((((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1)))) & (~(op(e2, op(e0, e2)) = op(e0, e2)))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1)))) & (~(op(e2, op(e1, e2)) = op(e1, e2)))) & (~(op(e3, op(e1, e3)) = op(e1, e3))))) | ((((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1)))) & (~(op(e2, op(e2, e2)) = op(e2, e2)))) & (~(op(e3, op(e2, e3)) = op(e2, e3))))) | ((((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1)))) & (~(op(e2, op(e3, e2)) = op(e3, e2)))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.68 inference(and_elim,[status(thm)],[212])).
% 0.49/0.68 tff(796,plain,
% 0.49/0.68 (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.49/0.68 tff(797,plain,
% 0.49/0.68 (((~(op(e0, op(e0, e0)) = op(e0, e0))) & (~(op(e1, op(e0, e1)) = op(e0, e1))) & (~(op(e2, op(e0, e2)) = op(e0, e2))) & (~(op(e3, op(e0, e3)) = op(e0, e3)))) | ((~(op(e0, op(e1, e0)) = op(e1, e0))) & (~(op(e1, op(e1, e1)) = op(e1, e1))) & (~(op(e2, op(e1, e2)) = op(e1, e2))) & (~(op(e3, op(e1, e3)) = op(e1, e3)))) | ((~(op(e0, op(e2, e0)) = op(e2, e0))) & (~(op(e1, op(e2, e1)) = op(e2, e1))) & (~(op(e2, op(e2, e2)) = op(e2, e2))) & (~(op(e3, op(e2, e3)) = op(e2, e3)))) | ((~(op(e0, op(e3, e0)) = op(e3, e0))) & (~(op(e1, op(e3, e1)) = op(e3, e1))) & (~(op(e2, op(e3, e2)) = op(e3, e2))) & (~(op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[796, 779])).
% 0.49/0.68 tff(798,plain,
% 0.49/0.68 ((~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))) | (~((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))))),
% 0.55/0.68 inference(modus_ponens,[status(thm)],[797, 778])).
% 0.55/0.68 tff(799,plain,
% 0.55/0.68 (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[798, 777, 758, 757])).
% 0.55/0.68 tff(800,plain,
% 0.55/0.68 (((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (~(op(e0, op(e3, e0)) = op(e3, e0)))),
% 0.55/0.68 inference(tautology,[status(thm)],[])).
% 0.55/0.68 tff(801,plain,
% 0.55/0.68 (~(op(e0, op(e3, e0)) = op(e3, e0))),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[800, 799])).
% 0.55/0.68 tff(802,plain,
% 0.55/0.68 ($false),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[801, 726])).
% 0.55/0.68 tff(803,plain,((op(e3, e2) = e1) | (~(op(e3, e0) = e3)) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e3, e3) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e3, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e2) = e3) | (op(e3, e2) = e0) | (op(e2, e2) = e1) | (op(e1, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.68 tff(804,plain,
% 0.55/0.68 (op(e3, e2) = e1),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[803, 559, 651, 648, 643, 639, 632, 626, 26, 618, 218, 614])).
% 0.55/0.68 tff(805,plain,
% 0.55/0.68 ((op(e3, e2) = e2) <=> (e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.68 inference(monotonicity,[status(thm)],[804, 233])).
% 0.55/0.68 tff(806,plain,
% 0.55/0.68 ((e1 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e3, e2) = e2)),
% 0.55/0.68 inference(symmetry,[status(thm)],[805])).
% 0.55/0.68 tff(807,plain,
% 0.55/0.68 ((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e3, e2) = e2))),
% 0.55/0.68 inference(monotonicity,[status(thm)],[806])).
% 0.55/0.68 tff(808,plain,
% 0.55/0.68 ((~(e1 = e2)) <=> (~(e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.55/0.68 inference(monotonicity,[status(thm)],[597])).
% 0.55/0.68 tff(809,plain,
% 0.55/0.68 (~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.68 inference(modus_ponens,[status(thm)],[353, 808])).
% 0.55/0.68 tff(810,plain,
% 0.55/0.68 (~(op(e3, e2) = e2)),
% 0.55/0.68 inference(modus_ponens,[status(thm)],[809, 807])).
% 0.55/0.68 tff(811,plain,
% 0.55/0.68 (((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))),
% 0.55/0.68 inference(rewrite,[status(thm)],[])).
% 0.55/0.68 tff(812,plain,
% 0.55/0.68 ((((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))),
% 0.55/0.68 inference(rewrite,[status(thm)],[])).
% 0.55/0.68 tff(813,plain,
% 0.55/0.68 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2))),
% 0.55/0.68 inference(rewrite,[status(thm)],[])).
% 0.55/0.68 tff(814,plain,
% 0.55/0.68 (((((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))),
% 0.55/0.68 inference(monotonicity,[status(thm)],[813])).
% 0.55/0.68 tff(815,plain,
% 0.55/0.68 (((((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))),
% 0.55/0.69 inference(transitivity,[status(thm)],[814, 812])).
% 0.55/0.69 tff(816,plain,
% 0.55/0.69 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)),
% 0.55/0.69 inference(and_elim,[status(thm)],[180])).
% 0.55/0.69 tff(817,plain,
% 0.55/0.69 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.55/0.69 tff(818,plain,
% 0.55/0.69 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[817, 811])).
% 0.55/0.69 tff(819,plain,
% 0.55/0.69 (op(e3, e1) = e2),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[818, 810, 590, 581])).
% 0.55/0.69 tff(820,plain,
% 0.55/0.69 ((e0 = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 0.55/0.69 inference(commutativity,[status(thm)],[])).
% 0.55/0.69 tff(821,plain,
% 0.55/0.69 ((op(e0, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[248])).
% 0.55/0.69 tff(822,plain,
% 0.55/0.69 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 0.55/0.69 inference(transitivity,[status(thm)],[821, 820])).
% 0.55/0.69 tff(823,plain,
% 0.55/0.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e0))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[822])).
% 0.55/0.69 tff(824,plain,
% 0.55/0.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = op(e0, e1)))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(825,plain,
% 0.55/0.69 (~(op(e0, e0) = op(e0, e1))),
% 0.55/0.69 inference(and_elim,[status(thm)],[137])).
% 0.55/0.69 tff(826,plain,
% 0.55/0.69 (~(op(e0, e0) = op(e0, e1))),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.55/0.69 tff(827,plain,
% 0.55/0.69 (~(op(e0, e1) = e0)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[826, 823])).
% 0.55/0.69 tff(828,assumption,(op(e3, e1) = e2), introduced(assumption)).
% 0.55/0.69 tff(829,plain,
% 0.55/0.69 (op(e1, op(e3, e1)) = op(e1, e2)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[828])).
% 0.55/0.69 tff(830,plain,
% 0.55/0.69 ((op(e1, op(e3, e1)) = op(e3, e1)) <=> (op(e1, e2) = e2)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[829, 828])).
% 0.55/0.69 tff(831,plain,
% 0.55/0.69 ((op(e1, e2) = e2) <=> (op(e1, op(e3, e1)) = op(e3, e1))),
% 0.55/0.69 inference(symmetry,[status(thm)],[830])).
% 0.55/0.69 tff(832,assumption,(op(e1, e0) = e1), introduced(assumption)).
% 0.55/0.69 tff(833,plain,
% 0.55/0.69 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[832])).
% 0.55/0.69 tff(834,plain,
% 0.55/0.69 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.55/0.69 inference(transitivity,[status(thm)],[833, 591])).
% 0.55/0.69 tff(835,plain,
% 0.55/0.69 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[834])).
% 0.55/0.69 tff(836,plain,
% 0.55/0.69 (~(op(e1, e2) = e1)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[613, 835])).
% 0.55/0.69 tff(837,assumption,(~(op(e1, e2) = e0)), introduced(assumption)).
% 0.55/0.69 tff(838,assumption,(~(op(e1, e2) = e3)), introduced(assumption)).
% 0.55/0.69 tff(839,plain,
% 0.55/0.69 (((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))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(840,plain,
% 0.55/0.69 ((((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))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(841,plain,
% 0.55/0.69 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(842,plain,
% 0.55/0.69 (((((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))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[841])).
% 0.55/0.69 tff(843,plain,
% 0.55/0.69 (((((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))),
% 0.55/0.69 inference(transitivity,[status(thm)],[842, 840])).
% 0.55/0.69 tff(844,plain,
% 0.55/0.69 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)),
% 0.55/0.69 inference(and_elim,[status(thm)],[431])).
% 0.55/0.69 tff(845,plain,
% 0.55/0.69 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.55/0.69 tff(846,plain,
% 0.55/0.69 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[845, 839])).
% 0.55/0.69 tff(847,plain,
% 0.55/0.69 (op(e1, e2) = e2),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[846, 838, 837, 836])).
% 0.55/0.69 tff(848,plain,
% 0.55/0.69 (op(e1, op(e3, e1)) = op(e3, e1)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[847, 831])).
% 0.55/0.69 tff(849,plain,
% 0.55/0.69 (((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (~(op(e1, op(e3, e1)) = op(e3, e1)))),
% 0.55/0.69 inference(tautology,[status(thm)],[])).
% 0.55/0.69 tff(850,plain,
% 0.55/0.69 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[849, 848])).
% 0.55/0.69 tff(851,plain,
% 0.55/0.69 (op(e0, op(e1, e0)) = op(e0, e1)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[832])).
% 0.55/0.69 tff(852,plain,
% 0.55/0.69 ((op(e0, op(e1, e0)) = op(e1, e0)) <=> (op(e0, e1) = e1)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[851, 832])).
% 0.55/0.69 tff(853,plain,
% 0.55/0.69 ((op(e0, e1) = e1) <=> (op(e0, op(e1, e0)) = op(e1, e0))),
% 0.55/0.69 inference(symmetry,[status(thm)],[852])).
% 0.55/0.69 tff(854,assumption,(~(op(e0, e1) = e0)), introduced(assumption)).
% 0.55/0.69 tff(855,plain,
% 0.55/0.69 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[828])).
% 0.55/0.69 tff(856,plain,
% 0.55/0.69 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[855])).
% 0.55/0.69 tff(857,plain,
% 0.55/0.69 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = op(e3, e1)))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(858,plain,
% 0.55/0.69 (~(op(e0, e1) = op(e3, e1))),
% 0.55/0.69 inference(and_elim,[status(thm)],[153])).
% 0.55/0.69 tff(859,plain,
% 0.55/0.69 (~(op(e0, e1) = op(e3, e1))),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[858, 857])).
% 0.55/0.69 tff(860,plain,
% 0.55/0.69 (~(op(e0, e1) = e2)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[859, 856])).
% 0.55/0.69 tff(861,assumption,(~(op(e3, e2) = e3)), introduced(assumption)).
% 0.55/0.69 tff(862,plain,
% 0.55/0.69 (op(e0, e2) = e3),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[684, 838, 26, 861])).
% 0.55/0.69 tff(863,plain,
% 0.55/0.69 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[862])).
% 0.55/0.69 tff(864,plain,
% 0.55/0.69 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[863])).
% 0.55/0.69 tff(865,plain,
% 0.55/0.69 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = op(e0, e2)))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(866,plain,
% 0.55/0.69 (~(op(e0, e1) = op(e0, e2))),
% 0.55/0.69 inference(and_elim,[status(thm)],[134])).
% 0.55/0.69 tff(867,plain,
% 0.55/0.69 (~(op(e0, e1) = op(e0, e2))),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.55/0.69 tff(868,plain,
% 0.55/0.69 (~(op(e0, e1) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[867, 864])).
% 0.55/0.69 tff(869,plain,
% 0.55/0.69 (((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(870,plain,
% 0.55/0.69 ((((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(871,plain,
% 0.55/0.69 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(872,plain,
% 0.55/0.69 (((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)) <=> (((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[871])).
% 0.55/0.69 tff(873,plain,
% 0.55/0.69 (((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3))),
% 0.55/0.69 inference(transitivity,[status(thm)],[872, 870])).
% 0.55/0.69 tff(874,plain,
% 0.55/0.69 ((((((((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))),
% 0.55/0.69 inference(and_elim,[status(thm)],[432])).
% 0.55/0.69 tff(875,plain,
% 0.55/0.69 (((((((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))),
% 0.55/0.69 inference(and_elim,[status(thm)],[874])).
% 0.55/0.69 tff(876,plain,
% 0.55/0.69 ((((((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))),
% 0.55/0.69 inference(and_elim,[status(thm)],[875])).
% 0.55/0.69 tff(877,plain,
% 0.55/0.69 (((((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))),
% 0.55/0.69 inference(and_elim,[status(thm)],[876])).
% 0.55/0.69 tff(878,plain,
% 0.55/0.69 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)),
% 0.55/0.69 inference(and_elim,[status(thm)],[877])).
% 0.55/0.69 tff(879,plain,
% 0.55/0.69 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[878, 873])).
% 0.55/0.69 tff(880,plain,
% 0.55/0.69 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[879, 869])).
% 0.55/0.69 tff(881,plain,
% 0.55/0.69 (op(e0, e1) = e1),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[880, 868, 860, 854])).
% 0.55/0.69 tff(882,plain,
% 0.55/0.69 (op(e0, op(e1, e0)) = op(e1, e0)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[881, 853])).
% 0.55/0.69 tff(883,plain,
% 0.55/0.69 (((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))) | (~(op(e0, op(e1, e0)) = op(e1, e0)))),
% 0.55/0.69 inference(tautology,[status(thm)],[])).
% 0.55/0.69 tff(884,plain,
% 0.55/0.69 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[883, 882])).
% 0.55/0.69 tff(885,assumption,(~(op(e2, e0) = e3)), introduced(assumption)).
% 0.55/0.69 tff(886,plain,
% 0.55/0.69 ((e3 = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.55/0.69 inference(commutativity,[status(thm)],[])).
% 0.55/0.69 tff(887,assumption,(~(op(e1, e0) = e3)), introduced(assumption)).
% 0.55/0.69 tff(888,plain,
% 0.55/0.69 (op(e1, e3) = e3),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[530, 838, 887, 423])).
% 0.55/0.69 tff(889,plain,
% 0.55/0.69 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[888])).
% 0.55/0.69 tff(890,plain,
% 0.55/0.69 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.55/0.69 inference(transitivity,[status(thm)],[889, 886])).
% 0.55/0.69 tff(891,plain,
% 0.55/0.69 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.55/0.69 inference(monotonicity,[status(thm)],[890])).
% 0.55/0.69 tff(892,plain,
% 0.55/0.69 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = op(e2, e3)))),
% 0.55/0.69 inference(rewrite,[status(thm)],[])).
% 0.55/0.69 tff(893,plain,
% 0.55/0.69 (~(op(e1, e3) = op(e2, e3))),
% 0.55/0.69 inference(and_elim,[status(thm)],[140])).
% 0.55/0.69 tff(894,plain,
% 0.55/0.69 (~(op(e1, e3) = op(e2, e3))),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.55/0.69 tff(895,plain,
% 0.55/0.69 (~(op(e2, e3) = e3)),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[894, 891])).
% 0.55/0.69 tff(896,plain,
% 0.55/0.69 (op(e2, e1) = e3),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[189, 895, 26, 885])).
% 0.55/0.69 tff(897,plain,
% 0.55/0.69 (e3 = op(e2, e1)),
% 0.55/0.69 inference(symmetry,[status(thm)],[896])).
% 0.55/0.69 tff(898,plain,
% 0.55/0.69 (op(e1, op(e2, e1)) = op(e1, e3)),
% 0.55/0.69 inference(monotonicity,[status(thm)],[896])).
% 0.55/0.69 tff(899,plain,
% 0.55/0.69 (op(e1, op(e2, e1)) = op(e2, e1)),
% 0.55/0.69 inference(transitivity,[status(thm)],[898, 888, 897])).
% 0.55/0.69 tff(900,plain,
% 0.55/0.70 (((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))) | (~(op(e1, op(e2, e1)) = op(e2, e1)))),
% 0.55/0.70 inference(tautology,[status(thm)],[])).
% 0.55/0.70 tff(901,plain,
% 0.55/0.70 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[900, 899])).
% 0.55/0.70 tff(902,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[798, 901, 884, 758, 850])).
% 0.55/0.70 tff(903,plain,((op(e1, e2) = e3) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~(op(e1, e0) = e1)) | (op(e0, e1) = e0) | (op(e2, e2) = e3) | (op(e2, e0) = e3) | (~(op(e3, e1) = e2)) | (op(e3, e2) = e3) | (op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(904,plain,
% 0.55/0.70 (op(e1, e2) = e3),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[903, 651, 607, 827, 26, 238, 819, 573, 565, 555, 244])).
% 0.55/0.70 tff(905,plain,
% 0.55/0.70 (op(e2, op(e1, e2)) = op(e2, e3)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[904])).
% 0.55/0.70 tff(906,plain,
% 0.55/0.70 ((op(e2, op(e1, e2)) = op(e1, e2)) <=> (op(e2, e3) = e3)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[905, 904])).
% 0.55/0.70 tff(907,plain,
% 0.55/0.70 ((~(op(e2, op(e1, e2)) = op(e1, e2))) <=> (~(op(e2, e3) = e3))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[906])).
% 0.55/0.70 tff(908,plain,
% 0.55/0.70 (op(e0, op(e2, e0)) = op(e0, e2)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[231])).
% 0.55/0.70 tff(909,plain,
% 0.55/0.70 (op(e0, e2) = op(e0, op(e2, e0))),
% 0.55/0.70 inference(symmetry,[status(thm)],[908])).
% 0.55/0.70 tff(910,plain,
% 0.55/0.70 ((op(e0, e2) = e2) <=> (op(e0, op(e2, e0)) = op(e2, e0))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[909, 232])).
% 0.55/0.70 tff(911,plain,
% 0.55/0.70 ((op(e1, e2) = e2) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[904, 233])).
% 0.55/0.70 tff(912,plain,
% 0.55/0.70 ((e3 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e1, e2) = e2)),
% 0.55/0.70 inference(symmetry,[status(thm)],[911])).
% 0.55/0.70 tff(913,plain,
% 0.55/0.70 ((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e1, e2) = e2))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[912])).
% 0.55/0.70 tff(914,plain,
% 0.55/0.70 ((~(e2 = e3)) <=> (~(e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[235])).
% 0.55/0.70 tff(915,plain,
% 0.55/0.70 (~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[170, 914])).
% 0.55/0.70 tff(916,plain,
% 0.55/0.70 (~(op(e1, e2) = e2)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[915, 913])).
% 0.55/0.70 tff(917,plain,
% 0.55/0.70 (((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))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(918,plain,
% 0.55/0.70 ((((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))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(919,plain,
% 0.55/0.70 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(920,plain,
% 0.55/0.70 (((((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))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[919])).
% 0.55/0.70 tff(921,plain,
% 0.55/0.70 (((((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))),
% 0.55/0.70 inference(transitivity,[status(thm)],[920, 918])).
% 0.55/0.70 tff(922,plain,
% 0.55/0.70 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)),
% 0.55/0.70 inference(and_elim,[status(thm)],[385])).
% 0.55/0.70 tff(923,plain,
% 0.55/0.70 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.55/0.70 tff(924,plain,
% 0.55/0.70 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[923, 917])).
% 0.55/0.70 tff(925,plain,
% 0.55/0.70 (op(e0, e2) = e2),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[924, 916, 810, 19])).
% 0.55/0.70 tff(926,plain,
% 0.55/0.70 (op(e0, op(e2, e0)) = op(e2, e0)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[925, 910])).
% 0.55/0.70 tff(927,plain,
% 0.55/0.70 (((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))) | (~(op(e0, op(e2, e0)) = op(e2, e0)))),
% 0.55/0.70 inference(tautology,[status(thm)],[])).
% 0.55/0.70 tff(928,plain,
% 0.55/0.70 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[927, 926])).
% 0.55/0.70 tff(929,plain,
% 0.55/0.70 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[904])).
% 0.55/0.70 tff(930,plain,
% 0.55/0.70 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.55/0.70 inference(transitivity,[status(thm)],[929, 656])).
% 0.55/0.70 tff(931,plain,
% 0.55/0.70 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[930])).
% 0.55/0.70 tff(932,plain,
% 0.55/0.70 (~(op(e1, e3) = e3)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[691, 931])).
% 0.55/0.70 tff(933,assumption,(~(op(e1, e3) = e3)), introduced(assumption)).
% 0.55/0.70 tff(934,plain,
% 0.55/0.70 ((~(op(e0, op(e3, e0)) = op(e3, e0))) <=> (~(op(e0, e3) = e3))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[654])).
% 0.55/0.70 tff(935,assumption,(~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))), introduced(assumption)).
% 0.55/0.70 tff(936,plain,
% 0.55/0.70 (~(op(e0, op(e3, e0)) = op(e3, e0))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[800, 935])).
% 0.55/0.70 tff(937,plain,
% 0.55/0.70 (~(op(e0, e3) = e3)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[936, 934])).
% 0.55/0.70 tff(938,plain,
% 0.55/0.70 (op(e2, e3) = e3),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[724, 937, 693, 933])).
% 0.55/0.70 tff(939,assumption,(op(e3, e2) = e1), introduced(assumption)).
% 0.55/0.70 tff(940,plain,
% 0.55/0.70 (op(e2, op(e3, e2)) = op(e2, e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[939])).
% 0.55/0.70 tff(941,plain,
% 0.55/0.70 ((op(e2, op(e3, e2)) = op(e3, e2)) <=> (op(e2, e1) = e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[940, 939])).
% 0.55/0.70 tff(942,plain,
% 0.55/0.70 ((~(op(e2, op(e3, e2)) = op(e3, e2))) <=> (~(op(e2, e1) = e1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[941])).
% 0.55/0.70 tff(943,plain,
% 0.55/0.70 (((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (~(op(e2, op(e3, e2)) = op(e3, e2)))),
% 0.55/0.70 inference(tautology,[status(thm)],[])).
% 0.55/0.70 tff(944,plain,
% 0.55/0.70 (~(op(e2, op(e3, e2)) = op(e3, e2))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[943, 935])).
% 0.55/0.70 tff(945,plain,
% 0.55/0.70 (~(op(e2, e1) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[944, 942])).
% 0.55/0.70 tff(946,plain,
% 0.55/0.70 (((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(947,plain,
% 0.55/0.70 ((((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(948,plain,
% 0.55/0.70 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(949,plain,
% 0.55/0.70 (((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)) <=> (((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[948])).
% 0.55/0.70 tff(950,plain,
% 0.55/0.70 (((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1))),
% 0.55/0.70 inference(transitivity,[status(thm)],[949, 947])).
% 0.55/0.70 tff(951,plain,
% 0.55/0.70 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)),
% 0.55/0.70 inference(and_elim,[status(thm)],[388])).
% 0.55/0.70 tff(952,plain,
% 0.55/0.70 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.55/0.70 tff(953,plain,
% 0.55/0.70 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[952, 946])).
% 0.55/0.70 tff(954,plain,
% 0.55/0.70 (op(e2, e3) = e1),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[953, 945, 662, 422])).
% 0.55/0.70 tff(955,plain,
% 0.55/0.70 (e1 = op(e2, e3)),
% 0.55/0.70 inference(symmetry,[status(thm)],[954])).
% 0.55/0.70 tff(956,plain,
% 0.55/0.70 (e1 = e3),
% 0.55/0.70 inference(transitivity,[status(thm)],[955, 938])).
% 0.55/0.70 tff(957,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[521, 956])).
% 0.55/0.70 tff(958,plain,(((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (op(e2, e2) = e1) | (op(e2, e0) = e1) | (op(e3, e3) = e3) | (op(e1, e3) = e3) | (~(op(e3, e2) = e1)) | (~(op(e3, e0) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(959,plain,
% 0.55/0.70 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[958, 218, 600, 648, 932, 804, 559])).
% 0.55/0.70 tff(960,plain,
% 0.55/0.70 (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[798, 959, 651, 928])).
% 0.55/0.70 tff(961,plain,
% 0.55/0.70 (((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))) | (~(op(e2, op(e1, e2)) = op(e1, e2)))),
% 0.55/0.70 inference(tautology,[status(thm)],[])).
% 0.55/0.70 tff(962,plain,
% 0.55/0.70 (~(op(e2, op(e1, e2)) = op(e1, e2))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[961, 960])).
% 0.55/0.70 tff(963,plain,
% 0.55/0.70 (~(op(e2, e3) = e3)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[962, 907])).
% 0.55/0.70 tff(964,plain,
% 0.55/0.70 (op(e2, e1) = e3),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[189, 963, 26, 238])).
% 0.55/0.70 tff(965,plain,
% 0.55/0.70 ((op(e1, e1) = e1) <=> (op(op(e2, e2), op(e2, e2)) = e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[550])).
% 0.55/0.70 tff(966,plain,
% 0.55/0.70 ((op(e1, e1) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.55/0.70 inference(transitivity,[status(thm)],[965, 27])).
% 0.55/0.70 tff(967,plain,
% 0.55/0.70 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e1, e1) = e1)),
% 0.55/0.70 inference(symmetry,[status(thm)],[966])).
% 0.55/0.70 tff(968,plain,
% 0.55/0.70 ((~(e1 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e1, e1) = e1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[967])).
% 0.55/0.70 tff(969,plain,
% 0.55/0.70 (~(op(e1, e1) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[41, 968])).
% 0.55/0.70 tff(970,plain,
% 0.55/0.70 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[804])).
% 0.55/0.70 tff(971,plain,
% 0.55/0.70 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[970])).
% 0.55/0.70 tff(972,plain,
% 0.55/0.70 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e3, e2)))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(973,plain,
% 0.55/0.70 (~(op(e3, e1) = op(e3, e2))),
% 0.55/0.70 inference(and_elim,[status(thm)],[59])).
% 0.55/0.70 tff(974,plain,
% 0.55/0.70 (~(op(e3, e1) = op(e3, e2))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.55/0.70 tff(975,plain,
% 0.55/0.70 (~(op(e3, e1) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[974, 971])).
% 0.55/0.70 tff(976,plain,
% 0.55/0.70 (op(e0, op(e1, e0)) = op(e0, e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[607])).
% 0.55/0.70 tff(977,plain,
% 0.55/0.70 ((op(e0, op(e1, e0)) = op(e1, e0)) <=> (op(e0, e1) = e1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[976, 607])).
% 0.55/0.70 tff(978,plain,
% 0.55/0.70 ((~(op(e0, op(e1, e0)) = op(e1, e0))) <=> (~(op(e0, e1) = e1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[977])).
% 0.55/0.70 tff(979,plain,
% 0.55/0.70 (~(op(e0, op(e1, e0)) = op(e1, e0))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[883, 960])).
% 0.55/0.70 tff(980,plain,
% 0.55/0.70 (~(op(e0, e1) = e1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.55/0.70 tff(981,plain,
% 0.55/0.70 (((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(982,plain,
% 0.55/0.71 ((((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(983,plain,
% 0.55/0.71 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(984,plain,
% 0.55/0.71 (((((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))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[983])).
% 0.55/0.71 tff(985,plain,
% 0.55/0.71 (((((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))),
% 0.55/0.71 inference(transitivity,[status(thm)],[984, 982])).
% 0.55/0.71 tff(986,plain,
% 0.55/0.71 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)),
% 0.55/0.71 inference(and_elim,[status(thm)],[449])).
% 0.55/0.71 tff(987,plain,
% 0.55/0.71 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.55/0.71 tff(988,plain,
% 0.55/0.71 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[987, 981])).
% 0.55/0.71 tff(989,plain,
% 0.55/0.71 (op(e2, e1) = e1),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[988, 980, 975, 969])).
% 0.55/0.71 tff(990,plain,
% 0.55/0.71 (e1 = op(e2, e1)),
% 0.55/0.71 inference(symmetry,[status(thm)],[989])).
% 0.55/0.71 tff(991,plain,
% 0.55/0.71 (e1 = e3),
% 0.55/0.71 inference(transitivity,[status(thm)],[990, 964])).
% 0.55/0.71 tff(992,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[521, 991])).
% 0.55/0.71 tff(993,plain,((op(e2, e2) = e3) | (~(e0 = op(op(e2, e2), op(e2, e2))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(994,plain,
% 0.55/0.71 (op(e2, e2) = e3),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[993, 3])).
% 0.55/0.71 tff(995,plain,
% 0.55/0.71 (e3 = op(e2, e2)),
% 0.55/0.71 inference(symmetry,[status(thm)],[994])).
% 0.55/0.71 tff(996,plain,
% 0.55/0.71 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[995, 995])).
% 0.55/0.71 tff(997,plain,
% 0.55/0.71 ((op(e3, e3) = e3) <=> (op(op(e2, e2), op(e2, e2)) = e3)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[996])).
% 0.55/0.71 tff(998,plain,
% 0.55/0.71 ((op(e3, e3) = e3) <=> (e3 = op(op(e2, e2), op(e2, e2)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[997, 20])).
% 0.55/0.71 tff(999,plain,
% 0.55/0.71 ((e3 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e3)),
% 0.55/0.71 inference(symmetry,[status(thm)],[998])).
% 0.55/0.71 tff(1000,plain,
% 0.55/0.71 ((~(e3 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e3))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[999])).
% 0.55/0.71 tff(1001,plain,
% 0.55/0.71 (~(op(e3, e3) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[510, 1000])).
% 0.55/0.71 tff(1002,plain,
% 0.55/0.71 (((~(op(e2, e2) = e3)) | (op(e2, e3) = e2)) <=> ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1003,plain,
% 0.55/0.71 ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2)),
% 0.55/0.71 inference(and_elim,[status(thm)],[48])).
% 0.55/0.71 tff(1004,plain,
% 0.55/0.71 ((~(op(e2, e2) = e3)) | (op(e2, e3) = e2)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.55/0.71 tff(1005,plain,
% 0.55/0.71 (op(e2, e3) = e2),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1004, 994])).
% 0.55/0.71 tff(1006,plain,
% 0.55/0.71 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1005])).
% 0.55/0.71 tff(1007,plain,
% 0.55/0.71 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1006])).
% 0.55/0.71 tff(1008,plain,
% 0.55/0.71 (~(op(e2, e0) = e2)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[369, 1007])).
% 0.55/0.71 tff(1009,plain,
% 0.55/0.71 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e3)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[75, 994])).
% 0.55/0.71 tff(1010,plain,
% 0.55/0.71 ((op(e2, e0) = op(e2, e2)) <=> (e3 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.71 inference(transitivity,[status(thm)],[1009, 21])).
% 0.55/0.71 tff(1011,plain,
% 0.55/0.71 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 0.55/0.71 inference(transitivity,[status(thm)],[1010, 89])).
% 0.55/0.71 tff(1012,plain,
% 0.55/0.71 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1011])).
% 0.55/0.71 tff(1013,plain,
% 0.55/0.71 (~(op(e2, e0) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[85, 1012])).
% 0.55/0.71 tff(1014,plain,
% 0.55/0.71 ((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e2, e0) = e1))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[78])).
% 0.55/0.71 tff(1015,plain,
% 0.55/0.71 ((e3 = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1016,plain,
% 0.55/0.71 ((op(e2, e2) = e3) <=> (e3 = op(e2, e2))),
% 0.55/0.71 inference(symmetry,[status(thm)],[1015])).
% 0.55/0.71 tff(1017,plain,
% 0.55/0.71 (e3 = op(e2, e2)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[994, 1016])).
% 0.55/0.71 tff(1018,plain,
% 0.55/0.71 ((~(~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2)))))))) <=> ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1019,plain,
% 0.55/0.71 (((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2)))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1020,plain,
% 0.55/0.71 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1019])).
% 0.55/0.71 tff(1021,plain,
% 0.55/0.71 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.55/0.71 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.55/0.71 tff(1022,plain,
% 0.55/0.71 ((~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1023,plain,
% 0.55/0.71 ((~(((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1024,axiom,(~(((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax10')).
% 0.55/0.71 tff(1025,plain,
% 0.55/0.71 (~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.55/0.71 tff(1026,plain,
% 0.55/0.71 (~((e0 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1025, 1022])).
% 0.55/0.71 tff(1027,plain,
% 0.55/0.71 ((~(e0 = op(op(e2, e2), op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1026, 1021])).
% 0.55/0.71 tff(1028,plain,
% 0.55/0.71 (~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1027, 1017, 3])).
% 0.55/0.71 tff(1029,plain,
% 0.55/0.71 (~(op(e2, e0) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1028, 1014])).
% 0.55/0.71 tff(1030,plain,
% 0.55/0.71 (op(e2, e0) = e0),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[121, 1029, 1013, 1008])).
% 0.55/0.71 tff(1031,plain,
% 0.55/0.71 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1030])).
% 0.55/0.71 tff(1032,plain,
% 0.55/0.71 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1031])).
% 0.55/0.71 tff(1033,plain,
% 0.55/0.71 (~(op(e0, e0) = e0)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[162, 1032])).
% 0.55/0.71 tff(1034,plain,
% 0.55/0.71 ((e2 = e1) <=> (e1 = e2)),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1035,plain,
% 0.55/0.71 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1005])).
% 0.55/0.71 tff(1036,plain,
% 0.55/0.71 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.55/0.71 inference(transitivity,[status(thm)],[1035, 1034])).
% 0.55/0.71 tff(1037,plain,
% 0.55/0.71 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.55/0.71 inference(symmetry,[status(thm)],[1036])).
% 0.55/0.71 tff(1038,plain,
% 0.55/0.71 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1037])).
% 0.55/0.71 tff(1039,plain,
% 0.55/0.71 (~(op(e2, e3) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[353, 1038])).
% 0.55/0.71 tff(1040,plain,
% 0.55/0.71 ((e1 = e3) <=> (e1 = op(e2, e2))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[995])).
% 0.55/0.71 tff(1041,plain,
% 0.55/0.71 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 0.55/0.71 inference(transitivity,[status(thm)],[1040, 91])).
% 0.55/0.71 tff(1042,plain,
% 0.55/0.71 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1041])).
% 0.55/0.71 tff(1043,plain,
% 0.55/0.71 (~(op(e2, e2) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[521, 1042])).
% 0.55/0.71 tff(1044,plain,
% 0.55/0.71 (op(e2, e1) = e1),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[953, 1029, 1043, 1039])).
% 0.55/0.71 tff(1045,plain,
% 0.55/0.71 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1044])).
% 0.55/0.71 tff(1046,plain,
% 0.55/0.71 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1045])).
% 0.55/0.71 tff(1047,plain,
% 0.55/0.71 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = op(e2, e1)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1048,plain,
% 0.55/0.71 (~(op(e1, e1) = op(e2, e1))),
% 0.55/0.71 inference(and_elim,[status(thm)],[152])).
% 0.55/0.71 tff(1049,plain,
% 0.55/0.71 (~(op(e1, e1) = op(e2, e1))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.55/0.71 tff(1050,plain,
% 0.55/0.71 (~(op(e1, e1) = e1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 0.55/0.71 tff(1051,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[215, 1050, 1033, 1001, 19])).
% 0.55/0.71 tff(1052,plain,(~(e0 = op(op(e2, e2), op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1053,assumption,(~(e2 = op(op(e3, e3), op(e3, e3)))), introduced(assumption)).
% 0.55/0.71 tff(1054,assumption,(~(e0 = op(op(e2, e2), op(e2, e2)))), introduced(assumption)).
% 0.55/0.71 tff(1055,assumption,(~(op(e0, e0) = e0)), introduced(assumption)).
% 0.55/0.71 tff(1056,assumption,(~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))), introduced(assumption)).
% 0.55/0.71 tff(1057,plain,
% 0.55/0.71 (((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (~(op(e2, op(e0, e2)) = op(e0, e2)))),
% 0.55/0.71 inference(tautology,[status(thm)],[])).
% 0.55/0.71 tff(1058,plain,
% 0.55/0.71 (~(op(e2, op(e0, e2)) = op(e0, e2))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1057, 1056])).
% 0.55/0.71 tff(1059,plain,
% 0.55/0.71 (((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (~(op(e1, op(e0, e1)) = op(e0, e1)))),
% 0.55/0.71 inference(tautology,[status(thm)],[])).
% 0.55/0.71 tff(1060,plain,
% 0.55/0.71 (~(op(e1, op(e0, e1)) = op(e0, e1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1059, 1056])).
% 0.55/0.71 tff(1061,plain,
% 0.55/0.71 (((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (~(op(e3, op(e0, e3)) = op(e0, e3)))),
% 0.55/0.71 inference(tautology,[status(thm)],[])).
% 0.55/0.71 tff(1062,plain,
% 0.55/0.71 (~(op(e3, op(e0, e3)) = op(e0, e3))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1061, 1056])).
% 0.55/0.71 tff(1063,assumption,(~(op(e2, op(e0, e2)) = op(e0, e2))), introduced(assumption)).
% 0.55/0.71 tff(1064,assumption,(~(op(e1, op(e0, e1)) = op(e0, e1))), introduced(assumption)).
% 0.55/0.71 tff(1065,assumption,(~(op(e3, op(e0, e3)) = op(e0, e3))), introduced(assumption)).
% 0.55/0.71 tff(1066,assumption,(~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))), introduced(assumption)).
% 0.55/0.71 tff(1067,assumption,(~(op(e3, e0) = e1)), introduced(assumption)).
% 0.55/0.71 tff(1068,plain,
% 0.55/0.71 ((e1 = op(e0, e0)) <=> (op(e0, e0) = e1)),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1069,plain,
% 0.55/0.71 ((op(e0, e0) = e1) <=> (e1 = op(e0, e0))),
% 0.55/0.71 inference(symmetry,[status(thm)],[1068])).
% 0.55/0.71 tff(1070,plain,
% 0.55/0.71 ((op(e3, e3) = e0) <=> (e0 = op(e3, e3))),
% 0.55/0.71 inference(symmetry,[status(thm)],[2])).
% 0.55/0.71 tff(1071,plain,
% 0.55/0.71 ((e1 = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1072,assumption,(~(op(e0, e2) = e3)), introduced(assumption)).
% 0.55/0.71 tff(1073,assumption,(~(op(e0, op(e3, e0)) = op(e3, e0))), introduced(assumption)).
% 0.55/0.71 tff(1074,assumption,(op(e3, e3) = e0), introduced(assumption)).
% 0.55/0.71 tff(1075,plain,
% 0.55/0.71 (op(e3, e0) = e3),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[558, 1074])).
% 0.55/0.71 tff(1076,plain,
% 0.55/0.71 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1075])).
% 0.55/0.71 tff(1077,plain,
% 0.55/0.71 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1076])).
% 0.55/0.71 tff(1078,plain,
% 0.55/0.71 (~(op(e0, e0) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[270, 1077])).
% 0.55/0.71 tff(1079,plain,
% 0.55/0.71 (op(e0, op(e3, e0)) = op(e0, e3)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1075])).
% 0.55/0.71 tff(1080,plain,
% 0.55/0.71 ((op(e0, op(e3, e0)) = op(e3, e0)) <=> (op(e0, e3) = e3)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1079, 1075])).
% 0.55/0.71 tff(1081,plain,
% 0.55/0.71 ((~(op(e0, op(e3, e0)) = op(e3, e0))) <=> (~(op(e0, e3) = e3))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1080])).
% 0.55/0.71 tff(1082,plain,
% 0.55/0.71 (~(op(e0, e3) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1073, 1081])).
% 0.55/0.71 tff(1083,plain,
% 0.55/0.71 (((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1084,plain,
% 0.55/0.71 ((((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1085,plain,
% 0.55/0.71 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1086,plain,
% 0.55/0.71 (((((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))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1085])).
% 0.55/0.71 tff(1087,plain,
% 0.55/0.71 (((((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))),
% 0.55/0.71 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.55/0.71 tff(1088,plain,
% 0.55/0.71 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)),
% 0.55/0.71 inference(and_elim,[status(thm)],[454])).
% 0.55/0.71 tff(1089,plain,
% 0.55/0.71 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.55/0.71 tff(1090,plain,
% 0.55/0.71 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1089, 1083])).
% 0.55/0.71 tff(1091,plain,
% 0.55/0.71 (op(e0, e1) = e3),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1090, 1082, 1072, 1078])).
% 0.55/0.71 tff(1092,plain,
% 0.55/0.71 ((e2 = op(e0, e0)) <=> (op(e0, e0) = e2)),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1093,plain,
% 0.55/0.71 (op(op(e3, e3), op(e3, e3)) = op(e0, e0)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1074, 1074])).
% 0.55/0.71 tff(1094,plain,
% 0.55/0.71 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (e2 = op(e0, e0))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1093])).
% 0.55/0.71 tff(1095,plain,
% 0.55/0.71 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (op(e0, e0) = e2)),
% 0.55/0.71 inference(transitivity,[status(thm)],[1094, 1092])).
% 0.55/0.71 tff(1096,plain,
% 0.55/0.71 ((~(e2 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e0, e0) = e2))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1095])).
% 0.55/0.71 tff(1097,plain,
% 0.55/0.71 (~(op(e0, e0) = e2)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1053, 1096])).
% 0.55/0.71 tff(1098,plain,
% 0.55/0.71 (((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1099,plain,
% 0.55/0.71 ((((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))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1100,plain,
% 0.55/0.72 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1101,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1100])).
% 0.55/0.72 tff(1102,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1101, 1099])).
% 0.55/0.72 tff(1103,plain,
% 0.55/0.72 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)),
% 0.55/0.72 inference(and_elim,[status(thm)],[877])).
% 0.55/0.72 tff(1104,plain,
% 0.55/0.72 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.55/0.72 tff(1105,plain,
% 0.55/0.72 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1104, 1098])).
% 0.55/0.72 tff(1106,plain,
% 0.55/0.72 (op(e0, e0) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1105, 1097, 1055, 1078])).
% 0.55/0.72 tff(1107,plain,
% 0.55/0.72 (((~(op(e0, e0) = e1)) | (op(e0, e1) = e0)) <=> ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1108,plain,
% 0.55/0.72 ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0)),
% 0.55/0.72 inference(and_elim,[status(thm)],[210])).
% 0.55/0.72 tff(1109,plain,
% 0.55/0.72 ((~(op(e0, e0) = e1)) | (op(e0, e1) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.55/0.72 tff(1110,plain,
% 0.55/0.72 (op(e0, e1) = e0),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1109, 1106])).
% 0.55/0.72 tff(1111,plain,
% 0.55/0.72 (e0 = op(e0, e1)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1110])).
% 0.55/0.72 tff(1112,plain,
% 0.55/0.72 (e0 = e3),
% 0.55/0.72 inference(transitivity,[status(thm)],[1111, 1091])).
% 0.55/0.72 tff(1113,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[509, 1112])).
% 0.55/0.72 tff(1114,plain,((~(op(e3, e3) = e0)) | (op(e0, e2) = e3) | (op(e0, e0) = e0) | (op(e0, op(e3, e0)) = op(e3, e0)) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1115,plain,
% 0.55/0.72 (~(op(e3, e3) = e0)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1114, 1072, 1055, 1073, 1053])).
% 0.55/0.72 tff(1116,plain,
% 0.55/0.72 (((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))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1117,plain,
% 0.55/0.72 ((((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))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1118,plain,
% 0.55/0.72 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1119,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1118])).
% 0.55/0.72 tff(1120,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.55/0.72 tff(1121,plain,
% 0.55/0.72 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)),
% 0.55/0.72 inference(and_elim,[status(thm)],[111])).
% 0.55/0.72 tff(1122,plain,
% 0.55/0.72 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.55/0.72 tff(1123,plain,
% 0.55/0.72 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1122, 1116])).
% 0.55/0.72 tff(1124,plain,
% 0.55/0.72 (op(e3, e3) = e2),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1123, 695, 280, 693])).
% 0.55/0.72 tff(1125,plain,
% 0.55/0.72 (((~(op(e3, e3) = e2)) | (op(e3, e2) = e3)) <=> ((~(op(e3, e3) = e2)) | (op(e3, e2) = e3))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1126,plain,
% 0.55/0.72 ((~(op(e3, e3) = e2)) | (op(e3, e2) = e3)),
% 0.55/0.72 inference(and_elim,[status(thm)],[45])).
% 0.55/0.72 tff(1127,plain,
% 0.55/0.72 ((~(op(e3, e3) = e2)) | (op(e3, e2) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.55/0.72 tff(1128,plain,
% 0.55/0.72 (op(e3, e2) = e3),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1127, 1124])).
% 0.55/0.72 tff(1129,plain,
% 0.55/0.72 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1128])).
% 0.55/0.72 tff(1130,plain,
% 0.55/0.72 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1129, 601])).
% 0.55/0.72 tff(1131,plain,
% 0.55/0.72 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1130])).
% 0.55/0.72 tff(1132,plain,
% 0.55/0.72 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1131])).
% 0.55/0.72 tff(1133,plain,
% 0.55/0.72 (~(op(e3, e2) = e1)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[521, 1132])).
% 0.55/0.72 tff(1134,plain,
% 0.55/0.72 (op(e3, e1) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[772, 1133, 1067, 695])).
% 0.55/0.72 tff(1135,plain,
% 0.55/0.72 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1134])).
% 0.55/0.72 tff(1136,plain,
% 0.55/0.72 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e3, e1))),
% 0.55/0.72 inference(symmetry,[status(thm)],[1135])).
% 0.55/0.72 tff(1137,plain,
% 0.55/0.72 ((e2 = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.55/0.72 inference(commutativity,[status(thm)],[])).
% 0.55/0.72 tff(1138,plain,
% 0.55/0.72 (op(op(e3, e3), op(e3, e3)) = op(e2, e2)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1124, 1124])).
% 0.55/0.72 tff(1139,plain,
% 0.55/0.72 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (e2 = op(e2, e2))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1138])).
% 0.55/0.72 tff(1140,plain,
% 0.55/0.72 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e2)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1139, 1137])).
% 0.55/0.72 tff(1141,plain,
% 0.55/0.72 ((~(e2 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e2))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1140])).
% 0.55/0.72 tff(1142,plain,
% 0.55/0.72 (~(op(e2, e2) = e2)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1053, 1141])).
% 0.55/0.72 tff(1143,plain,
% 0.55/0.72 (op(e1, e1) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[215, 1142, 1055, 693])).
% 0.55/0.72 tff(1144,plain,
% 0.55/0.72 (op(e1, e1) = op(e3, e1)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1143, 1136])).
% 0.55/0.72 tff(1145,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[338, 1144])).
% 0.55/0.72 tff(1146,plain,((op(e3, e3) = e1) | (op(e0, e0) = e0) | (op(e3, e3) = e3) | (op(e3, e0) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1147,plain,
% 0.55/0.72 (op(e3, e3) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1146, 693, 1115, 1067, 1053, 1055])).
% 0.55/0.72 tff(1148,plain,
% 0.55/0.72 (((~(op(e3, e3) = e1)) | (op(e3, e1) = e3)) <=> ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1149,plain,
% 0.55/0.72 ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3)),
% 0.55/0.72 inference(and_elim,[status(thm)],[46])).
% 0.55/0.72 tff(1150,plain,
% 0.55/0.72 ((~(op(e3, e3) = e1)) | (op(e3, e1) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.55/0.72 tff(1151,plain,
% 0.55/0.72 (op(e3, e1) = e3),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1150, 1147])).
% 0.55/0.72 tff(1152,plain,
% 0.55/0.72 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1151])).
% 0.55/0.72 tff(1153,plain,
% 0.55/0.72 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1152])).
% 0.55/0.72 tff(1154,plain,
% 0.55/0.72 (~(op(e0, e1) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[859, 1153])).
% 0.55/0.72 tff(1155,assumption,(op(e3, e3) = e1), introduced(assumption)).
% 0.55/0.72 tff(1156,plain,
% 0.55/0.72 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1155])).
% 0.55/0.72 tff(1157,plain,
% 0.55/0.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1156])).
% 0.55/0.72 tff(1158,plain,
% 0.55/0.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = op(e3, e3)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1159,plain,
% 0.55/0.72 (~(op(e3, e2) = op(e3, e3))),
% 0.55/0.72 inference(and_elim,[status(thm)],[57])).
% 0.55/0.72 tff(1160,plain,
% 0.55/0.72 (~(op(e3, e2) = op(e3, e3))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.55/0.72 tff(1161,plain,
% 0.55/0.72 (~(op(e3, e2) = e1)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1160, 1157])).
% 0.55/0.72 tff(1162,plain,
% 0.55/0.72 (op(e3, e1) = e3),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1150, 1155])).
% 0.55/0.72 tff(1163,plain,
% 0.55/0.72 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1162])).
% 0.55/0.72 tff(1164,plain,
% 0.55/0.72 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1163, 566])).
% 0.55/0.72 tff(1165,plain,
% 0.55/0.72 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1164])).
% 0.55/0.72 tff(1166,plain,
% 0.55/0.72 (~(op(e3, e2) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[974, 1165])).
% 0.55/0.72 tff(1167,plain,
% 0.55/0.72 (op(e1, e2) = e3),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[684, 1166, 26, 1072])).
% 0.55/0.72 tff(1168,plain,
% 0.55/0.72 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1167])).
% 0.55/0.72 tff(1169,plain,
% 0.55/0.72 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1168, 601])).
% 0.55/0.72 tff(1170,plain,
% 0.55/0.72 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1169])).
% 0.55/0.72 tff(1171,plain,
% 0.55/0.72 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1170])).
% 0.55/0.72 tff(1172,plain,
% 0.55/0.72 (~(op(e1, e2) = e1)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[521, 1171])).
% 0.55/0.72 tff(1173,plain,
% 0.55/0.72 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1162])).
% 0.55/0.72 tff(1174,plain,
% 0.55/0.72 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1173, 1])).
% 0.55/0.72 tff(1175,plain,
% 0.55/0.72 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1174])).
% 0.55/0.72 tff(1176,plain,
% 0.55/0.72 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1175])).
% 0.55/0.72 tff(1177,plain,
% 0.55/0.72 (~(op(e3, e1) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[509, 1176])).
% 0.55/0.72 tff(1178,plain,
% 0.55/0.72 ((e3 = e2) <=> (e2 = e3)),
% 0.55/0.72 inference(commutativity,[status(thm)],[])).
% 0.55/0.72 tff(1179,assumption,(~(op(e2, e3) = e3)), introduced(assumption)).
% 0.55/0.72 tff(1180,plain,
% 0.55/0.72 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1162])).
% 0.55/0.72 tff(1181,plain,
% 0.55/0.72 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1180])).
% 0.55/0.72 tff(1182,plain,
% 0.55/0.72 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e3, e1)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1183,plain,
% 0.55/0.72 (~(op(e2, e1) = op(e3, e1))),
% 0.55/0.72 inference(and_elim,[status(thm)],[150])).
% 0.55/0.72 tff(1184,plain,
% 0.55/0.72 (~(op(e2, e1) = op(e3, e1))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 0.55/0.72 tff(1185,plain,
% 0.55/0.72 (~(op(e2, e1) = e3)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1184, 1181])).
% 0.55/0.72 tff(1186,plain,
% 0.55/0.72 (op(e2, e0) = e3),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[189, 1185, 26, 1179])).
% 0.55/0.72 tff(1187,plain,
% 0.55/0.72 ((op(e2, e0) = e2) <=> (e3 = e2)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1186])).
% 0.55/0.72 tff(1188,plain,
% 0.55/0.72 ((op(e2, e0) = e2) <=> (e2 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1187, 1178])).
% 0.55/0.72 tff(1189,plain,
% 0.55/0.72 ((e2 = e3) <=> (op(e2, e0) = e2)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1188])).
% 0.55/0.72 tff(1190,plain,
% 0.55/0.72 ((~(e2 = e3)) <=> (~(op(e2, e0) = e2))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1189])).
% 0.55/0.72 tff(1191,plain,
% 0.55/0.72 (~(op(e2, e0) = e2)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[170, 1190])).
% 0.55/0.72 tff(1192,plain,
% 0.55/0.72 (~(op(e2, e2) = e0)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[230, 1191])).
% 0.55/0.72 tff(1193,plain,
% 0.55/0.72 ((op(e2, e0) = e0) <=> (e3 = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1186])).
% 0.55/0.72 tff(1194,plain,
% 0.55/0.72 ((op(e2, e0) = e0) <=> (e0 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1193, 1])).
% 0.55/0.72 tff(1195,plain,
% 0.55/0.72 ((e0 = e3) <=> (op(e2, e0) = e0)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1194])).
% 0.55/0.72 tff(1196,plain,
% 0.55/0.72 ((~(e0 = e3)) <=> (~(op(e2, e0) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1195])).
% 0.55/0.72 tff(1197,plain,
% 0.55/0.72 (~(op(e2, e0) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[509, 1196])).
% 0.55/0.72 tff(1198,plain,
% 0.55/0.72 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1167])).
% 0.55/0.72 tff(1199,plain,
% 0.55/0.72 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1198, 1])).
% 0.55/0.72 tff(1200,plain,
% 0.55/0.72 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1199])).
% 0.55/0.72 tff(1201,plain,
% 0.55/0.72 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1200])).
% 0.55/0.72 tff(1202,plain,
% 0.55/0.72 (~(op(e1, e2) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[509, 1201])).
% 0.55/0.72 tff(1203,plain,
% 0.55/0.72 ((e1 = e0) <=> (e0 = e1)),
% 0.55/0.72 inference(commutativity,[status(thm)],[])).
% 0.55/0.72 tff(1204,assumption,(~(op(e2, e2) = e2)), introduced(assumption)).
% 0.55/0.72 tff(1205,plain,
% 0.55/0.72 (op(e1, e1) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[215, 1204, 1055, 693])).
% 0.55/0.72 tff(1206,plain,
% 0.55/0.72 ((op(e1, e1) = e0) <=> (e1 = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1205])).
% 0.55/0.72 tff(1207,plain,
% 0.55/0.72 ((op(e1, e1) = e0) <=> (e0 = e1)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1206, 1203])).
% 0.55/0.72 tff(1208,plain,
% 0.55/0.72 ((e0 = e1) <=> (op(e1, e1) = e0)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1207])).
% 0.55/0.72 tff(1209,plain,
% 0.55/0.72 ((~(e0 = e1)) <=> (~(op(e1, e1) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1208])).
% 0.55/0.72 tff(1210,plain,
% 0.55/0.72 (~(op(e1, e1) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[40, 1209])).
% 0.55/0.72 tff(1211,assumption,(~(op(e2, e2) = e0)), introduced(assumption)).
% 0.55/0.72 tff(1212,assumption,(~(op(e2, e0) = e0)), introduced(assumption)).
% 0.55/0.72 tff(1213,plain,
% 0.55/0.72 ((e2 = e0) <=> (e0 = e2)),
% 0.55/0.72 inference(commutativity,[status(thm)],[])).
% 0.55/0.72 tff(1214,plain,
% 0.55/0.72 (op(e2, e2) = e1),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[226, 1204, 1211, 26])).
% 0.55/0.72 tff(1215,plain,
% 0.55/0.72 (op(e2, e1) = e2),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[52, 1214])).
% 0.55/0.72 tff(1216,plain,
% 0.55/0.72 ((op(e2, e1) = e0) <=> (e2 = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1215])).
% 0.55/0.72 tff(1217,plain,
% 0.55/0.72 ((op(e2, e1) = e0) <=> (e0 = e2)),
% 0.55/0.72 inference(transitivity,[status(thm)],[1216, 1213])).
% 0.55/0.72 tff(1218,plain,
% 0.55/0.72 ((e0 = e2) <=> (op(e2, e1) = e0)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1217])).
% 0.55/0.72 tff(1219,plain,
% 0.55/0.72 ((~(e0 = e2)) <=> (~(op(e2, e1) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1218])).
% 0.55/0.72 tff(1220,plain,
% 0.55/0.72 (~(op(e2, e1) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[16, 1219])).
% 0.55/0.72 tff(1221,plain,
% 0.55/0.72 (((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))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1222,plain,
% 0.55/0.72 ((((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))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1223,plain,
% 0.55/0.72 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1224,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1223])).
% 0.55/0.72 tff(1225,plain,
% 0.55/0.72 (((((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))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1224, 1222])).
% 0.55/0.72 tff(1226,plain,
% 0.55/0.72 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)),
% 0.55/0.72 inference(and_elim,[status(thm)],[390])).
% 0.55/0.72 tff(1227,plain,
% 0.55/0.72 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 0.55/0.72 tff(1228,plain,
% 0.55/0.72 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1227, 1221])).
% 0.55/0.72 tff(1229,plain,
% 0.55/0.72 (op(e2, e3) = e0),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1228, 1220, 1212, 1211])).
% 0.55/0.72 tff(1230,plain,
% 0.55/0.72 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e0)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1229])).
% 0.55/0.72 tff(1231,plain,
% 0.55/0.72 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e0))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1230])).
% 0.55/0.73 tff(1232,plain,
% 0.55/0.73 (~(op(e1, e3) = e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[894, 1231])).
% 0.55/0.73 tff(1233,assumption,(~(op(e3, e1) = e0)), introduced(assumption)).
% 0.55/0.73 tff(1234,plain,
% 0.55/0.73 (((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))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1235,plain,
% 0.55/0.73 ((((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))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1236,plain,
% 0.55/0.73 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1237,plain,
% 0.55/0.73 (((((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))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1236])).
% 0.55/0.73 tff(1238,plain,
% 0.55/0.73 (((((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))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.55/0.73 tff(1239,plain,
% 0.55/0.73 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)),
% 0.55/0.73 inference(and_elim,[status(thm)],[451])).
% 0.55/0.73 tff(1240,plain,
% 0.55/0.73 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.55/0.73 tff(1241,plain,
% 0.55/0.73 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1240, 1234])).
% 0.55/0.73 tff(1242,plain,
% 0.55/0.73 (op(e0, e1) = e0),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1241, 1210, 1220, 1233])).
% 0.55/0.73 tff(1243,plain,
% 0.55/0.73 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1242])).
% 0.55/0.73 tff(1244,plain,
% 0.55/0.73 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1243, 1242])).
% 0.55/0.73 tff(1245,plain,
% 0.55/0.73 ((~(op(e1, op(e0, e1)) = op(e0, e1))) <=> (~(op(e1, e0) = e0))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1244])).
% 0.55/0.73 tff(1246,plain,
% 0.55/0.73 (~(op(e1, e0) = e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1064, 1245])).
% 0.55/0.73 tff(1247,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[548, 1246, 1232, 837, 1210])).
% 0.55/0.73 tff(1248,plain,((op(e2, e2) = e2) | (op(e1, e2) = e0) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, e0) = e0) | (op(e2, e2) = e0) | (op(e3, e1) = e0) | (op(e2, e2) = e3) | (op(e0, e0) = e0) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1249,plain,
% 0.55/0.73 (op(e2, e2) = e2),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1248, 1202, 1064, 1197, 1192, 1177, 26, 1055, 693])).
% 0.55/0.73 tff(1250,plain,
% 0.55/0.73 ((op(e2, e2) = e1) <=> (e2 = e1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1249])).
% 0.55/0.73 tff(1251,plain,
% 0.55/0.73 ((op(e2, e2) = e1) <=> (e1 = e2)),
% 0.55/0.73 inference(transitivity,[status(thm)],[1250, 1034])).
% 0.55/0.73 tff(1252,plain,
% 0.55/0.73 ((e1 = e2) <=> (op(e2, e2) = e1)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1251])).
% 0.55/0.73 tff(1253,plain,
% 0.55/0.73 ((~(e1 = e2)) <=> (~(op(e2, e2) = e1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1252])).
% 0.55/0.73 tff(1254,plain,
% 0.55/0.73 (~(op(e2, e2) = e1)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[353, 1253])).
% 0.55/0.73 tff(1255,plain,
% 0.55/0.73 (op(e0, e2) = e1),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[671, 1254, 1172, 1161])).
% 0.55/0.73 tff(1256,plain,
% 0.55/0.73 (e1 = op(e0, e2)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1255])).
% 0.55/0.73 tff(1257,plain,
% 0.55/0.73 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1155])).
% 0.55/0.73 tff(1258,plain,
% 0.55/0.73 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1257])).
% 0.55/0.73 tff(1259,plain,
% 0.55/0.73 (~(op(e2, e3) = e1)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[196, 1258])).
% 0.55/0.73 tff(1260,plain,
% 0.55/0.73 ((op(e2, e0) = e1) <=> (e3 = e1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1186])).
% 0.55/0.73 tff(1261,plain,
% 0.55/0.73 ((op(e2, e0) = e1) <=> (e1 = e3)),
% 0.55/0.73 inference(transitivity,[status(thm)],[1260, 601])).
% 0.55/0.73 tff(1262,plain,
% 0.55/0.73 ((e1 = e3) <=> (op(e2, e0) = e1)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1261])).
% 0.55/0.73 tff(1263,plain,
% 0.55/0.73 ((~(e1 = e3)) <=> (~(op(e2, e0) = e1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1262])).
% 0.55/0.73 tff(1264,plain,
% 0.55/0.73 (~(op(e2, e0) = e1)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[521, 1263])).
% 0.55/0.73 tff(1265,plain,
% 0.55/0.73 (op(e2, e1) = e1),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[953, 1254, 1264, 1259])).
% 0.55/0.73 tff(1266,plain,
% 0.55/0.73 (op(e2, op(e0, e2)) = op(e2, e1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1255])).
% 0.55/0.73 tff(1267,plain,
% 0.55/0.73 (op(e2, op(e0, e2)) = op(e0, e2)),
% 0.55/0.73 inference(transitivity,[status(thm)],[1266, 1265, 1256])).
% 0.55/0.73 tff(1268,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1063, 1267])).
% 0.55/0.73 tff(1269,plain,((~(op(e3, e3) = e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, e2) = e3) | (op(e0, e0) = e0) | (op(e3, e3) = e3) | (op(e0, e2) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1270,plain,
% 0.55/0.73 (op(e2, e3) = e3),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1269, 1147, 1064, 26, 1055, 693, 1072, 1063])).
% 0.55/0.73 tff(1271,plain,
% 0.55/0.73 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1270])).
% 0.55/0.73 tff(1272,plain,
% 0.55/0.73 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1271])).
% 0.55/0.73 tff(1273,plain,
% 0.55/0.73 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = op(e2, e3)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1274,plain,
% 0.55/0.73 (~(op(e0, e3) = op(e2, e3))),
% 0.55/0.73 inference(and_elim,[status(thm)],[142])).
% 0.55/0.73 tff(1275,plain,
% 0.55/0.73 (~(op(e0, e3) = op(e2, e3))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.55/0.73 tff(1276,plain,
% 0.55/0.73 (~(op(e0, e3) = e3)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1275, 1272])).
% 0.55/0.73 tff(1277,plain,
% 0.55/0.73 (op(e0, e0) = e3),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1090, 1276, 1072, 1154])).
% 0.55/0.73 tff(1278,plain,
% 0.55/0.73 (((~(op(e0, e0) = e3)) | (op(e0, e3) = e0)) <=> ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1279,plain,
% 0.55/0.73 ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0)),
% 0.55/0.73 inference(and_elim,[status(thm)],[208])).
% 0.55/0.73 tff(1280,plain,
% 0.55/0.73 ((~(op(e0, e0) = e3)) | (op(e0, e3) = e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.55/0.73 tff(1281,plain,
% 0.55/0.73 (op(e0, e3) = e0),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1280, 1277])).
% 0.55/0.73 tff(1282,plain,
% 0.55/0.73 ((op(e0, e3) = e2) <=> (e0 = e2)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1281])).
% 0.55/0.73 tff(1283,plain,
% 0.55/0.73 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1282])).
% 0.55/0.73 tff(1284,plain,
% 0.55/0.73 ((~(e0 = e2)) <=> (~(op(e0, e3) = e2))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1283])).
% 0.55/0.73 tff(1285,plain,
% 0.55/0.73 (~(op(e0, e3) = e2)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[16, 1284])).
% 0.55/0.73 tff(1286,plain,
% 0.55/0.73 ((op(e0, e0) = e2) <=> (e3 = e2)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1277])).
% 0.55/0.73 tff(1287,plain,
% 0.55/0.73 ((op(e0, e0) = e2) <=> (e2 = e3)),
% 0.55/0.73 inference(transitivity,[status(thm)],[1286, 1178])).
% 0.55/0.73 tff(1288,plain,
% 0.55/0.73 ((e2 = e3) <=> (op(e0, e0) = e2)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1287])).
% 0.55/0.73 tff(1289,plain,
% 0.55/0.73 ((~(e2 = e3)) <=> (~(op(e0, e0) = e2))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1288])).
% 0.55/0.73 tff(1290,plain,
% 0.55/0.73 (~(op(e0, e0) = e2)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[170, 1289])).
% 0.55/0.73 tff(1291,plain,
% 0.55/0.73 ((e2 = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.55/0.73 inference(commutativity,[status(thm)],[])).
% 0.55/0.73 tff(1292,plain,
% 0.55/0.73 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1277, 1277])).
% 0.55/0.73 tff(1293,plain,
% 0.55/0.73 (op(op(e0, e0), op(e0, e0)) = e1),
% 0.55/0.73 inference(transitivity,[status(thm)],[1292, 1147])).
% 0.55/0.73 tff(1294,plain,
% 0.55/0.73 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1293])).
% 0.55/0.73 tff(1295,plain,
% 0.55/0.73 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e2 = op(e0, e1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1294])).
% 0.55/0.73 tff(1296,plain,
% 0.55/0.73 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e1) = e2)),
% 0.55/0.73 inference(transitivity,[status(thm)],[1295, 1291])).
% 0.55/0.73 tff(1297,plain,
% 0.55/0.73 ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e1) = e2))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1296])).
% 0.55/0.73 tff(1298,plain,
% 0.55/0.73 ((e3 = op(e0, e0)) <=> (op(e0, e0) = e3)),
% 0.55/0.73 inference(commutativity,[status(thm)],[])).
% 0.55/0.73 tff(1299,plain,
% 0.55/0.73 ((op(e0, e0) = e3) <=> (e3 = op(e0, e0))),
% 0.55/0.73 inference(symmetry,[status(thm)],[1298])).
% 0.55/0.73 tff(1300,plain,
% 0.55/0.73 (e3 = op(e0, e0)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1277, 1299])).
% 0.55/0.73 tff(1301,plain,
% 0.55/0.73 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.55/0.73 inference(symmetry,[status(thm)],[1292])).
% 0.55/0.73 tff(1302,plain,
% 0.55/0.73 (e1 = op(e3, e3)),
% 0.55/0.73 inference(symmetry,[status(thm)],[1147])).
% 0.55/0.73 tff(1303,plain,
% 0.55/0.73 (e1 = op(op(e0, e0), op(e0, e0))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1302, 1301])).
% 0.55/0.73 tff(1304,plain,
% 0.55/0.73 ((~(~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0)))))))) <=> ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1305,plain,
% 0.55/0.73 (((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0)))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1306,plain,
% 0.55/0.73 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1305])).
% 0.55/0.73 tff(1307,plain,
% 0.55/0.73 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1306, 1304])).
% 0.55/0.73 tff(1308,plain,
% 0.55/0.73 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1309,plain,
% 0.55/0.73 ((~(((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1310,axiom,(~(((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax17')).
% 0.55/0.73 tff(1311,plain,
% 0.55/0.73 (~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.55/0.73 tff(1312,plain,
% 0.55/0.73 (~((e1 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1311, 1308])).
% 0.55/0.73 tff(1313,plain,
% 0.55/0.73 ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1312, 1307])).
% 0.55/0.73 tff(1314,plain,
% 0.55/0.73 (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1313, 1303, 1300])).
% 0.55/0.73 tff(1315,plain,
% 0.55/0.73 (~(op(e0, e1) = e2)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1314, 1297])).
% 0.55/0.73 tff(1316,plain,
% 0.55/0.73 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1151])).
% 0.55/0.73 tff(1317,plain,
% 0.55/0.73 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1316])).
% 0.55/0.73 tff(1318,plain,
% 0.55/0.73 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = op(e3, e1)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1319,plain,
% 0.55/0.73 (~(op(e3, e0) = op(e3, e1))),
% 0.55/0.73 inference(and_elim,[status(thm)],[62])).
% 0.55/0.73 tff(1320,plain,
% 0.55/0.73 (~(op(e3, e0) = op(e3, e1))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 0.55/0.74 tff(1321,plain,
% 0.55/0.74 (~(op(e3, e0) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1320, 1317])).
% 0.55/0.74 tff(1322,plain,
% 0.55/0.74 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1281])).
% 0.55/0.74 tff(1323,plain,
% 0.55/0.74 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1322, 1281])).
% 0.55/0.74 tff(1324,plain,
% 0.55/0.74 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1323])).
% 0.55/0.74 tff(1325,plain,
% 0.55/0.74 (~(op(e3, e0) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1065, 1324])).
% 0.55/0.74 tff(1326,plain,
% 0.55/0.74 (((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))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1327,plain,
% 0.55/0.74 ((((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))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1328,plain,
% 0.55/0.74 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1329,plain,
% 0.55/0.74 (((((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))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1328])).
% 0.55/0.74 tff(1330,plain,
% 0.55/0.74 (((((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))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1329, 1327])).
% 0.55/0.74 tff(1331,plain,
% 0.55/0.74 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)),
% 0.55/0.74 inference(and_elim,[status(thm)],[114])).
% 0.55/0.74 tff(1332,plain,
% 0.55/0.74 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.55/0.74 tff(1333,plain,
% 0.55/0.74 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1332, 1326])).
% 0.55/0.74 tff(1334,plain,
% 0.55/0.74 (op(e3, e0) = e2),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1333, 1325, 1067, 1321])).
% 0.55/0.74 tff(1335,plain,
% 0.55/0.74 (op(e0, op(e3, e0)) = op(e0, e2)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1334])).
% 0.55/0.74 tff(1336,plain,
% 0.55/0.74 ((op(e0, op(e3, e0)) = op(e3, e0)) <=> (op(e0, e2) = e2)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1335, 1334])).
% 0.55/0.74 tff(1337,plain,
% 0.55/0.74 ((~(op(e0, op(e3, e0)) = op(e3, e0))) <=> (~(op(e0, e2) = e2))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1336])).
% 0.55/0.74 tff(1338,plain,
% 0.55/0.74 (~(op(e0, e2) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1073, 1337])).
% 0.55/0.74 tff(1339,plain,
% 0.55/0.74 (((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))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1340,plain,
% 0.55/0.74 ((((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))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1341,plain,
% 0.55/0.74 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1342,plain,
% 0.55/0.74 (((((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))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1341])).
% 0.55/0.74 tff(1343,plain,
% 0.55/0.74 (((((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))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1342, 1340])).
% 0.55/0.74 tff(1344,plain,
% 0.55/0.74 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)),
% 0.55/0.74 inference(and_elim,[status(thm)],[456])).
% 0.55/0.74 tff(1345,plain,
% 0.55/0.74 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 0.55/0.74 tff(1346,plain,
% 0.55/0.74 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1345, 1339])).
% 0.55/0.74 tff(1347,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1346, 1338, 1315, 1290, 1285])).
% 0.55/0.74 tff(1348,plain,((op(e3, e3) = e3) | (op(e0, op(e3, e0)) = op(e3, e0)) | (op(e3, e0) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e0, e2) = e3) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, e2) = e3) | (op(e0, e0) = e0) | (op(e2, op(e0, e2)) = op(e0, e2)) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1349,plain,
% 0.55/0.74 (op(e0, op(e3, e0)) = op(e3, e0)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1348, 1072, 1067, 1065, 693, 1064, 26, 1055, 1063, 1053])).
% 0.55/0.74 tff(1350,plain,
% 0.55/0.74 ((e1 = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.55/0.74 inference(commutativity,[status(thm)],[])).
% 0.55/0.74 tff(1351,plain,
% 0.55/0.74 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1162])).
% 0.55/0.74 tff(1352,plain,
% 0.55/0.74 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1351])).
% 0.55/0.74 tff(1353,plain,
% 0.55/0.74 (~(op(e0, e1) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[859, 1352])).
% 0.55/0.74 tff(1354,plain,
% 0.55/0.74 (op(e2, e3) = e3),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1269, 1155, 1064, 26, 1055, 693, 1072, 1063])).
% 0.55/0.74 tff(1355,plain,
% 0.55/0.74 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1354])).
% 0.55/0.74 tff(1356,plain,
% 0.55/0.74 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1355])).
% 0.55/0.74 tff(1357,plain,
% 0.55/0.74 (~(op(e0, e3) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1275, 1356])).
% 0.55/0.74 tff(1358,plain,
% 0.55/0.74 (op(e0, e0) = e3),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1090, 1357, 1072, 1353])).
% 0.55/0.74 tff(1359,plain,
% 0.55/0.74 (op(e0, e3) = e0),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1280, 1358])).
% 0.55/0.74 tff(1360,plain,
% 0.55/0.74 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1359])).
% 0.55/0.74 tff(1361,plain,
% 0.55/0.74 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1360])).
% 0.55/0.74 tff(1362,plain,
% 0.55/0.74 (~(op(e0, e1) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[403, 1361])).
% 0.55/0.74 tff(1363,plain,
% 0.55/0.74 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1358, 1358])).
% 0.55/0.74 tff(1364,plain,
% 0.55/0.74 (op(op(e0, e0), op(e0, e0)) = e1),
% 0.55/0.74 inference(transitivity,[status(thm)],[1363, 1155])).
% 0.55/0.74 tff(1365,plain,
% 0.55/0.74 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e1)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1364])).
% 0.55/0.74 tff(1366,plain,
% 0.55/0.74 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e2 = op(e0, e1))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1365])).
% 0.55/0.74 tff(1367,plain,
% 0.55/0.74 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e1) = e2)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1366, 1291])).
% 0.55/0.74 tff(1368,plain,
% 0.55/0.74 ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e1) = e2))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1367])).
% 0.55/0.74 tff(1369,plain,
% 0.55/0.74 (e3 = op(e0, e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1358, 1299])).
% 0.55/0.74 tff(1370,plain,
% 0.55/0.74 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1363])).
% 0.55/0.74 tff(1371,plain,
% 0.55/0.74 (e1 = op(e3, e3)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1155])).
% 0.55/0.74 tff(1372,plain,
% 0.55/0.74 (e1 = op(op(e0, e0), op(e0, e0))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1371, 1370])).
% 0.55/0.74 tff(1373,plain,
% 0.55/0.74 (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1313, 1372, 1369])).
% 0.55/0.74 tff(1374,plain,
% 0.55/0.74 (~(op(e0, e1) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1373, 1368])).
% 0.55/0.74 tff(1375,plain,
% 0.55/0.74 (op(e0, e1) = e1),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[880, 1374, 1362, 1353])).
% 0.55/0.74 tff(1376,plain,
% 0.55/0.74 ((op(e0, e1) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1375])).
% 0.55/0.74 tff(1377,plain,
% 0.55/0.74 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1376, 1350])).
% 0.55/0.74 tff(1378,plain,
% 0.55/0.74 ((op(e1, e1) = e1) <=> (op(e0, e1) = op(e1, e1))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1377])).
% 0.55/0.74 tff(1379,plain,
% 0.55/0.74 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1162])).
% 0.55/0.74 tff(1380,plain,
% 0.55/0.74 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1379])).
% 0.55/0.74 tff(1381,plain,
% 0.55/0.74 (~(op(e3, e0) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1320, 1380])).
% 0.55/0.74 tff(1382,plain,
% 0.55/0.74 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1359])).
% 0.55/0.74 tff(1383,plain,
% 0.55/0.74 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1382, 1359])).
% 0.55/0.74 tff(1384,plain,
% 0.55/0.74 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1383])).
% 0.55/0.74 tff(1385,plain,
% 0.55/0.74 (~(op(e3, e0) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1065, 1384])).
% 0.55/0.74 tff(1386,plain,
% 0.55/0.74 (op(e3, e0) = e2),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1333, 1385, 1067, 1381])).
% 0.55/0.74 tff(1387,assumption,(op(e0, op(e3, e0)) = op(e3, e0)), introduced(assumption)).
% 0.55/0.74 tff(1388,plain,
% 0.55/0.74 (e2 = op(e3, e0)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1386])).
% 0.55/0.74 tff(1389,plain,
% 0.55/0.74 (op(e0, e2) = op(e0, op(e3, e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1388])).
% 0.55/0.74 tff(1390,plain,
% 0.55/0.74 (op(e0, e2) = e2),
% 0.55/0.74 inference(transitivity,[status(thm)],[1389, 1387, 1386])).
% 0.55/0.74 tff(1391,plain,
% 0.55/0.74 ((op(e0, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1390])).
% 0.55/0.74 tff(1392,plain,
% 0.55/0.74 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1391, 1137])).
% 0.55/0.74 tff(1393,plain,
% 0.55/0.74 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1392])).
% 0.55/0.74 tff(1394,plain,
% 0.55/0.74 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = op(e2, e2)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1395,plain,
% 0.55/0.74 (~(op(e0, e2) = op(e2, e2))),
% 0.55/0.74 inference(and_elim,[status(thm)],[148])).
% 0.55/0.74 tff(1396,plain,
% 0.55/0.74 (~(op(e0, e2) = op(e2, e2))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.55/0.74 tff(1397,plain,
% 0.55/0.74 (~(op(e2, e2) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1396, 1393])).
% 0.55/0.74 tff(1398,plain,
% 0.55/0.74 (op(e1, e1) = e1),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[215, 1397, 1055, 693])).
% 0.55/0.74 tff(1399,plain,
% 0.55/0.74 (op(e0, e1) = op(e1, e1)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1398, 1378])).
% 0.55/0.74 tff(1400,plain,
% 0.55/0.74 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = op(e1, e1)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1401,plain,
% 0.55/0.74 (~(op(e0, e1) = op(e1, e1))),
% 0.55/0.74 inference(and_elim,[status(thm)],[155])).
% 0.55/0.74 tff(1402,plain,
% 0.55/0.74 (~(op(e0, e1) = op(e1, e1))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.55/0.74 tff(1403,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1402, 1399])).
% 0.55/0.74 tff(1404,plain,((~(op(e3, e3) = e1)) | (op(e0, e0) = e0) | (op(e3, e3) = e3) | (~(op(e0, op(e3, e0)) = op(e3, e0))) | (op(e3, e0) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e0, e2) = e3) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, e2) = e3) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1405,plain,
% 0.55/0.74 (~(op(e3, e3) = e1)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1404, 1349, 693, 1055, 1067, 1065, 1072, 1064, 26, 1063])).
% 0.55/0.74 tff(1406,plain,
% 0.55/0.74 (op(e3, e3) = e0),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1146, 1405, 693, 1067, 1053, 1055])).
% 0.55/0.74 tff(1407,plain,
% 0.55/0.74 (op(e3, e0) = e3),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[558, 1406])).
% 0.55/0.74 tff(1408,plain,
% 0.55/0.74 (e3 = op(e3, e0)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1407])).
% 0.55/0.74 tff(1409,plain,
% 0.55/0.74 ((op(e3, e2) = op(e3, e0)) <=> (op(e3, e0) = op(e3, e2))),
% 0.55/0.74 inference(commutativity,[status(thm)],[])).
% 0.55/0.74 tff(1410,plain,
% 0.55/0.74 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1408])).
% 0.55/0.74 tff(1411,plain,
% 0.55/0.74 ((op(e3, e2) = e3) <=> (op(e3, e0) = op(e3, e2))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1410, 1409])).
% 0.55/0.74 tff(1412,plain,
% 0.55/0.74 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1411])).
% 0.55/0.74 tff(1413,plain,
% 0.55/0.74 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1412])).
% 0.55/0.74 tff(1414,plain,
% 0.55/0.74 (~(op(e3, e2) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[572, 1413])).
% 0.55/0.74 tff(1415,plain,
% 0.55/0.74 (op(e1, e2) = e3),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[684, 1414, 26, 1072])).
% 0.55/0.74 tff(1416,plain,
% 0.55/0.74 (op(e1, e2) = op(e3, e0)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1415, 1408])).
% 0.55/0.74 tff(1417,plain,
% 0.55/0.74 ((op(e1, e2) = e0) <=> (op(e3, e0) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1416])).
% 0.55/0.74 tff(1418,plain,
% 0.55/0.74 ((op(e3, e0) = e0) <=> (op(e1, e2) = e0)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1417])).
% 0.55/0.74 tff(1419,plain,
% 0.55/0.74 ((~(op(e3, e0) = e0)) <=> (~(op(e1, e2) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1418])).
% 0.55/0.74 tff(1420,plain,
% 0.55/0.74 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1406])).
% 0.55/0.74 tff(1421,plain,
% 0.55/0.74 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1420])).
% 0.55/0.74 tff(1422,plain,
% 0.55/0.74 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = op(e3, e3)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1423,plain,
% 0.55/0.74 (~(op(e3, e0) = op(e3, e3))),
% 0.55/0.74 inference(and_elim,[status(thm)],[60])).
% 0.55/0.74 tff(1424,plain,
% 0.55/0.74 (~(op(e3, e0) = op(e3, e3))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 0.55/0.74 tff(1425,plain,
% 0.55/0.74 (~(op(e3, e0) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1424, 1421])).
% 0.55/0.74 tff(1426,plain,
% 0.55/0.74 (~(op(e1, e2) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1425, 1419])).
% 0.55/0.74 tff(1427,plain,
% 0.55/0.74 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1406])).
% 0.55/0.74 tff(1428,plain,
% 0.55/0.74 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1427])).
% 0.55/0.74 tff(1429,plain,
% 0.55/0.74 (~(op(e1, e3) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[539, 1428])).
% 0.55/0.74 tff(1430,plain,
% 0.55/0.74 ((e0 = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.55/0.74 inference(commutativity,[status(thm)],[])).
% 0.55/0.74 tff(1431,plain,
% 0.55/0.74 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1407])).
% 0.55/0.74 tff(1432,plain,
% 0.55/0.74 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1431])).
% 0.55/0.74 tff(1433,plain,
% 0.55/0.74 (~(op(e0, e0) = e3)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[270, 1432])).
% 0.55/0.74 tff(1434,plain,
% 0.55/0.74 (op(op(e3, e3), op(e3, e3)) = op(e0, e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1406, 1406])).
% 0.55/0.74 tff(1435,plain,
% 0.55/0.74 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (e2 = op(e0, e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1434])).
% 0.55/0.74 tff(1436,plain,
% 0.55/0.74 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (op(e0, e0) = e2)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1435, 1092])).
% 0.55/0.74 tff(1437,plain,
% 0.55/0.74 ((~(e2 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e0, e0) = e2))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1436])).
% 0.55/0.74 tff(1438,plain,
% 0.55/0.74 (~(op(e0, e0) = e2)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1053, 1437])).
% 0.55/0.74 tff(1439,plain,
% 0.55/0.74 (op(e0, e0) = e1),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1105, 1438, 1055, 1433])).
% 0.55/0.74 tff(1440,plain,
% 0.55/0.74 (op(e0, e1) = e0),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1109, 1439])).
% 0.55/0.74 tff(1441,plain,
% 0.55/0.74 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1440])).
% 0.55/0.74 tff(1442,plain,
% 0.55/0.74 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1441, 1430])).
% 0.55/0.74 tff(1443,plain,
% 0.55/0.74 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1442])).
% 0.55/0.74 tff(1444,plain,
% 0.55/0.74 (~(op(e1, e1) = e0)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1402, 1443])).
% 0.55/0.74 tff(1445,plain,
% 0.55/0.74 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1440])).
% 0.55/0.74 tff(1446,plain,
% 0.55/0.74 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1445, 1440])).
% 0.55/0.74 tff(1447,plain,
% 0.55/0.74 ((~(op(e1, op(e0, e1)) = op(e0, e1))) <=> (~(op(e1, e0) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1446])).
% 0.55/0.75 tff(1448,plain,
% 0.55/0.75 (~(op(e1, e0) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1064, 1447])).
% 0.55/0.75 tff(1449,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[548, 1448, 1444, 1429, 1426])).
% 0.55/0.75 tff(1450,plain,((op(e0, e2) = e3) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e0, e0) = e0) | (op(e2, e2) = e3) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e3) | (op(e3, e0) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1451,plain,
% 0.55/0.75 (op(e0, e2) = e3),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1450, 693, 1055, 26, 1053, 1064, 1067, 1065, 1063])).
% 0.55/0.75 tff(1452,plain,
% 0.55/0.75 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1453,plain,
% 0.55/0.75 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1452, 566])).
% 0.55/0.75 tff(1454,plain,
% 0.55/0.75 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1453])).
% 0.55/0.75 tff(1455,plain,
% 0.55/0.75 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = op(e3, e2)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1456,plain,
% 0.55/0.75 (~(op(e0, e2) = op(e3, e2))),
% 0.55/0.75 inference(and_elim,[status(thm)],[147])).
% 0.55/0.75 tff(1457,plain,
% 0.55/0.75 (~(op(e0, e2) = op(e3, e2))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 0.55/0.75 tff(1458,plain,
% 0.55/0.75 (~(op(e3, e2) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1457, 1454])).
% 0.55/0.75 tff(1459,plain,
% 0.55/0.75 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1460,plain,
% 0.55/0.75 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1459])).
% 0.55/0.75 tff(1461,plain,
% 0.55/0.75 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = op(e0, e2)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1462,plain,
% 0.55/0.75 (~(op(e0, e0) = op(e0, e2))),
% 0.55/0.75 inference(and_elim,[status(thm)],[136])).
% 0.55/0.75 tff(1463,plain,
% 0.55/0.75 (~(op(e0, e0) = op(e0, e2))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.55/0.75 tff(1464,plain,
% 0.55/0.75 (~(op(e0, e0) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1463, 1460])).
% 0.55/0.75 tff(1465,plain,
% 0.55/0.75 ((op(e0, e2) = e0) <=> (e3 = e0)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1466,plain,
% 0.55/0.75 ((op(e0, e2) = e0) <=> (e0 = e3)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1465, 1])).
% 0.55/0.75 tff(1467,plain,
% 0.55/0.75 ((e0 = e3) <=> (op(e0, e2) = e0)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1466])).
% 0.55/0.75 tff(1468,plain,
% 0.55/0.75 ((~(e0 = e3)) <=> (~(op(e0, e2) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1467])).
% 0.55/0.75 tff(1469,plain,
% 0.55/0.75 (~(op(e0, e2) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[509, 1468])).
% 0.55/0.75 tff(1470,plain,
% 0.55/0.75 (((~(op(e0, e0) = e2)) | (op(e0, e2) = e0)) <=> ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1471,plain,
% 0.55/0.75 ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0)),
% 0.55/0.75 inference(and_elim,[status(thm)],[209])).
% 0.55/0.75 tff(1472,plain,
% 0.55/0.75 ((~(op(e0, e0) = e2)) | (op(e0, e2) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.55/0.75 tff(1473,plain,
% 0.55/0.75 (~(op(e0, e0) = e2)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1472, 1469])).
% 0.55/0.75 tff(1474,plain,
% 0.55/0.75 (op(e0, e0) = e1),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1105, 1473, 1055, 1464])).
% 0.55/0.75 tff(1475,plain,
% 0.55/0.75 (op(e0, e1) = e0),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1109, 1474])).
% 0.55/0.75 tff(1476,plain,
% 0.55/0.75 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1475])).
% 0.55/0.75 tff(1477,plain,
% 0.55/0.75 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1476, 1430])).
% 0.55/0.75 tff(1478,plain,
% 0.55/0.75 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1477])).
% 0.55/0.75 tff(1479,plain,
% 0.55/0.75 (~(op(e1, e1) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1402, 1478])).
% 0.55/0.75 tff(1480,plain,
% 0.55/0.75 ((e3 = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 0.55/0.75 inference(commutativity,[status(thm)],[])).
% 0.55/0.75 tff(1481,plain,
% 0.55/0.75 ((op(e0, e2) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1482,plain,
% 0.55/0.75 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1481, 1480])).
% 0.55/0.75 tff(1483,plain,
% 0.55/0.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1482])).
% 0.55/0.75 tff(1484,plain,
% 0.55/0.75 (~(op(e0, e3) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[702, 1483])).
% 0.55/0.75 tff(1485,plain,
% 0.55/0.75 (op(e2, op(e0, e2)) = op(e2, e3)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1486,plain,
% 0.55/0.75 ((op(e2, op(e0, e2)) = op(e0, e2)) <=> (op(e2, e3) = e3)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1485, 1451])).
% 0.55/0.75 tff(1487,plain,
% 0.55/0.75 ((~(op(e2, op(e0, e2)) = op(e0, e2))) <=> (~(op(e2, e3) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1486])).
% 0.55/0.75 tff(1488,plain,
% 0.55/0.75 (~(op(e2, e3) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1063, 1487])).
% 0.55/0.75 tff(1489,plain,
% 0.55/0.75 (op(e1, e3) = e3),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[724, 1488, 1484, 693])).
% 0.55/0.75 tff(1490,plain,
% 0.55/0.75 ((op(e1, e3) = e0) <=> (e3 = e0)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1489])).
% 0.55/0.75 tff(1491,plain,
% 0.55/0.75 ((op(e1, e3) = e0) <=> (e0 = e3)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1490, 1])).
% 0.55/0.75 tff(1492,plain,
% 0.55/0.75 ((e0 = e3) <=> (op(e1, e3) = e0)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1491])).
% 0.55/0.75 tff(1493,plain,
% 0.55/0.75 ((~(e0 = e3)) <=> (~(op(e1, e3) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1492])).
% 0.55/0.75 tff(1494,plain,
% 0.55/0.75 (~(op(e1, e3) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[509, 1493])).
% 0.55/0.75 tff(1495,plain,
% 0.55/0.75 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1475])).
% 0.55/0.75 tff(1496,plain,
% 0.55/0.75 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1495, 1475])).
% 0.55/0.75 tff(1497,plain,
% 0.55/0.75 ((~(op(e1, op(e0, e1)) = op(e0, e1))) <=> (~(op(e1, e0) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1496])).
% 0.55/0.75 tff(1498,plain,
% 0.55/0.75 (~(op(e1, e0) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1064, 1497])).
% 0.55/0.75 tff(1499,plain,
% 0.55/0.75 (op(e1, e2) = e0),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[548, 1498, 1494, 1479])).
% 0.55/0.75 tff(1500,plain,
% 0.55/0.75 ((op(e1, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1499])).
% 0.55/0.75 tff(1501,plain,
% 0.55/0.75 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1500, 272])).
% 0.55/0.75 tff(1502,plain,
% 0.55/0.75 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1501])).
% 0.55/0.75 tff(1503,plain,
% 0.55/0.75 (~(op(e3, e2) = e0)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[742, 1502])).
% 0.55/0.75 tff(1504,plain,
% 0.55/0.75 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1505,plain,
% 0.55/0.75 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1504, 1178])).
% 0.55/0.75 tff(1506,plain,
% 0.55/0.75 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1505])).
% 0.55/0.75 tff(1507,plain,
% 0.55/0.75 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1506])).
% 0.55/0.75 tff(1508,plain,
% 0.55/0.75 (~(op(e0, e2) = e2)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[170, 1507])).
% 0.55/0.75 tff(1509,plain,
% 0.55/0.75 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1475])).
% 0.55/0.75 tff(1510,plain,
% 0.55/0.75 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1509])).
% 0.55/0.75 tff(1511,plain,
% 0.55/0.75 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1510])).
% 0.55/0.75 tff(1512,plain,
% 0.55/0.75 (~(op(e0, e1) = e2)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[16, 1511])).
% 0.55/0.75 tff(1513,plain,
% 0.55/0.75 (op(e0, e3) = e2),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1346, 1512, 1473, 1508])).
% 0.55/0.75 tff(1514,plain,
% 0.55/0.75 (op(e3, op(e0, e3)) = op(e3, e2)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1513])).
% 0.55/0.75 tff(1515,plain,
% 0.55/0.75 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e2) = e2)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1514, 1513])).
% 0.55/0.75 tff(1516,plain,
% 0.55/0.75 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e2) = e2))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1515])).
% 0.55/0.75 tff(1517,plain,
% 0.55/0.75 (~(op(e3, e2) = e2)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1065, 1516])).
% 0.55/0.75 tff(1518,plain,
% 0.55/0.75 (op(e3, e2) = e1),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[736, 1517, 1503, 1458])).
% 0.55/0.75 tff(1519,plain,
% 0.55/0.75 ((op(e3, e2) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1518])).
% 0.55/0.75 tff(1520,plain,
% 0.55/0.75 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1519, 1071])).
% 0.55/0.75 tff(1521,plain,
% 0.55/0.75 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1520])).
% 0.55/0.75 tff(1522,plain,
% 0.55/0.75 (~(op(e3, e3) = e1)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1160, 1521])).
% 0.55/0.75 tff(1523,plain,
% 0.55/0.75 (op(e3, e3) = e0),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1146, 1522, 693, 1067, 1053, 1055])).
% 0.55/0.75 tff(1524,plain,
% 0.55/0.75 (e0 = op(e3, e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1523, 1070])).
% 0.55/0.75 tff(1525,plain,
% 0.55/0.75 (op(op(e3, e3), op(e3, e3)) = op(e0, e0)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1523, 1523])).
% 0.55/0.75 tff(1526,plain,
% 0.55/0.75 (op(e0, e0) = op(op(e3, e3), op(e3, e3))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1525])).
% 0.55/0.75 tff(1527,plain,
% 0.55/0.75 (e1 = op(e0, e0)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1474])).
% 0.55/0.75 tff(1528,plain,
% 0.55/0.75 (e1 = op(op(e3, e3), op(e3, e3))),
% 0.55/0.75 inference(transitivity,[status(thm)],[1527, 1526])).
% 0.55/0.75 tff(1529,plain,
% 0.55/0.75 (op(op(e3, e3), op(e3, e3)) = e1),
% 0.55/0.75 inference(transitivity,[status(thm)],[1525, 1474])).
% 0.55/0.75 tff(1530,plain,
% 0.55/0.75 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e1)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1529])).
% 0.55/0.75 tff(1531,plain,
% 0.55/0.75 (op(e3, e1) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1530])).
% 0.55/0.75 tff(1532,plain,
% 0.55/0.75 ((e2 = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.55/0.75 inference(commutativity,[status(thm)],[])).
% 0.55/0.75 tff(1533,plain,
% 0.55/0.75 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1489])).
% 0.55/0.75 tff(1534,plain,
% 0.55/0.75 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1533])).
% 0.55/0.75 tff(1535,plain,
% 0.55/0.75 (~(op(e1, e0) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[625, 1534])).
% 0.55/0.75 tff(1536,plain,
% 0.55/0.75 ((e1 = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.55/0.75 inference(commutativity,[status(thm)],[])).
% 0.55/0.75 tff(1537,plain,
% 0.55/0.75 ((op(e0, e0) = op(e1, e0)) <=> (e1 = op(e1, e0))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1474])).
% 0.55/0.75 tff(1538,plain,
% 0.55/0.75 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1537, 1536])).
% 0.55/0.75 tff(1539,plain,
% 0.55/0.75 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1538])).
% 0.55/0.75 tff(1540,plain,
% 0.55/0.75 (~(op(e1, e0) = e1)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[254, 1539])).
% 0.55/0.75 tff(1541,plain,
% 0.55/0.75 (((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3)) <=> ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1542,plain,
% 0.55/0.75 ((((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2)) | (op(e1, e0) = e3)) <=> ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1543,plain,
% 0.55/0.75 ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) <=> ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1544,plain,
% 0.55/0.75 (((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3)) <=> (((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1543])).
% 0.55/0.75 tff(1545,plain,
% 0.55/0.75 (((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3)) <=> ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3))),
% 0.55/0.75 inference(transitivity,[status(thm)],[1544, 1542])).
% 0.55/0.75 tff(1546,plain,
% 0.55/0.75 ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3)),
% 0.55/0.75 inference(and_elim,[status(thm)],[874])).
% 0.55/0.75 tff(1547,plain,
% 0.55/0.75 ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 0.62/0.75 tff(1548,plain,
% 0.62/0.75 ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3)),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[1547, 1541])).
% 0.62/0.75 tff(1549,plain,
% 0.62/0.75 (op(e1, e0) = e2),
% 0.62/0.75 inference(unit_resolution,[status(thm)],[1548, 1498, 1540, 1535])).
% 0.62/0.75 tff(1550,plain,
% 0.62/0.75 ((op(e1, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.62/0.75 inference(monotonicity,[status(thm)],[1549])).
% 0.62/0.75 tff(1551,plain,
% 0.62/0.75 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.62/0.75 inference(transitivity,[status(thm)],[1550, 1532])).
% 0.62/0.75 tff(1552,plain,
% 0.62/0.75 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.62/0.75 inference(monotonicity,[status(thm)],[1551])).
% 0.62/0.75 tff(1553,plain,
% 0.62/0.75 (~(op(e3, e0) = e2)),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[564, 1552])).
% 0.62/0.75 tff(1554,plain,
% 0.62/0.75 (~(op(e3, e3) = e2)),
% 0.62/0.75 inference(unit_resolution,[status(thm)],[1127, 1458])).
% 0.62/0.75 tff(1555,plain,
% 0.62/0.75 (op(e3, e1) = e2),
% 0.62/0.75 inference(unit_resolution,[status(thm)],[818, 1517, 1554, 1553])).
% 0.62/0.75 tff(1556,plain,
% 0.62/0.75 (e2 = op(e3, e1)),
% 0.62/0.75 inference(symmetry,[status(thm)],[1555])).
% 0.62/0.75 tff(1557,plain,
% 0.62/0.75 (e2 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.62/0.75 inference(transitivity,[status(thm)],[1556, 1531])).
% 0.62/0.75 tff(1558,plain,
% 0.62/0.75 ((~(~((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3)))))) <=> ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(1559,plain,
% 0.62/0.75 (((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3)))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(1560,plain,
% 0.62/0.75 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3))))))),
% 0.62/0.75 inference(monotonicity,[status(thm)],[1559])).
% 0.62/0.75 tff(1561,plain,
% 0.62/0.75 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3))))),
% 0.62/0.75 inference(transitivity,[status(thm)],[1560, 1558])).
% 0.62/0.75 tff(1562,plain,
% 0.62/0.75 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(1563,plain,
% 0.62/0.75 ((~(((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3))) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(1564,axiom,(~(((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3))) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax12')).
% 0.62/0.75 tff(1565,plain,
% 0.62/0.75 (~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.62/0.75 tff(1566,plain,
% 0.62/0.75 (~((e1 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[1565, 1562])).
% 0.62/0.75 tff(1567,plain,
% 0.62/0.75 ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, e3)))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[1566, 1561])).
% 0.62/0.75 tff(1568,plain,
% 0.62/0.75 ($false),
% 0.62/0.75 inference(unit_resolution,[status(thm)],[1567, 1557, 1528, 1524])).
% 0.62/0.75 tff(1569,plain,((op(e3, e3) = e3) | (op(e3, e0) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e0, e0) = e0) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.75 tff(1570,plain,
% 0.62/0.75 (op(e3, e3) = e3),
% 0.62/0.75 inference(unit_resolution,[status(thm)],[1569, 26, 1053, 1055, 1065, 1064, 1063, 1067])).
% 0.62/0.76 tff(1571,plain,
% 0.62/0.76 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1570])).
% 0.62/0.76 tff(1572,plain,
% 0.62/0.76 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1571])).
% 0.62/0.76 tff(1573,plain,
% 0.62/0.76 (~(op(e3, e2) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1160, 1572])).
% 0.62/0.76 tff(1574,plain,
% 0.62/0.76 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1570])).
% 0.62/0.76 tff(1575,plain,
% 0.62/0.76 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1574])).
% 0.62/0.76 tff(1576,plain,
% 0.62/0.76 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = op(e3, e3)))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1577,plain,
% 0.62/0.76 (~(op(e0, e3) = op(e3, e3))),
% 0.62/0.76 inference(and_elim,[status(thm)],[141])).
% 0.62/0.76 tff(1578,plain,
% 0.62/0.76 (~(op(e0, e3) = op(e3, e3))),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.62/0.76 tff(1579,plain,
% 0.62/0.76 (~(op(e0, e3) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1578, 1575])).
% 0.62/0.76 tff(1580,plain,
% 0.62/0.76 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1570])).
% 0.62/0.76 tff(1581,plain,
% 0.62/0.76 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1580])).
% 0.62/0.76 tff(1582,plain,
% 0.62/0.76 (~(op(e2, e3) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[196, 1581])).
% 0.62/0.76 tff(1583,plain,
% 0.62/0.76 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1570])).
% 0.62/0.76 tff(1584,plain,
% 0.62/0.76 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1583])).
% 0.62/0.76 tff(1585,plain,
% 0.62/0.76 (~(op(e3, e0) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1424, 1584])).
% 0.62/0.76 tff(1586,plain,
% 0.62/0.76 ((e3 = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.62/0.76 inference(commutativity,[status(thm)],[])).
% 0.62/0.76 tff(1587,assumption,(~(op(e0, e3) = e3)), introduced(assumption)).
% 0.62/0.76 tff(1588,assumption,(~(op(e3, e0) = e3)), introduced(assumption)).
% 0.62/0.76 tff(1589,plain,
% 0.62/0.76 (op(e1, e2) = e3),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[684, 1072, 26, 861])).
% 0.62/0.76 tff(1590,assumption,(~(op(e0, e0) = e3)), introduced(assumption)).
% 0.62/0.76 tff(1591,plain,
% 0.62/0.76 (op(e0, e1) = e3),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1090, 1590, 1587, 1072])).
% 0.62/0.76 tff(1592,plain,
% 0.62/0.76 ((op(e0, e1) = e0) <=> (e3 = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1591])).
% 0.62/0.76 tff(1593,plain,
% 0.62/0.76 ((op(e0, e1) = e0) <=> (e0 = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1592, 1])).
% 0.62/0.76 tff(1594,plain,
% 0.62/0.76 ((e0 = e3) <=> (op(e0, e1) = e0)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1593])).
% 0.62/0.76 tff(1595,plain,
% 0.62/0.76 ((~(e0 = e3)) <=> (~(op(e0, e1) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1594])).
% 0.62/0.76 tff(1596,plain,
% 0.62/0.76 (~(op(e0, e1) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[509, 1595])).
% 0.62/0.76 tff(1597,plain,
% 0.62/0.76 (~(op(e0, e0) = e1)),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1109, 1596])).
% 0.62/0.76 tff(1598,plain,
% 0.62/0.76 (op(e0, e0) = e2),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1105, 1597, 1055, 1590])).
% 0.62/0.76 tff(1599,assumption,(op(e1, e2) = e3), introduced(assumption)).
% 0.62/0.76 tff(1600,plain,
% 0.62/0.76 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1599])).
% 0.62/0.76 tff(1601,plain,
% 0.62/0.76 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1600])).
% 0.62/0.76 tff(1602,plain,
% 0.62/0.76 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = op(e1, e2)))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1603,plain,
% 0.62/0.76 (~(op(e1, e1) = op(e1, e2))),
% 0.62/0.76 inference(and_elim,[status(thm)],[128])).
% 0.62/0.76 tff(1604,plain,
% 0.62/0.76 (~(op(e1, e1) = op(e1, e2))),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.62/0.76 tff(1605,plain,
% 0.62/0.76 (~(op(e1, e1) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1604, 1601])).
% 0.62/0.76 tff(1606,plain,
% 0.62/0.76 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1599])).
% 0.62/0.76 tff(1607,plain,
% 0.62/0.76 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1606])).
% 0.62/0.76 tff(1608,plain,
% 0.62/0.76 (~(op(e1, e0) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[613, 1607])).
% 0.62/0.76 tff(1609,plain,
% 0.62/0.76 (((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))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1610,plain,
% 0.62/0.76 ((((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))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1611,plain,
% 0.62/0.76 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1612,plain,
% 0.62/0.76 (((((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))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1611])).
% 0.62/0.76 tff(1613,plain,
% 0.62/0.76 (((((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))),
% 0.62/0.76 inference(transitivity,[status(thm)],[1612, 1610])).
% 0.62/0.76 tff(1614,plain,
% 0.62/0.76 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)),
% 0.62/0.76 inference(and_elim,[status(thm)],[453])).
% 0.62/0.76 tff(1615,plain,
% 0.62/0.76 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.62/0.76 tff(1616,plain,
% 0.62/0.76 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1615, 1609])).
% 0.62/0.76 tff(1617,plain,
% 0.62/0.76 (op(e2, e0) = e3),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1616, 1590, 1588, 1608])).
% 0.62/0.76 tff(1618,plain,
% 0.62/0.76 ((op(e2, e0) = e1) <=> (e3 = e1)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1617])).
% 0.62/0.76 tff(1619,plain,
% 0.62/0.76 ((op(e2, e0) = e1) <=> (e1 = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1618, 601])).
% 0.62/0.76 tff(1620,plain,
% 0.62/0.76 ((e1 = e3) <=> (op(e2, e0) = e1)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1619])).
% 0.62/0.76 tff(1621,plain,
% 0.62/0.76 ((~(e1 = e3)) <=> (~(op(e2, e0) = e1))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1620])).
% 0.62/0.76 tff(1622,plain,
% 0.62/0.76 (~(op(e2, e0) = e1)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[521, 1621])).
% 0.62/0.76 tff(1623,plain,
% 0.62/0.76 (op(e1, e0) = e1),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[460, 1597, 1622, 1067])).
% 0.62/0.76 tff(1624,plain,
% 0.62/0.76 ((op(e1, e0) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1623])).
% 0.62/0.76 tff(1625,plain,
% 0.62/0.76 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1624, 1350])).
% 0.62/0.76 tff(1626,plain,
% 0.62/0.76 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1625])).
% 0.62/0.76 tff(1627,plain,
% 0.62/0.76 (~(op(e1, e1) = e1)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[441, 1626])).
% 0.62/0.76 tff(1628,plain,
% 0.62/0.76 (op(e1, e1) = e0),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[435, 1627, 379, 1605])).
% 0.62/0.76 tff(1629,plain,
% 0.62/0.76 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1628, 1628])).
% 0.62/0.76 tff(1630,plain,
% 0.62/0.76 (op(op(e1, e1), op(e1, e1)) = e2),
% 0.62/0.76 inference(transitivity,[status(thm)],[1629, 1598])).
% 0.62/0.76 tff(1631,plain,
% 0.62/0.76 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e2)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1630])).
% 0.62/0.76 tff(1632,plain,
% 0.62/0.76 (op(e1, e2) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.62/0.76 inference(symmetry,[status(thm)],[1631])).
% 0.62/0.76 tff(1633,plain,
% 0.62/0.76 (e3 = op(e1, e2)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1599])).
% 0.62/0.76 tff(1634,plain,
% 0.62/0.76 (e3 = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.62/0.76 inference(transitivity,[status(thm)],[1633, 1632])).
% 0.62/0.76 tff(1635,plain,
% 0.62/0.76 ($false),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1066, 1634])).
% 0.62/0.76 tff(1636,plain,((op(e0, e0) = e3) | (e3 = op(e1, op(op(e1, e1), op(e1, e1)))) | (~(op(e1, e2) = e3)) | (op(e1, e1) = e2) | (op(e3, e0) = e1) | (op(e0, e0) = e0) | (op(e3, e0) = e3) | (op(e0, e3) = e3) | (op(e0, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.76 tff(1637,plain,
% 0.62/0.76 (op(e0, e0) = e3),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1636, 1589, 1066, 379, 1067, 1055, 1588, 1587, 1072])).
% 0.62/0.76 tff(1638,plain,
% 0.62/0.76 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1637])).
% 0.62/0.76 tff(1639,plain,
% 0.62/0.76 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1638, 1586])).
% 0.62/0.76 tff(1640,plain,
% 0.62/0.76 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1639])).
% 0.62/0.76 tff(1641,plain,
% 0.62/0.76 (~(op(e2, e0) = e3)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[162, 1640])).
% 0.62/0.76 tff(1642,plain,
% 0.62/0.76 (op(e2, e1) = e3),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[189, 1641, 26, 1179])).
% 0.62/0.76 tff(1643,plain,
% 0.62/0.76 ((op(e2, e1) = e0) <=> (e3 = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1642])).
% 0.62/0.76 tff(1644,plain,
% 0.62/0.76 ((op(e2, e1) = e0) <=> (e0 = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1643, 1])).
% 0.62/0.76 tff(1645,plain,
% 0.62/0.76 ((e0 = e3) <=> (op(e2, e1) = e0)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1644])).
% 0.62/0.76 tff(1646,plain,
% 0.62/0.76 ((~(e0 = e3)) <=> (~(op(e2, e1) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1645])).
% 0.62/0.76 tff(1647,plain,
% 0.62/0.76 (~(op(e2, e1) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[509, 1646])).
% 0.62/0.76 tff(1648,plain,
% 0.62/0.76 (op(e0, e3) = e0),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1280, 1637])).
% 0.62/0.76 tff(1649,plain,
% 0.62/0.76 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1648])).
% 0.62/0.76 tff(1650,plain,
% 0.62/0.76 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1649])).
% 0.62/0.76 tff(1651,plain,
% 0.62/0.76 (~(op(e0, e1) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[403, 1650])).
% 0.62/0.76 tff(1652,plain,
% 0.62/0.76 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1648])).
% 0.62/0.76 tff(1653,plain,
% 0.62/0.76 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1652])).
% 0.62/0.76 tff(1654,plain,
% 0.62/0.76 (~(op(e0, e2) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[702, 1653])).
% 0.62/0.76 tff(1655,plain,
% 0.62/0.76 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1589])).
% 0.62/0.76 tff(1656,plain,
% 0.62/0.76 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1655, 1])).
% 0.62/0.76 tff(1657,plain,
% 0.62/0.76 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1656])).
% 0.62/0.76 tff(1658,plain,
% 0.62/0.76 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1657])).
% 0.62/0.76 tff(1659,plain,
% 0.62/0.76 (~(op(e1, e2) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[509, 1658])).
% 0.62/0.76 tff(1660,plain,
% 0.62/0.76 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1648])).
% 0.62/0.76 tff(1661,plain,
% 0.62/0.76 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1660, 1648])).
% 0.62/0.76 tff(1662,plain,
% 0.62/0.76 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1661])).
% 0.62/0.76 tff(1663,plain,
% 0.62/0.76 (~(op(e3, e0) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1065, 1662])).
% 0.62/0.76 tff(1664,plain,
% 0.62/0.76 (op(e3, e0) = e2),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1333, 1663, 1067, 1588])).
% 0.62/0.76 tff(1665,plain,
% 0.62/0.76 (e2 = op(e3, e0)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1664])).
% 0.62/0.76 tff(1666,plain,
% 0.62/0.76 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1665])).
% 0.62/0.76 tff(1667,plain,
% 0.62/0.76 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1666])).
% 0.62/0.76 tff(1668,plain,
% 0.62/0.76 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1667])).
% 0.62/0.76 tff(1669,plain,
% 0.62/0.76 (~(op(e2, e0) = e2)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[589, 1668])).
% 0.62/0.76 tff(1670,plain,
% 0.62/0.76 (~(op(e2, e2) = e0)),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[230, 1669])).
% 0.62/0.76 tff(1671,plain,
% 0.62/0.76 (((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))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1672,plain,
% 0.62/0.76 ((((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))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1673,plain,
% 0.62/0.76 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(1674,plain,
% 0.62/0.76 (((((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))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1673])).
% 0.62/0.76 tff(1675,plain,
% 0.62/0.76 (((((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))),
% 0.62/0.76 inference(transitivity,[status(thm)],[1674, 1672])).
% 0.62/0.76 tff(1676,plain,
% 0.62/0.76 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)),
% 0.62/0.76 inference(and_elim,[status(thm)],[389])).
% 0.62/0.76 tff(1677,plain,
% 0.62/0.76 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.62/0.76 tff(1678,plain,
% 0.62/0.76 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1677, 1671])).
% 0.62/0.76 tff(1679,plain,
% 0.62/0.76 (op(e3, e2) = e0),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1678, 1670, 1659, 1654])).
% 0.62/0.76 tff(1680,plain,
% 0.62/0.76 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1679])).
% 0.62/0.76 tff(1681,plain,
% 0.62/0.76 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1680])).
% 0.62/0.76 tff(1682,plain,
% 0.62/0.76 (~(op(e3, e1) = e0)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[974, 1681])).
% 0.62/0.76 tff(1683,plain,
% 0.62/0.76 (op(e1, e1) = e0),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[1241, 1682, 1651, 1647])).
% 0.62/0.76 tff(1684,plain,
% 0.62/0.76 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1683, 1683])).
% 0.62/0.76 tff(1685,plain,
% 0.62/0.76 (op(e0, e0) = op(op(e1, e1), op(e1, e1))),
% 0.62/0.76 inference(symmetry,[status(thm)],[1684])).
% 0.62/0.76 tff(1686,plain,
% 0.62/0.76 (e3 = op(e0, e0)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1637])).
% 0.62/0.76 tff(1687,plain,
% 0.62/0.76 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.62/0.76 inference(transitivity,[status(thm)],[1686, 1685])).
% 0.62/0.76 tff(1688,plain,
% 0.62/0.76 ((op(e1, e1) = e0) <=> (e0 = op(e1, e1))),
% 0.62/0.76 inference(symmetry,[status(thm)],[1430])).
% 0.62/0.76 tff(1689,plain,
% 0.62/0.76 (e0 = op(e1, e1)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[1683, 1688])).
% 0.62/0.76 tff(1690,plain,
% 0.62/0.76 (op(op(e1, e1), op(e1, e1)) = e3),
% 0.62/0.76 inference(transitivity,[status(thm)],[1684, 1637])).
% 0.62/0.76 tff(1691,plain,
% 0.62/0.76 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e3)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1690])).
% 0.62/0.76 tff(1692,plain,
% 0.62/0.76 (op(e1, e3) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.62/0.76 inference(symmetry,[status(thm)],[1691])).
% 0.62/0.76 tff(1693,plain,
% 0.62/0.76 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1589])).
% 0.62/0.76 tff(1694,plain,
% 0.62/0.76 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 0.62/0.76 inference(transitivity,[status(thm)],[1693, 1178])).
% 0.62/0.76 tff(1695,plain,
% 0.62/0.76 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1694])).
% 0.62/0.76 tff(1696,plain,
% 0.62/0.76 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1695])).
% 0.62/0.76 tff(1697,plain,
% 0.62/0.76 (~(op(e1, e2) = e2)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[170, 1696])).
% 0.62/0.76 tff(1698,plain,
% 0.62/0.76 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e3, e0))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1665])).
% 0.62/0.76 tff(1699,plain,
% 0.62/0.76 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1698])).
% 0.62/0.76 tff(1700,plain,
% 0.62/0.76 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.62/0.76 inference(monotonicity,[status(thm)],[1699])).
% 0.62/0.76 tff(1701,plain,
% 0.62/0.76 (~(op(e1, e0) = e2)),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[564, 1700])).
% 0.62/0.76 tff(1702,plain,
% 0.62/0.76 (op(e1, e3) = e2),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[751, 1701, 379, 1697])).
% 0.62/0.76 tff(1703,plain,
% 0.62/0.76 (e2 = op(e1, e3)),
% 0.62/0.76 inference(symmetry,[status(thm)],[1702])).
% 0.62/0.76 tff(1704,plain,
% 0.62/0.76 (e2 = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.62/0.76 inference(transitivity,[status(thm)],[1703, 1692])).
% 0.63/0.77 tff(1705,plain,
% 0.63/0.77 ((~(~((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1))))))) <=> ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1706,plain,
% 0.63/0.77 (((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1))))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1707,plain,
% 0.63/0.77 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1706])).
% 0.63/0.77 tff(1708,plain,
% 0.63/0.77 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1707, 1705])).
% 0.63/0.77 tff(1709,plain,
% 0.63/0.77 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1710,plain,
% 0.63/0.77 ((~(((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1))) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1711,axiom,(~(((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1))) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax25')).
% 0.63/0.77 tff(1712,plain,
% 0.63/0.77 (~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.63/0.77 tff(1713,plain,
% 0.63/0.77 (~((e3 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1712, 1709])).
% 0.63/0.77 tff(1714,plain,
% 0.63/0.77 ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(op(e1, e1), op(e1, e1))))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1713, 1708])).
% 0.63/0.77 tff(1715,plain,
% 0.63/0.77 ($false),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1714, 1704, 1689, 1687])).
% 0.63/0.77 tff(1716,plain,((op(e0, e2) = e3) | (op(e1, e1) = e2) | (op(e3, e0) = e1) | (op(e3, e0) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3) | (op(e3, op(e0, e3)) = op(e0, e3)) | (e3 = op(e1, op(op(e1, e1), op(e1, e1)))) | (op(e0, e0) = e0) | (op(e0, e3) = e3) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.77 tff(1717,plain,
% 0.63/0.77 (op(e0, e2) = e3),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1716, 1585, 1067, 379, 26, 1582, 1065, 1066, 1055, 1579, 1573])).
% 0.63/0.77 tff(1718,plain,
% 0.63/0.77 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1719,plain,
% 0.63/0.77 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1718])).
% 0.63/0.77 tff(1720,plain,
% 0.63/0.77 (~(op(e0, e0) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1463, 1719])).
% 0.63/0.77 tff(1721,plain,
% 0.63/0.77 ((op(e0, e2) = e0) <=> (e3 = e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1722,plain,
% 0.63/0.77 ((op(e0, e2) = e0) <=> (e0 = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1721, 1])).
% 0.63/0.77 tff(1723,plain,
% 0.63/0.77 ((e0 = e3) <=> (op(e0, e2) = e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1722])).
% 0.63/0.77 tff(1724,plain,
% 0.63/0.77 ((~(e0 = e3)) <=> (~(op(e0, e2) = e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1723])).
% 0.63/0.77 tff(1725,plain,
% 0.63/0.77 (~(op(e0, e2) = e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[509, 1724])).
% 0.63/0.77 tff(1726,plain,
% 0.63/0.77 (~(op(e0, e0) = e2)),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1472, 1725])).
% 0.63/0.77 tff(1727,plain,
% 0.63/0.77 (op(e0, e0) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1105, 1726, 1055, 1720])).
% 0.63/0.77 tff(1728,plain,
% 0.63/0.77 (e1 = op(e0, e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1727, 1069])).
% 0.63/0.77 tff(1729,plain,
% 0.63/0.77 ((e3 = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1730,plain,
% 0.63/0.77 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1727, 1727])).
% 0.63/0.77 tff(1731,plain,
% 0.63/0.77 ((e3 = op(op(e0, e0), op(e0, e0))) <=> (e3 = op(e1, e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1730])).
% 0.63/0.77 tff(1732,plain,
% 0.63/0.77 ((e3 = op(op(e0, e0), op(e0, e0))) <=> (op(e1, e1) = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1731, 1729])).
% 0.63/0.77 tff(1733,plain,
% 0.63/0.77 ((op(e1, e1) = e3) <=> (e3 = op(op(e0, e0), op(e0, e0)))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1732])).
% 0.63/0.77 tff(1734,plain,
% 0.63/0.77 ((e3 = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1735,plain,
% 0.63/0.77 ((op(e0, e2) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1736,plain,
% 0.63/0.77 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1735, 1734])).
% 0.63/0.77 tff(1737,plain,
% 0.63/0.77 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1736])).
% 0.63/0.77 tff(1738,plain,
% 0.63/0.77 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = op(e1, e2)))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1739,plain,
% 0.63/0.77 (~(op(e0, e2) = op(e1, e2))),
% 0.63/0.77 inference(and_elim,[status(thm)],[149])).
% 0.63/0.77 tff(1740,plain,
% 0.63/0.77 (~(op(e0, e2) = op(e1, e2))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 0.63/0.77 tff(1741,plain,
% 0.63/0.77 (~(op(e1, e2) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1740, 1737])).
% 0.63/0.77 tff(1742,plain,
% 0.63/0.77 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1570])).
% 0.63/0.77 tff(1743,plain,
% 0.63/0.77 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1742])).
% 0.63/0.77 tff(1744,plain,
% 0.63/0.77 (~(op(e1, e3) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[539, 1743])).
% 0.63/0.77 tff(1745,plain,
% 0.63/0.77 ((e2 = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1746,plain,
% 0.63/0.77 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1747,plain,
% 0.63/0.77 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1746, 1178])).
% 0.63/0.77 tff(1748,plain,
% 0.63/0.77 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1747])).
% 0.63/0.77 tff(1749,plain,
% 0.63/0.77 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1748])).
% 0.63/0.77 tff(1750,plain,
% 0.63/0.77 (~(op(e0, e2) = e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[170, 1749])).
% 0.63/0.77 tff(1751,plain,
% 0.63/0.77 (op(e0, e1) = e0),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1109, 1727])).
% 0.63/0.77 tff(1752,plain,
% 0.63/0.77 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1751])).
% 0.63/0.77 tff(1753,plain,
% 0.63/0.77 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1752])).
% 0.63/0.77 tff(1754,plain,
% 0.63/0.77 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1753])).
% 0.63/0.77 tff(1755,plain,
% 0.63/0.77 (~(op(e0, e1) = e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[16, 1754])).
% 0.63/0.77 tff(1756,plain,
% 0.63/0.77 (op(e0, e3) = e2),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1346, 1755, 1726, 1750])).
% 0.63/0.77 tff(1757,plain,
% 0.63/0.77 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1756])).
% 0.63/0.77 tff(1758,plain,
% 0.63/0.77 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1757, 1745])).
% 0.63/0.77 tff(1759,plain,
% 0.63/0.77 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1758])).
% 0.63/0.77 tff(1760,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(1761,plain,
% 0.63/0.77 (~(op(e0, e3) = op(e1, e3))),
% 0.63/0.77 inference(and_elim,[status(thm)],[143])).
% 0.63/0.77 tff(1762,plain,
% 0.63/0.77 (~(op(e0, e3) = op(e1, e3))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.63/0.77 tff(1763,plain,
% 0.63/0.77 (~(op(e1, e3) = e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1762, 1759])).
% 0.63/0.77 tff(1764,plain,
% 0.63/0.77 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1751])).
% 0.63/0.77 tff(1765,plain,
% 0.63/0.77 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1764, 1751])).
% 0.63/0.77 tff(1766,plain,
% 0.63/0.77 ((~(op(e1, op(e0, e1)) = op(e0, e1))) <=> (~(op(e1, e0) = e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1765])).
% 0.63/0.77 tff(1767,plain,
% 0.63/0.77 (~(op(e1, e0) = e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1064, 1766])).
% 0.63/0.77 tff(1768,plain,
% 0.63/0.77 (e3 = op(e3, e3)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1570])).
% 0.63/0.77 tff(1769,plain,
% 0.63/0.77 ((e1 = e3) <=> (e1 = op(e3, e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1768])).
% 0.63/0.77 tff(1770,plain,
% 0.63/0.77 ((e1 = e3) <=> (op(e3, e3) = e1)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1769, 1071])).
% 0.63/0.77 tff(1771,plain,
% 0.63/0.77 ((~(e1 = e3)) <=> (~(op(e3, e3) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1770])).
% 0.63/0.77 tff(1772,plain,
% 0.63/0.77 (~(op(e3, e3) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[521, 1771])).
% 0.63/0.77 tff(1773,plain,
% 0.63/0.77 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1774,plain,
% 0.63/0.77 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1773])).
% 0.63/0.77 tff(1775,plain,
% 0.63/0.77 (~(op(e0, e1) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[867, 1774])).
% 0.63/0.77 tff(1776,plain,
% 0.63/0.77 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1570])).
% 0.63/0.77 tff(1777,plain,
% 0.63/0.77 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1776])).
% 0.63/0.77 tff(1778,plain,
% 0.63/0.77 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = op(e3, e3)))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1779,plain,
% 0.63/0.77 (~(op(e3, e1) = op(e3, e3))),
% 0.63/0.77 inference(and_elim,[status(thm)],[58])).
% 0.63/0.77 tff(1780,plain,
% 0.63/0.77 (~(op(e3, e1) = op(e3, e3))),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 0.63/0.77 tff(1781,plain,
% 0.63/0.77 (~(op(e3, e1) = e3)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1780, 1777])).
% 0.63/0.77 tff(1782,plain,
% 0.63/0.77 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1717])).
% 0.63/0.77 tff(1783,plain,
% 0.63/0.77 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1782, 601])).
% 0.63/0.77 tff(1784,plain,
% 0.63/0.77 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1783])).
% 0.63/0.77 tff(1785,plain,
% 0.63/0.77 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1784])).
% 0.63/0.77 tff(1786,plain,
% 0.63/0.77 (~(op(e0, e2) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[521, 1785])).
% 0.63/0.77 tff(1787,plain,
% 0.63/0.77 ((e0 = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.63/0.77 inference(commutativity,[status(thm)],[])).
% 0.63/0.77 tff(1788,plain,
% 0.63/0.77 ((op(e2, e2) = e0) <=> (e0 = op(e2, e2))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1787])).
% 0.63/0.77 tff(1789,assumption,(~(op(e0, e2) = e0)), introduced(assumption)).
% 0.63/0.77 tff(1790,assumption,(op(e0, e0) = e1), introduced(assumption)).
% 0.63/0.77 tff(1791,plain,
% 0.63/0.77 (op(e0, e1) = e0),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1109, 1790])).
% 0.63/0.77 tff(1792,plain,
% 0.63/0.77 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1791])).
% 0.63/0.77 tff(1793,plain,
% 0.63/0.77 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1792, 1430])).
% 0.63/0.77 tff(1794,plain,
% 0.63/0.77 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1793])).
% 0.63/0.77 tff(1795,plain,
% 0.63/0.77 (~(op(e1, e1) = e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1402, 1794])).
% 0.63/0.77 tff(1796,assumption,(~(op(e1, e0) = e0)), introduced(assumption)).
% 0.63/0.77 tff(1797,plain,
% 0.63/0.77 (op(e1, e3) = e0),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[548, 837, 1795, 1796])).
% 0.63/0.77 tff(1798,plain,
% 0.63/0.77 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1797])).
% 0.63/0.77 tff(1799,plain,
% 0.63/0.77 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1798])).
% 0.63/0.77 tff(1800,plain,
% 0.63/0.77 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1799])).
% 0.63/0.77 tff(1801,plain,
% 0.63/0.77 (~(op(e1, e3) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[40, 1800])).
% 0.63/0.77 tff(1802,plain,
% 0.63/0.77 (~(op(e1, e1) = e3)),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[332, 1801])).
% 0.63/0.77 tff(1803,plain,
% 0.63/0.77 (op(e1, e1) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[435, 1802, 379, 1795])).
% 0.63/0.77 tff(1804,plain,
% 0.63/0.77 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1803])).
% 0.63/0.77 tff(1805,plain,
% 0.63/0.77 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1804, 591])).
% 0.63/0.77 tff(1806,plain,
% 0.63/0.77 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1805])).
% 0.63/0.77 tff(1807,plain,
% 0.63/0.77 (~(op(e1, e2) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1604, 1806])).
% 0.63/0.77 tff(1808,assumption,(~(op(e0, e2) = e1)), introduced(assumption)).
% 0.63/0.77 tff(1809,plain,
% 0.63/0.77 ((op(e0, e0) = op(e0, e3)) <=> (e1 = op(e0, e3))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1790])).
% 0.63/0.77 tff(1810,plain,
% 0.63/0.77 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1809, 696])).
% 0.63/0.77 tff(1811,plain,
% 0.63/0.77 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1810])).
% 0.63/0.77 tff(1812,plain,
% 0.63/0.77 (~(op(e0, e3) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[305, 1811])).
% 0.63/0.77 tff(1813,plain,
% 0.63/0.77 (op(e2, e3) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[711, 1801, 695, 1812])).
% 0.63/0.77 tff(1814,plain,
% 0.63/0.77 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1813])).
% 0.63/0.77 tff(1815,plain,
% 0.63/0.77 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1814])).
% 0.63/0.77 tff(1816,plain,
% 0.63/0.77 (~(op(e2, e2) = e1)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[313, 1815])).
% 0.63/0.77 tff(1817,plain,
% 0.63/0.77 (op(e3, e2) = e1),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[671, 1816, 1808, 1807])).
% 0.63/0.77 tff(1818,plain,
% 0.63/0.77 ((op(e3, e2) = e0) <=> (e1 = e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1817])).
% 0.63/0.77 tff(1819,plain,
% 0.63/0.77 ((op(e3, e2) = e0) <=> (e0 = e1)),
% 0.63/0.77 inference(transitivity,[status(thm)],[1818, 1203])).
% 0.63/0.77 tff(1820,plain,
% 0.63/0.77 ((e0 = e1) <=> (op(e3, e2) = e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1819])).
% 0.63/0.77 tff(1821,plain,
% 0.63/0.77 ((~(e0 = e1)) <=> (~(op(e3, e2) = e0))),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1820])).
% 0.63/0.77 tff(1822,plain,
% 0.63/0.77 (~(op(e3, e2) = e0)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[40, 1821])).
% 0.63/0.77 tff(1823,plain,
% 0.63/0.77 (op(e2, e2) = e0),
% 0.63/0.77 inference(unit_resolution,[status(thm)],[1678, 1822, 837, 1789])).
% 0.63/0.77 tff(1824,plain,
% 0.63/0.77 (e0 = op(e2, e2)),
% 0.63/0.77 inference(modus_ponens,[status(thm)],[1823, 1788])).
% 0.63/0.77 tff(1825,plain,
% 0.63/0.77 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1823, 1823])).
% 0.63/0.77 tff(1826,plain,
% 0.63/0.77 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1825])).
% 0.63/0.77 tff(1827,plain,
% 0.63/0.77 (e1 = op(e0, e0)),
% 0.63/0.77 inference(symmetry,[status(thm)],[1790])).
% 0.63/0.77 tff(1828,plain,
% 0.63/0.77 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.63/0.77 inference(transitivity,[status(thm)],[1827, 1826])).
% 0.63/0.77 tff(1829,plain,
% 0.63/0.77 (op(op(e2, e2), op(e2, e2)) = e1),
% 0.63/0.77 inference(transitivity,[status(thm)],[1825, 1790])).
% 0.63/0.77 tff(1830,plain,
% 0.63/0.77 (op(e2, op(op(e2, e2), op(e2, e2))) = op(e2, e1)),
% 0.63/0.77 inference(monotonicity,[status(thm)],[1829])).
% 0.63/0.77 tff(1831,plain,
% 0.63/0.77 (op(e2, e1) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.63/0.77 inference(symmetry,[status(thm)],[1830])).
% 0.63/0.77 tff(1832,assumption,(~(op(e0, e1) = e3)), introduced(assumption)).
% 0.63/0.77 tff(1833,assumption,(~(op(e3, e1) = e3)), introduced(assumption)).
% 0.63/0.77 tff(1834,plain,
% 0.63/0.77 (((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))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1835,plain,
% 0.63/0.77 ((((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))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1836,plain,
% 0.63/0.77 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3))),
% 0.63/0.77 inference(rewrite,[status(thm)],[])).
% 0.63/0.77 tff(1837,plain,
% 0.63/0.77 (((((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))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1836])).
% 0.63/0.78 tff(1838,plain,
% 0.63/0.78 (((((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))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1837, 1835])).
% 0.63/0.78 tff(1839,plain,
% 0.63/0.78 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)),
% 0.63/0.78 inference(and_elim,[status(thm)],[391])).
% 0.63/0.78 tff(1840,plain,
% 0.63/0.78 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 0.63/0.78 tff(1841,plain,
% 0.63/0.78 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1840, 1834])).
% 0.63/0.78 tff(1842,plain,
% 0.63/0.78 (op(e2, e1) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1841, 1802, 1833, 1832])).
% 0.63/0.78 tff(1843,plain,
% 0.63/0.78 (e3 = op(e2, e1)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1842])).
% 0.63/0.78 tff(1844,plain,
% 0.63/0.78 (e3 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1843, 1831])).
% 0.63/0.78 tff(1845,plain,
% 0.63/0.78 ((~(~((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2)))))) <=> ((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1846,plain,
% 0.63/0.78 (((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2)))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1847,plain,
% 0.63/0.78 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2))))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1846])).
% 0.63/0.78 tff(1848,plain,
% 0.63/0.78 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1847, 1845])).
% 0.63/0.78 tff(1849,plain,
% 0.63/0.78 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1850,plain,
% 0.63/0.78 ((~(((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2))) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1851,axiom,(~(((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2))) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax13')).
% 0.63/0.78 tff(1852,plain,
% 0.63/0.78 (~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 0.63/0.78 tff(1853,plain,
% 0.63/0.78 (~((e1 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1852, 1849])).
% 0.63/0.78 tff(1854,plain,
% 0.63/0.78 ((~(e3 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, e2)))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1853, 1848])).
% 0.63/0.78 tff(1855,plain,
% 0.63/0.78 ($false),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1854, 1844, 1828, 1824])).
% 0.63/0.78 tff(1856,plain,((op(e1, e2) = e0) | (~(op(e0, e0) = e1)) | (op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e1, e1) = e2) | (op(e3, e1) = e3) | (op(e0, e1) = e3) | (op(e3, e3) = e1) | (op(e1, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.78 tff(1857,plain,
% 0.63/0.78 (op(e1, e2) = e0),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1856, 1727, 1725, 1786, 379, 1781, 1775, 1772, 1767])).
% 0.63/0.78 tff(1858,plain,
% 0.63/0.78 ((op(e1, e2) = e2) <=> (e0 = e2)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1857])).
% 0.63/0.78 tff(1859,plain,
% 0.63/0.78 ((e0 = e2) <=> (op(e1, e2) = e2)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1858])).
% 0.63/0.78 tff(1860,plain,
% 0.63/0.78 ((~(e0 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1859])).
% 0.63/0.78 tff(1861,plain,
% 0.63/0.78 (~(op(e1, e2) = e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[16, 1860])).
% 0.63/0.78 tff(1862,plain,
% 0.63/0.78 (op(e1, e0) = e2),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[751, 1861, 379, 1763])).
% 0.63/0.78 tff(1863,plain,
% 0.63/0.78 ((op(e1, e0) = e3) <=> (e2 = e3)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1862])).
% 0.63/0.78 tff(1864,plain,
% 0.63/0.78 ((e2 = e3) <=> (op(e1, e0) = e3)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1863])).
% 0.63/0.78 tff(1865,plain,
% 0.63/0.78 ((~(e2 = e3)) <=> (~(op(e1, e0) = e3))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1864])).
% 0.63/0.78 tff(1866,plain,
% 0.63/0.78 (~(op(e1, e0) = e3)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[170, 1865])).
% 0.63/0.78 tff(1867,plain,
% 0.63/0.78 (op(e1, e1) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[530, 1866, 1744, 1741])).
% 0.63/0.78 tff(1868,plain,
% 0.63/0.78 (e3 = op(op(e0, e0), op(e0, e0))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1867, 1733])).
% 0.63/0.78 tff(1869,plain,
% 0.63/0.78 (op(op(e0, e0), op(e0, e0)) = e3),
% 0.63/0.78 inference(transitivity,[status(thm)],[1730, 1867])).
% 0.63/0.78 tff(1870,plain,
% 0.63/0.78 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e3)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1869])).
% 0.63/0.78 tff(1871,plain,
% 0.63/0.78 (op(e0, e3) = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.63/0.78 inference(symmetry,[status(thm)],[1870])).
% 0.63/0.78 tff(1872,plain,
% 0.63/0.78 (e2 = op(e0, e3)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1756])).
% 0.63/0.78 tff(1873,plain,
% 0.63/0.78 (e2 = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1872, 1871])).
% 0.63/0.78 tff(1874,plain,
% 0.63/0.78 ((~(~((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0))))))) <=> ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1875,plain,
% 0.63/0.78 (((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1876,plain,
% 0.63/0.78 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1875])).
% 0.63/0.78 tff(1877,plain,
% 0.63/0.78 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1876, 1874])).
% 0.63/0.78 tff(1878,plain,
% 0.63/0.78 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1879,plain,
% 0.63/0.78 ((~(((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0))) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1880,axiom,(~(((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0))) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax27')).
% 0.63/0.78 tff(1881,plain,
% 0.63/0.78 (~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.63/0.78 tff(1882,plain,
% 0.63/0.78 (~((e3 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1881, 1878])).
% 0.63/0.78 tff(1883,plain,
% 0.63/0.78 ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(op(e0, e0), op(e0, e0))))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1882, 1877])).
% 0.63/0.78 tff(1884,plain,
% 0.63/0.78 ($false),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1883, 1873, 1868, 1728])).
% 0.63/0.78 tff(1885,plain,((op(e2, e2) = e3) | (op(e1, e1) = e2) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e0, e0) = e0) | (op(e3, e0) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (e3 = op(e1, op(op(e1, e1), op(e1, e1)))) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.78 tff(1886,plain,
% 0.63/0.78 (op(e2, e2) = e3),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1885, 1067, 1064, 1055, 379, 1065, 1066, 1053, 1063])).
% 0.63/0.78 tff(1887,plain,
% 0.63/0.78 (op(e2, e3) = e2),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1004, 1886])).
% 0.63/0.78 tff(1888,plain,
% 0.63/0.78 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1887])).
% 0.63/0.78 tff(1889,plain,
% 0.63/0.78 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1888])).
% 0.63/0.78 tff(1890,plain,
% 0.63/0.78 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e2, e3)))),
% 0.63/0.78 inference(rewrite,[status(thm)],[])).
% 0.63/0.78 tff(1891,plain,
% 0.63/0.78 (~(op(e2, e1) = op(e2, e3))),
% 0.63/0.78 inference(and_elim,[status(thm)],[64])).
% 0.63/0.78 tff(1892,plain,
% 0.63/0.78 (~(op(e2, e1) = op(e2, e3))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.63/0.78 tff(1893,plain,
% 0.63/0.78 (~(op(e2, e1) = e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1892, 1889])).
% 0.63/0.78 tff(1894,plain,
% 0.63/0.78 ((e2 = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.63/0.78 inference(commutativity,[status(thm)],[])).
% 0.63/0.78 tff(1895,plain,
% 0.63/0.78 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1886, 1886])).
% 0.63/0.78 tff(1896,plain,
% 0.63/0.78 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (e0 = op(e3, e3))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1895])).
% 0.63/0.78 tff(1897,plain,
% 0.63/0.78 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e0)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1896, 2])).
% 0.63/0.78 tff(1898,plain,
% 0.63/0.78 ((~(e0 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1897])).
% 0.63/0.78 tff(1899,plain,
% 0.63/0.78 (~(op(e3, e3) = e0)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1054, 1898])).
% 0.63/0.78 tff(1900,assumption,(op(e2, e2) = e3), introduced(assumption)).
% 0.63/0.78 tff(1901,plain,
% 0.63/0.78 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1900, 1900])).
% 0.63/0.78 tff(1902,plain,
% 0.63/0.78 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.63/0.78 inference(symmetry,[status(thm)],[1901])).
% 0.63/0.78 tff(1903,plain,
% 0.63/0.78 (op(e3, e3) = e1),
% 0.63/0.78 inference(unit_resolution,[status(thm)],[1146, 693, 280, 1067, 1053, 1055])).
% 0.63/0.78 tff(1904,plain,
% 0.63/0.78 (e1 = op(e3, e3)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1903])).
% 0.63/0.78 tff(1905,plain,
% 0.63/0.78 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1904, 1902])).
% 0.63/0.78 tff(1906,plain,
% 0.63/0.78 (op(e2, e1) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1905])).
% 0.63/0.78 tff(1907,plain,
% 0.63/0.78 ((op(e2, e1) = e0) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e0)),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1906])).
% 0.63/0.78 tff(1908,plain,
% 0.63/0.78 ((op(e2, e1) = e0) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.63/0.78 inference(transitivity,[status(thm)],[1907, 293])).
% 0.63/0.78 tff(1909,plain,
% 0.63/0.78 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e1) = e0)),
% 0.63/0.78 inference(symmetry,[status(thm)],[1908])).
% 0.63/0.78 tff(1910,plain,
% 0.63/0.78 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e2, e1) = e0))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1909])).
% 0.63/0.78 tff(1911,plain,
% 0.63/0.78 (e3 = op(e2, e2)),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1900, 1016])).
% 0.63/0.78 tff(1912,plain,
% 0.63/0.78 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (e1 = op(e3, e3))),
% 0.63/0.78 inference(monotonicity,[status(thm)],[1901])).
% 0.63/0.78 tff(1913,plain,
% 0.63/0.78 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e1)),
% 0.63/0.78 inference(transitivity,[status(thm)],[1912, 1071])).
% 0.63/0.78 tff(1914,plain,
% 0.63/0.78 ((op(e3, e3) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.63/0.78 inference(symmetry,[status(thm)],[1913])).
% 0.63/0.78 tff(1915,plain,
% 0.63/0.78 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.63/0.78 inference(modus_ponens,[status(thm)],[1903, 1914])).
% 0.63/0.79 tff(1916,plain,
% 0.63/0.79 ((~(~((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2)))))))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1917,plain,
% 0.63/0.79 (((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2)))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1918,plain,
% 0.63/0.79 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1917])).
% 0.63/0.79 tff(1919,plain,
% 0.63/0.79 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1918, 1916])).
% 0.63/0.79 tff(1920,plain,
% 0.63/0.79 ((~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1921,plain,
% 0.63/0.79 ((~(((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1922,axiom,(~(((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax16')).
% 0.63/0.79 tff(1923,plain,
% 0.63/0.79 (~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 0.63/0.79 tff(1924,plain,
% 0.63/0.79 (~((e1 = op(op(e2, e2), op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1923, 1920])).
% 0.63/0.79 tff(1925,plain,
% 0.63/0.79 ((~(e3 = op(e2, e2))) | (~(e1 = op(op(e2, e2), op(e2, e2)))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1924, 1919])).
% 0.63/0.79 tff(1926,plain,
% 0.63/0.79 (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1925, 1915, 1911])).
% 0.63/0.79 tff(1927,plain,
% 0.63/0.79 (~(op(e2, e1) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1926, 1910])).
% 0.63/0.79 tff(1928,plain,
% 0.63/0.79 (op(e2, e3) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1004, 1900])).
% 0.63/0.79 tff(1929,plain,
% 0.63/0.79 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1928])).
% 0.63/0.79 tff(1930,plain,
% 0.63/0.79 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1929])).
% 0.63/0.79 tff(1931,plain,
% 0.63/0.79 (~(op(e2, e1) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1892, 1930])).
% 0.63/0.79 tff(1932,plain,
% 0.63/0.79 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1900])).
% 0.63/0.79 tff(1933,plain,
% 0.63/0.79 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1932])).
% 0.63/0.79 tff(1934,plain,
% 0.63/0.79 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = op(e2, e2)))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1935,plain,
% 0.63/0.79 (~(op(e2, e1) = op(e2, e2))),
% 0.63/0.79 inference(and_elim,[status(thm)],[65])).
% 0.63/0.79 tff(1936,plain,
% 0.63/0.79 (~(op(e2, e1) = op(e2, e2))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 0.63/0.79 tff(1937,plain,
% 0.63/0.79 (~(op(e2, e1) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1936, 1933])).
% 0.63/0.79 tff(1938,plain,
% 0.63/0.79 ((e1 = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.63/0.79 inference(commutativity,[status(thm)],[])).
% 0.63/0.79 tff(1939,plain,
% 0.63/0.79 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1900])).
% 0.63/0.79 tff(1940,plain,
% 0.63/0.79 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1939, 1178])).
% 0.63/0.79 tff(1941,plain,
% 0.63/0.79 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1940])).
% 0.63/0.79 tff(1942,plain,
% 0.63/0.79 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1941])).
% 0.63/0.79 tff(1943,plain,
% 0.63/0.79 (~(op(e2, e2) = e2)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[170, 1942])).
% 0.63/0.79 tff(1944,plain,
% 0.63/0.79 (op(e1, e1) = e1),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[215, 693, 1055, 1943])).
% 0.63/0.79 tff(1945,plain,
% 0.63/0.79 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1944])).
% 0.63/0.79 tff(1946,plain,
% 0.63/0.79 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1945, 1938])).
% 0.63/0.79 tff(1947,plain,
% 0.63/0.79 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1946])).
% 0.63/0.79 tff(1948,plain,
% 0.63/0.79 (~(op(e2, e1) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1049, 1947])).
% 0.63/0.79 tff(1949,plain,
% 0.63/0.79 (((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))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1950,plain,
% 0.63/0.79 ((((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))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1951,plain,
% 0.63/0.79 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1952,plain,
% 0.63/0.79 (((((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))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1951])).
% 0.63/0.79 tff(1953,plain,
% 0.63/0.79 (((((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))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1952, 1950])).
% 0.63/0.79 tff(1954,plain,
% 0.63/0.79 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)),
% 0.63/0.79 inference(and_elim,[status(thm)],[117])).
% 0.63/0.79 tff(1955,plain,
% 0.63/0.79 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 0.63/0.79 tff(1956,plain,
% 0.63/0.79 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1955, 1949])).
% 0.63/0.79 tff(1957,plain,
% 0.63/0.79 (op(e2, e1) = e0),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1956, 1948, 1937, 1931])).
% 0.63/0.79 tff(1958,plain,
% 0.63/0.79 ($false),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1957, 1927])).
% 0.63/0.79 tff(1959,plain,((op(e3, e3) = e3) | (~(op(e2, e2) = e3)) | (op(e0, e0) = e0) | (op(e3, e3) = e0) | (op(e3, e0) = e1) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.79 tff(1960,plain,
% 0.63/0.79 (op(e3, e3) = e3),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1959, 1886, 1055, 1899, 1067, 1053])).
% 0.63/0.79 tff(1961,plain,
% 0.63/0.79 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1960])).
% 0.63/0.79 tff(1962,plain,
% 0.63/0.79 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1961])).
% 0.63/0.79 tff(1963,plain,
% 0.63/0.79 (~(op(e3, e0) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1424, 1962])).
% 0.63/0.79 tff(1964,plain,
% 0.63/0.79 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1960])).
% 0.63/0.79 tff(1965,plain,
% 0.63/0.79 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1964])).
% 0.63/0.79 tff(1966,plain,
% 0.63/0.79 (~(op(e0, e3) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1578, 1965])).
% 0.63/0.79 tff(1967,plain,
% 0.63/0.79 ((op(e3, e3) = e1) <=> (e3 = e1)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1960])).
% 0.63/0.79 tff(1968,plain,
% 0.63/0.79 ((op(e3, e3) = e1) <=> (e1 = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1967, 601])).
% 0.63/0.79 tff(1969,plain,
% 0.63/0.79 ((e1 = e3) <=> (op(e3, e3) = e1)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1968])).
% 0.63/0.79 tff(1970,plain,
% 0.63/0.79 ((~(e1 = e3)) <=> (~(op(e3, e3) = e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1969])).
% 0.63/0.79 tff(1971,plain,
% 0.63/0.79 (~(op(e3, e3) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[521, 1970])).
% 0.63/0.79 tff(1972,plain,
% 0.63/0.79 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1900])).
% 0.63/0.79 tff(1973,plain,
% 0.63/0.79 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1972])).
% 0.63/0.79 tff(1974,plain,
% 0.63/0.79 (~(op(e0, e2) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1396, 1973])).
% 0.63/0.79 tff(1975,plain,
% 0.63/0.79 (op(e0, e1) = e3),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1090, 1590, 1974, 1587])).
% 0.63/0.79 tff(1976,plain,
% 0.63/0.79 ((op(e0, e1) = e0) <=> (e3 = e0)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1975])).
% 0.63/0.79 tff(1977,plain,
% 0.63/0.79 ((op(e0, e1) = e0) <=> (e0 = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1976, 1])).
% 0.63/0.79 tff(1978,plain,
% 0.63/0.79 ((e0 = e3) <=> (op(e0, e1) = e0)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1977])).
% 0.63/0.79 tff(1979,plain,
% 0.63/0.79 ((~(e0 = e3)) <=> (~(op(e0, e1) = e0))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1978])).
% 0.63/0.79 tff(1980,plain,
% 0.63/0.79 (~(op(e0, e1) = e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[509, 1979])).
% 0.63/0.79 tff(1981,plain,
% 0.63/0.79 (~(op(e0, e0) = e1)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1109, 1980])).
% 0.63/0.79 tff(1982,plain,
% 0.63/0.79 (op(e0, e0) = e2),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1105, 1981, 1055, 1590])).
% 0.63/0.79 tff(1983,plain,
% 0.63/0.79 (op(op(e0, e0), op(e0, e0)) = op(e2, e2)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1982, 1982])).
% 0.63/0.79 tff(1984,plain,
% 0.63/0.79 (op(op(e0, e0), op(e0, e0)) = e3),
% 0.63/0.79 inference(transitivity,[status(thm)],[1983, 1900])).
% 0.63/0.79 tff(1985,plain,
% 0.63/0.79 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1984])).
% 0.63/0.79 tff(1986,plain,
% 0.63/0.79 ((e1 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e1 = op(e0, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1985])).
% 0.63/0.79 tff(1987,plain,
% 0.63/0.79 ((e1 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e3) = e1)),
% 0.63/0.79 inference(transitivity,[status(thm)],[1986, 696])).
% 0.63/0.79 tff(1988,plain,
% 0.63/0.79 ((~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e3) = e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1987])).
% 0.63/0.79 tff(1989,plain,
% 0.63/0.79 ((op(e0, e0) = e2) <=> (e2 = op(e0, e0))),
% 0.63/0.79 inference(symmetry,[status(thm)],[1092])).
% 0.63/0.79 tff(1990,plain,
% 0.63/0.79 (e2 = op(e0, e0)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1982, 1989])).
% 0.63/0.79 tff(1991,plain,
% 0.63/0.79 (op(e2, e2) = op(op(e0, e0), op(e0, e0))),
% 0.63/0.79 inference(symmetry,[status(thm)],[1983])).
% 0.63/0.79 tff(1992,plain,
% 0.63/0.79 (e3 = op(e2, e2)),
% 0.63/0.79 inference(symmetry,[status(thm)],[1900])).
% 0.63/0.79 tff(1993,plain,
% 0.63/0.79 (e3 = op(op(e0, e0), op(e0, e0))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1992, 1991])).
% 0.63/0.79 tff(1994,plain,
% 0.63/0.79 ((~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0))))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1995,plain,
% 0.63/0.79 (((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1996,plain,
% 0.63/0.79 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1995])).
% 0.63/0.79 tff(1997,plain,
% 0.63/0.79 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.79 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.63/0.79 tff(1998,plain,
% 0.63/0.79 ((~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(1999,plain,
% 0.63/0.79 ((~(((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0))) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(2000,axiom,(~(((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0))) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax29')).
% 0.63/0.79 tff(2001,plain,
% 0.63/0.79 (~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 0.63/0.79 tff(2002,plain,
% 0.63/0.79 (~((e3 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[2001, 1998])).
% 0.63/0.79 tff(2003,plain,
% 0.63/0.79 ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e3 = op(op(e0, e0), op(e0, e0))))),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[2002, 1997])).
% 0.63/0.79 tff(2004,plain,
% 0.63/0.79 (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[2003, 1993, 1990])).
% 0.63/0.79 tff(2005,plain,
% 0.63/0.79 (~(op(e0, e3) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[2004, 1988])).
% 0.63/0.79 tff(2006,plain,
% 0.63/0.79 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1928])).
% 0.63/0.79 tff(2007,plain,
% 0.63/0.79 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.63/0.79 inference(transitivity,[status(thm)],[2006, 1034])).
% 0.63/0.79 tff(2008,plain,
% 0.63/0.79 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.63/0.79 inference(symmetry,[status(thm)],[2007])).
% 0.63/0.79 tff(2009,plain,
% 0.63/0.79 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2008])).
% 0.63/0.79 tff(2010,plain,
% 0.63/0.79 (~(op(e2, e3) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[353, 2009])).
% 0.63/0.79 tff(2011,plain,
% 0.63/0.79 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1975])).
% 0.63/0.79 tff(2012,plain,
% 0.63/0.79 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[2011, 1729])).
% 0.63/0.79 tff(2013,plain,
% 0.63/0.79 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2012])).
% 0.63/0.79 tff(2014,plain,
% 0.63/0.79 (~(op(e1, e1) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[1402, 2013])).
% 0.63/0.79 tff(2015,plain,
% 0.63/0.79 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[1900])).
% 0.63/0.79 tff(2016,plain,
% 0.63/0.79 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2015])).
% 0.63/0.79 tff(2017,plain,
% 0.63/0.79 (~(op(e2, e0) = e3)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[85, 2016])).
% 0.63/0.79 tff(2018,plain,
% 0.63/0.79 (op(e1, e0) = e3),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[1616, 1590, 2017, 1588])).
% 0.63/0.79 tff(2019,plain,
% 0.63/0.79 ((op(e1, e0) = e1) <=> (e3 = e1)),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2018])).
% 0.63/0.79 tff(2020,plain,
% 0.63/0.79 ((op(e1, e0) = e1) <=> (e1 = e3)),
% 0.63/0.79 inference(transitivity,[status(thm)],[2019, 601])).
% 0.63/0.79 tff(2021,plain,
% 0.63/0.79 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 0.63/0.79 inference(symmetry,[status(thm)],[2020])).
% 0.63/0.79 tff(2022,plain,
% 0.63/0.79 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2021])).
% 0.63/0.79 tff(2023,plain,
% 0.63/0.79 (~(op(e1, e0) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[521, 2022])).
% 0.63/0.79 tff(2024,plain,
% 0.63/0.79 (((~(op(e1, e1) = e0)) | (op(e1, e0) = e1)) <=> ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1))),
% 0.63/0.79 inference(rewrite,[status(thm)],[])).
% 0.63/0.79 tff(2025,plain,
% 0.63/0.79 ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1)),
% 0.63/0.79 inference(and_elim,[status(thm)],[207])).
% 0.63/0.79 tff(2026,plain,
% 0.63/0.79 ((~(op(e1, e1) = e0)) | (op(e1, e0) = e1)),
% 0.63/0.79 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.63/0.79 tff(2027,plain,
% 0.63/0.79 (~(op(e1, e1) = e0)),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[2026, 2023])).
% 0.63/0.79 tff(2028,plain,
% 0.63/0.79 (op(e1, e1) = e1),
% 0.63/0.79 inference(unit_resolution,[status(thm)],[435, 2027, 379, 2014])).
% 0.63/0.79 tff(2029,plain,
% 0.63/0.79 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.63/0.79 inference(monotonicity,[status(thm)],[2028])).
% 0.63/0.79 tff(2030,plain,
% 0.63/0.79 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2029, 619])).
% 0.63/0.80 tff(2031,plain,
% 0.63/0.80 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2030])).
% 0.63/0.80 tff(2032,plain,
% 0.63/0.80 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = op(e1, e3)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2033,plain,
% 0.63/0.80 (~(op(e1, e1) = op(e1, e3))),
% 0.63/0.80 inference(and_elim,[status(thm)],[127])).
% 0.63/0.80 tff(2034,plain,
% 0.63/0.80 (~(op(e1, e1) = op(e1, e3))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 0.63/0.80 tff(2035,plain,
% 0.63/0.80 (~(op(e1, e3) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2034, 2031])).
% 0.63/0.80 tff(2036,plain,
% 0.63/0.80 (op(e0, e3) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[711, 2035, 2010, 695])).
% 0.63/0.80 tff(2037,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2036, 2005])).
% 0.63/0.80 tff(2038,plain,((op(e0, e0) = e3) | (~(op(e2, e2) = e3)) | (op(e3, e3) = e1) | (op(e1, e1) = e2) | (op(e0, e0) = e0) | (op(e3, e0) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2039,plain,
% 0.63/0.80 (op(e0, e0) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2038, 1886, 1971, 379, 1055, 1963, 1966])).
% 0.63/0.80 tff(2040,plain,
% 0.63/0.80 (op(e0, e3) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1280, 2039])).
% 0.63/0.80 tff(2041,plain,
% 0.63/0.80 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2040])).
% 0.63/0.80 tff(2042,plain,
% 0.63/0.80 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2041, 2040])).
% 0.63/0.80 tff(2043,plain,
% 0.63/0.80 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2042])).
% 0.63/0.80 tff(2044,plain,
% 0.63/0.80 (~(op(e3, e0) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1065, 2043])).
% 0.63/0.80 tff(2045,plain,
% 0.63/0.80 (op(e3, e0) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1333, 2044, 1067, 1963])).
% 0.63/0.80 tff(2046,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2045])).
% 0.63/0.80 tff(2047,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2046, 1894])).
% 0.63/0.80 tff(2048,plain,
% 0.63/0.80 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2047])).
% 0.63/0.80 tff(2049,plain,
% 0.63/0.80 (~(op(e3, e1) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1320, 2048])).
% 0.63/0.80 tff(2050,plain,
% 0.63/0.80 (op(e0, e1) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[396, 2049, 379, 1893])).
% 0.63/0.80 tff(2051,plain,
% 0.63/0.80 (e2 = op(e0, e1)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2050])).
% 0.63/0.80 tff(2052,plain,
% 0.63/0.80 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[1887])).
% 0.63/0.80 tff(2053,plain,
% 0.63/0.80 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2052])).
% 0.63/0.80 tff(2054,plain,
% 0.63/0.80 (~(op(e1, e3) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[894, 2053])).
% 0.63/0.80 tff(2055,plain,
% 0.63/0.80 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2045])).
% 0.63/0.80 tff(2056,plain,
% 0.63/0.80 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2055])).
% 0.63/0.80 tff(2057,plain,
% 0.63/0.80 (~(op(e1, e0) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[564, 2056])).
% 0.63/0.80 tff(2058,plain,
% 0.63/0.80 (op(e1, e2) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[751, 2057, 379, 2054])).
% 0.63/0.80 tff(2059,plain,
% 0.63/0.80 (op(e1, op(e0, e1)) = op(e1, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2050])).
% 0.63/0.80 tff(2060,plain,
% 0.63/0.80 (op(e1, op(e0, e1)) = op(e0, e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2059, 2058, 2051])).
% 0.63/0.80 tff(2061,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1064, 2060])).
% 0.63/0.80 tff(2062,plain,((op(e3, e0) = e1) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e1, e1) = e2) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (e0 = op(op(e2, e2), op(e2, e2))) | (e3 = op(e1, op(op(e1, e1), op(e1, e1)))) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2063,plain,
% 0.63/0.80 (op(e3, e0) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2062, 379, 1064, 1065, 1055, 1053, 1054, 1066, 1063])).
% 0.63/0.80 tff(2064,plain,
% 0.63/0.80 ((op(e3, e0) = e3) <=> (e1 = e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2063])).
% 0.63/0.80 tff(2065,plain,
% 0.63/0.80 ((e1 = e3) <=> (op(e3, e0) = e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2064])).
% 0.63/0.80 tff(2066,plain,
% 0.63/0.80 ((~(e1 = e3)) <=> (~(op(e3, e0) = e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2065])).
% 0.63/0.80 tff(2067,plain,
% 0.63/0.80 (~(op(e3, e0) = e3)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[521, 2066])).
% 0.63/0.80 tff(2068,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2063])).
% 0.63/0.80 tff(2069,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2068, 1071])).
% 0.63/0.80 tff(2070,plain,
% 0.63/0.80 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2069])).
% 0.63/0.80 tff(2071,plain,
% 0.63/0.80 (~(op(e3, e3) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1424, 2070])).
% 0.63/0.80 tff(2072,plain,
% 0.63/0.80 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2063])).
% 0.63/0.80 tff(2073,plain,
% 0.63/0.80 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2072])).
% 0.63/0.80 tff(2074,plain,
% 0.63/0.80 (~(op(e0, e0) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[270, 2073])).
% 0.63/0.80 tff(2075,plain,
% 0.63/0.80 ((op(e3, e0) = e0) <=> (e1 = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2063])).
% 0.63/0.80 tff(2076,plain,
% 0.63/0.80 ((op(e3, e0) = e0) <=> (e0 = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2075, 1203])).
% 0.63/0.80 tff(2077,plain,
% 0.63/0.80 ((e0 = e1) <=> (op(e3, e0) = e0)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2076])).
% 0.63/0.80 tff(2078,plain,
% 0.63/0.80 ((~(e0 = e1)) <=> (~(op(e3, e0) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2077])).
% 0.63/0.80 tff(2079,plain,
% 0.63/0.80 (~(op(e3, e0) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[40, 2078])).
% 0.63/0.80 tff(2080,plain,
% 0.63/0.80 (~(op(e3, e3) = e0)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[558, 2067])).
% 0.63/0.80 tff(2081,plain,
% 0.63/0.80 ((e1 = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.63/0.80 inference(commutativity,[status(thm)],[])).
% 0.63/0.80 tff(2082,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2063])).
% 0.63/0.80 tff(2083,plain,
% 0.63/0.80 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2082, 2081])).
% 0.63/0.80 tff(2084,plain,
% 0.63/0.80 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2083])).
% 0.63/0.80 tff(2085,plain,
% 0.63/0.80 (~(op(e3, e2) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[572, 2084])).
% 0.63/0.80 tff(2086,plain,
% 0.63/0.80 ((e1 = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.63/0.80 inference(commutativity,[status(thm)],[])).
% 0.63/0.80 tff(2087,plain,
% 0.63/0.80 (op(e3, e3) = e2),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1123, 693, 695, 280])).
% 0.63/0.80 tff(2088,plain,
% 0.63/0.80 (op(op(e3, e3), op(e3, e3)) = op(e2, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2087, 2087])).
% 0.63/0.80 tff(2089,plain,
% 0.63/0.80 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (e2 = op(e2, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2088])).
% 0.63/0.80 tff(2090,plain,
% 0.63/0.80 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2089, 1137])).
% 0.63/0.80 tff(2091,plain,
% 0.63/0.80 ((~(e2 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2090])).
% 0.63/0.80 tff(2092,plain,
% 0.63/0.80 (~(op(e2, e2) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1053, 2091])).
% 0.63/0.80 tff(2093,plain,
% 0.63/0.80 (op(e1, e1) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[215, 2092, 1055, 693])).
% 0.63/0.80 tff(2094,plain,
% 0.63/0.80 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2093])).
% 0.63/0.80 tff(2095,plain,
% 0.63/0.80 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2094])).
% 0.63/0.80 tff(2096,plain,
% 0.63/0.80 (~(op(e0, e1) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1402, 2095])).
% 0.63/0.80 tff(2097,assumption,(~(op(e3, e0) = e0)), introduced(assumption)).
% 0.63/0.80 tff(2098,plain,
% 0.63/0.80 (op(e3, e2) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1127, 2087])).
% 0.63/0.80 tff(2099,plain,
% 0.63/0.80 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2098])).
% 0.63/0.80 tff(2100,plain,
% 0.63/0.80 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2099, 1])).
% 0.63/0.80 tff(2101,plain,
% 0.63/0.80 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2100])).
% 0.63/0.80 tff(2102,plain,
% 0.63/0.80 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2101])).
% 0.63/0.80 tff(2103,plain,
% 0.63/0.80 (~(op(e3, e2) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[509, 2102])).
% 0.63/0.80 tff(2104,plain,
% 0.63/0.80 (op(e3, e1) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[288, 2103, 280, 2097])).
% 0.63/0.80 tff(2105,plain,
% 0.63/0.80 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2104])).
% 0.63/0.80 tff(2106,plain,
% 0.63/0.80 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2105])).
% 0.63/0.80 tff(2107,plain,
% 0.63/0.80 (~(op(e0, e1) = e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[859, 2106])).
% 0.63/0.80 tff(2108,plain,
% 0.63/0.80 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2093])).
% 0.63/0.80 tff(2109,plain,
% 0.63/0.80 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2108, 591])).
% 0.63/0.80 tff(2110,plain,
% 0.63/0.80 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2109])).
% 0.63/0.80 tff(2111,plain,
% 0.63/0.80 (~(op(e1, e2) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[1604, 2110])).
% 0.63/0.80 tff(2112,assumption,(op(e0, e0) = e2), introduced(assumption)).
% 0.63/0.80 tff(2113,plain,
% 0.63/0.80 (e2 = op(e0, e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2112, 1989])).
% 0.63/0.80 tff(2114,plain,
% 0.63/0.80 (op(op(e0, e0), op(e0, e0)) = op(e2, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2112, 2112])).
% 0.63/0.80 tff(2115,plain,
% 0.63/0.80 ((e1 = op(op(e0, e0), op(e0, e0))) <=> (e1 = op(e2, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2114])).
% 0.63/0.80 tff(2116,plain,
% 0.63/0.80 ((e1 = op(op(e0, e0), op(e0, e0))) <=> (op(e2, e2) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2115, 91])).
% 0.63/0.80 tff(2117,plain,
% 0.63/0.80 ((op(e2, e2) = e1) <=> (e1 = op(op(e0, e0), op(e0, e0)))),
% 0.63/0.80 inference(symmetry,[status(thm)],[2116])).
% 0.63/0.80 tff(2118,plain,
% 0.63/0.80 (op(e0, e2) = e0),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1472, 2112])).
% 0.63/0.80 tff(2119,plain,
% 0.63/0.80 ((op(e0, e2) = e1) <=> (e0 = e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2118])).
% 0.63/0.80 tff(2120,plain,
% 0.63/0.80 ((e0 = e1) <=> (op(e0, e2) = e1)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2119])).
% 0.63/0.80 tff(2121,plain,
% 0.63/0.80 ((~(e0 = e1)) <=> (~(op(e0, e2) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2120])).
% 0.63/0.80 tff(2122,plain,
% 0.63/0.80 (~(op(e0, e2) = e1)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[40, 2121])).
% 0.63/0.80 tff(2123,plain,
% 0.63/0.80 (op(e2, e2) = e1),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[671, 2122, 663, 661])).
% 0.63/0.80 tff(2124,plain,
% 0.63/0.80 (e1 = op(op(e0, e0), op(e0, e0))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2123, 2117])).
% 0.63/0.80 tff(2125,plain,
% 0.63/0.80 (op(op(e0, e0), op(e0, e0)) = e1),
% 0.63/0.80 inference(transitivity,[status(thm)],[2114, 2123])).
% 0.63/0.80 tff(2126,plain,
% 0.63/0.80 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e1)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2125])).
% 0.63/0.80 tff(2127,plain,
% 0.63/0.80 (op(e0, e1) = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.63/0.80 inference(symmetry,[status(thm)],[2126])).
% 0.63/0.80 tff(2128,assumption,(~(op(e0, e1) = e1)), introduced(assumption)).
% 0.63/0.80 tff(2129,plain,
% 0.63/0.80 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2112])).
% 0.63/0.80 tff(2130,plain,
% 0.63/0.80 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2129, 1291])).
% 0.63/0.80 tff(2131,plain,
% 0.63/0.80 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2130])).
% 0.63/0.80 tff(2132,plain,
% 0.63/0.80 (~(op(e0, e1) = e2)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[826, 2131])).
% 0.63/0.80 tff(2133,plain,
% 0.63/0.80 (op(e0, e1) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[880, 2132, 854, 2128])).
% 0.63/0.80 tff(2134,plain,
% 0.63/0.80 (e3 = op(e0, e1)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2133])).
% 0.63/0.80 tff(2135,plain,
% 0.63/0.80 (e3 = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2134, 2127])).
% 0.63/0.80 tff(2136,plain,
% 0.63/0.80 ((~(~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0)))))))) <=> ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2137,plain,
% 0.63/0.80 (((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0)))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2138,plain,
% 0.63/0.80 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2137])).
% 0.63/0.80 tff(2139,plain,
% 0.63/0.80 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2138, 2136])).
% 0.63/0.80 tff(2140,plain,
% 0.63/0.80 ((~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2141,plain,
% 0.63/0.80 ((~(((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0))) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2142,axiom,(~(((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0))) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax15')).
% 0.63/0.80 tff(2143,plain,
% 0.63/0.80 (~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 0.63/0.80 tff(2144,plain,
% 0.63/0.80 (~((e1 = op(op(e0, e0), op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2143, 2140])).
% 0.63/0.80 tff(2145,plain,
% 0.63/0.80 ((~(e1 = op(op(e0, e0), op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2144, 2139])).
% 0.63/0.80 tff(2146,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2145, 2135, 2124, 2113])).
% 0.63/0.80 tff(2147,plain,((~(op(e0, e0) = e2)) | (op(e3, e2) = e1) | (op(e1, e2) = e1) | (op(e0, e1) = e0) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2148,plain,
% 0.63/0.80 (~(op(e0, e0) = e2)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2147, 2111, 663, 2107, 2096])).
% 0.63/0.80 tff(2149,plain,
% 0.63/0.80 (op(e0, e0) = e3),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1105, 2148, 1055, 421])).
% 0.63/0.80 tff(2150,plain,
% 0.63/0.80 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2149, 2149])).
% 0.63/0.80 tff(2151,plain,
% 0.63/0.80 (op(op(e0, e0), op(e0, e0)) = e2),
% 0.63/0.80 inference(transitivity,[status(thm)],[2150, 2087])).
% 0.63/0.80 tff(2152,plain,
% 0.63/0.80 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e2)),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2151])).
% 0.63/0.80 tff(2153,plain,
% 0.63/0.80 ((e1 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e1 = op(e0, e2))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2152])).
% 0.63/0.80 tff(2154,plain,
% 0.63/0.80 ((e1 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e2) = e1)),
% 0.63/0.80 inference(transitivity,[status(thm)],[2153, 2086])).
% 0.63/0.80 tff(2155,plain,
% 0.63/0.80 ((~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e2) = e1))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2154])).
% 0.63/0.80 tff(2156,plain,
% 0.63/0.80 (e3 = op(e0, e0)),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2149, 1299])).
% 0.63/0.80 tff(2157,plain,
% 0.63/0.80 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.63/0.80 inference(symmetry,[status(thm)],[2150])).
% 0.63/0.80 tff(2158,plain,
% 0.63/0.80 (e2 = op(e3, e3)),
% 0.63/0.80 inference(symmetry,[status(thm)],[2087])).
% 0.63/0.80 tff(2159,plain,
% 0.63/0.80 (e2 = op(op(e0, e0), op(e0, e0))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2158, 2157])).
% 0.63/0.80 tff(2160,plain,
% 0.63/0.80 ((~(~((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0)))))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2161,plain,
% 0.63/0.81 (((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2162,plain,
% 0.63/0.81 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2161])).
% 0.63/0.81 tff(2163,plain,
% 0.63/0.81 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2162, 2160])).
% 0.63/0.81 tff(2164,plain,
% 0.63/0.81 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2165,plain,
% 0.63/0.81 ((~(((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2166,axiom,(~(((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax23')).
% 0.63/0.81 tff(2167,plain,
% 0.63/0.81 (~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.63/0.81 tff(2168,plain,
% 0.63/0.81 (~((e2 = op(op(e0, e0), op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2167, 2164])).
% 0.63/0.81 tff(2169,plain,
% 0.63/0.81 ((~(e3 = op(e0, e0))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2168, 2163])).
% 0.63/0.81 tff(2170,plain,
% 0.63/0.81 (~(e1 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2169, 2159, 2156])).
% 0.63/0.81 tff(2171,plain,
% 0.63/0.81 (~(op(e0, e2) = e1)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2170, 2155])).
% 0.63/0.81 tff(2172,plain,
% 0.63/0.81 (op(e0, e3) = e0),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1280, 2149])).
% 0.63/0.81 tff(2173,plain,
% 0.63/0.81 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2172])).
% 0.63/0.81 tff(2174,plain,
% 0.63/0.81 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 0.63/0.81 inference(symmetry,[status(thm)],[2173])).
% 0.63/0.81 tff(2175,plain,
% 0.63/0.81 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2174])).
% 0.63/0.81 tff(2176,plain,
% 0.63/0.81 (~(op(e0, e3) = e1)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[40, 2175])).
% 0.63/0.81 tff(2177,plain,
% 0.63/0.81 (((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))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2178,plain,
% 0.63/0.81 ((((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))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2179,plain,
% 0.63/0.81 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2180,plain,
% 0.63/0.81 (((((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))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2179])).
% 0.63/0.81 tff(2181,plain,
% 0.63/0.81 (((((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))),
% 0.68/0.81 inference(transitivity,[status(thm)],[2180, 2178])).
% 0.68/0.81 tff(2182,plain,
% 0.68/0.81 ((((((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))),
% 0.68/0.81 inference(and_elim,[status(thm)],[457])).
% 0.68/0.81 tff(2183,plain,
% 0.68/0.81 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)),
% 0.68/0.81 inference(and_elim,[status(thm)],[2182])).
% 0.68/0.81 tff(2184,plain,
% 0.68/0.81 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[2183, 2181])).
% 0.68/0.81 tff(2185,plain,
% 0.68/0.81 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[2184, 2177])).
% 0.68/0.81 tff(2186,plain,
% 0.68/0.81 (op(e0, e2) = e1),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2185, 2176, 421, 2096])).
% 0.68/0.81 tff(2187,plain,
% 0.68/0.81 ($false),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2186, 2171])).
% 0.68/0.81 tff(2188,plain,((op(e3, e3) = e3) | (op(e0, e0) = e1) | (op(e0, e0) = e0) | (op(e3, e2) = e1) | (op(e3, e3) = e0) | (op(e3, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.81 tff(2189,plain,
% 0.68/0.81 (op(e3, e3) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2188, 2074, 1055, 2085, 2080, 2079, 1053, 2071])).
% 0.68/0.81 tff(2190,plain,
% 0.68/0.81 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2189])).
% 0.68/0.81 tff(2191,plain,
% 0.68/0.81 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2190])).
% 0.68/0.81 tff(2192,plain,
% 0.68/0.81 (~(op(e0, e3) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[1578, 2191])).
% 0.68/0.81 tff(2193,plain,
% 0.68/0.81 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2189])).
% 0.68/0.81 tff(2194,plain,
% 0.68/0.81 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2193])).
% 0.68/0.81 tff(2195,plain,
% 0.68/0.81 (~(op(e3, e2) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[1160, 2194])).
% 0.68/0.81 tff(2196,plain,
% 0.68/0.81 (op(e0, e0) = e2),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1105, 1590, 1055, 421])).
% 0.68/0.81 tff(2197,plain,
% 0.68/0.81 (op(e0, e2) = e0),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1472, 2196])).
% 0.68/0.81 tff(2198,plain,
% 0.68/0.81 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2197])).
% 0.68/0.81 tff(2199,plain,
% 0.68/0.81 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2198])).
% 0.68/0.81 tff(2200,plain,
% 0.68/0.81 (~(op(e0, e1) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[867, 2199])).
% 0.68/0.81 tff(2201,plain,
% 0.68/0.81 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2197])).
% 0.68/0.81 tff(2202,plain,
% 0.68/0.81 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2201])).
% 0.68/0.81 tff(2203,plain,
% 0.68/0.81 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2202])).
% 0.68/0.81 tff(2204,plain,
% 0.68/0.81 (~(op(e0, e2) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[509, 2203])).
% 0.68/0.81 tff(2205,plain,
% 0.68/0.81 (op(e0, e1) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1090, 2204, 1587, 1590])).
% 0.68/0.81 tff(2206,plain,
% 0.68/0.81 ((op(e0, e1) = e1) <=> (e3 = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2205])).
% 0.68/0.81 tff(2207,plain,
% 0.68/0.81 ((op(e0, e1) = e1) <=> (e1 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2206, 601])).
% 0.68/0.81 tff(2208,plain,
% 0.68/0.81 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2207])).
% 0.68/0.81 tff(2209,plain,
% 0.68/0.81 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2208])).
% 0.68/0.81 tff(2210,plain,
% 0.68/0.81 (~(op(e0, e1) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[521, 2209])).
% 0.68/0.81 tff(2211,plain,
% 0.68/0.81 (~(op(e2, e2) = e3)),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2038, 1590, 695, 379, 1055, 1588, 1587])).
% 0.68/0.81 tff(2212,plain,
% 0.68/0.81 (op(e1, e2) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[684, 2204, 861, 2211])).
% 0.68/0.81 tff(2213,plain,
% 0.68/0.81 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2212])).
% 0.68/0.81 tff(2214,plain,
% 0.68/0.81 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2213, 601])).
% 0.68/0.81 tff(2215,plain,
% 0.68/0.81 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2214])).
% 0.68/0.81 tff(2216,plain,
% 0.68/0.81 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2215])).
% 0.68/0.81 tff(2217,plain,
% 0.68/0.81 (~(op(e1, e2) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[521, 2216])).
% 0.68/0.81 tff(2218,plain,
% 0.68/0.81 ($false),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2147, 2217, 2210, 663, 2196, 2200])).
% 0.68/0.81 tff(2219,plain,((op(e0, e0) = e3) | (op(e3, e2) = e1) | (op(e3, e2) = e3) | (op(e0, e3) = e3) | (op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e3, e3) = e1) | (op(e1, e1) = e2) | (op(e3, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.81 tff(2220,plain,
% 0.68/0.81 (op(e0, e0) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2219, 2085, 2195, 2192, 1055, 2074, 2071, 379, 2067])).
% 0.68/0.81 tff(2221,plain,
% 0.68/0.81 (op(e0, e3) = e0),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1280, 2220])).
% 0.68/0.81 tff(2222,plain,
% 0.68/0.81 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2221])).
% 0.68/0.81 tff(2223,plain,
% 0.68/0.81 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2222])).
% 0.68/0.81 tff(2224,plain,
% 0.68/0.81 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2223])).
% 0.68/0.81 tff(2225,plain,
% 0.68/0.81 (~(op(e0, e3) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[40, 2224])).
% 0.68/0.81 tff(2226,plain,
% 0.68/0.81 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2189])).
% 0.68/0.81 tff(2227,plain,
% 0.68/0.81 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2226])).
% 0.68/0.81 tff(2228,plain,
% 0.68/0.81 (~(op(e2, e3) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[196, 2227])).
% 0.68/0.81 tff(2229,plain,
% 0.68/0.81 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2063])).
% 0.68/0.81 tff(2230,plain,
% 0.68/0.81 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2229])).
% 0.68/0.81 tff(2231,plain,
% 0.68/0.81 (~(op(e1, e0) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[564, 2230])).
% 0.68/0.81 tff(2232,plain,
% 0.68/0.81 (~(op(e1, e1) = e0)),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[2026, 2231])).
% 0.68/0.81 tff(2233,plain,
% 0.68/0.81 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2063])).
% 0.68/0.81 tff(2234,plain,
% 0.68/0.81 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2233])).
% 0.68/0.81 tff(2235,plain,
% 0.68/0.81 (~(op(e2, e0) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[589, 2234])).
% 0.68/0.81 tff(2236,plain,
% 0.68/0.81 ((e3 = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.68/0.81 inference(commutativity,[status(thm)],[])).
% 0.68/0.81 tff(2237,assumption,(op(e0, e0) = e3), introduced(assumption)).
% 0.68/0.81 tff(2238,plain,
% 0.68/0.81 ((op(e0, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2237])).
% 0.68/0.81 tff(2239,plain,
% 0.68/0.81 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2238, 2236])).
% 0.68/0.81 tff(2240,plain,
% 0.68/0.81 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2239])).
% 0.68/0.81 tff(2241,plain,
% 0.68/0.81 (~(op(e0, e2) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[1463, 2240])).
% 0.68/0.81 tff(2242,plain,
% 0.68/0.81 (op(e1, e2) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[684, 26, 861, 2241])).
% 0.68/0.81 tff(2243,plain,
% 0.68/0.81 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2242])).
% 0.68/0.81 tff(2244,plain,
% 0.68/0.81 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2243, 1])).
% 0.68/0.81 tff(2245,plain,
% 0.68/0.81 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2244])).
% 0.68/0.81 tff(2246,plain,
% 0.68/0.81 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2245])).
% 0.68/0.81 tff(2247,plain,
% 0.68/0.81 (~(op(e1, e2) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[509, 2246])).
% 0.68/0.81 tff(2248,plain,
% 0.68/0.81 (op(e0, e3) = e0),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1280, 2237])).
% 0.68/0.81 tff(2249,plain,
% 0.68/0.81 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2248])).
% 0.68/0.81 tff(2250,plain,
% 0.68/0.81 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2249])).
% 0.68/0.81 tff(2251,plain,
% 0.68/0.81 (~(op(e0, e2) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[702, 2250])).
% 0.68/0.81 tff(2252,plain,
% 0.68/0.81 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2248])).
% 0.68/0.81 tff(2253,plain,
% 0.68/0.81 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2252])).
% 0.68/0.81 tff(2254,plain,
% 0.68/0.81 (~(op(e0, e1) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[403, 2253])).
% 0.68/0.81 tff(2255,plain,
% 0.68/0.81 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2237])).
% 0.68/0.81 tff(2256,plain,
% 0.68/0.81 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2255, 1586])).
% 0.68/0.81 tff(2257,plain,
% 0.68/0.81 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2256])).
% 0.68/0.81 tff(2258,plain,
% 0.68/0.81 (~(op(e2, e0) = e3)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[162, 2257])).
% 0.68/0.81 tff(2259,plain,
% 0.68/0.81 (op(e2, e1) = e3),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[189, 26, 1179, 2258])).
% 0.68/0.81 tff(2260,plain,
% 0.68/0.81 ((op(e2, e1) = e0) <=> (e3 = e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2259])).
% 0.68/0.81 tff(2261,plain,
% 0.68/0.81 ((op(e2, e1) = e0) <=> (e0 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2260, 1])).
% 0.68/0.81 tff(2262,plain,
% 0.68/0.81 ((e0 = e3) <=> (op(e2, e1) = e0)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2261])).
% 0.68/0.81 tff(2263,plain,
% 0.68/0.81 ((~(e0 = e3)) <=> (~(op(e2, e1) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2262])).
% 0.68/0.81 tff(2264,plain,
% 0.68/0.81 (~(op(e2, e1) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[509, 2263])).
% 0.68/0.81 tff(2265,plain,
% 0.68/0.81 (op(e3, e1) = e0),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1241, 2264, 2254, 424])).
% 0.68/0.81 tff(2266,plain,
% 0.68/0.81 ((op(e3, e1) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2265])).
% 0.68/0.81 tff(2267,plain,
% 0.68/0.81 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2266, 272])).
% 0.68/0.81 tff(2268,plain,
% 0.68/0.81 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2267])).
% 0.68/0.81 tff(2269,plain,
% 0.68/0.81 (~(op(e3, e2) = e0)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[974, 2268])).
% 0.68/0.81 tff(2270,plain,
% 0.68/0.81 (op(e2, e2) = e0),
% 0.68/0.81 inference(unit_resolution,[status(thm)],[1678, 2269, 2251, 2247])).
% 0.68/0.81 tff(2271,plain,
% 0.68/0.81 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2270, 2270])).
% 0.68/0.81 tff(2272,plain,
% 0.68/0.81 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.68/0.81 inference(symmetry,[status(thm)],[2271])).
% 0.68/0.81 tff(2273,plain,
% 0.68/0.81 (e3 = op(e0, e0)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2237])).
% 0.68/0.81 tff(2274,plain,
% 0.68/0.81 (e3 = op(op(e2, e2), op(e2, e2))),
% 0.68/0.81 inference(transitivity,[status(thm)],[2273, 2272])).
% 0.68/0.81 tff(2275,plain,
% 0.68/0.81 (e0 = op(e2, e2)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[2270, 1788])).
% 0.68/0.81 tff(2276,plain,
% 0.68/0.81 (op(op(e2, e2), op(e2, e2)) = e3),
% 0.68/0.81 inference(transitivity,[status(thm)],[2271, 2237])).
% 0.68/0.81 tff(2277,plain,
% 0.68/0.81 (op(e2, op(op(e2, e2), op(e2, e2))) = op(e2, e3)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2276])).
% 0.68/0.81 tff(2278,plain,
% 0.68/0.81 (op(e2, e3) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.68/0.81 inference(symmetry,[status(thm)],[2277])).
% 0.68/0.81 tff(2279,plain,
% 0.68/0.81 ((op(e2, e1) = e1) <=> (e3 = e1)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2259])).
% 0.68/0.81 tff(2280,plain,
% 0.68/0.81 ((op(e2, e1) = e1) <=> (e1 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2279, 601])).
% 0.68/0.81 tff(2281,plain,
% 0.68/0.81 ((e1 = e3) <=> (op(e2, e1) = e1)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2280])).
% 0.68/0.81 tff(2282,plain,
% 0.68/0.81 ((~(e1 = e3)) <=> (~(op(e2, e1) = e1))),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2281])).
% 0.68/0.81 tff(2283,plain,
% 0.68/0.81 (~(op(e2, e1) = e1)),
% 0.68/0.81 inference(modus_ponens,[status(thm)],[521, 2282])).
% 0.68/0.81 tff(2284,plain,
% 0.68/0.81 ((op(e2, e1) = e2) <=> (e3 = e2)),
% 0.68/0.81 inference(monotonicity,[status(thm)],[2259])).
% 0.68/0.81 tff(2285,plain,
% 0.68/0.81 ((op(e2, e1) = e2) <=> (e2 = e3)),
% 0.68/0.81 inference(transitivity,[status(thm)],[2284, 1178])).
% 0.68/0.81 tff(2286,plain,
% 0.68/0.81 ((e2 = e3) <=> (op(e2, e1) = e2)),
% 0.68/0.81 inference(symmetry,[status(thm)],[2285])).
% 0.68/0.82 tff(2287,plain,
% 0.68/0.82 ((~(e2 = e3)) <=> (~(op(e2, e1) = e2))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2286])).
% 0.68/0.82 tff(2288,plain,
% 0.68/0.82 (~(op(e2, e1) = e2)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[170, 2287])).
% 0.68/0.82 tff(2289,plain,
% 0.68/0.82 (~(op(e2, e2) = e1)),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[52, 2288])).
% 0.68/0.82 tff(2290,plain,
% 0.68/0.82 (op(e2, e3) = e1),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[953, 2289, 422, 2283])).
% 0.68/0.82 tff(2291,plain,
% 0.68/0.82 (e1 = op(e2, e3)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2290])).
% 0.68/0.82 tff(2292,plain,
% 0.68/0.82 (e1 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2291, 2278])).
% 0.68/0.82 tff(2293,plain,
% 0.68/0.82 ((~(~((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2))))))) <=> ((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2294,plain,
% 0.68/0.82 (((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2295,plain,
% 0.68/0.82 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2294])).
% 0.68/0.82 tff(2296,plain,
% 0.68/0.82 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2295, 2293])).
% 0.68/0.82 tff(2297,plain,
% 0.68/0.82 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2298,plain,
% 0.68/0.82 ((~(((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2))) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2299,axiom,(~(((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2))) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax24')).
% 0.68/0.82 tff(2300,plain,
% 0.68/0.82 (~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 0.68/0.82 tff(2301,plain,
% 0.68/0.82 (~((e3 = op(op(e2, e2), op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2300, 2297])).
% 0.68/0.82 tff(2302,plain,
% 0.68/0.82 ((~(e1 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(op(e2, e2), op(e2, e2))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2301, 2296])).
% 0.68/0.82 tff(2303,plain,
% 0.68/0.82 ($false),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2302, 2292, 2275, 2274])).
% 0.68/0.82 tff(2304,plain,((op(e2, e2) = e3) | (~(op(e0, e0) = e3)) | (op(e2, e0) = e1) | (op(e1, e1) = e0) | (op(e3, e2) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.82 tff(2305,plain,
% 0.68/0.82 (op(e2, e2) = e3),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2304, 2220, 2235, 2232, 2195, 2228])).
% 0.68/0.82 tff(2306,plain,
% 0.68/0.82 ((op(e2, e2) = e1) <=> (e3 = e1)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2305])).
% 0.68/0.82 tff(2307,plain,
% 0.68/0.82 ((op(e2, e2) = e1) <=> (e1 = e3)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2306, 601])).
% 0.68/0.82 tff(2308,plain,
% 0.68/0.82 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2307])).
% 0.68/0.82 tff(2309,plain,
% 0.68/0.82 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2308])).
% 0.68/0.82 tff(2310,plain,
% 0.68/0.82 (~(op(e2, e2) = e1)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[521, 2309])).
% 0.68/0.82 tff(2311,plain,
% 0.68/0.82 (op(e2, e3) = e2),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[1004, 2305])).
% 0.68/0.82 tff(2312,plain,
% 0.68/0.82 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2311])).
% 0.68/0.82 tff(2313,plain,
% 0.68/0.82 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2312, 1034])).
% 0.68/0.82 tff(2314,plain,
% 0.68/0.82 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2313])).
% 0.68/0.82 tff(2315,plain,
% 0.68/0.82 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2314])).
% 0.68/0.82 tff(2316,plain,
% 0.68/0.82 (~(op(e2, e3) = e1)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[353, 2315])).
% 0.68/0.82 tff(2317,plain,
% 0.68/0.82 (op(e2, e1) = e1),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[953, 2316, 2235, 2310])).
% 0.68/0.82 tff(2318,plain,
% 0.68/0.82 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e1)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2317])).
% 0.68/0.82 tff(2319,plain,
% 0.68/0.82 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e1))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2318])).
% 0.68/0.82 tff(2320,plain,
% 0.68/0.82 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = op(e2, e1)))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2321,plain,
% 0.68/0.82 (~(op(e0, e1) = op(e2, e1))),
% 0.68/0.82 inference(and_elim,[status(thm)],[154])).
% 0.68/0.82 tff(2322,plain,
% 0.68/0.82 (~(op(e0, e1) = op(e2, e1))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 0.68/0.82 tff(2323,plain,
% 0.68/0.82 (~(op(e0, e1) = e1)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2322, 2319])).
% 0.68/0.82 tff(2324,plain,
% 0.68/0.82 (op(e0, e2) = e1),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2185, 2323, 2074, 2225])).
% 0.68/0.82 tff(2325,plain,
% 0.68/0.82 (e1 = op(e0, e2)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2324])).
% 0.68/0.82 tff(2326,plain,
% 0.68/0.82 (op(e2, op(e0, e2)) = op(e2, e1)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2324])).
% 0.68/0.82 tff(2327,plain,
% 0.68/0.82 (op(e2, op(e0, e2)) = op(e0, e2)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2326, 2317, 2325])).
% 0.68/0.82 tff(2328,plain,
% 0.68/0.82 ($false),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[1063, 2327])).
% 0.68/0.82 tff(2329,plain,((op(e1, e1) = e2) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e3, op(e0, e3)) = op(e0, e3)) | (e0 = op(op(e2, e2), op(e2, e2))) | (e3 = op(e1, op(op(e1, e1), op(e1, e1))))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.82 tff(2330,plain,
% 0.68/0.82 (op(e1, e1) = e2),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2329, 1066, 1055, 1053, 1064, 1065, 1054, 1063])).
% 0.68/0.82 tff(2331,plain,
% 0.68/0.82 (op(e1, e2) = e1),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[514, 2330])).
% 0.68/0.82 tff(2332,plain,
% 0.68/0.82 ((op(e1, e2) = e3) <=> (e1 = e3)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2331])).
% 0.68/0.82 tff(2333,plain,
% 0.68/0.82 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2332])).
% 0.68/0.82 tff(2334,plain,
% 0.68/0.82 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2333])).
% 0.68/0.82 tff(2335,plain,
% 0.68/0.82 (~(op(e1, e2) = e3)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[521, 2334])).
% 0.68/0.82 tff(2336,plain,
% 0.68/0.82 (e2 = op(e1, e1)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2330])).
% 0.68/0.82 tff(2337,plain,
% 0.68/0.82 ((e2 = e3) <=> (op(e1, e1) = e3)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2336])).
% 0.68/0.82 tff(2338,plain,
% 0.68/0.82 ((~(e2 = e3)) <=> (~(op(e1, e1) = e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2337])).
% 0.68/0.82 tff(2339,plain,
% 0.68/0.82 (~(op(e1, e1) = e3)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[170, 2338])).
% 0.68/0.82 tff(2340,plain,
% 0.68/0.82 ((op(e1, op(op(e1, e1), op(e1, e1))) = e0) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(commutativity,[status(thm)],[])).
% 0.68/0.82 tff(2341,assumption,(op(e1, e1) = e2), introduced(assumption)).
% 0.68/0.82 tff(2342,plain,
% 0.68/0.82 (op(op(e1, e1), op(e1, e1)) = op(e2, e2)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2341, 2341])).
% 0.68/0.82 tff(2343,plain,
% 0.68/0.82 (op(e2, e2) = op(op(e1, e1), op(e1, e1))),
% 0.68/0.82 inference(symmetry,[status(thm)],[2342])).
% 0.68/0.82 tff(2344,plain,
% 0.68/0.82 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.68/0.82 inference(transitivity,[status(thm)],[1992, 2343])).
% 0.68/0.82 tff(2345,plain,
% 0.68/0.82 (op(e1, e3) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2344])).
% 0.68/0.82 tff(2346,plain,
% 0.68/0.82 ((op(e1, e3) = e0) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e0)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2345])).
% 0.68/0.82 tff(2347,plain,
% 0.68/0.82 ((op(e1, e3) = e0) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2346, 2340])).
% 0.68/0.82 tff(2348,plain,
% 0.68/0.82 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e3) = e0)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2347])).
% 0.68/0.82 tff(2349,plain,
% 0.68/0.82 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e3) = e0))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2348])).
% 0.68/0.82 tff(2350,plain,
% 0.68/0.82 (e2 = op(e1, e1)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2341, 484])).
% 0.68/0.82 tff(2351,plain,
% 0.68/0.82 ((e3 = op(op(e1, e1), op(e1, e1))) <=> (e3 = op(e2, e2))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2342])).
% 0.68/0.82 tff(2352,plain,
% 0.68/0.82 ((e3 = op(op(e1, e1), op(e1, e1))) <=> (op(e2, e2) = e3)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2351, 1015])).
% 0.68/0.82 tff(2353,plain,
% 0.68/0.82 ((op(e2, e2) = e3) <=> (e3 = op(op(e1, e1), op(e1, e1)))),
% 0.68/0.82 inference(symmetry,[status(thm)],[2352])).
% 0.68/0.82 tff(2354,plain,
% 0.68/0.82 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[1900, 2353])).
% 0.68/0.82 tff(2355,plain,
% 0.68/0.82 ((~(~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1))))))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2356,plain,
% 0.68/0.82 (((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2357,plain,
% 0.68/0.82 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2356])).
% 0.68/0.82 tff(2358,plain,
% 0.68/0.82 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1)))))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2357, 2355])).
% 0.68/0.82 tff(2359,plain,
% 0.68/0.82 ((~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2360,plain,
% 0.68/0.82 ((~(((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2361,axiom,(~(((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax28')).
% 0.68/0.82 tff(2362,plain,
% 0.68/0.82 (~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2361, 2360])).
% 0.68/0.82 tff(2363,plain,
% 0.68/0.82 (~((e3 = op(op(e1, e1), op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2362, 2359])).
% 0.68/0.82 tff(2364,plain,
% 0.68/0.82 ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e3 = op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2363, 2358])).
% 0.68/0.82 tff(2365,plain,
% 0.68/0.82 (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2364, 2354, 2350])).
% 0.68/0.82 tff(2366,plain,
% 0.68/0.82 (~(op(e1, e3) = e0)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2365, 2349])).
% 0.68/0.82 tff(2367,plain,
% 0.68/0.82 (op(e1, e2) = e1),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[514, 2341])).
% 0.68/0.82 tff(2368,plain,
% 0.68/0.82 ((op(e1, e2) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2367])).
% 0.68/0.82 tff(2369,plain,
% 0.68/0.82 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2368, 619])).
% 0.68/0.82 tff(2370,plain,
% 0.68/0.82 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2369])).
% 0.68/0.82 tff(2371,plain,
% 0.68/0.82 (~(op(e1, e3) = e1)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[691, 2370])).
% 0.68/0.82 tff(2372,plain,
% 0.68/0.82 ((op(e1, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2341])).
% 0.68/0.82 tff(2373,plain,
% 0.68/0.82 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.68/0.82 inference(transitivity,[status(thm)],[2372, 1745])).
% 0.68/0.82 tff(2374,plain,
% 0.68/0.82 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2373])).
% 0.68/0.82 tff(2375,plain,
% 0.68/0.82 (~(op(e1, e3) = e2)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2034, 2374])).
% 0.68/0.82 tff(2376,plain,
% 0.68/0.82 ((op(e1, op(op(e1, e1), op(e1, e1))) = e3) <=> (e3 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(commutativity,[status(thm)],[])).
% 0.68/0.82 tff(2377,plain,
% 0.68/0.82 ((op(e1, e3) = e3) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e3)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2345])).
% 0.68/0.82 tff(2378,plain,
% 0.68/0.82 ((op(e1, e3) = e3) <=> (e3 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2377, 2376])).
% 0.68/0.82 tff(2379,plain,
% 0.68/0.82 ((e3 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e3) = e3)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2378])).
% 0.68/0.82 tff(2380,plain,
% 0.68/0.82 ((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e3) = e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2379])).
% 0.68/0.82 tff(2381,plain,
% 0.68/0.82 (~(op(e1, e3) = e3)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[1066, 2380])).
% 0.68/0.82 tff(2382,plain,
% 0.68/0.82 (((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2383,plain,
% 0.68/0.82 ((((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2384,plain,
% 0.68/0.82 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(2385,plain,
% 0.68/0.82 (((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)) <=> (((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[2384])).
% 0.68/0.82 tff(2386,plain,
% 0.68/0.82 (((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2385, 2383])).
% 0.68/0.82 tff(2387,plain,
% 0.68/0.82 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)),
% 0.68/0.82 inference(and_elim,[status(thm)],[430])).
% 0.68/0.82 tff(2388,plain,
% 0.68/0.82 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 0.68/0.82 tff(2389,plain,
% 0.68/0.82 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.68/0.82 inference(modus_ponens,[status(thm)],[2388, 2382])).
% 0.68/0.82 tff(2390,plain,
% 0.68/0.82 (op(e1, e3) = e0),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2389, 2381, 2375, 2371])).
% 0.68/0.82 tff(2391,plain,
% 0.68/0.82 ($false),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2390, 2366])).
% 0.68/0.82 tff(2392,plain,((~(op(e2, e2) = e3)) | (~(op(e1, e1) = e2)) | (e3 = op(e1, op(op(e1, e1), op(e1, e1))))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.82 tff(2393,plain,
% 0.68/0.82 (~(op(e2, e2) = e3)),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[2392, 2330, 1066])).
% 0.68/0.82 tff(2394,plain,
% 0.68/0.82 (op(op(e3, e3), op(e3, e3)) = op(e1, e1)),
% 0.68/0.82 inference(monotonicity,[status(thm)],[1155, 1155])).
% 0.68/0.82 tff(2395,plain,
% 0.68/0.82 (op(e1, e1) = op(op(e3, e3), op(e3, e3))),
% 0.68/0.82 inference(symmetry,[status(thm)],[2394])).
% 0.68/0.82 tff(2396,plain,
% 0.68/0.82 (e2 = op(e1, e1)),
% 0.68/0.82 inference(symmetry,[status(thm)],[2341])).
% 0.68/0.82 tff(2397,plain,
% 0.68/0.82 (e2 = op(op(e3, e3), op(e3, e3))),
% 0.68/0.82 inference(transitivity,[status(thm)],[2396, 2395])).
% 0.68/0.82 tff(2398,plain,
% 0.68/0.82 ($false),
% 0.68/0.82 inference(unit_resolution,[status(thm)],[1053, 2397])).
% 0.68/0.82 tff(2399,plain,((~(op(e3, e3) = e1)) | (e2 = op(op(e3, e3), op(e3, e3))) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(2400,plain,
% 0.68/0.83 (~(op(e3, e3) = e1)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2399, 2330, 1053])).
% 0.68/0.83 tff(2401,plain,
% 0.68/0.83 ((op(e1, e2) = e3) <=> (e1 = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2367])).
% 0.68/0.83 tff(2402,plain,
% 0.68/0.83 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2401])).
% 0.68/0.83 tff(2403,plain,
% 0.68/0.83 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2402])).
% 0.68/0.83 tff(2404,plain,
% 0.68/0.83 (~(op(e1, e2) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[521, 2403])).
% 0.68/0.83 tff(2405,plain,
% 0.68/0.83 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2367])).
% 0.68/0.83 tff(2406,plain,
% 0.68/0.83 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2405, 2081])).
% 0.68/0.83 tff(2407,plain,
% 0.68/0.83 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2406])).
% 0.68/0.83 tff(2408,plain,
% 0.68/0.83 (~(op(e3, e2) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[742, 2407])).
% 0.68/0.83 tff(2409,plain,
% 0.68/0.83 (op(e0, e0) = e2),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1105, 421, 1055, 1590])).
% 0.68/0.83 tff(2410,plain,
% 0.68/0.83 (op(e0, e2) = e0),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1472, 2409])).
% 0.68/0.83 tff(2411,plain,
% 0.68/0.83 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2410])).
% 0.68/0.83 tff(2412,plain,
% 0.68/0.83 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2411])).
% 0.68/0.83 tff(2413,plain,
% 0.68/0.83 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2412])).
% 0.68/0.83 tff(2414,plain,
% 0.68/0.83 (~(op(e0, e2) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[509, 2413])).
% 0.68/0.83 tff(2415,plain,
% 0.68/0.83 (op(e3, e2) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[684, 2414, 838, 26])).
% 0.68/0.83 tff(2416,plain,
% 0.68/0.83 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2415])).
% 0.68/0.83 tff(2417,plain,
% 0.68/0.83 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2416, 164])).
% 0.68/0.83 tff(2418,plain,
% 0.68/0.83 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2417])).
% 0.68/0.83 tff(2419,plain,
% 0.68/0.83 (~(op(e3, e3) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1160, 2418])).
% 0.68/0.83 tff(2420,plain,
% 0.68/0.83 (op(e3, e0) = e1),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1569, 2419, 1053, 1055, 1065, 1064, 1063, 26])).
% 0.68/0.83 tff(2421,plain,
% 0.68/0.83 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2415])).
% 0.68/0.83 tff(2422,plain,
% 0.68/0.83 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2421])).
% 0.68/0.83 tff(2423,plain,
% 0.68/0.83 (~(op(e3, e0) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[572, 2422])).
% 0.68/0.83 tff(2424,plain,
% 0.68/0.83 (~(op(e3, e3) = e0)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[558, 2423])).
% 0.68/0.83 tff(2425,plain,
% 0.68/0.83 (op(e3, e0) = e0),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2188, 2424, 1055, 663, 421, 2419, 1053, 695])).
% 0.68/0.83 tff(2426,plain,
% 0.68/0.83 (e0 = op(e3, e0)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2425])).
% 0.68/0.83 tff(2427,plain,
% 0.68/0.83 (e0 = e1),
% 0.68/0.83 inference(transitivity,[status(thm)],[2426, 2420])).
% 0.68/0.83 tff(2428,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[40, 2427])).
% 0.68/0.83 tff(2429,plain,((op(e0, e0) = e1) | (op(e0, e0) = e0) | (op(e3, e2) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e2, e2) = e3) | (op(e1, e2) = e3) | (op(e0, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(2430,plain,
% 0.68/0.83 (op(e0, e0) = e1),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2429, 26, 2408, 1053, 695, 1065, 1064, 1063, 1055, 2404, 1590])).
% 0.68/0.83 tff(2431,plain,
% 0.68/0.83 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2430, 2430])).
% 0.68/0.83 tff(2432,plain,
% 0.68/0.83 (op(op(e0, e0), op(e0, e0)) = e2),
% 0.68/0.83 inference(transitivity,[status(thm)],[2431, 2341])).
% 0.68/0.83 tff(2433,plain,
% 0.68/0.83 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e2)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2432])).
% 0.68/0.83 tff(2434,plain,
% 0.68/0.83 ((e3 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e3 = op(e0, e2))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2433])).
% 0.68/0.83 tff(2435,plain,
% 0.68/0.83 ((e3 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e2) = e3)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2434, 2236])).
% 0.68/0.83 tff(2436,plain,
% 0.68/0.83 ((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e2) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2435])).
% 0.68/0.83 tff(2437,plain,
% 0.68/0.83 (e1 = op(e0, e0)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2430, 1069])).
% 0.68/0.83 tff(2438,plain,
% 0.68/0.83 (op(e1, e1) = op(op(e0, e0), op(e0, e0))),
% 0.68/0.83 inference(symmetry,[status(thm)],[2431])).
% 0.68/0.83 tff(2439,plain,
% 0.68/0.83 (e2 = op(op(e0, e0), op(e0, e0))),
% 0.68/0.83 inference(transitivity,[status(thm)],[2396, 2438])).
% 0.68/0.83 tff(2440,plain,
% 0.68/0.83 ((~(~((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0)))))) <=> ((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0))))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(2441,plain,
% 0.68/0.83 (((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0)))))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(2442,plain,
% 0.68/0.83 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~(~((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0))))))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2441])).
% 0.68/0.83 tff(2443,plain,
% 0.68/0.83 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> ((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0))))),
% 0.68/0.83 inference(transitivity,[status(thm)],[2442, 2440])).
% 0.68/0.83 tff(2444,plain,
% 0.68/0.83 ((~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(2445,plain,
% 0.68/0.83 ((~(((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0))) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))) <=> (~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0))))))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(2446,axiom,(~(((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0))) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax21')).
% 0.68/0.83 tff(2447,plain,
% 0.68/0.83 (~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 0.68/0.83 tff(2448,plain,
% 0.68/0.83 (~((e2 = op(op(e0, e0), op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(op(e0, e0), op(e0, e0)))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2447, 2444])).
% 0.68/0.83 tff(2449,plain,
% 0.68/0.83 ((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) | (~(e2 = op(op(e0, e0), op(e0, e0)))) | (~(e1 = op(e0, e0)))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2448, 2443])).
% 0.68/0.83 tff(2450,plain,
% 0.68/0.83 (~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2449, 2439, 2437])).
% 0.68/0.83 tff(2451,plain,
% 0.68/0.83 (~(op(e0, e2) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2450, 2436])).
% 0.68/0.83 tff(2452,plain,
% 0.68/0.83 ((e1 = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.68/0.83 inference(commutativity,[status(thm)],[])).
% 0.68/0.83 tff(2453,plain,
% 0.68/0.83 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2430])).
% 0.68/0.83 tff(2454,plain,
% 0.68/0.83 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2453, 2452])).
% 0.68/0.83 tff(2455,plain,
% 0.68/0.83 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2454])).
% 0.68/0.83 tff(2456,plain,
% 0.68/0.83 (~(op(e3, e0) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[270, 2455])).
% 0.68/0.83 tff(2457,plain,
% 0.68/0.83 (op(e3, e3) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1569, 2456, 1053, 1055, 1065, 1064, 1063, 26])).
% 0.68/0.83 tff(2458,plain,
% 0.68/0.83 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2457])).
% 0.68/0.83 tff(2459,plain,
% 0.68/0.83 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2458])).
% 0.68/0.83 tff(2460,plain,
% 0.68/0.83 (~(op(e3, e2) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1160, 2459])).
% 0.68/0.83 tff(2461,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[684, 2460, 2451, 2404, 26])).
% 0.68/0.83 tff(2462,plain,((op(e2, e2) = e3) | (~(op(e1, e1) = e2)) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e0, e0) = e0) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, e3) = e1) | (op(e0, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(2463,plain,
% 0.68/0.83 (op(e0, e0) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2462, 2400, 1053, 1055, 1065, 1064, 1063, 2330, 2393])).
% 0.68/0.83 tff(2464,plain,
% 0.68/0.83 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2463])).
% 0.68/0.83 tff(2465,plain,
% 0.68/0.83 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2464, 256])).
% 0.68/0.83 tff(2466,plain,
% 0.68/0.83 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2465])).
% 0.68/0.83 tff(2467,plain,
% 0.68/0.83 (~(op(e1, e0) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[254, 2466])).
% 0.68/0.83 tff(2468,plain,
% 0.68/0.83 (op(e1, e3) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[530, 2467, 2339, 2335])).
% 0.68/0.83 tff(2469,plain,
% 0.68/0.83 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2468])).
% 0.68/0.83 tff(2470,plain,
% 0.68/0.83 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2469, 164])).
% 0.68/0.83 tff(2471,plain,
% 0.68/0.83 ((op(e3, e3) = e3) <=> (op(e1, e3) = op(e3, e3))),
% 0.68/0.83 inference(symmetry,[status(thm)],[2470])).
% 0.68/0.83 tff(2472,plain,
% 0.68/0.83 ((op(e0, e0) = e1) <=> (e3 = e1)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2463])).
% 0.68/0.83 tff(2473,plain,
% 0.68/0.83 ((op(e0, e0) = e1) <=> (e1 = e3)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2472, 601])).
% 0.68/0.83 tff(2474,plain,
% 0.68/0.83 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2473])).
% 0.68/0.83 tff(2475,plain,
% 0.68/0.83 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2474])).
% 0.68/0.83 tff(2476,plain,
% 0.68/0.83 (~(op(e0, e0) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[521, 2475])).
% 0.68/0.83 tff(2477,plain,
% 0.68/0.83 (op(e0, e3) = e0),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1280, 2463])).
% 0.68/0.83 tff(2478,plain,
% 0.68/0.83 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2477])).
% 0.68/0.83 tff(2479,plain,
% 0.68/0.83 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2478, 2])).
% 0.68/0.83 tff(2480,plain,
% 0.68/0.83 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2479])).
% 0.68/0.83 tff(2481,plain,
% 0.68/0.83 (~(op(e3, e3) = e0)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1578, 2480])).
% 0.68/0.83 tff(2482,plain,
% 0.68/0.83 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2331])).
% 0.68/0.83 tff(2483,plain,
% 0.68/0.83 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2482, 2081])).
% 0.68/0.83 tff(2484,plain,
% 0.68/0.83 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2483])).
% 0.68/0.83 tff(2485,plain,
% 0.68/0.83 (~(op(e3, e2) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[742, 2484])).
% 0.68/0.83 tff(2486,plain,
% 0.68/0.83 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2477])).
% 0.68/0.83 tff(2487,plain,
% 0.68/0.83 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2486, 2477])).
% 0.68/0.83 tff(2488,plain,
% 0.68/0.83 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2487])).
% 0.68/0.83 tff(2489,plain,
% 0.68/0.83 (~(op(e3, e0) = e0)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1065, 2488])).
% 0.68/0.83 tff(2490,plain,
% 0.68/0.83 (op(e3, e3) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2188, 2489, 1055, 2485, 2481, 2476, 1053, 2400])).
% 0.68/0.83 tff(2491,plain,
% 0.68/0.83 (op(e1, e3) = op(e3, e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[2490, 2471])).
% 0.68/0.83 tff(2492,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[539, 2491])).
% 0.68/0.83 tff(2493,plain,((e3 = op(e1, op(op(e1, e1), op(e1, e1)))) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (e0 = op(op(e2, e2), op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(2494,plain,
% 0.68/0.83 (e3 = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2493, 1065, 1053, 1055, 1064, 1063, 1054])).
% 0.68/0.83 tff(2495,plain,
% 0.68/0.83 (op(e1, op(op(e1, e1), op(e1, e1))) = e3),
% 0.68/0.83 inference(symmetry,[status(thm)],[2494])).
% 0.68/0.83 tff(2496,assumption,(e3 = op(e1, op(op(e1, e1), op(e1, e1)))), introduced(assumption)).
% 0.68/0.83 tff(2497,plain,
% 0.68/0.83 (op(e3, e0) = e1),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1569, 693, 1053, 1055, 1065, 1064, 1063, 26])).
% 0.68/0.83 tff(2498,plain,
% 0.68/0.83 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2497])).
% 0.68/0.83 tff(2499,plain,
% 0.68/0.83 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2498])).
% 0.68/0.83 tff(2500,plain,
% 0.68/0.83 (~(op(e0, e0) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[270, 2499])).
% 0.68/0.83 tff(2501,plain,
% 0.68/0.83 ((op(e3, e0) = e0) <=> (e1 = e0)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2497])).
% 0.68/0.83 tff(2502,plain,
% 0.68/0.83 ((op(e3, e0) = e0) <=> (e0 = e1)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2501, 1203])).
% 0.68/0.83 tff(2503,plain,
% 0.68/0.83 ((e0 = e1) <=> (op(e3, e0) = e0)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2502])).
% 0.68/0.83 tff(2504,plain,
% 0.68/0.83 ((~(e0 = e1)) <=> (~(op(e3, e0) = e0))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2503])).
% 0.68/0.83 tff(2505,plain,
% 0.68/0.83 (~(op(e3, e0) = e0)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[40, 2504])).
% 0.68/0.83 tff(2506,plain,
% 0.68/0.83 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2497])).
% 0.68/0.83 tff(2507,plain,
% 0.68/0.83 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.68/0.83 inference(transitivity,[status(thm)],[2506, 2081])).
% 0.68/0.83 tff(2508,plain,
% 0.68/0.83 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2507])).
% 0.68/0.83 tff(2509,plain,
% 0.68/0.83 (~(op(e3, e2) = e1)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[572, 2508])).
% 0.68/0.83 tff(2510,plain,
% 0.68/0.83 ((op(e3, e0) = e3) <=> (e1 = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2497])).
% 0.68/0.83 tff(2511,plain,
% 0.68/0.83 ((e1 = e3) <=> (op(e3, e0) = e3)),
% 0.68/0.83 inference(symmetry,[status(thm)],[2510])).
% 0.68/0.83 tff(2512,plain,
% 0.68/0.83 ((~(e1 = e3)) <=> (~(op(e3, e0) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2511])).
% 0.68/0.83 tff(2513,plain,
% 0.68/0.83 (~(op(e3, e0) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[521, 2512])).
% 0.68/0.83 tff(2514,plain,
% 0.68/0.83 (~(op(e3, e3) = e0)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[558, 2513])).
% 0.68/0.83 tff(2515,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2188, 2514, 2509, 1055, 693, 2505, 2500, 1053, 695])).
% 0.68/0.83 tff(2516,plain,((op(e3, e3) = e3) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(2517,plain,
% 0.68/0.83 (op(e3, e3) = e3),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[2516, 26, 1053, 695, 1065, 1064, 1063, 1055])).
% 0.68/0.83 tff(2518,plain,
% 0.68/0.83 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2517])).
% 0.68/0.83 tff(2519,plain,
% 0.68/0.83 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2518])).
% 0.68/0.83 tff(2520,plain,
% 0.68/0.83 (~(op(e3, e2) = e3)),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1160, 2519])).
% 0.68/0.83 tff(2521,plain,
% 0.68/0.83 (op(e1, op(op(e1, e1), op(e1, e1))) = e3),
% 0.68/0.83 inference(symmetry,[status(thm)],[2496])).
% 0.68/0.83 tff(2522,plain,
% 0.68/0.83 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2517])).
% 0.68/0.83 tff(2523,plain,
% 0.68/0.83 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[2522])).
% 0.68/0.83 tff(2524,plain,
% 0.68/0.84 (~(op(e0, e3) = e3)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1578, 2523])).
% 0.68/0.84 tff(2525,plain,
% 0.68/0.84 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2517])).
% 0.68/0.84 tff(2526,plain,
% 0.68/0.84 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2525])).
% 0.68/0.84 tff(2527,plain,
% 0.68/0.84 (~(op(e3, e0) = e3)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1424, 2526])).
% 0.68/0.84 tff(2528,plain,
% 0.68/0.84 (~(op(e1, e1) = e2)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[2462, 1590, 1053, 1055, 1065, 1064, 1063, 695, 26])).
% 0.68/0.84 tff(2529,plain,
% 0.68/0.84 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2409])).
% 0.68/0.84 tff(2530,plain,
% 0.68/0.84 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.68/0.84 inference(transitivity,[status(thm)],[2529, 1532])).
% 0.68/0.84 tff(2531,plain,
% 0.68/0.84 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2530])).
% 0.68/0.84 tff(2532,plain,
% 0.68/0.84 (~(op(e3, e0) = e2)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[270, 2531])).
% 0.68/0.84 tff(2533,plain,
% 0.68/0.84 (op(e3, e2) = e1),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[2219, 421, 1587, 861, 1055, 1590, 695, 379, 1588])).
% 0.68/0.84 tff(2534,plain,
% 0.68/0.84 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2533])).
% 0.68/0.84 tff(2535,plain,
% 0.68/0.84 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2534])).
% 0.68/0.84 tff(2536,plain,
% 0.68/0.84 (~(op(e3, e0) = e1)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[572, 2535])).
% 0.68/0.84 tff(2537,plain,
% 0.68/0.84 (op(e3, e0) = e0),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1333, 2536, 2532, 1588])).
% 0.68/0.84 tff(2538,plain,
% 0.68/0.84 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2537])).
% 0.68/0.84 tff(2539,plain,
% 0.68/0.84 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2538])).
% 0.68/0.84 tff(2540,plain,
% 0.68/0.84 (~(op(e1, e0) = e0)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[564, 2539])).
% 0.68/0.84 tff(2541,plain,
% 0.68/0.84 ((e0 = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.68/0.84 inference(commutativity,[status(thm)],[])).
% 0.68/0.84 tff(2542,plain,
% 0.68/0.84 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2410])).
% 0.68/0.84 tff(2543,plain,
% 0.68/0.84 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.68/0.84 inference(transitivity,[status(thm)],[2542, 2541])).
% 0.68/0.84 tff(2544,plain,
% 0.68/0.84 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2543])).
% 0.68/0.84 tff(2545,plain,
% 0.68/0.84 (~(op(e1, e2) = e0)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1740, 2544])).
% 0.68/0.84 tff(2546,plain,
% 0.68/0.84 ((e2 = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.68/0.84 inference(commutativity,[status(thm)],[])).
% 0.68/0.84 tff(2547,plain,
% 0.68/0.84 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2409])).
% 0.68/0.84 tff(2548,plain,
% 0.68/0.84 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.68/0.84 inference(transitivity,[status(thm)],[2547, 2546])).
% 0.68/0.84 tff(2549,plain,
% 0.68/0.84 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2548])).
% 0.68/0.84 tff(2550,plain,
% 0.68/0.84 (~(op(e1, e0) = e2)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[254, 2549])).
% 0.68/0.84 tff(2551,plain,
% 0.68/0.84 ((op(e1, op(op(e1, e1), op(e1, e1))) = e2) <=> (e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(commutativity,[status(thm)],[])).
% 0.68/0.84 tff(2552,plain,
% 0.68/0.84 ((op(e0, e2) = e3) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2410, 2496])).
% 0.68/0.84 tff(2553,plain,
% 0.68/0.84 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e0, e2) = e3)),
% 0.68/0.84 inference(symmetry,[status(thm)],[2552])).
% 0.68/0.84 tff(2554,plain,
% 0.68/0.84 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e0, e2) = e3))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2553])).
% 0.68/0.84 tff(2555,plain,
% 0.68/0.84 ((e0 = e3) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2496])).
% 0.68/0.84 tff(2556,plain,
% 0.68/0.84 ((~(e0 = e3)) <=> (~(e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2555])).
% 0.68/0.84 tff(2557,plain,
% 0.68/0.84 (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[509, 2556])).
% 0.68/0.84 tff(2558,plain,
% 0.68/0.84 (~(op(e0, e2) = e3)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[2557, 2554])).
% 0.68/0.84 tff(2559,plain,
% 0.68/0.84 (op(e1, e2) = e3),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[684, 2558, 861, 26])).
% 0.68/0.84 tff(2560,plain,
% 0.68/0.84 (op(e1, e2) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[2559, 2496])).
% 0.68/0.84 tff(2561,plain,
% 0.68/0.84 ((op(e1, e2) = e2) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e2)),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2560])).
% 0.68/0.84 tff(2562,plain,
% 0.68/0.84 ((op(e1, e2) = e2) <=> (e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(transitivity,[status(thm)],[2561, 2551])).
% 0.68/0.84 tff(2563,plain,
% 0.68/0.84 ((e2 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e2) = e2)),
% 0.68/0.84 inference(symmetry,[status(thm)],[2562])).
% 0.68/0.84 tff(2564,plain,
% 0.68/0.84 ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e2) = e2))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2563])).
% 0.68/0.84 tff(2565,plain,
% 0.68/0.84 ((e2 = e3) <=> (e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[2496])).
% 0.71/0.84 tff(2566,plain,
% 0.71/0.84 ((~(e2 = e3)) <=> (~(e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2565])).
% 0.71/0.84 tff(2567,plain,
% 0.71/0.84 (~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[170, 2566])).
% 0.71/0.84 tff(2568,plain,
% 0.71/0.84 (~(op(e1, e2) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2567, 2564])).
% 0.71/0.84 tff(2569,plain,
% 0.71/0.84 (op(e1, e3) = e2),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[751, 2568, 379, 2550])).
% 0.71/0.84 tff(2570,plain,
% 0.71/0.84 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2569])).
% 0.71/0.84 tff(2571,plain,
% 0.71/0.84 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2570, 1213])).
% 0.71/0.84 tff(2572,plain,
% 0.71/0.84 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2571])).
% 0.71/0.84 tff(2573,plain,
% 0.71/0.84 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2572])).
% 0.71/0.84 tff(2574,plain,
% 0.71/0.84 (~(op(e1, e3) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[16, 2573])).
% 0.71/0.84 tff(2575,plain,
% 0.71/0.84 (op(e1, e1) = e0),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[548, 2574, 2545, 2540])).
% 0.71/0.84 tff(2576,plain,
% 0.71/0.84 (e0 = op(e1, e1)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2575, 1688])).
% 0.71/0.84 tff(2577,plain,
% 0.71/0.84 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2575, 2575])).
% 0.71/0.84 tff(2578,plain,
% 0.71/0.84 (op(e0, e0) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.84 inference(symmetry,[status(thm)],[2577])).
% 0.71/0.84 tff(2579,plain,
% 0.71/0.84 (e2 = op(e0, e0)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2409])).
% 0.71/0.84 tff(2580,plain,
% 0.71/0.84 (e2 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2579, 2578])).
% 0.71/0.84 tff(2581,plain,
% 0.71/0.84 ((~(~((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1)))))) <=> ((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1))))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2582,plain,
% 0.71/0.84 (((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1)))))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2583,plain,
% 0.71/0.84 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1))))))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2582])).
% 0.71/0.84 tff(2584,plain,
% 0.71/0.84 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1))))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2583, 2581])).
% 0.71/0.84 tff(2585,plain,
% 0.71/0.84 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2586,plain,
% 0.71/0.84 ((~(((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1))) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2587,axiom,(~(((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1))) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax19')).
% 0.71/0.84 tff(2588,plain,
% 0.71/0.84 (~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 0.71/0.84 tff(2589,plain,
% 0.71/0.84 (~((e2 = op(op(e1, e1), op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2588, 2585])).
% 0.71/0.84 tff(2590,plain,
% 0.71/0.84 ((~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, e1)))),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2589, 2584])).
% 0.71/0.84 tff(2591,plain,
% 0.71/0.84 ($false),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[2590, 2580, 2576, 2496])).
% 0.71/0.84 tff(2592,plain,((op(e0, e0) = e1) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (op(e1, e1) = e2) | (op(e3, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e0) = e3) | (op(e0, e3) = e3) | (op(e0, e0) = e0) | (op(e0, e0) = e3) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.84 tff(2593,plain,
% 0.71/0.84 (op(e0, e0) = e1),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[2592, 2528, 2496, 2520, 26, 2527, 2524, 1055, 1590, 695])).
% 0.71/0.84 tff(2594,plain,
% 0.71/0.84 (op(e0, e1) = e0),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[1109, 2593])).
% 0.71/0.84 tff(2595,plain,
% 0.71/0.84 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2594])).
% 0.71/0.84 tff(2596,plain,
% 0.71/0.84 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2595, 1430])).
% 0.71/0.84 tff(2597,plain,
% 0.71/0.84 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2596])).
% 0.71/0.84 tff(2598,plain,
% 0.71/0.84 (~(op(e1, e1) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1402, 2597])).
% 0.71/0.84 tff(2599,plain,
% 0.71/0.84 ((e0 = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.84 inference(commutativity,[status(thm)],[])).
% 0.71/0.84 tff(2600,plain,
% 0.71/0.84 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2594])).
% 0.71/0.84 tff(2601,plain,
% 0.71/0.84 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2600, 2594])).
% 0.71/0.84 tff(2602,plain,
% 0.71/0.84 ((~(op(e1, op(e0, e1)) = op(e0, e1))) <=> (~(op(e1, e0) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2601])).
% 0.71/0.84 tff(2603,plain,
% 0.71/0.84 (~(op(e1, e0) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1064, 2602])).
% 0.71/0.84 tff(2604,plain,
% 0.71/0.84 ((op(e0, e1) = e3) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2594, 2496])).
% 0.71/0.84 tff(2605,plain,
% 0.71/0.84 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e0, e1) = e3)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2604])).
% 0.71/0.84 tff(2606,plain,
% 0.71/0.84 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e0, e1) = e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2605])).
% 0.71/0.84 tff(2607,plain,
% 0.71/0.84 (~(op(e0, e1) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2557, 2606])).
% 0.71/0.84 tff(2608,plain,
% 0.71/0.84 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2517])).
% 0.71/0.84 tff(2609,plain,
% 0.71/0.84 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2608])).
% 0.71/0.84 tff(2610,plain,
% 0.71/0.84 (~(op(e3, e1) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1780, 2609])).
% 0.71/0.84 tff(2611,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2593])).
% 0.71/0.84 tff(2612,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2611, 2086])).
% 0.71/0.84 tff(2613,plain,
% 0.71/0.84 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2612])).
% 0.71/0.84 tff(2614,plain,
% 0.71/0.84 (~(op(e0, e2) = e1)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1463, 2613])).
% 0.71/0.84 tff(2615,plain,
% 0.71/0.84 ((e0 = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.84 inference(commutativity,[status(thm)],[])).
% 0.71/0.84 tff(2616,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2594])).
% 0.71/0.84 tff(2617,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2616, 2615])).
% 0.71/0.84 tff(2618,plain,
% 0.71/0.84 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2617])).
% 0.71/0.84 tff(2619,plain,
% 0.71/0.84 (~(op(e0, e2) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[867, 2618])).
% 0.71/0.84 tff(2620,plain,
% 0.71/0.84 (op(e1, e2) = e0),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[1856, 2619, 2528, 2614, 2593, 2610, 2607, 695, 2603])).
% 0.71/0.84 tff(2621,plain,
% 0.71/0.84 ((op(e1, e2) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2620])).
% 0.71/0.84 tff(2622,plain,
% 0.71/0.84 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2621, 2599])).
% 0.71/0.84 tff(2623,plain,
% 0.71/0.84 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2622])).
% 0.71/0.84 tff(2624,plain,
% 0.71/0.84 (~(op(e1, e3) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[691, 2623])).
% 0.71/0.84 tff(2625,plain,
% 0.71/0.84 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2517])).
% 0.71/0.84 tff(2626,plain,
% 0.71/0.84 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2625])).
% 0.71/0.84 tff(2627,plain,
% 0.71/0.84 (~(op(e1, e3) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[539, 2626])).
% 0.71/0.84 tff(2628,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e3)) <=> (e1 = op(e0, e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2593])).
% 0.71/0.84 tff(2629,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2628, 696])).
% 0.71/0.84 tff(2630,plain,
% 0.71/0.84 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e1))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2629])).
% 0.71/0.84 tff(2631,plain,
% 0.71/0.84 (~(op(e0, e3) = e1)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[305, 2630])).
% 0.71/0.84 tff(2632,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2594])).
% 0.71/0.84 tff(2633,plain,
% 0.71/0.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2632, 299])).
% 0.71/0.84 tff(2634,plain,
% 0.71/0.84 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2633])).
% 0.71/0.84 tff(2635,plain,
% 0.71/0.84 (~(op(e0, e3) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[403, 2634])).
% 0.71/0.84 tff(2636,plain,
% 0.71/0.84 (((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))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2637,plain,
% 0.71/0.84 ((((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))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2638,plain,
% 0.71/0.84 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2))),
% 0.71/0.84 inference(rewrite,[status(thm)],[])).
% 0.71/0.84 tff(2639,plain,
% 0.71/0.84 (((((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))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2638])).
% 0.71/0.84 tff(2640,plain,
% 0.71/0.84 (((((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))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2639, 2637])).
% 0.71/0.84 tff(2641,plain,
% 0.71/0.84 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)),
% 0.71/0.84 inference(and_elim,[status(thm)],[875])).
% 0.71/0.84 tff(2642,plain,
% 0.71/0.84 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2641, 2640])).
% 0.71/0.84 tff(2643,plain,
% 0.71/0.84 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2642, 2636])).
% 0.71/0.84 tff(2644,plain,
% 0.71/0.84 (op(e0, e3) = e2),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[2643, 2635, 2631, 2524])).
% 0.71/0.84 tff(2645,plain,
% 0.71/0.84 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2644])).
% 0.71/0.84 tff(2646,plain,
% 0.71/0.84 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2645, 1745])).
% 0.71/0.84 tff(2647,plain,
% 0.71/0.84 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2646])).
% 0.71/0.84 tff(2648,plain,
% 0.71/0.84 (~(op(e1, e3) = e2)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1762, 2647])).
% 0.71/0.84 tff(2649,plain,
% 0.71/0.84 (op(e1, e3) = e1),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[2389, 2648, 2627, 2624])).
% 0.71/0.84 tff(2650,plain,
% 0.71/0.84 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2649])).
% 0.71/0.84 tff(2651,plain,
% 0.71/0.84 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2650])).
% 0.71/0.84 tff(2652,plain,
% 0.71/0.84 (~(op(e1, e1) = e1)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2034, 2651])).
% 0.71/0.84 tff(2653,plain,
% 0.71/0.84 (op(e1, e1) = e3),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[435, 2652, 2528, 2598])).
% 0.71/0.84 tff(2654,plain,
% 0.71/0.84 (op(op(e1, e1), op(e1, e1)) = op(e3, e3)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2653, 2653])).
% 0.71/0.84 tff(2655,plain,
% 0.71/0.84 (op(e3, e3) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.84 inference(symmetry,[status(thm)],[2654])).
% 0.71/0.84 tff(2656,plain,
% 0.71/0.84 (e3 = op(e3, e3)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2517])).
% 0.71/0.84 tff(2657,plain,
% 0.71/0.84 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2656, 2655])).
% 0.71/0.84 tff(2658,plain,
% 0.71/0.84 (op(e1, e3) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2657])).
% 0.71/0.84 tff(2659,plain,
% 0.71/0.84 (e1 = op(e1, e3)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2649])).
% 0.71/0.84 tff(2660,plain,
% 0.71/0.84 (e1 = e3),
% 0.71/0.84 inference(transitivity,[status(thm)],[2659, 2658, 2521])).
% 0.71/0.84 tff(2661,plain,
% 0.71/0.84 ($false),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[521, 2660])).
% 0.71/0.84 tff(2662,plain,((op(e0, e0) = e3) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (op(e3, e3) = e1) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, e2) = e3) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.84 tff(2663,plain,
% 0.71/0.84 (op(e0, e0) = e3),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[2662, 26, 695, 1064, 2496, 1055, 1053, 1065, 1063])).
% 0.71/0.84 tff(2664,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2663])).
% 0.71/0.84 tff(2665,plain,
% 0.71/0.84 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.71/0.84 inference(transitivity,[status(thm)],[2664, 2236])).
% 0.71/0.84 tff(2666,plain,
% 0.71/0.84 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2665])).
% 0.71/0.84 tff(2667,plain,
% 0.71/0.84 (~(op(e0, e2) = e3)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[1463, 2666])).
% 0.71/0.84 tff(2668,plain,
% 0.71/0.84 (op(e1, e2) = e3),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[684, 2667, 2520, 26])).
% 0.71/0.84 tff(2669,plain,
% 0.71/0.84 (op(e1, e2) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2668, 2496])).
% 0.71/0.84 tff(2670,plain,
% 0.71/0.84 ((op(e1, e2) = e0) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2669])).
% 0.71/0.84 tff(2671,plain,
% 0.71/0.84 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.84 inference(transitivity,[status(thm)],[2670, 2340])).
% 0.71/0.84 tff(2672,plain,
% 0.71/0.84 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 0.71/0.84 inference(symmetry,[status(thm)],[2671])).
% 0.71/0.84 tff(2673,plain,
% 0.71/0.84 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2672])).
% 0.71/0.84 tff(2674,plain,
% 0.71/0.84 (~(op(e1, e2) = e0)),
% 0.71/0.84 inference(modus_ponens,[status(thm)],[2557, 2673])).
% 0.71/0.84 tff(2675,plain,
% 0.71/0.84 (op(e0, e3) = e0),
% 0.71/0.84 inference(unit_resolution,[status(thm)],[1280, 2663])).
% 0.71/0.84 tff(2676,plain,
% 0.71/0.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 0.71/0.84 inference(monotonicity,[status(thm)],[2675])).
% 0.71/0.84 tff(2677,plain,
% 0.71/0.84 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2676])).
% 0.71/0.85 tff(2678,plain,
% 0.71/0.85 (~(op(e0, e2) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[702, 2677])).
% 0.71/0.85 tff(2679,plain,
% 0.71/0.85 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2675])).
% 0.71/0.85 tff(2680,plain,
% 0.71/0.85 ((op(e3, op(e0, e3)) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2679, 2675])).
% 0.71/0.85 tff(2681,plain,
% 0.71/0.85 ((~(op(e3, op(e0, e3)) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2680])).
% 0.71/0.85 tff(2682,plain,
% 0.71/0.85 (~(op(e3, e0) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1065, 2681])).
% 0.71/0.85 tff(2683,plain,
% 0.71/0.85 ((op(e1, e2) = e2) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2669])).
% 0.71/0.85 tff(2684,plain,
% 0.71/0.85 ((op(e1, e2) = e2) <=> (e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2683, 2551])).
% 0.71/0.85 tff(2685,plain,
% 0.71/0.85 ((e2 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e2) = e2)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2684])).
% 0.71/0.85 tff(2686,plain,
% 0.71/0.85 ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2685])).
% 0.71/0.85 tff(2687,plain,
% 0.71/0.85 (~(op(e1, e2) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2567, 2686])).
% 0.71/0.85 tff(2688,plain,
% 0.71/0.85 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2668])).
% 0.71/0.85 tff(2689,plain,
% 0.71/0.85 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2688, 601])).
% 0.71/0.85 tff(2690,plain,
% 0.71/0.85 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2689])).
% 0.71/0.85 tff(2691,plain,
% 0.71/0.85 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2690])).
% 0.71/0.85 tff(2692,plain,
% 0.71/0.85 (~(op(e1, e2) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[521, 2691])).
% 0.71/0.85 tff(2693,plain,
% 0.71/0.85 (~(op(e1, e1) = e2)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[514, 2692])).
% 0.71/0.85 tff(2694,plain,
% 0.71/0.85 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2517])).
% 0.71/0.85 tff(2695,plain,
% 0.71/0.85 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2694])).
% 0.71/0.85 tff(2696,plain,
% 0.71/0.85 (~(op(e2, e3) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[196, 2695])).
% 0.71/0.85 tff(2697,plain,
% 0.71/0.85 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2663])).
% 0.71/0.85 tff(2698,plain,
% 0.71/0.85 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2697, 1586])).
% 0.71/0.85 tff(2699,plain,
% 0.71/0.85 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2698])).
% 0.71/0.85 tff(2700,plain,
% 0.71/0.85 (~(op(e2, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[162, 2699])).
% 0.71/0.85 tff(2701,plain,
% 0.71/0.85 (op(e2, e1) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[189, 2700, 26, 2696])).
% 0.71/0.85 tff(2702,plain,
% 0.71/0.85 (op(e2, e1) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2701, 2496])).
% 0.71/0.85 tff(2703,plain,
% 0.71/0.85 ((op(e2, e1) = e0) <=> (op(e1, op(op(e1, e1), op(e1, e1))) = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2702])).
% 0.71/0.85 tff(2704,plain,
% 0.71/0.85 ((op(e2, e1) = e0) <=> (e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2703, 2340])).
% 0.71/0.85 tff(2705,plain,
% 0.71/0.85 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e2, e1) = e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2704])).
% 0.71/0.85 tff(2706,plain,
% 0.71/0.85 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e2, e1) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2705])).
% 0.71/0.85 tff(2707,plain,
% 0.71/0.85 (~(op(e2, e1) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2557, 2706])).
% 0.71/0.85 tff(2708,assumption,(op(e3, e0) = e1), introduced(assumption)).
% 0.71/0.85 tff(2709,plain,
% 0.71/0.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2708])).
% 0.71/0.85 tff(2710,plain,
% 0.71/0.85 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2709])).
% 0.71/0.85 tff(2711,plain,
% 0.71/0.85 (~(op(e2, e0) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[589, 2710])).
% 0.71/0.85 tff(2712,plain,
% 0.71/0.85 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2708])).
% 0.71/0.85 tff(2713,plain,
% 0.71/0.85 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2712])).
% 0.71/0.85 tff(2714,plain,
% 0.71/0.85 (~(op(e1, e0) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[564, 2713])).
% 0.71/0.85 tff(2715,plain,
% 0.71/0.85 (~(op(e1, e1) = e0)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2026, 2714])).
% 0.71/0.85 tff(2716,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2304, 2715, 2711, 26, 861, 2237, 1179])).
% 0.71/0.85 tff(2717,plain,((~(op(e3, e0) = e1)) | (op(e2, e2) = e3) | (op(e3, e2) = e3) | (~(op(e0, e0) = e3)) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2718,plain,
% 0.71/0.85 (~(op(e3, e0) = e1)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2717, 26, 2520, 2663, 2696])).
% 0.71/0.85 tff(2719,assumption,(~(op(e2, e1) = e0)), introduced(assumption)).
% 0.71/0.85 tff(2720,plain,
% 0.71/0.85 (op(e3, e1) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[772, 1067, 663, 695])).
% 0.71/0.85 tff(2721,plain,
% 0.71/0.85 ((op(e3, e1) = e0) <=> (e1 = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2720])).
% 0.71/0.85 tff(2722,plain,
% 0.71/0.85 ((op(e3, e1) = e0) <=> (e0 = e1)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2721, 1203])).
% 0.71/0.85 tff(2723,plain,
% 0.71/0.85 ((e0 = e1) <=> (op(e3, e1) = e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2722])).
% 0.71/0.85 tff(2724,plain,
% 0.71/0.85 ((~(e0 = e1)) <=> (~(op(e3, e1) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2723])).
% 0.71/0.85 tff(2725,plain,
% 0.71/0.85 (~(op(e3, e1) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[40, 2724])).
% 0.71/0.85 tff(2726,plain,
% 0.71/0.85 (op(e1, e1) = e0),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1241, 2725, 2254, 2719])).
% 0.71/0.85 tff(2727,plain,
% 0.71/0.85 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2726, 2726])).
% 0.71/0.85 tff(2728,plain,
% 0.71/0.85 (op(e0, e0) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2727])).
% 0.71/0.85 tff(2729,plain,
% 0.71/0.85 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2273, 2728])).
% 0.71/0.85 tff(2730,plain,
% 0.71/0.85 (op(e1, e3) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2729])).
% 0.71/0.85 tff(2731,assumption,(~(op(e1, e2) = e2)), introduced(assumption)).
% 0.71/0.85 tff(2732,plain,
% 0.71/0.85 (op(e3, e0) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1333, 1067, 2097, 1588])).
% 0.71/0.85 tff(2733,plain,
% 0.71/0.85 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2732])).
% 0.71/0.85 tff(2734,plain,
% 0.71/0.85 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2733])).
% 0.71/0.85 tff(2735,plain,
% 0.71/0.85 (~(op(e1, e0) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[564, 2734])).
% 0.71/0.85 tff(2736,plain,
% 0.71/0.85 (op(e1, e3) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[751, 2735, 379, 2731])).
% 0.71/0.85 tff(2737,plain,
% 0.71/0.85 (e2 = op(e1, e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2736])).
% 0.71/0.85 tff(2738,plain,
% 0.71/0.85 (e2 = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2737, 2730])).
% 0.71/0.85 tff(2739,assumption,(~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))), introduced(assumption)).
% 0.71/0.85 tff(2740,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2739, 2738])).
% 0.71/0.85 tff(2741,plain,((op(e3, e0) = e1) | (e2 = op(e1, op(op(e1, e1), op(e1, e1)))) | (~(op(e0, e0) = e3)) | (op(e2, e1) = e0) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e3, e2) = e1) | (op(e3, e3) = e1) | (op(e3, e0) = e0) | (op(e3, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2742,plain,
% 0.71/0.85 (op(e3, e2) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2741, 2718, 2663, 2707, 2693, 2687, 2567, 695, 2682, 2527])).
% 0.71/0.85 tff(2743,plain,
% 0.71/0.85 ((op(e3, e2) = e0) <=> (e1 = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2742])).
% 0.71/0.85 tff(2744,plain,
% 0.71/0.85 ((op(e3, e2) = e0) <=> (e0 = e1)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2743, 1203])).
% 0.71/0.85 tff(2745,plain,
% 0.71/0.85 ((e0 = e1) <=> (op(e3, e2) = e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2744])).
% 0.71/0.85 tff(2746,plain,
% 0.71/0.85 ((~(e0 = e1)) <=> (~(op(e3, e2) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2745])).
% 0.71/0.85 tff(2747,plain,
% 0.71/0.85 (~(op(e3, e2) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[40, 2746])).
% 0.71/0.85 tff(2748,plain,
% 0.71/0.85 (op(e3, e0) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1333, 2718, 2682, 2527])).
% 0.71/0.85 tff(2749,plain,
% 0.71/0.85 (e2 = op(e3, e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2748])).
% 0.71/0.85 tff(2750,plain,
% 0.71/0.85 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2749])).
% 0.71/0.85 tff(2751,plain,
% 0.71/0.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2750])).
% 0.71/0.85 tff(2752,plain,
% 0.71/0.85 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2751])).
% 0.71/0.85 tff(2753,plain,
% 0.71/0.85 (~(op(e2, e0) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[589, 2752])).
% 0.71/0.85 tff(2754,plain,
% 0.71/0.85 (~(op(e2, e2) = e0)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[230, 2753])).
% 0.71/0.85 tff(2755,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1678, 2754, 2747, 2678, 2674])).
% 0.71/0.85 tff(2756,plain,((op(e2, e2) = e3) | (op(e3, e3) = e1) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2757,plain,
% 0.71/0.85 (op(e2, e2) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2756, 695, 2494, 1065, 1064, 1055, 1053, 1063])).
% 0.71/0.85 tff(2758,plain,
% 0.71/0.85 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2757, 2757])).
% 0.71/0.85 tff(2759,plain,
% 0.71/0.85 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (e0 = op(e3, e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2758])).
% 0.71/0.85 tff(2760,plain,
% 0.71/0.85 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e0)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2759, 2])).
% 0.71/0.85 tff(2761,plain,
% 0.71/0.85 ((~(e0 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2760])).
% 0.71/0.85 tff(2762,plain,
% 0.71/0.85 (~(op(e3, e3) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1054, 2761])).
% 0.71/0.85 tff(2763,plain,
% 0.71/0.85 (op(e2, e3) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1004, 2757])).
% 0.71/0.85 tff(2764,plain,
% 0.71/0.85 ((op(e2, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2763])).
% 0.71/0.85 tff(2765,plain,
% 0.71/0.85 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2764, 359])).
% 0.71/0.85 tff(2766,plain,
% 0.71/0.85 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2765])).
% 0.71/0.85 tff(2767,plain,
% 0.71/0.85 (~(op(e3, e3) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[196, 2766])).
% 0.71/0.85 tff(2768,plain,
% 0.71/0.85 (op(e3, e3) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1123, 2767, 695, 2762])).
% 0.71/0.85 tff(2769,plain,
% 0.71/0.85 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2768])).
% 0.71/0.85 tff(2770,plain,
% 0.71/0.85 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2769])).
% 0.71/0.85 tff(2771,plain,
% 0.71/0.85 (~(op(e1, e3) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[539, 2770])).
% 0.71/0.85 tff(2772,plain,
% 0.71/0.85 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2757])).
% 0.71/0.85 tff(2773,plain,
% 0.71/0.85 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2772])).
% 0.71/0.85 tff(2774,plain,
% 0.71/0.85 (~(op(e1, e2) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[243, 2773])).
% 0.71/0.85 tff(2775,plain,
% 0.71/0.85 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2768])).
% 0.71/0.85 tff(2776,plain,
% 0.71/0.85 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2775])).
% 0.71/0.85 tff(2777,plain,
% 0.71/0.85 (~(op(e0, e3) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1578, 2776])).
% 0.71/0.85 tff(2778,plain,
% 0.71/0.85 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2768])).
% 0.71/0.85 tff(2779,plain,
% 0.71/0.85 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2778])).
% 0.71/0.85 tff(2780,plain,
% 0.71/0.85 (~(op(e3, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1424, 2779])).
% 0.71/0.85 tff(2781,plain,
% 0.71/0.85 (op(e1, e3) = e3),
% 0.71/0.85 inference(transitivity,[status(thm)],[2345, 2521])).
% 0.71/0.85 tff(2782,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[933, 2781])).
% 0.71/0.85 tff(2783,plain,((~(op(e1, e1) = e2)) | (op(e1, e3) = e3) | (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))) | (~(op(e2, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2784,plain,
% 0.71/0.85 (~(op(e1, e1) = e2)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2783, 2771, 2494, 2757])).
% 0.71/0.85 tff(2785,plain,
% 0.71/0.85 (op(e0, e0) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2038, 2784, 2757, 695, 1055, 2780, 2777])).
% 0.71/0.85 tff(2786,plain,
% 0.71/0.85 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2785])).
% 0.71/0.85 tff(2787,plain,
% 0.71/0.85 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2786, 256])).
% 0.71/0.85 tff(2788,plain,
% 0.71/0.85 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2787])).
% 0.71/0.85 tff(2789,plain,
% 0.71/0.85 (~(op(e1, e0) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[254, 2788])).
% 0.71/0.85 tff(2790,plain,
% 0.71/0.85 (op(e1, e1) = e3),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[530, 2789, 2774, 2771])).
% 0.71/0.85 tff(2791,plain,
% 0.71/0.85 (op(op(e1, e1), op(e1, e1)) = op(e3, e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2790, 2790])).
% 0.71/0.85 tff(2792,plain,
% 0.71/0.85 (op(e3, e3) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2791])).
% 0.71/0.85 tff(2793,plain,
% 0.71/0.85 (e3 = op(e3, e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2768])).
% 0.71/0.85 tff(2794,plain,
% 0.71/0.85 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2793, 2792])).
% 0.71/0.85 tff(2795,plain,
% 0.71/0.85 (op(e1, e3) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2794])).
% 0.71/0.85 tff(2796,plain,
% 0.71/0.85 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2763])).
% 0.71/0.85 tff(2797,plain,
% 0.71/0.85 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2796, 1034])).
% 0.71/0.85 tff(2798,plain,
% 0.71/0.85 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2797])).
% 0.71/0.85 tff(2799,plain,
% 0.71/0.85 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2798])).
% 0.71/0.85 tff(2800,plain,
% 0.71/0.85 (~(op(e2, e3) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[353, 2799])).
% 0.71/0.85 tff(2801,plain,
% 0.71/0.85 (op(e0, e3) = e0),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1280, 2785])).
% 0.71/0.85 tff(2802,plain,
% 0.71/0.85 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2801])).
% 0.71/0.85 tff(2803,plain,
% 0.71/0.85 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2802])).
% 0.71/0.85 tff(2804,plain,
% 0.71/0.85 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2803])).
% 0.71/0.85 tff(2805,plain,
% 0.71/0.85 (~(op(e0, e3) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[40, 2804])).
% 0.71/0.85 tff(2806,plain,
% 0.71/0.85 (op(e1, e3) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[711, 2805, 2800, 695])).
% 0.71/0.85 tff(2807,plain,
% 0.71/0.85 (e1 = op(e1, e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2806])).
% 0.71/0.85 tff(2808,plain,
% 0.71/0.85 (e1 = e3),
% 0.71/0.85 inference(transitivity,[status(thm)],[2807, 2795, 2495])).
% 0.71/0.85 tff(2809,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[521, 2808])).
% 0.71/0.85 tff(2810,plain,((op(e3, e3) = e1) | (op(e0, e0) = e0) | (e0 = op(op(e2, e2), op(e2, e2))) | (op(e3, op(e0, e3)) = op(e0, e3)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e2, op(e0, e2)) = op(e0, e2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2811,plain,
% 0.71/0.85 (op(e3, e3) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2810, 1062, 1054, 1055, 1060, 1053, 1058])).
% 0.71/0.85 tff(2812,plain,
% 0.71/0.85 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2811])).
% 0.71/0.85 tff(2813,plain,
% 0.71/0.85 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2812])).
% 0.71/0.85 tff(2814,plain,
% 0.71/0.85 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2813])).
% 0.71/0.85 tff(2815,plain,
% 0.71/0.85 (~(op(e3, e3) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[521, 2814])).
% 0.71/0.85 tff(2816,plain,
% 0.71/0.85 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2811])).
% 0.71/0.85 tff(2817,plain,
% 0.71/0.85 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2816])).
% 0.71/0.85 tff(2818,plain,
% 0.71/0.85 (~(op(e3, e0) = e1)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1424, 2817])).
% 0.71/0.85 tff(2819,plain,
% 0.71/0.85 (e1 = op(e3, e3)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2811])).
% 0.71/0.85 tff(2820,plain,
% 0.71/0.85 ((e0 = e1) <=> (e0 = op(e3, e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2819])).
% 0.71/0.85 tff(2821,plain,
% 0.71/0.85 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2820, 2])).
% 0.71/0.85 tff(2822,plain,
% 0.71/0.85 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2821])).
% 0.71/0.85 tff(2823,plain,
% 0.71/0.85 (~(op(e3, e3) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[40, 2822])).
% 0.71/0.85 tff(2824,plain,
% 0.71/0.85 (~(op(e2, e2) = e3)),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1959, 2815, 1055, 2823, 2818, 1053])).
% 0.71/0.85 tff(2825,plain,
% 0.71/0.85 ($false),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1569, 2824, 2818, 1053, 1055, 1062, 1060, 1058, 2815])).
% 0.71/0.85 tff(2826,plain,(((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e0, e0) = e0) | (e0 = op(op(e2, e2), op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.85 tff(2827,plain,
% 0.71/0.85 ((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2826, 1055, 1053, 1054])).
% 0.71/0.85 tff(2828,plain,
% 0.71/0.85 (op(e0, e0) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1105, 1097, 1055, 1590])).
% 0.71/0.85 tff(2829,plain,
% 0.71/0.85 (op(e0, e1) = e0),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1109, 2828])).
% 0.71/0.85 tff(2830,plain,
% 0.71/0.85 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2829])).
% 0.71/0.85 tff(2831,plain,
% 0.71/0.85 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2830])).
% 0.71/0.85 tff(2832,plain,
% 0.71/0.85 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2831])).
% 0.71/0.85 tff(2833,plain,
% 0.71/0.85 (~(op(e0, e1) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[16, 2832])).
% 0.71/0.85 tff(2834,plain,
% 0.71/0.85 ((op(e3, op(op(e3, e3), op(e3, e3))) = e2) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.71/0.85 inference(commutativity,[status(thm)],[])).
% 0.71/0.85 tff(2835,plain,
% 0.71/0.85 (op(op(e3, e3), op(e3, e3)) = e1),
% 0.71/0.85 inference(transitivity,[status(thm)],[1093, 2828])).
% 0.71/0.85 tff(2836,plain,
% 0.71/0.85 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2835])).
% 0.71/0.85 tff(2837,plain,
% 0.71/0.85 (op(e3, e1) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2836])).
% 0.71/0.85 tff(2838,plain,
% 0.71/0.85 ((op(e3, e1) = e2) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e2)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2837])).
% 0.71/0.85 tff(2839,plain,
% 0.71/0.85 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2838, 2834])).
% 0.71/0.85 tff(2840,plain,
% 0.71/0.85 ((e2 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e3, e1) = e2)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2839])).
% 0.71/0.85 tff(2841,plain,
% 0.71/0.85 ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e3, e1) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2840])).
% 0.71/0.85 tff(2842,plain,
% 0.71/0.85 (e0 = op(e3, e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1074, 1070])).
% 0.71/0.85 tff(2843,plain,
% 0.71/0.85 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (e1 = op(e0, e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[1093])).
% 0.71/0.85 tff(2844,plain,
% 0.71/0.85 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e0, e0) = e1)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2843, 1068])).
% 0.71/0.85 tff(2845,plain,
% 0.71/0.85 ((op(e0, e0) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.71/0.85 inference(symmetry,[status(thm)],[2844])).
% 0.71/0.85 tff(2846,plain,
% 0.71/0.85 (e1 = op(op(e3, e3), op(e3, e3))),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2828, 2845])).
% 0.71/0.85 tff(2847,plain,
% 0.71/0.85 (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[1567, 2846, 2842])).
% 0.71/0.85 tff(2848,plain,
% 0.71/0.85 (~(op(e3, e1) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2847, 2841])).
% 0.71/0.85 tff(2849,plain,
% 0.71/0.85 (op(e2, e1) = e2),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[396, 2848, 2833, 379])).
% 0.71/0.85 tff(2850,plain,
% 0.71/0.85 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2849])).
% 0.71/0.85 tff(2851,plain,
% 0.71/0.85 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2850, 1137])).
% 0.71/0.85 tff(2852,plain,
% 0.71/0.85 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2851])).
% 0.71/0.85 tff(2853,plain,
% 0.71/0.85 (~(op(e2, e2) = e2)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1936, 2852])).
% 0.71/0.85 tff(2854,plain,
% 0.71/0.85 ((op(op(e0, e0), op(e0, e0)) = e1) <=> (e1 = op(op(e0, e0), op(e0, e0)))),
% 0.71/0.85 inference(commutativity,[status(thm)],[])).
% 0.71/0.85 tff(2855,plain,
% 0.71/0.85 (e1 = op(e0, e0)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2828])).
% 0.71/0.85 tff(2856,plain,
% 0.71/0.85 (op(e1, e1) = op(op(e0, e0), op(e0, e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2855, 2855])).
% 0.71/0.85 tff(2857,plain,
% 0.71/0.85 ((op(e1, e1) = e1) <=> (op(op(e0, e0), op(e0, e0)) = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2856])).
% 0.71/0.85 tff(2858,plain,
% 0.71/0.85 ((op(e1, e1) = e1) <=> (e1 = op(op(e0, e0), op(e0, e0)))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2857, 2854])).
% 0.71/0.85 tff(2859,plain,
% 0.71/0.85 ((e1 = op(op(e0, e0), op(e0, e0))) <=> (op(e1, e1) = e1)),
% 0.71/0.85 inference(symmetry,[status(thm)],[2858])).
% 0.71/0.85 tff(2860,plain,
% 0.71/0.85 ((e3 = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.71/0.85 inference(commutativity,[status(thm)],[])).
% 0.71/0.85 tff(2861,plain,
% 0.71/0.85 ((op(e3, e0) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[1075])).
% 0.71/0.85 tff(2862,plain,
% 0.71/0.85 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.71/0.85 inference(transitivity,[status(thm)],[2861, 2860])).
% 0.71/0.85 tff(2863,plain,
% 0.71/0.85 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2862])).
% 0.71/0.85 tff(2864,plain,
% 0.71/0.85 (~(op(e3, e1) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1320, 2863])).
% 0.71/0.85 tff(2865,plain,
% 0.71/0.85 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[1074])).
% 0.71/0.85 tff(2866,plain,
% 0.71/0.85 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2865])).
% 0.71/0.85 tff(2867,plain,
% 0.71/0.85 (~(op(e3, e1) = e0)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[1780, 2866])).
% 0.71/0.85 tff(2868,plain,
% 0.71/0.85 (((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))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2869,plain,
% 0.71/0.85 ((((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))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2870,plain,
% 0.71/0.85 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2))),
% 0.71/0.85 inference(rewrite,[status(thm)],[])).
% 0.71/0.85 tff(2871,plain,
% 0.71/0.85 (((((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))),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2870])).
% 0.71/0.85 tff(2872,plain,
% 0.71/0.85 (((((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))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2871, 2869])).
% 0.71/0.85 tff(2873,plain,
% 0.71/0.85 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)),
% 0.71/0.85 inference(and_elim,[status(thm)],[113])).
% 0.71/0.85 tff(2874,plain,
% 0.71/0.85 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 0.71/0.85 tff(2875,plain,
% 0.71/0.85 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.71/0.85 inference(modus_ponens,[status(thm)],[2874, 2868])).
% 0.71/0.85 tff(2876,plain,
% 0.71/0.85 (op(e3, e1) = e1),
% 0.71/0.85 inference(unit_resolution,[status(thm)],[2875, 2848, 2867, 2864])).
% 0.71/0.85 tff(2877,plain,
% 0.71/0.85 ((op(e1, e1) = op(e3, e1)) <=> (op(op(e0, e0), op(e0, e0)) = e1)),
% 0.71/0.85 inference(monotonicity,[status(thm)],[2856, 2876])).
% 0.71/0.85 tff(2878,plain,
% 0.71/0.85 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(op(e0, e0), op(e0, e0)))),
% 0.71/0.85 inference(transitivity,[status(thm)],[2877, 2854])).
% 0.71/0.86 tff(2879,plain,
% 0.71/0.86 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2878, 2859])).
% 0.71/0.86 tff(2880,plain,
% 0.71/0.86 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2879])).
% 0.71/0.86 tff(2881,plain,
% 0.71/0.86 (~(op(e1, e1) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[338, 2880])).
% 0.71/0.86 tff(2882,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[215, 2881, 2853, 1055, 693])).
% 0.71/0.86 tff(2883,plain,((~(op(e3, e3) = e0)) | (op(e0, e0) = e0) | (op(e3, e3) = e3) | (op(e1, e1) = e2) | (op(e0, e0) = e3) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2884,plain,
% 0.71/0.86 (~(op(e3, e3) = e0)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2883, 693, 1055, 379, 1590, 1053])).
% 0.71/0.86 tff(2885,plain,
% 0.71/0.86 (op(e3, e0) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1146, 2884, 695, 693, 1053, 1055])).
% 0.71/0.86 tff(2886,plain,
% 0.71/0.86 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2885])).
% 0.71/0.86 tff(2887,plain,
% 0.71/0.86 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2886])).
% 0.71/0.86 tff(2888,plain,
% 0.71/0.86 (~(op(e0, e0) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[270, 2887])).
% 0.71/0.86 tff(2889,plain,
% 0.71/0.86 ((op(e3, e0) = e0) <=> (e1 = e0)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2885])).
% 0.71/0.86 tff(2890,plain,
% 0.71/0.86 ((op(e3, e0) = e0) <=> (e0 = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2889, 1203])).
% 0.71/0.86 tff(2891,plain,
% 0.71/0.86 ((e0 = e1) <=> (op(e3, e0) = e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2890])).
% 0.71/0.86 tff(2892,plain,
% 0.71/0.86 ((~(e0 = e1)) <=> (~(op(e3, e0) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2891])).
% 0.71/0.86 tff(2893,plain,
% 0.71/0.86 (~(op(e3, e0) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[40, 2892])).
% 0.71/0.86 tff(2894,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2885])).
% 0.71/0.86 tff(2895,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2894, 2081])).
% 0.71/0.86 tff(2896,plain,
% 0.71/0.86 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2895])).
% 0.71/0.86 tff(2897,plain,
% 0.71/0.86 (~(op(e3, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[572, 2896])).
% 0.71/0.86 tff(2898,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2188, 2897, 2893, 1055, 2884, 693, 2888, 1053, 695])).
% 0.71/0.86 tff(2899,plain,((op(e3, e3) = e3) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1) | (op(e1, e1) = e2) | (op(e0, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2900,plain,
% 0.71/0.86 (op(e3, e3) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2899, 379, 1053, 695, 1055, 1590])).
% 0.71/0.86 tff(2901,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.86 tff(2902,plain,
% 0.71/0.86 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2901])).
% 0.71/0.86 tff(2903,plain,
% 0.71/0.86 (~(op(e3, e0) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1424, 2902])).
% 0.71/0.86 tff(2904,plain,
% 0.71/0.86 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.86 tff(2905,plain,
% 0.71/0.86 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2904])).
% 0.71/0.86 tff(2906,plain,
% 0.71/0.86 (~(op(e0, e3) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1578, 2905])).
% 0.71/0.86 tff(2907,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.86 tff(2908,plain,
% 0.71/0.86 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2907])).
% 0.71/0.86 tff(2909,plain,
% 0.71/0.86 (~(op(e3, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1160, 2908])).
% 0.71/0.86 tff(2910,plain,
% 0.71/0.86 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.86 tff(2911,plain,
% 0.71/0.86 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2910])).
% 0.71/0.86 tff(2912,plain,
% 0.71/0.86 (~(op(e1, e3) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[539, 2911])).
% 0.71/0.86 tff(2913,plain,
% 0.71/0.86 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2900])).
% 0.71/0.86 tff(2914,plain,
% 0.71/0.86 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2913])).
% 0.71/0.86 tff(2915,plain,
% 0.71/0.86 (~(op(e3, e1) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1780, 2914])).
% 0.71/0.86 tff(2916,plain,
% 0.71/0.86 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1791])).
% 0.71/0.86 tff(2917,plain,
% 0.71/0.86 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2916, 299])).
% 0.71/0.86 tff(2918,plain,
% 0.71/0.86 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2917])).
% 0.71/0.86 tff(2919,plain,
% 0.71/0.86 (~(op(e0, e3) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[403, 2918])).
% 0.71/0.86 tff(2920,plain,
% 0.71/0.86 (op(e0, e3) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2643, 2919, 1587, 1812])).
% 0.71/0.86 tff(2921,plain,
% 0.71/0.86 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2920])).
% 0.71/0.86 tff(2922,plain,
% 0.71/0.86 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2921, 1745])).
% 0.71/0.86 tff(2923,plain,
% 0.71/0.86 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2922])).
% 0.71/0.86 tff(2924,plain,
% 0.71/0.86 (~(op(e1, e3) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1762, 2923])).
% 0.71/0.86 tff(2925,plain,
% 0.71/0.86 ((op(e0, e1) = e3) <=> (e0 = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1791])).
% 0.71/0.86 tff(2926,plain,
% 0.71/0.86 ((e0 = e3) <=> (op(e0, e1) = e3)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2925])).
% 0.71/0.86 tff(2927,plain,
% 0.71/0.86 ((~(e0 = e3)) <=> (~(op(e0, e1) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2926])).
% 0.71/0.86 tff(2928,plain,
% 0.71/0.86 (~(op(e0, e1) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[509, 2927])).
% 0.71/0.86 tff(2929,plain,
% 0.71/0.86 (op(e0, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1090, 2928, 1590, 1587])).
% 0.71/0.86 tff(2930,plain,
% 0.71/0.86 ((op(e0, e2) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2929])).
% 0.71/0.86 tff(2931,plain,
% 0.71/0.86 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2930, 1734])).
% 0.71/0.86 tff(2932,plain,
% 0.71/0.86 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2931])).
% 0.71/0.86 tff(2933,plain,
% 0.71/0.86 (~(op(e1, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1740, 2932])).
% 0.71/0.86 tff(2934,plain,
% 0.71/0.86 (e1 = op(e0, e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1790, 1069])).
% 0.71/0.86 tff(2935,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1790, 1790])).
% 0.71/0.86 tff(2936,plain,
% 0.71/0.86 ((e3 = op(op(e0, e0), op(e0, e0))) <=> (e3 = op(e1, e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2935])).
% 0.71/0.86 tff(2937,plain,
% 0.71/0.86 ((e3 = op(op(e0, e0), op(e0, e0))) <=> (op(e1, e1) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2936, 1729])).
% 0.71/0.86 tff(2938,plain,
% 0.71/0.86 ((op(e1, e1) = e3) <=> (e3 = op(op(e0, e0), op(e0, e0)))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2937])).
% 0.71/0.86 tff(2939,assumption,(op(e1, e1) = e3), introduced(assumption)).
% 0.71/0.86 tff(2940,plain,
% 0.71/0.86 (e3 = op(op(e0, e0), op(e0, e0))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[2939, 2938])).
% 0.71/0.86 tff(2941,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = e3),
% 0.71/0.86 inference(transitivity,[status(thm)],[2935, 2939])).
% 0.71/0.86 tff(2942,plain,
% 0.71/0.86 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2941])).
% 0.71/0.86 tff(2943,plain,
% 0.71/0.86 (op(e0, e3) = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2942])).
% 0.71/0.86 tff(2944,assumption,(op(e0, e3) = e2), introduced(assumption)).
% 0.71/0.86 tff(2945,plain,
% 0.71/0.86 (e2 = op(e0, e3)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2944])).
% 0.71/0.86 tff(2946,plain,
% 0.71/0.86 (e2 = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[2945, 2943])).
% 0.71/0.86 tff(2947,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1883, 2946, 2940, 2934])).
% 0.71/0.86 tff(2948,plain,((~(op(e1, e1) = e3)) | (~(op(e0, e3) = e2)) | (~(op(e0, e0) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2949,plain,
% 0.71/0.86 (~(op(e1, e1) = e3)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2948, 2920, 1790])).
% 0.71/0.86 tff(2950,plain,
% 0.71/0.86 (op(e1, e0) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[530, 2949, 2933, 933])).
% 0.71/0.86 tff(2951,plain,
% 0.71/0.86 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2950])).
% 0.71/0.86 tff(2952,plain,
% 0.71/0.86 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2951, 1178])).
% 0.71/0.86 tff(2953,plain,
% 0.71/0.86 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2952])).
% 0.71/0.86 tff(2954,plain,
% 0.71/0.86 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2953])).
% 0.71/0.86 tff(2955,plain,
% 0.71/0.86 (~(op(e1, e0) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[170, 2954])).
% 0.71/0.86 tff(2956,plain,
% 0.71/0.86 (op(e1, e2) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[751, 2955, 2924, 379])).
% 0.71/0.86 tff(2957,plain,
% 0.71/0.86 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1791])).
% 0.71/0.86 tff(2958,plain,
% 0.71/0.86 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2957, 2615])).
% 0.71/0.86 tff(2959,plain,
% 0.71/0.86 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2958])).
% 0.71/0.86 tff(2960,plain,
% 0.71/0.86 (~(op(e0, e2) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[867, 2959])).
% 0.71/0.86 tff(2961,plain,
% 0.71/0.86 ((op(e0, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1790])).
% 0.71/0.86 tff(2962,plain,
% 0.71/0.86 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2961, 2086])).
% 0.71/0.86 tff(2963,plain,
% 0.71/0.86 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2962])).
% 0.71/0.86 tff(2964,plain,
% 0.71/0.86 (~(op(e0, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1463, 2963])).
% 0.71/0.86 tff(2965,plain,
% 0.71/0.86 ((op(e1, e0) = e0) <=> (e3 = e0)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2950])).
% 0.71/0.86 tff(2966,plain,
% 0.71/0.86 ((op(e1, e0) = e0) <=> (e0 = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2965, 1])).
% 0.71/0.86 tff(2967,plain,
% 0.71/0.86 ((e0 = e3) <=> (op(e1, e0) = e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2966])).
% 0.71/0.86 tff(2968,plain,
% 0.71/0.86 ((~(e0 = e3)) <=> (~(op(e1, e0) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2967])).
% 0.71/0.86 tff(2969,plain,
% 0.71/0.86 (~(op(e1, e0) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[509, 2968])).
% 0.71/0.86 tff(2970,plain,
% 0.71/0.86 (op(e1, e2) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1856, 2969, 1790, 2964, 379, 1833, 2928, 695, 2960])).
% 0.71/0.86 tff(2971,plain,
% 0.71/0.86 (e0 = op(e1, e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2970])).
% 0.71/0.86 tff(2972,plain,
% 0.71/0.86 (e0 = e2),
% 0.71/0.86 inference(transitivity,[status(thm)],[2971, 2956])).
% 0.71/0.86 tff(2973,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[16, 2972])).
% 0.71/0.86 tff(2974,plain,((~(op(e0, e0) = e1)) | (op(e1, e1) = e2) | (op(e3, e1) = e3) | (op(e3, e3) = e1) | (op(e1, e3) = e3) | (op(e0, e3) = e3) | (op(e0, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2975,plain,
% 0.71/0.86 (~(op(e0, e0) = e1)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2974, 379, 2915, 695, 2912, 2906, 1590])).
% 0.71/0.86 tff(2976,plain,
% 0.71/0.86 (op(e3, e2) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2219, 2975, 1590, 2909, 1055, 2906, 695, 379, 2903])).
% 0.71/0.86 tff(2977,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2976])).
% 0.71/0.86 tff(2978,plain,
% 0.71/0.86 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e2))),
% 0.71/0.86 inference(symmetry,[status(thm)],[2977])).
% 0.71/0.86 tff(2979,plain,
% 0.71/0.86 (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2592, 421, 26, 379, 1590, 861, 1587, 1055, 1588, 695])).
% 0.71/0.86 tff(2980,plain,
% 0.71/0.86 (op(e1, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[684, 2414, 26, 861])).
% 0.71/0.86 tff(2981,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1636, 2980, 2414, 1067, 379, 1590, 1055, 1588, 1587, 2979])).
% 0.71/0.86 tff(2982,plain,((op(e0, e0) = e1) | (op(e3, e0) = e1) | (op(e1, e1) = e2) | (op(e0, e0) = e3) | (op(e0, e0) = e0) | (op(e3, e0) = e3) | (op(e0, e3) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2983,plain,
% 0.71/0.86 (op(e3, e0) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2982, 2975, 379, 1590, 1055, 2903, 2906, 26, 2909, 695])).
% 0.71/0.86 tff(2984,plain,
% 0.71/0.86 (op(e3, e0) = op(e3, e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[2983, 2978])).
% 0.71/0.86 tff(2985,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[572, 2984])).
% 0.71/0.86 tff(2986,plain,((op(e1, e1) = e2) | (op(e0, e0) = e3) | (op(e0, e0) = e0) | (op(e2, e2) = e3) | (op(e3, e3) = e1) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(2987,plain,
% 0.71/0.86 (op(e1, e1) = e2),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2986, 1590, 1055, 26, 695, 1053])).
% 0.71/0.86 tff(2988,plain,
% 0.71/0.86 (op(e1, e2) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[514, 2987])).
% 0.71/0.86 tff(2989,plain,
% 0.71/0.86 ((op(e1, e2) = e3) <=> (e1 = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2988])).
% 0.71/0.86 tff(2990,plain,
% 0.71/0.86 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2989])).
% 0.71/0.86 tff(2991,plain,
% 0.71/0.86 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2990])).
% 0.71/0.86 tff(2992,plain,
% 0.71/0.86 (~(op(e1, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[521, 2991])).
% 0.71/0.86 tff(2993,plain,
% 0.71/0.86 (op(e3, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[684, 2414, 26, 2992])).
% 0.71/0.86 tff(2994,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2993])).
% 0.71/0.86 tff(2995,plain,
% 0.71/0.86 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2994])).
% 0.71/0.86 tff(2996,plain,
% 0.71/0.86 (~(op(e3, e0) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[572, 2995])).
% 0.71/0.86 tff(2997,plain,
% 0.71/0.86 (~(op(e3, e3) = e0)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[558, 2996])).
% 0.71/0.86 tff(2998,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2993])).
% 0.71/0.86 tff(2999,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[2998, 164])).
% 0.71/0.86 tff(3000,plain,
% 0.71/0.86 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2999])).
% 0.71/0.86 tff(3001,plain,
% 0.71/0.86 (~(op(e3, e3) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1160, 3000])).
% 0.71/0.86 tff(3002,plain,
% 0.71/0.86 (op(e3, e0) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1146, 3001, 695, 2997, 1053, 1055])).
% 0.71/0.86 tff(3003,plain,
% 0.71/0.86 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[2988])).
% 0.71/0.86 tff(3004,plain,
% 0.71/0.86 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3003, 2081])).
% 0.71/0.86 tff(3005,plain,
% 0.71/0.86 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3004])).
% 0.71/0.86 tff(3006,plain,
% 0.71/0.86 (~(op(e3, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[742, 3005])).
% 0.71/0.86 tff(3007,plain,
% 0.71/0.86 (op(e3, e0) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2188, 3001, 1055, 2997, 3006, 421, 1053, 695])).
% 0.71/0.86 tff(3008,plain,
% 0.71/0.86 (e0 = op(e3, e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3007])).
% 0.71/0.86 tff(3009,plain,
% 0.71/0.86 (e0 = e1),
% 0.71/0.86 inference(transitivity,[status(thm)],[3008, 3002])).
% 0.71/0.86 tff(3010,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[40, 3009])).
% 0.71/0.86 tff(3011,plain,((op(e0, e0) = e1) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1) | (op(e2, e2) = e3) | (op(e0, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(3012,plain,
% 0.71/0.86 (op(e0, e0) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[3011, 1590, 1053, 695, 26, 1055])).
% 0.71/0.86 tff(3013,plain,
% 0.71/0.86 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3012])).
% 0.71/0.86 tff(3014,plain,
% 0.71/0.86 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3013, 2452])).
% 0.71/0.86 tff(3015,plain,
% 0.71/0.86 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3014])).
% 0.71/0.86 tff(3016,plain,
% 0.71/0.86 (~(op(e3, e0) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[270, 3015])).
% 0.71/0.86 tff(3017,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = op(e1, e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3012, 3012])).
% 0.71/0.86 tff(3018,plain,
% 0.71/0.86 (op(op(e0, e0), op(e0, e0)) = e2),
% 0.71/0.86 inference(transitivity,[status(thm)],[3017, 2987])).
% 0.71/0.86 tff(3019,plain,
% 0.71/0.86 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3018])).
% 0.71/0.86 tff(3020,plain,
% 0.71/0.86 ((e3 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e3 = op(e0, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3019])).
% 0.71/0.86 tff(3021,plain,
% 0.71/0.86 ((e3 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e2) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3020, 2236])).
% 0.71/0.86 tff(3022,plain,
% 0.71/0.86 ((~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3021])).
% 0.71/0.86 tff(3023,plain,
% 0.71/0.86 (e1 = op(e0, e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[3012, 1069])).
% 0.71/0.86 tff(3024,plain,
% 0.71/0.86 (op(e1, e1) = op(op(e0, e0), op(e0, e0))),
% 0.71/0.86 inference(symmetry,[status(thm)],[3017])).
% 0.71/0.86 tff(3025,plain,
% 0.71/0.86 (e2 = op(e1, e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[2987])).
% 0.71/0.86 tff(3026,plain,
% 0.71/0.86 (e2 = op(op(e0, e0), op(e0, e0))),
% 0.71/0.86 inference(transitivity,[status(thm)],[3025, 3024])).
% 0.71/0.86 tff(3027,plain,
% 0.71/0.86 (~(e3 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2449, 3026, 3023])).
% 0.71/0.86 tff(3028,plain,
% 0.71/0.86 (~(op(e0, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[3027, 3022])).
% 0.71/0.86 tff(3029,plain,
% 0.71/0.86 (op(e3, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[684, 3028, 26, 2992])).
% 0.71/0.86 tff(3030,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3029])).
% 0.71/0.86 tff(3031,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3030, 164])).
% 0.71/0.86 tff(3032,plain,
% 0.71/0.86 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3031])).
% 0.71/0.86 tff(3033,plain,
% 0.71/0.86 (~(op(e3, e3) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1160, 3032])).
% 0.71/0.86 tff(3034,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3029])).
% 0.71/0.86 tff(3035,plain,
% 0.71/0.86 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3034])).
% 0.71/0.86 tff(3036,plain,
% 0.71/0.86 (~(op(e3, e0) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[572, 3035])).
% 0.71/0.86 tff(3037,plain,
% 0.71/0.86 (~(op(e3, e3) = e0)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[558, 3036])).
% 0.71/0.86 tff(3038,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1146, 3037, 3033, 695, 3016, 1053, 1055])).
% 0.71/0.86 tff(3039,plain,((op(e0, e0) = e3) | (op(e3, e3) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e0, e0) = e0) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(3040,plain,
% 0.71/0.86 (op(e0, e0) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[3039, 695, 1053, 1055, 26])).
% 0.71/0.86 tff(3041,plain,
% 0.71/0.86 (e3 = op(e0, e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3040])).
% 0.71/0.86 tff(3042,plain,
% 0.71/0.86 ((e1 = e3) <=> (e1 = op(e0, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3041])).
% 0.71/0.86 tff(3043,plain,
% 0.71/0.86 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3042, 1068])).
% 0.71/0.86 tff(3044,plain,
% 0.71/0.86 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3043])).
% 0.71/0.86 tff(3045,plain,
% 0.71/0.86 (~(op(e0, e0) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[521, 3044])).
% 0.71/0.86 tff(3046,plain,
% 0.71/0.86 (op(e0, e3) = e0),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1280, 3040])).
% 0.71/0.86 tff(3047,plain,
% 0.71/0.86 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3046])).
% 0.71/0.86 tff(3048,plain,
% 0.71/0.86 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3047, 2])).
% 0.71/0.86 tff(3049,plain,
% 0.71/0.86 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3048])).
% 0.71/0.86 tff(3050,plain,
% 0.71/0.86 (~(op(e3, e3) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1578, 3049])).
% 0.71/0.86 tff(3051,plain,
% 0.71/0.86 (op(e3, e0) = e1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1146, 693, 695, 280, 1053, 1055])).
% 0.71/0.86 tff(3052,plain,
% 0.71/0.86 (e1 = op(e3, e0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3051])).
% 0.71/0.86 tff(3053,plain,
% 0.71/0.86 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3052])).
% 0.71/0.86 tff(3054,plain,
% 0.71/0.86 ((op(e3, e2) = e1) <=> (op(e3, e0) = op(e3, e2))),
% 0.71/0.86 inference(transitivity,[status(thm)],[3053, 1409])).
% 0.71/0.86 tff(3055,plain,
% 0.71/0.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3054])).
% 0.71/0.86 tff(3056,plain,
% 0.71/0.86 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3055])).
% 0.71/0.86 tff(3057,plain,
% 0.71/0.86 (~(op(e3, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[572, 3056])).
% 0.71/0.86 tff(3058,plain,
% 0.71/0.86 ((e0 = e1) <=> (e0 = op(e3, e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3052])).
% 0.71/0.86 tff(3059,plain,
% 0.71/0.86 ((e0 = e1) <=> (op(e3, e0) = e0)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3058, 261])).
% 0.71/0.86 tff(3060,plain,
% 0.71/0.86 ((~(e0 = e1)) <=> (~(op(e3, e0) = e0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3059])).
% 0.71/0.86 tff(3061,plain,
% 0.71/0.86 (~(op(e3, e0) = e0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[40, 3060])).
% 0.71/0.86 tff(3062,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[2188, 3061, 3057, 1055, 280, 693, 421, 1053, 695])).
% 0.71/0.86 tff(3063,plain,((op(e3, e3) = e3) | (op(e0, e0) = e0) | (op(e3, e3) = e0) | (op(e0, e0) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(3064,plain,
% 0.71/0.86 (op(e3, e3) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[3063, 3050, 1055, 3045, 1053, 695])).
% 0.71/0.86 tff(3065,plain,
% 0.71/0.86 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3064])).
% 0.71/0.86 tff(3066,plain,
% 0.71/0.86 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3065])).
% 0.71/0.86 tff(3067,plain,
% 0.71/0.86 (~(op(e2, e3) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[196, 3066])).
% 0.71/0.86 tff(3068,plain,
% 0.71/0.86 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3064])).
% 0.71/0.86 tff(3069,plain,
% 0.71/0.86 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3068])).
% 0.71/0.86 tff(3070,plain,
% 0.71/0.86 (~(op(e3, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1160, 3069])).
% 0.71/0.86 tff(3071,plain,
% 0.71/0.86 ((op(e0, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3040])).
% 0.71/0.86 tff(3072,plain,
% 0.71/0.86 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3071, 2236])).
% 0.71/0.86 tff(3073,plain,
% 0.71/0.86 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3072])).
% 0.71/0.86 tff(3074,plain,
% 0.71/0.86 (~(op(e0, e2) = e3)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1463, 3073])).
% 0.71/0.86 tff(3075,plain,
% 0.71/0.86 (op(e1, e2) = e3),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[684, 3070, 26, 3074])).
% 0.71/0.86 tff(3076,plain,
% 0.71/0.86 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3075])).
% 0.71/0.86 tff(3077,plain,
% 0.71/0.86 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3076, 1178])).
% 0.71/0.86 tff(3078,plain,
% 0.71/0.86 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3077])).
% 0.71/0.86 tff(3079,plain,
% 0.71/0.86 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3078])).
% 0.71/0.86 tff(3080,plain,
% 0.71/0.86 (~(op(e1, e2) = e2)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[170, 3079])).
% 0.71/0.86 tff(3081,plain,
% 0.71/0.86 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3075])).
% 0.71/0.86 tff(3082,plain,
% 0.71/0.86 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 0.71/0.86 inference(transitivity,[status(thm)],[3081, 601])).
% 0.71/0.86 tff(3083,plain,
% 0.71/0.86 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[3082])).
% 0.71/0.86 tff(3084,plain,
% 0.71/0.86 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3083])).
% 0.71/0.86 tff(3085,plain,
% 0.71/0.86 (~(op(e1, e2) = e1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[521, 3084])).
% 0.71/0.86 tff(3086,plain,
% 0.71/0.86 (~(op(e1, e1) = e2)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[514, 3085])).
% 0.71/0.86 tff(3087,assumption,(op(e1, e1) = e0), introduced(assumption)).
% 0.71/0.86 tff(3088,plain,
% 0.71/0.86 (op(op(e1, e1), op(e1, e1)) = op(e0, e0)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[3087, 3087])).
% 0.71/0.86 tff(3089,plain,
% 0.71/0.86 (op(op(e1, e1), op(e1, e1)) = e3),
% 0.71/0.86 inference(transitivity,[status(thm)],[3088, 2237])).
% 0.71/0.87 tff(3090,plain,
% 0.71/0.87 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3089])).
% 0.71/0.87 tff(3091,plain,
% 0.71/0.87 ((e2 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (e2 = op(e1, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3090])).
% 0.71/0.87 tff(3092,plain,
% 0.71/0.87 ((e2 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e3) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3091, 1745])).
% 0.71/0.87 tff(3093,plain,
% 0.71/0.87 ((~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3092])).
% 0.71/0.87 tff(3094,plain,
% 0.71/0.87 (op(e0, e0) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.87 inference(symmetry,[status(thm)],[3088])).
% 0.71/0.87 tff(3095,plain,
% 0.71/0.87 (e3 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.87 inference(transitivity,[status(thm)],[2273, 3094])).
% 0.71/0.87 tff(3096,plain,
% 0.71/0.87 (e0 = op(e1, e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[3087, 1688])).
% 0.71/0.87 tff(3097,plain,
% 0.71/0.87 (~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1714, 3096, 3095])).
% 0.71/0.87 tff(3098,plain,
% 0.71/0.87 (~(op(e1, e3) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[3097, 3093])).
% 0.71/0.87 tff(3099,plain,
% 0.71/0.87 (op(e1, e0) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2026, 3087])).
% 0.71/0.87 tff(3100,plain,
% 0.71/0.87 ((op(e1, e0) = e2) <=> (e1 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3099])).
% 0.71/0.87 tff(3101,plain,
% 0.71/0.87 ((e1 = e2) <=> (op(e1, e0) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3100])).
% 0.71/0.87 tff(3102,plain,
% 0.71/0.87 ((~(e1 = e2)) <=> (~(op(e1, e0) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3101])).
% 0.71/0.87 tff(3103,plain,
% 0.71/0.87 (~(op(e1, e0) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[353, 3102])).
% 0.71/0.87 tff(3104,plain,
% 0.71/0.87 (op(e1, e3) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[751, 3103, 379, 2731])).
% 0.71/0.87 tff(3105,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[3104, 3098])).
% 0.71/0.87 tff(3106,plain,((~(op(e1, e1) = e0)) | (~(op(e0, e0) = e3)) | (op(e1, e1) = e2) | (op(e1, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(3107,plain,
% 0.71/0.87 (~(op(e1, e1) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[3106, 3040, 3086, 3080])).
% 0.71/0.87 tff(3108,plain,
% 0.71/0.87 (op(e2, e0) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2304, 3107, 26, 3040, 3070, 3067])).
% 0.71/0.87 tff(3109,plain,
% 0.71/0.87 ((op(e2, e0) = e2) <=> (e1 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3108])).
% 0.71/0.87 tff(3110,plain,
% 0.71/0.87 ((e1 = e2) <=> (op(e2, e0) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3109])).
% 0.71/0.87 tff(3111,plain,
% 0.71/0.87 ((~(e1 = e2)) <=> (~(op(e2, e0) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3110])).
% 0.71/0.87 tff(3112,plain,
% 0.71/0.87 (~(op(e2, e0) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[353, 3111])).
% 0.71/0.87 tff(3113,plain,
% 0.71/0.87 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3040])).
% 0.71/0.87 tff(3114,plain,
% 0.71/0.87 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3113, 1586])).
% 0.71/0.87 tff(3115,plain,
% 0.71/0.87 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3114])).
% 0.71/0.87 tff(3116,plain,
% 0.71/0.87 (~(op(e2, e0) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[162, 3115])).
% 0.71/0.87 tff(3117,plain,
% 0.71/0.87 (op(e2, e1) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[189, 3067, 26, 3116])).
% 0.71/0.87 tff(3118,plain,
% 0.71/0.87 ((op(e2, e1) = e0) <=> (e3 = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3117])).
% 0.71/0.87 tff(3119,plain,
% 0.71/0.87 ((op(e2, e1) = e0) <=> (e0 = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3118, 1])).
% 0.71/0.87 tff(3120,plain,
% 0.71/0.87 ((e0 = e3) <=> (op(e2, e1) = e0)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3119])).
% 0.71/0.87 tff(3121,plain,
% 0.71/0.87 ((~(e0 = e3)) <=> (~(op(e2, e1) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3120])).
% 0.71/0.87 tff(3122,plain,
% 0.71/0.87 (~(op(e2, e1) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[509, 3121])).
% 0.71/0.87 tff(3123,plain,
% 0.71/0.87 ((op(e0, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3046])).
% 0.71/0.87 tff(3124,plain,
% 0.71/0.87 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3123, 307])).
% 0.71/0.87 tff(3125,plain,
% 0.71/0.87 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3124])).
% 0.71/0.87 tff(3126,plain,
% 0.71/0.87 (~(op(e2, e3) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1275, 3125])).
% 0.71/0.87 tff(3127,plain,
% 0.71/0.87 ((op(e2, e0) = e0) <=> (e1 = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3108])).
% 0.71/0.87 tff(3128,plain,
% 0.71/0.87 ((op(e2, e0) = e0) <=> (e0 = e1)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3127, 1203])).
% 0.71/0.87 tff(3129,plain,
% 0.71/0.87 ((e0 = e1) <=> (op(e2, e0) = e0)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3128])).
% 0.71/0.87 tff(3130,plain,
% 0.71/0.87 ((~(e0 = e1)) <=> (~(op(e2, e0) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3129])).
% 0.71/0.87 tff(3131,plain,
% 0.71/0.87 (~(op(e2, e0) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[40, 3130])).
% 0.71/0.87 tff(3132,plain,
% 0.71/0.87 (op(e2, e2) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1228, 3131, 3126, 3122])).
% 0.71/0.87 tff(3133,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[230, 3132, 3112])).
% 0.71/0.87 tff(3134,plain,((op(e3, e3) = e1) | (op(e2, e2) = e3) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(3135,plain,
% 0.71/0.87 (op(e3, e3) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[3134, 26, 1055, 1053])).
% 0.71/0.87 tff(3136,plain,
% 0.71/0.87 (op(e3, e1) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1150, 3135])).
% 0.71/0.87 tff(3137,plain,
% 0.71/0.87 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3136])).
% 0.71/0.87 tff(3138,plain,
% 0.71/0.87 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3137, 1178])).
% 0.71/0.87 tff(3139,plain,
% 0.71/0.87 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3138])).
% 0.71/0.87 tff(3140,plain,
% 0.71/0.87 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3139])).
% 0.71/0.87 tff(3141,plain,
% 0.71/0.87 (~(op(e3, e1) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[170, 3140])).
% 0.71/0.87 tff(3142,plain,
% 0.71/0.87 (~(op(e1, e1) = e2)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[2399, 3135, 1053])).
% 0.71/0.87 tff(3143,plain,
% 0.71/0.87 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3136])).
% 0.71/0.87 tff(3144,plain,
% 0.71/0.87 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3143])).
% 0.71/0.87 tff(3145,plain,
% 0.71/0.87 (~(op(e3, e0) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1320, 3144])).
% 0.71/0.87 tff(3146,plain,
% 0.71/0.87 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3135])).
% 0.71/0.87 tff(3147,plain,
% 0.71/0.87 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3146])).
% 0.71/0.87 tff(3148,plain,
% 0.71/0.87 (~(op(e3, e0) = e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1424, 3147])).
% 0.71/0.87 tff(3149,plain,
% 0.71/0.87 (e1 = op(e3, e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3135])).
% 0.71/0.87 tff(3150,plain,
% 0.71/0.87 ((e1 = e2) <=> (op(e3, e3) = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3149])).
% 0.71/0.87 tff(3151,plain,
% 0.71/0.87 ((~(e1 = e2)) <=> (~(op(e3, e3) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3150])).
% 0.71/0.87 tff(3152,plain,
% 0.71/0.87 (~(op(e3, e3) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[353, 3151])).
% 0.71/0.87 tff(3153,plain,
% 0.71/0.87 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3136])).
% 0.71/0.87 tff(3154,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3153])).
% 0.71/0.87 tff(3155,plain,
% 0.71/0.87 (~(op(e0, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[859, 3154])).
% 0.71/0.87 tff(3156,plain,
% 0.71/0.87 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3135])).
% 0.71/0.87 tff(3157,plain,
% 0.71/0.87 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3156])).
% 0.71/0.87 tff(3158,plain,
% 0.71/0.87 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3157])).
% 0.71/0.87 tff(3159,plain,
% 0.71/0.87 (~(op(e3, e3) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[521, 3158])).
% 0.71/0.87 tff(3160,plain,
% 0.71/0.87 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3136])).
% 0.71/0.87 tff(3161,plain,
% 0.71/0.87 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3160, 1])).
% 0.71/0.87 tff(3162,plain,
% 0.71/0.87 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3161])).
% 0.71/0.87 tff(3163,plain,
% 0.71/0.87 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3162])).
% 0.71/0.87 tff(3164,plain,
% 0.71/0.87 (~(op(e3, e1) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[509, 3163])).
% 0.71/0.87 tff(3165,plain,
% 0.71/0.87 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2118])).
% 0.71/0.87 tff(3166,plain,
% 0.71/0.87 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3165, 2541])).
% 0.71/0.87 tff(3167,plain,
% 0.71/0.87 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3166])).
% 0.71/0.87 tff(3168,plain,
% 0.71/0.87 (~(op(e1, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1740, 3167])).
% 0.71/0.87 tff(3169,assumption,(~(op(e3, e3) = e2)), introduced(assumption)).
% 0.71/0.87 tff(3170,plain,
% 0.71/0.87 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2112])).
% 0.71/0.87 tff(3171,plain,
% 0.71/0.87 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3170, 1532])).
% 0.71/0.87 tff(3172,plain,
% 0.71/0.87 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3171])).
% 0.71/0.87 tff(3173,plain,
% 0.71/0.87 (~(op(e3, e0) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[270, 3172])).
% 0.71/0.87 tff(3174,plain,
% 0.71/0.87 (op(e3, e2) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[818, 3173, 3169, 372])).
% 0.71/0.87 tff(3175,plain,
% 0.71/0.87 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3174])).
% 0.71/0.87 tff(3176,plain,
% 0.71/0.87 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3175])).
% 0.71/0.87 tff(3177,plain,
% 0.71/0.87 (~(op(e2, e2) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[278, 3176])).
% 0.71/0.87 tff(3178,plain,
% 0.71/0.87 ((op(e0, e2) = op(e2, e2)) <=> (e0 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2118])).
% 0.71/0.87 tff(3179,plain,
% 0.71/0.87 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3178, 1787])).
% 0.71/0.87 tff(3180,plain,
% 0.71/0.87 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3179])).
% 0.71/0.87 tff(3181,plain,
% 0.71/0.87 (~(op(e2, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1396, 3180])).
% 0.71/0.87 tff(3182,plain,
% 0.71/0.87 (op(e3, e0) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1333, 3173, 1067, 1588])).
% 0.71/0.87 tff(3183,plain,
% 0.71/0.87 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3182])).
% 0.71/0.87 tff(3184,plain,
% 0.71/0.87 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3183])).
% 0.71/0.87 tff(3185,plain,
% 0.71/0.87 (~(op(e2, e0) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[589, 3184])).
% 0.71/0.87 tff(3186,plain,
% 0.71/0.87 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[2118])).
% 0.71/0.87 tff(3187,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3186])).
% 0.71/0.87 tff(3188,plain,
% 0.71/0.87 (~(op(e0, e1) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[867, 3187])).
% 0.71/0.87 tff(3189,plain,
% 0.71/0.87 (op(e0, e1) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[880, 2132, 1832, 3188])).
% 0.71/0.87 tff(3190,plain,
% 0.71/0.87 (op(e1, op(e0, e1)) = op(e1, e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3189])).
% 0.71/0.87 tff(3191,plain,
% 0.71/0.87 ((op(e1, op(e0, e1)) = op(e0, e1)) <=> (op(e1, e1) = e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3190, 3189])).
% 0.71/0.87 tff(3192,plain,
% 0.71/0.87 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e1)) = op(e0, e1))),
% 0.71/0.87 inference(symmetry,[status(thm)],[3191])).
% 0.71/0.87 tff(3193,plain,
% 0.71/0.87 ((~(op(e1, e1) = e1)) <=> (~(op(e1, op(e0, e1)) = op(e0, e1)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3192])).
% 0.71/0.87 tff(3194,plain,
% 0.71/0.87 ((op(e0, e1) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3189])).
% 0.71/0.87 tff(3195,plain,
% 0.71/0.87 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3194, 1350])).
% 0.71/0.87 tff(3196,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3195])).
% 0.71/0.87 tff(3197,plain,
% 0.71/0.87 (~(op(e1, e1) = e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1402, 3196])).
% 0.71/0.87 tff(3198,plain,
% 0.71/0.87 (~(op(e1, op(e0, e1)) = op(e0, e1))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[3197, 3193])).
% 0.71/0.87 tff(3199,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1248, 3198, 3185, 26, 3181, 1233, 3177, 3168, 1055, 693])).
% 0.71/0.87 tff(3200,plain,((~(op(e0, e0) = e2)) | (op(e2, e2) = e3) | (op(e3, e1) = e0) | (op(e0, e0) = e0) | (op(e3, e3) = e3) | (op(e0, e1) = e3) | (op(e3, e3) = e2) | (op(e3, e1) = e2) | (op(e3, e0) = e1) | (op(e3, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(3201,plain,
% 0.71/0.87 (~(op(e0, e0) = e2)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[3200, 26, 3164, 1055, 3159, 3155, 3152, 3141, 3148, 3145])).
% 0.71/0.87 tff(3202,plain,
% 0.71/0.87 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3135])).
% 0.71/0.87 tff(3203,plain,
% 0.71/0.87 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3202])).
% 0.71/0.87 tff(3204,plain,
% 0.71/0.87 (~(op(e1, e3) = e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[539, 3203])).
% 0.71/0.87 tff(3205,plain,
% 0.71/0.87 ((e0 = e1) <=> (e0 = op(e3, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3149])).
% 0.71/0.87 tff(3206,plain,
% 0.71/0.87 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3205, 2])).
% 0.71/0.87 tff(3207,plain,
% 0.71/0.87 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3206])).
% 0.71/0.87 tff(3208,plain,
% 0.71/0.87 (~(op(e3, e3) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[40, 3207])).
% 0.71/0.87 tff(3209,assumption,(op(e3, e1) = e3), introduced(assumption)).
% 0.71/0.87 tff(3210,plain,
% 0.71/0.87 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.87 tff(3211,plain,
% 0.71/0.87 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3210])).
% 0.71/0.87 tff(3212,plain,
% 0.71/0.87 (~(op(e1, e1) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[338, 3211])).
% 0.71/0.87 tff(3213,assumption,(~(op(e0, e0) = e2)), introduced(assumption)).
% 0.71/0.87 tff(3214,plain,
% 0.71/0.87 (op(e0, e0) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1105, 1590, 1055, 3213])).
% 0.71/0.87 tff(3215,plain,
% 0.71/0.87 (op(e0, e1) = e0),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1109, 3214])).
% 0.71/0.87 tff(3216,plain,
% 0.71/0.87 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3215])).
% 0.71/0.87 tff(3217,plain,
% 0.71/0.87 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3216, 1430])).
% 0.71/0.87 tff(3218,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3217])).
% 0.71/0.87 tff(3219,plain,
% 0.71/0.87 (~(op(e1, e1) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1402, 3218])).
% 0.71/0.87 tff(3220,plain,
% 0.71/0.87 (op(e1, e1) = e1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[435, 3219, 3212, 379])).
% 0.71/0.87 tff(3221,plain,
% 0.71/0.87 (op(e1, op(e1, e1)) = op(e1, e1)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3220])).
% 0.71/0.87 tff(3222,plain,
% 0.71/0.87 (((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))) | (~(op(e1, op(e1, e1)) = op(e1, e1)))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(3223,plain,
% 0.71/0.87 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[3222, 3221])).
% 0.71/0.87 tff(3224,plain,
% 0.71/0.87 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.87 tff(3225,plain,
% 0.71/0.87 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3224])).
% 0.71/0.87 tff(3226,plain,
% 0.71/0.87 (~(op(e3, e0) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1320, 3225])).
% 0.71/0.87 tff(3227,plain,
% 0.71/0.87 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.87 tff(3228,plain,
% 0.71/0.87 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3227, 566])).
% 0.71/0.87 tff(3229,plain,
% 0.71/0.87 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3228])).
% 0.71/0.87 tff(3230,plain,
% 0.71/0.87 (~(op(e3, e2) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[974, 3229])).
% 0.71/0.87 tff(3231,plain,
% 0.71/0.87 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3215])).
% 0.71/0.87 tff(3232,plain,
% 0.71/0.87 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3231])).
% 0.71/0.87 tff(3233,plain,
% 0.71/0.87 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3232])).
% 0.71/0.87 tff(3234,plain,
% 0.71/0.87 (~(op(e0, e1) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[16, 3233])).
% 0.71/0.87 tff(3235,plain,
% 0.71/0.87 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.87 tff(3236,plain,
% 0.71/0.87 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3235, 1178])).
% 0.71/0.87 tff(3237,plain,
% 0.71/0.87 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3236])).
% 0.71/0.87 tff(3238,plain,
% 0.71/0.87 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3237])).
% 0.71/0.87 tff(3239,plain,
% 0.71/0.87 (~(op(e3, e1) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[170, 3238])).
% 0.71/0.87 tff(3240,plain,
% 0.71/0.87 (op(e2, e1) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[396, 3234, 379, 3239])).
% 0.71/0.87 tff(3241,plain,
% 0.71/0.87 ((e0 = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.71/0.87 inference(commutativity,[status(thm)],[])).
% 0.71/0.87 tff(3242,plain,
% 0.71/0.87 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3215])).
% 0.71/0.87 tff(3243,plain,
% 0.71/0.87 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3242, 3241])).
% 0.71/0.87 tff(3244,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3243])).
% 0.71/0.87 tff(3245,plain,
% 0.71/0.87 (~(op(e2, e1) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[2322, 3244])).
% 0.71/0.87 tff(3246,plain,
% 0.71/0.87 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3215])).
% 0.71/0.87 tff(3247,plain,
% 0.71/0.87 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3246, 2615])).
% 0.71/0.87 tff(3248,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3247])).
% 0.71/0.87 tff(3249,plain,
% 0.71/0.87 (~(op(e0, e2) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[867, 3248])).
% 0.71/0.87 tff(3250,plain,
% 0.71/0.87 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3215])).
% 0.71/0.87 tff(3251,plain,
% 0.71/0.87 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3250, 299])).
% 0.71/0.87 tff(3252,plain,
% 0.71/0.87 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3251])).
% 0.71/0.87 tff(3253,plain,
% 0.71/0.87 (~(op(e0, e3) = e0)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[403, 3252])).
% 0.71/0.87 tff(3254,assumption,((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))), introduced(assumption)).
% 0.71/0.87 tff(3255,plain,
% 0.71/0.87 (op(e1, op(e3, e1)) = op(e1, e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.87 tff(3256,plain,
% 0.71/0.87 ((op(e1, op(e3, e1)) = op(e3, e1)) <=> (op(e1, e3) = e3)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3255, 3209])).
% 0.71/0.87 tff(3257,plain,
% 0.71/0.87 ((op(e1, e3) = e3) <=> (op(e1, op(e3, e1)) = op(e3, e1))),
% 0.71/0.87 inference(symmetry,[status(thm)],[3256])).
% 0.71/0.87 tff(3258,assumption,(~(op(e0, e1) = e2)), introduced(assumption)).
% 0.71/0.87 tff(3259,assumption,(op(e0, e2) = e3), introduced(assumption)).
% 0.71/0.87 tff(3260,plain,
% 0.71/0.87 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3259])).
% 0.71/0.87 tff(3261,plain,
% 0.71/0.87 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3260, 1178])).
% 0.71/0.87 tff(3262,plain,
% 0.71/0.87 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3261])).
% 0.71/0.87 tff(3263,plain,
% 0.71/0.87 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3262])).
% 0.71/0.87 tff(3264,plain,
% 0.71/0.87 (~(op(e0, e2) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[170, 3263])).
% 0.71/0.87 tff(3265,plain,
% 0.71/0.87 (op(e0, e3) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1346, 3264, 3213, 3258])).
% 0.71/0.87 tff(3266,plain,
% 0.71/0.87 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3265])).
% 0.71/0.87 tff(3267,plain,
% 0.71/0.87 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3266, 1745])).
% 0.71/0.87 tff(3268,plain,
% 0.71/0.87 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3267])).
% 0.71/0.87 tff(3269,plain,
% 0.71/0.87 (~(op(e1, e3) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1762, 3268])).
% 0.71/0.87 tff(3270,assumption,(op(e2, e1) = e2), introduced(assumption)).
% 0.71/0.87 tff(3271,plain,
% 0.71/0.87 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3270])).
% 0.71/0.87 tff(3272,plain,
% 0.71/0.87 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3271])).
% 0.71/0.87 tff(3273,plain,
% 0.71/0.87 (~(op(e2, e0) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[70, 3272])).
% 0.71/0.87 tff(3274,plain,
% 0.71/0.87 (~(op(e2, e2) = e0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[230, 3273])).
% 0.71/0.87 tff(3275,plain,
% 0.71/0.87 ((op(e0, e2) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3259])).
% 0.71/0.87 tff(3276,plain,
% 0.71/0.87 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3275, 1480])).
% 0.71/0.87 tff(3277,plain,
% 0.71/0.87 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3276])).
% 0.71/0.87 tff(3278,plain,
% 0.71/0.87 (~(op(e0, e3) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[702, 3277])).
% 0.71/0.87 tff(3279,plain,
% 0.71/0.87 ((~(op(e1, op(e3, e1)) = op(e3, e1))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3256])).
% 0.71/0.87 tff(3280,plain,
% 0.71/0.87 (op(e1, op(e2, e1)) = op(e1, e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3270])).
% 0.71/0.87 tff(3281,plain,
% 0.71/0.87 ((op(e1, op(e2, e1)) = op(e2, e1)) <=> (op(e1, e2) = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3280, 3270])).
% 0.71/0.87 tff(3282,plain,
% 0.71/0.87 ((op(e1, e2) = e2) <=> (op(e1, op(e2, e1)) = op(e2, e1))),
% 0.71/0.87 inference(symmetry,[status(thm)],[3281])).
% 0.71/0.87 tff(3283,assumption,(~(op(e0, e2) = e2)), introduced(assumption)).
% 0.71/0.87 tff(3284,plain,
% 0.71/0.87 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3270])).
% 0.71/0.87 tff(3285,plain,
% 0.71/0.87 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.71/0.87 inference(transitivity,[status(thm)],[3284, 1137])).
% 0.71/0.87 tff(3286,plain,
% 0.71/0.87 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3285])).
% 0.71/0.87 tff(3287,plain,
% 0.71/0.87 (~(op(e2, e2) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1936, 3286])).
% 0.71/0.87 tff(3288,assumption,(op(e3, e2) = e0), introduced(assumption)).
% 0.71/0.87 tff(3289,plain,
% 0.71/0.87 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3288])).
% 0.71/0.87 tff(3290,plain,
% 0.71/0.87 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 0.71/0.87 inference(symmetry,[status(thm)],[3289])).
% 0.71/0.87 tff(3291,plain,
% 0.71/0.87 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3290])).
% 0.71/0.87 tff(3292,plain,
% 0.71/0.87 (~(op(e3, e2) = e2)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[16, 3291])).
% 0.71/0.87 tff(3293,plain,
% 0.71/0.87 (op(e1, e2) = e2),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[924, 3292, 3287, 3283])).
% 0.71/0.87 tff(3294,plain,
% 0.71/0.87 (op(e1, op(e2, e1)) = op(e2, e1)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[3293, 3282])).
% 0.71/0.87 tff(3295,plain,
% 0.71/0.87 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[900, 3294])).
% 0.71/0.87 tff(3296,plain,
% 0.71/0.87 (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[798, 3295, 758, 3254])).
% 0.71/0.87 tff(3297,plain,
% 0.71/0.87 (~(op(e1, op(e3, e1)) = op(e3, e1))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[849, 3296])).
% 0.71/0.87 tff(3298,plain,
% 0.71/0.87 (~(op(e1, e3) = e3)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[3297, 3279])).
% 0.71/0.87 tff(3299,plain,
% 0.71/0.87 (op(e2, e3) = e3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[724, 3298, 693, 1587])).
% 0.71/0.87 tff(3300,plain,
% 0.71/0.87 (op(e2, op(e3, e2)) = op(e2, e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3288])).
% 0.71/0.87 tff(3301,plain,
% 0.71/0.87 ((op(e2, op(e3, e2)) = op(e3, e2)) <=> (op(e2, e0) = e0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3300, 3288])).
% 0.71/0.87 tff(3302,plain,
% 0.71/0.87 ((~(op(e2, op(e3, e2)) = op(e3, e2))) <=> (~(op(e2, e0) = e0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[3301])).
% 0.71/0.88 tff(3303,plain,
% 0.71/0.88 (~(op(e2, op(e3, e2)) = op(e3, e2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[943, 3296])).
% 0.71/0.88 tff(3304,plain,
% 0.71/0.88 (~(op(e2, e0) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 0.71/0.88 tff(3305,plain,
% 0.71/0.88 (op(e2, e3) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1228, 3304, 3274, 2719])).
% 0.71/0.88 tff(3306,plain,
% 0.71/0.88 (e0 = op(e2, e3)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3305])).
% 0.71/0.88 tff(3307,plain,
% 0.71/0.88 (e0 = e3),
% 0.71/0.88 inference(transitivity,[status(thm)],[3306, 3299])).
% 0.71/0.88 tff(3308,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[509, 3307])).
% 0.71/0.88 tff(3309,plain,((~(op(e3, e2) = e0)) | (op(e2, e1) = e0) | (op(e3, e3) = e3) | (op(e0, e3) = e3) | (~(op(e3, e1) = e3)) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))) | (~(op(e2, e1) = e2)) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3310,plain,
% 0.71/0.88 (~(op(e3, e2) = e0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3309, 3278, 693, 2719, 3209, 758, 3254, 3270, 3264])).
% 0.71/0.88 tff(3311,plain,
% 0.71/0.88 (op(e1, e2) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1678, 3310, 1789, 3274])).
% 0.71/0.88 tff(3312,plain,
% 0.71/0.88 ((op(e1, e2) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3311])).
% 0.71/0.88 tff(3313,plain,
% 0.71/0.88 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3312, 2599])).
% 0.71/0.88 tff(3314,plain,
% 0.71/0.88 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3313])).
% 0.71/0.88 tff(3315,plain,
% 0.71/0.88 (~(op(e1, e3) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[691, 3314])).
% 0.71/0.88 tff(3316,plain,
% 0.71/0.88 (op(e1, e3) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[2389, 3315, 694, 3269])).
% 0.71/0.88 tff(3317,plain,
% 0.71/0.88 (op(e1, op(e3, e1)) = op(e3, e1)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3316, 3257])).
% 0.71/0.88 tff(3318,plain,
% 0.71/0.88 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[849, 3317])).
% 0.71/0.88 tff(3319,assumption,(~(op(e0, e3) = e0)), introduced(assumption)).
% 0.71/0.88 tff(3320,plain,
% 0.71/0.88 (op(e2, e3) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[322, 3315, 280, 3319])).
% 0.71/0.88 tff(3321,plain,
% 0.71/0.88 (e0 = op(e2, e3)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3320])).
% 0.71/0.88 tff(3322,plain,
% 0.71/0.88 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.88 tff(3323,plain,
% 0.71/0.88 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3322, 1])).
% 0.71/0.88 tff(3324,plain,
% 0.71/0.88 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3323])).
% 0.71/0.88 tff(3325,plain,
% 0.71/0.88 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3324])).
% 0.71/0.88 tff(3326,plain,
% 0.71/0.88 (~(op(e3, e1) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[509, 3325])).
% 0.71/0.88 tff(3327,plain,
% 0.71/0.88 (op(e3, e0) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[288, 3310, 280, 3326])).
% 0.71/0.88 tff(3328,plain,
% 0.71/0.88 (op(e3, op(e2, e3)) = op(e3, e0)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3320])).
% 0.71/0.88 tff(3329,plain,
% 0.71/0.88 (op(e3, op(e2, e3)) = op(e2, e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3328, 3327, 3321])).
% 0.71/0.88 tff(3330,plain,
% 0.71/0.88 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[776, 3329])).
% 0.71/0.88 tff(3331,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[798, 3330, 3318, 758, 3254])).
% 0.71/0.88 tff(3332,plain,((~(op(e0, e2) = e3)) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))) | (~(op(e3, e1) = e3)) | (op(e3, e3) = e0) | (op(e0, e3) = e0) | (op(e1, e3) = e1) | (op(e0, e2) = e0) | (op(e3, e3) = e3) | (op(e2, e1) = e0) | (~(op(e2, e1) = e2)) | (op(e0, e0) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3333,plain,
% 0.71/0.88 (~(op(e0, e2) = e3)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3332, 3223, 758, 3209, 280, 3253, 694, 3249, 693, 3245, 3240, 3213, 3234])).
% 0.71/0.88 tff(3334,plain,
% 0.71/0.88 (op(e1, e2) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[684, 3333, 26, 3230])).
% 0.71/0.88 tff(3335,plain,
% 0.71/0.88 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3334])).
% 0.71/0.88 tff(3336,plain,
% 0.71/0.88 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3335])).
% 0.71/0.88 tff(3337,plain,
% 0.71/0.88 (~(op(e1, e0) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[613, 3336])).
% 0.71/0.88 tff(3338,plain,
% 0.71/0.88 (op(e2, e0) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1616, 3337, 1590, 3226])).
% 0.71/0.88 tff(3339,plain,
% 0.71/0.88 (e3 = op(e2, e0)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3338])).
% 0.71/0.88 tff(3340,plain,
% 0.71/0.88 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3209])).
% 0.71/0.88 tff(3341,plain,
% 0.71/0.88 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3340])).
% 0.71/0.88 tff(3342,plain,
% 0.71/0.88 (~(op(e0, e1) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[859, 3341])).
% 0.71/0.88 tff(3343,plain,
% 0.71/0.88 (op(e0, e3) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1090, 3333, 1590, 3342])).
% 0.71/0.88 tff(3344,plain,
% 0.71/0.88 (op(e0, op(e2, e0)) = op(e0, e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3338])).
% 0.71/0.88 tff(3345,plain,
% 0.71/0.88 (op(e0, op(e2, e0)) = op(e2, e0)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3344, 3343, 3339])).
% 0.71/0.88 tff(3346,plain,
% 0.71/0.88 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[927, 3345])).
% 0.71/0.88 tff(3347,plain,
% 0.71/0.88 ((e2 = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.71/0.88 inference(commutativity,[status(thm)],[])).
% 0.71/0.88 tff(3348,plain,
% 0.71/0.88 ((op(e0, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3214])).
% 0.71/0.88 tff(3349,plain,
% 0.71/0.88 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3348, 2086])).
% 0.71/0.88 tff(3350,plain,
% 0.71/0.88 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3349])).
% 0.71/0.88 tff(3351,plain,
% 0.71/0.88 (~(op(e0, e2) = e1)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1463, 3350])).
% 0.71/0.88 tff(3352,plain,
% 0.71/0.88 (((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))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(3353,plain,
% 0.71/0.88 ((((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))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(3354,plain,
% 0.71/0.88 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(3355,plain,
% 0.71/0.88 (((((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))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3354])).
% 0.71/0.88 tff(3356,plain,
% 0.71/0.88 (((((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))),
% 0.71/0.88 inference(transitivity,[status(thm)],[3355, 3353])).
% 0.71/0.88 tff(3357,plain,
% 0.71/0.88 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)),
% 0.71/0.88 inference(and_elim,[status(thm)],[876])).
% 0.71/0.88 tff(3358,plain,
% 0.71/0.88 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 0.71/0.88 tff(3359,plain,
% 0.71/0.88 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3358, 3352])).
% 0.71/0.88 tff(3360,plain,
% 0.71/0.88 (op(e0, e2) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3359, 3333, 3351, 3249])).
% 0.71/0.88 tff(3361,plain,
% 0.71/0.88 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3360])).
% 0.71/0.88 tff(3362,plain,
% 0.71/0.88 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3361, 3347])).
% 0.71/0.88 tff(3363,plain,
% 0.71/0.88 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3362])).
% 0.71/0.88 tff(3364,plain,
% 0.71/0.88 (~(op(e3, e2) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1457, 3363])).
% 0.71/0.88 tff(3365,plain,
% 0.71/0.88 (op(e3, e0) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[818, 3364, 3169, 3239])).
% 0.71/0.88 tff(3366,plain,
% 0.71/0.88 (e2 = op(e3, e0)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3365])).
% 0.71/0.88 tff(3367,plain,
% 0.71/0.88 (op(e0, op(e3, e0)) = op(e0, e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3365])).
% 0.71/0.88 tff(3368,plain,
% 0.71/0.88 (op(e0, op(e3, e0)) = op(e3, e0)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3367, 3360, 3366])).
% 0.71/0.88 tff(3369,plain,
% 0.71/0.88 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[800, 3368])).
% 0.71/0.88 tff(3370,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[798, 3369, 3346, 758, 3223])).
% 0.71/0.88 tff(3371,plain,((op(e0, e0) = e3) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e3, e3) = e2) | (op(e2, e2) = e3) | (~(op(e3, e1) = e3)) | (op(e3, e3) = e0) | (op(e1, e3) = e1) | (op(e3, e3) = e3) | (op(e0, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3372,plain,
% 0.71/0.88 (op(e0, e0) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3371, 3152, 758, 26, 3136, 3208, 3204, 3159, 3201, 3142, 1055])).
% 0.71/0.88 tff(3373,plain,
% 0.71/0.88 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3372, 3372])).
% 0.71/0.88 tff(3374,plain,
% 0.71/0.88 (op(op(e0, e0), op(e0, e0)) = e1),
% 0.71/0.88 inference(transitivity,[status(thm)],[3373, 3135])).
% 0.71/0.88 tff(3375,plain,
% 0.71/0.88 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e1)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3374])).
% 0.71/0.88 tff(3376,plain,
% 0.71/0.88 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (e2 = op(e0, e1))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3375])).
% 0.71/0.88 tff(3377,plain,
% 0.71/0.88 ((e2 = op(e0, op(op(e0, e0), op(e0, e0)))) <=> (op(e0, e1) = e2)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3376, 1291])).
% 0.71/0.88 tff(3378,plain,
% 0.71/0.88 ((~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))) <=> (~(op(e0, e1) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3377])).
% 0.71/0.88 tff(3379,plain,
% 0.71/0.88 (e3 = op(e0, e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3372, 1299])).
% 0.71/0.88 tff(3380,plain,
% 0.71/0.88 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.71/0.88 inference(symmetry,[status(thm)],[3373])).
% 0.71/0.88 tff(3381,plain,
% 0.71/0.88 (e1 = op(op(e0, e0), op(e0, e0))),
% 0.71/0.88 inference(transitivity,[status(thm)],[3149, 3380])).
% 0.71/0.88 tff(3382,plain,
% 0.71/0.88 (~(e2 = op(e0, op(op(e0, e0), op(e0, e0))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1313, 3381, 3379])).
% 0.71/0.88 tff(3383,plain,
% 0.71/0.88 (~(op(e0, e1) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3382, 3378])).
% 0.71/0.88 tff(3384,plain,
% 0.71/0.88 (op(e2, e1) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[396, 3383, 3142, 3141])).
% 0.71/0.88 tff(3385,plain,
% 0.71/0.88 (op(e0, e3) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1280, 3372])).
% 0.71/0.88 tff(3386,plain,
% 0.71/0.88 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3385])).
% 0.71/0.88 tff(3387,plain,
% 0.71/0.88 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3386])).
% 0.71/0.88 tff(3388,plain,
% 0.71/0.88 (~(op(e0, e1) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[403, 3387])).
% 0.71/0.88 tff(3389,plain,
% 0.71/0.88 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3136])).
% 0.71/0.88 tff(3390,plain,
% 0.71/0.88 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3389, 566])).
% 0.71/0.88 tff(3391,plain,
% 0.71/0.88 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3390])).
% 0.71/0.88 tff(3392,plain,
% 0.71/0.88 (~(op(e3, e2) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[974, 3391])).
% 0.71/0.88 tff(3393,plain,
% 0.71/0.88 ((op(e0, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3372])).
% 0.71/0.88 tff(3394,plain,
% 0.71/0.88 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3393, 2236])).
% 0.71/0.88 tff(3395,plain,
% 0.71/0.88 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3394])).
% 0.71/0.88 tff(3396,plain,
% 0.71/0.88 (~(op(e0, e2) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1463, 3395])).
% 0.71/0.88 tff(3397,plain,
% 0.71/0.88 (op(e1, e2) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[684, 3396, 26, 3392])).
% 0.71/0.88 tff(3398,plain,
% 0.71/0.88 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3397])).
% 0.71/0.88 tff(3399,plain,
% 0.71/0.88 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3398, 1178])).
% 0.71/0.88 tff(3400,plain,
% 0.71/0.88 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3399])).
% 0.71/0.88 tff(3401,plain,
% 0.71/0.88 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3400])).
% 0.71/0.88 tff(3402,plain,
% 0.71/0.88 (~(op(e1, e2) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[170, 3401])).
% 0.71/0.88 tff(3403,plain,
% 0.71/0.88 (~(op(e1, e1) = e0)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3106, 3402, 3142, 3372])).
% 0.71/0.88 tff(3404,plain,
% 0.71/0.88 (op(e2, e1) = e0),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1241, 3403, 3164, 3388])).
% 0.71/0.88 tff(3405,plain,
% 0.71/0.88 (e0 = op(e2, e1)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3404])).
% 0.71/0.88 tff(3406,plain,
% 0.71/0.88 (e0 = e2),
% 0.71/0.88 inference(transitivity,[status(thm)],[3405, 3384])).
% 0.71/0.88 tff(3407,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[16, 3406])).
% 0.71/0.88 tff(3408,plain,((op(e2, e2) = e3) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3409,plain,
% 0.71/0.88 (op(e2, e2) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3408, 2827, 1055, 1053])).
% 0.71/0.88 tff(3410,plain,
% 0.71/0.88 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3409, 3409])).
% 0.71/0.88 tff(3411,plain,
% 0.71/0.88 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (e0 = op(e3, e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3410])).
% 0.71/0.88 tff(3412,plain,
% 0.71/0.88 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e0)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3411, 2])).
% 0.71/0.88 tff(3413,plain,
% 0.71/0.88 ((~(e0 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e0))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3412])).
% 0.71/0.88 tff(3414,plain,
% 0.71/0.88 (~(op(e3, e3) = e0)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1054, 3413])).
% 0.71/0.88 tff(3415,plain,
% 0.71/0.88 (op(e3, e0) = e1),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1959, 693, 1055, 1900, 280, 1053])).
% 0.71/0.88 tff(3416,plain,
% 0.71/0.88 ((op(e3, e0) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3415])).
% 0.71/0.88 tff(3417,plain,
% 0.71/0.88 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3416, 1071])).
% 0.71/0.88 tff(3418,plain,
% 0.71/0.88 ((op(e3, e3) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 0.71/0.88 inference(symmetry,[status(thm)],[3417])).
% 0.71/0.88 tff(3419,plain,
% 0.71/0.88 ((op(e2, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1928])).
% 0.71/0.88 tff(3420,plain,
% 0.71/0.88 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3419, 359])).
% 0.71/0.88 tff(3421,plain,
% 0.71/0.88 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3420])).
% 0.71/0.88 tff(3422,plain,
% 0.71/0.88 (~(op(e3, e3) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[196, 3421])).
% 0.71/0.88 tff(3423,plain,
% 0.71/0.88 (op(e3, e3) = e1),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1123, 693, 3422, 280])).
% 0.71/0.88 tff(3424,plain,
% 0.71/0.88 (op(e3, e0) = op(e3, e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[3423, 3418])).
% 0.71/0.88 tff(3425,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1424, 3424])).
% 0.71/0.88 tff(3426,plain,((op(e3, e3) = e3) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (~(op(e2, e2) = e3)) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3427,plain,
% 0.71/0.88 (op(e3, e3) = e3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3426, 3414, 1055, 3409, 1053])).
% 0.71/0.88 tff(3428,assumption,(op(e3, e3) = e3), introduced(assumption)).
% 0.71/0.88 tff(3429,plain,
% 0.71/0.88 (op(e3, op(e3, e3)) = op(e3, e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3428])).
% 0.71/0.88 tff(3430,assumption,(~(op(e3, op(e3, e3)) = op(e3, e3))), introduced(assumption)).
% 0.71/0.88 tff(3431,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3430, 3429])).
% 0.71/0.88 tff(3432,plain,((~(op(e3, e3) = e3)) | (op(e3, op(e3, e3)) = op(e3, e3))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(3433,plain,
% 0.71/0.88 (op(e3, op(e3, e3)) = op(e3, e3)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3432, 3427])).
% 0.71/0.88 tff(3434,plain,
% 0.71/0.88 (((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (~(op(e3, op(e3, e3)) = op(e3, e3)))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(3435,plain,
% 0.71/0.88 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[3434, 3433])).
% 0.71/0.88 tff(3436,plain,
% 0.71/0.88 (op(e2, e3) = e2),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1004, 3409])).
% 0.71/0.88 tff(3437,plain,
% 0.71/0.88 (op(e3, op(e2, e3)) = op(e3, e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3436])).
% 0.71/0.88 tff(3438,plain,
% 0.71/0.88 ((op(e3, op(e2, e3)) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3437, 3436])).
% 0.71/0.88 tff(3439,plain,
% 0.71/0.88 ((op(e3, e2) = e2) <=> (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.88 inference(symmetry,[status(thm)],[3438])).
% 0.71/0.88 tff(3440,plain,
% 0.71/0.88 ((e2 = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.88 inference(commutativity,[status(thm)],[])).
% 0.71/0.88 tff(3441,plain,
% 0.71/0.88 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3436])).
% 0.71/0.88 tff(3442,plain,
% 0.71/0.88 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3441])).
% 0.71/0.88 tff(3443,plain,
% 0.71/0.88 (~(op(e2, e0) = e2)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[369, 3442])).
% 0.71/0.88 tff(3444,plain,
% 0.71/0.88 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3427])).
% 0.71/0.88 tff(3445,plain,
% 0.71/0.88 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3444])).
% 0.71/0.88 tff(3446,plain,
% 0.71/0.88 (~(op(e0, e3) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1578, 3445])).
% 0.71/0.88 tff(3447,plain,
% 0.71/0.88 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3427])).
% 0.71/0.88 tff(3448,plain,
% 0.71/0.88 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3447])).
% 0.71/0.88 tff(3449,plain,
% 0.71/0.88 (~(op(e3, e0) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1424, 3448])).
% 0.71/0.88 tff(3450,plain,
% 0.71/0.88 ((op(e3, e3) = e1) <=> (e3 = e1)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3427])).
% 0.71/0.88 tff(3451,plain,
% 0.71/0.88 ((op(e3, e3) = e1) <=> (e1 = e3)),
% 0.71/0.88 inference(transitivity,[status(thm)],[3450, 601])).
% 0.71/0.88 tff(3452,plain,
% 0.71/0.88 ((e1 = e3) <=> (op(e3, e3) = e1)),
% 0.71/0.88 inference(symmetry,[status(thm)],[3451])).
% 0.71/0.88 tff(3453,plain,
% 0.71/0.88 ((~(e1 = e3)) <=> (~(op(e3, e3) = e1))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3452])).
% 0.71/0.88 tff(3454,plain,
% 0.71/0.88 (~(op(e3, e3) = e1)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[521, 3453])).
% 0.71/0.88 tff(3455,plain,
% 0.71/0.88 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3427])).
% 0.71/0.88 tff(3456,plain,
% 0.71/0.88 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[3455])).
% 0.71/0.88 tff(3457,plain,
% 0.71/0.88 (~(op(e1, e3) = e3)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[539, 3456])).
% 0.71/0.88 tff(3458,plain,
% 0.71/0.88 (~(e3 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[2783, 2341, 933, 1900])).
% 0.71/0.88 tff(3459,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[2392, 3458, 2341, 1900])).
% 0.71/0.89 tff(3460,plain,((~(op(e1, e1) = e2)) | (~(op(e2, e2) = e3)) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(3461,plain,
% 0.71/0.89 (~(op(e1, e1) = e2)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3460, 3409, 3457])).
% 0.71/0.89 tff(3462,plain,
% 0.71/0.89 (op(e0, e0) = e3),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[2038, 3461, 3409, 3454, 1055, 3449, 3446])).
% 0.71/0.89 tff(3463,plain,
% 0.71/0.89 ((op(e0, e0) = e2) <=> (e3 = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3462])).
% 0.71/0.89 tff(3464,plain,
% 0.71/0.89 ((op(e0, e0) = e2) <=> (e2 = e3)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3463, 1178])).
% 0.71/0.89 tff(3465,plain,
% 0.71/0.89 ((e2 = e3) <=> (op(e0, e0) = e2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3464])).
% 0.71/0.89 tff(3466,plain,
% 0.71/0.89 ((~(e2 = e3)) <=> (~(op(e0, e0) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3465])).
% 0.71/0.89 tff(3467,plain,
% 0.71/0.89 (~(op(e0, e0) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[170, 3466])).
% 0.71/0.89 tff(3468,plain,
% 0.71/0.89 (e3 = op(e2, e2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3409])).
% 0.71/0.89 tff(3469,plain,
% 0.71/0.89 ((e0 = e3) <=> (e0 = op(e2, e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3468])).
% 0.71/0.89 tff(3470,plain,
% 0.71/0.89 ((e0 = e3) <=> (op(e2, e2) = e0)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3469, 1787])).
% 0.71/0.89 tff(3471,plain,
% 0.71/0.89 ((~(e0 = e3)) <=> (~(op(e2, e2) = e0))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3470])).
% 0.71/0.89 tff(3472,plain,
% 0.71/0.89 (~(op(e2, e2) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[509, 3471])).
% 0.71/0.89 tff(3473,plain,
% 0.71/0.89 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3409])).
% 0.71/0.89 tff(3474,plain,
% 0.71/0.89 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3473, 566])).
% 0.71/0.89 tff(3475,plain,
% 0.71/0.89 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3474])).
% 0.71/0.89 tff(3476,plain,
% 0.71/0.89 (~(op(e3, e2) = e3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[278, 3475])).
% 0.71/0.89 tff(3477,plain,
% 0.71/0.89 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3409])).
% 0.71/0.89 tff(3478,plain,
% 0.71/0.89 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3477, 1178])).
% 0.71/0.89 tff(3479,plain,
% 0.71/0.89 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3478])).
% 0.71/0.89 tff(3480,plain,
% 0.71/0.89 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3479])).
% 0.71/0.89 tff(3481,plain,
% 0.71/0.89 (~(op(e2, e2) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[170, 3480])).
% 0.71/0.89 tff(3482,plain,
% 0.71/0.89 (op(e0, e3) = e0),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1280, 3462])).
% 0.71/0.89 tff(3483,plain,
% 0.71/0.89 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3482])).
% 0.71/0.89 tff(3484,plain,
% 0.71/0.89 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3483])).
% 0.71/0.89 tff(3485,plain,
% 0.71/0.89 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3484])).
% 0.71/0.89 tff(3486,plain,
% 0.71/0.89 (~(op(e0, e3) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[40, 3485])).
% 0.71/0.89 tff(3487,plain,
% 0.71/0.89 ((op(e0, e0) = e1) <=> (e3 = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3462])).
% 0.71/0.89 tff(3488,plain,
% 0.71/0.89 ((op(e0, e0) = e1) <=> (e1 = e3)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3487, 601])).
% 0.71/0.89 tff(3489,plain,
% 0.71/0.89 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3488])).
% 0.71/0.89 tff(3490,plain,
% 0.71/0.89 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3489])).
% 0.71/0.89 tff(3491,plain,
% 0.71/0.89 (~(op(e0, e0) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[521, 3490])).
% 0.71/0.89 tff(3492,assumption,((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))), introduced(assumption)).
% 0.71/0.89 tff(3493,assumption,(op(e2, e3) = e2), introduced(assumption)).
% 0.71/0.89 tff(3494,plain,
% 0.71/0.89 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3493])).
% 0.71/0.89 tff(3495,plain,
% 0.71/0.89 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3494])).
% 0.71/0.89 tff(3496,plain,
% 0.71/0.89 (~(op(e2, e0) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[369, 3495])).
% 0.71/0.89 tff(3497,plain,
% 0.71/0.89 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3493])).
% 0.71/0.89 tff(3498,plain,
% 0.71/0.89 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3497, 1034])).
% 0.71/0.89 tff(3499,plain,
% 0.71/0.89 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3498])).
% 0.71/0.89 tff(3500,plain,
% 0.71/0.89 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3499])).
% 0.71/0.89 tff(3501,plain,
% 0.71/0.89 (~(op(e2, e3) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[353, 3500])).
% 0.71/0.89 tff(3502,assumption,(~(op(e0, e3) = e1)), introduced(assumption)).
% 0.71/0.89 tff(3503,plain,
% 0.71/0.89 (op(e1, e3) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[711, 3502, 3501, 695])).
% 0.71/0.89 tff(3504,plain,
% 0.71/0.89 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3503])).
% 0.71/0.89 tff(3505,plain,
% 0.71/0.89 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3504])).
% 0.71/0.89 tff(3506,plain,
% 0.71/0.89 (~(op(e1, e0) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[625, 3505])).
% 0.71/0.89 tff(3507,plain,
% 0.71/0.89 (op(e2, e0) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[460, 1067, 421, 3506])).
% 0.71/0.89 tff(3508,plain,
% 0.71/0.89 ((op(e2, e0) = e0) <=> (e1 = e0)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3507])).
% 0.71/0.89 tff(3509,plain,
% 0.71/0.89 ((op(e2, e0) = e0) <=> (e0 = e1)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3508, 1203])).
% 0.71/0.89 tff(3510,plain,
% 0.71/0.89 ((e0 = e1) <=> (op(e2, e0) = e0)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3509])).
% 0.71/0.89 tff(3511,plain,
% 0.71/0.89 ((~(e0 = e1)) <=> (~(op(e2, e0) = e0))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3510])).
% 0.71/0.89 tff(3512,plain,
% 0.71/0.89 (~(op(e2, e0) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[40, 3511])).
% 0.71/0.89 tff(3513,plain,
% 0.71/0.89 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3493])).
% 0.71/0.89 tff(3514,plain,
% 0.71/0.89 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3513, 1213])).
% 0.71/0.89 tff(3515,plain,
% 0.71/0.89 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3514])).
% 0.71/0.89 tff(3516,plain,
% 0.71/0.89 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3515])).
% 0.71/0.89 tff(3517,plain,
% 0.71/0.89 (~(op(e2, e3) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[16, 3516])).
% 0.71/0.89 tff(3518,plain,
% 0.71/0.89 (op(e2, e1) = e0),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1228, 3512, 3517, 1211])).
% 0.71/0.89 tff(3519,assumption,(op(e1, e3) = e1), introduced(assumption)).
% 0.71/0.89 tff(3520,plain,
% 0.71/0.89 (op(e3, op(e1, e3)) = op(e3, e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3519])).
% 0.71/0.89 tff(3521,plain,
% 0.71/0.89 ((op(e3, op(e1, e3)) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3520, 3519])).
% 0.71/0.89 tff(3522,plain,
% 0.71/0.89 ((op(e3, e1) = e1) <=> (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.89 inference(symmetry,[status(thm)],[3521])).
% 0.71/0.89 tff(3523,plain,
% 0.71/0.89 ((e0 = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.71/0.89 inference(commutativity,[status(thm)],[])).
% 0.71/0.89 tff(3524,assumption,(op(e2, e1) = e0), introduced(assumption)).
% 0.71/0.89 tff(3525,plain,
% 0.71/0.89 ((op(e2, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3524])).
% 0.71/0.89 tff(3526,plain,
% 0.71/0.89 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3525, 3523])).
% 0.71/0.89 tff(3527,plain,
% 0.71/0.89 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3526])).
% 0.71/0.89 tff(3528,plain,
% 0.71/0.89 (~(op(e3, e1) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1184, 3527])).
% 0.71/0.89 tff(3529,plain,
% 0.71/0.89 (op(e3, e2) = e0),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[288, 2097, 280, 3528])).
% 0.71/0.89 tff(3530,plain,
% 0.71/0.89 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3529])).
% 0.71/0.89 tff(3531,plain,
% 0.71/0.89 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3530])).
% 0.71/0.89 tff(3532,plain,
% 0.71/0.89 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3531])).
% 0.71/0.89 tff(3533,plain,
% 0.71/0.89 (~(op(e3, e2) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[40, 3532])).
% 0.71/0.89 tff(3534,plain,
% 0.71/0.89 (op(e3, e1) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[772, 3533, 695, 1067])).
% 0.71/0.89 tff(3535,plain,
% 0.71/0.89 (op(e3, op(e1, e3)) = op(e1, e3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3534, 3522])).
% 0.71/0.89 tff(3536,plain,
% 0.71/0.89 (op(e1, op(e2, e1)) = op(e1, e0)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3524])).
% 0.71/0.89 tff(3537,plain,
% 0.71/0.89 ((op(e1, op(e2, e1)) = op(e2, e1)) <=> (op(e1, e0) = e0)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3536, 3524])).
% 0.71/0.89 tff(3538,plain,
% 0.71/0.89 ((op(e1, e0) = e0) <=> (op(e1, op(e2, e1)) = op(e2, e1))),
% 0.71/0.89 inference(symmetry,[status(thm)],[3537])).
% 0.71/0.89 tff(3539,plain,
% 0.71/0.89 (((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))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3540,plain,
% 0.71/0.89 ((((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))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3541,plain,
% 0.71/0.89 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3542,plain,
% 0.71/0.89 (((((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))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3541])).
% 0.71/0.89 tff(3543,plain,
% 0.71/0.89 (((((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))),
% 0.71/0.89 inference(transitivity,[status(thm)],[3542, 3540])).
% 0.71/0.89 tff(3544,plain,
% 0.71/0.89 (((((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))),
% 0.71/0.89 inference(and_elim,[status(thm)],[2182])).
% 0.71/0.89 tff(3545,plain,
% 0.71/0.89 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)),
% 0.71/0.89 inference(and_elim,[status(thm)],[3544])).
% 0.71/0.89 tff(3546,plain,
% 0.71/0.89 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3545, 3543])).
% 0.71/0.89 tff(3547,plain,
% 0.71/0.89 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3546, 3539])).
% 0.71/0.89 tff(3548,plain,
% 0.71/0.89 (op(e1, e0) = e0),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3547, 2097, 1055, 1212])).
% 0.71/0.89 tff(3549,plain,
% 0.71/0.89 (op(e1, op(e2, e1)) = op(e2, e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3548, 3538])).
% 0.71/0.89 tff(3550,plain,
% 0.71/0.89 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[900, 3549])).
% 0.71/0.89 tff(3551,plain,
% 0.71/0.89 (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[798, 3550, 758, 3492])).
% 0.71/0.89 tff(3552,plain,
% 0.71/0.89 (~(op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[756, 3551])).
% 0.71/0.89 tff(3553,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3552, 3535])).
% 0.71/0.89 tff(3554,plain,((op(e3, e0) = e0) | (~(op(e1, e3) = e1)) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))) | (op(e3, e3) = e1) | (op(e3, e0) = e1) | (~(op(e2, e1) = e0)) | (op(e0, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(3555,plain,
% 0.71/0.89 (op(e3, e0) = e0),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3554, 1067, 758, 3492, 695, 3503, 3518, 1055, 3512, 280])).
% 0.71/0.89 tff(3556,plain,
% 0.71/0.89 ((op(e3, e0) = e2) <=> (e0 = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3555])).
% 0.71/0.89 tff(3557,plain,
% 0.71/0.89 ((e0 = e2) <=> (op(e3, e0) = e2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3556])).
% 0.71/0.89 tff(3558,plain,
% 0.71/0.89 ((~(e0 = e2)) <=> (~(op(e3, e0) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3557])).
% 0.71/0.89 tff(3559,plain,
% 0.71/0.89 (~(op(e3, e0) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[16, 3558])).
% 0.71/0.89 tff(3560,plain,
% 0.71/0.89 (((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3561,plain,
% 0.71/0.89 ((((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3562,plain,
% 0.71/0.89 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(3563,plain,
% 0.71/0.89 (((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)) <=> (((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3562])).
% 0.71/0.89 tff(3564,plain,
% 0.71/0.89 (((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2))),
% 0.71/0.89 inference(transitivity,[status(thm)],[3563, 3561])).
% 0.71/0.89 tff(3565,plain,
% 0.71/0.89 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)),
% 0.71/0.89 inference(and_elim,[status(thm)],[455])).
% 0.71/0.89 tff(3566,plain,
% 0.71/0.89 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 0.71/0.89 tff(3567,plain,
% 0.71/0.89 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3566, 3560])).
% 0.71/0.89 tff(3568,plain,
% 0.71/0.89 (op(e1, e0) = e2),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3567, 3559, 3213, 3496])).
% 0.71/0.89 tff(3569,plain,
% 0.71/0.89 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3568])).
% 0.71/0.89 tff(3570,plain,
% 0.71/0.89 ((op(e0, op(e1, e0)) = op(e1, e0)) <=> (op(e0, e2) = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3569, 3568])).
% 0.71/0.89 tff(3571,plain,
% 0.71/0.89 ((op(e0, e2) = e2) <=> (op(e0, op(e1, e0)) = op(e1, e0))),
% 0.71/0.89 inference(symmetry,[status(thm)],[3570])).
% 0.71/0.89 tff(3572,plain,
% 0.71/0.89 ((op(e1, e0) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3568])).
% 0.71/0.89 tff(3573,plain,
% 0.71/0.89 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3572, 3440])).
% 0.71/0.89 tff(3574,plain,
% 0.71/0.89 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3573])).
% 0.71/0.89 tff(3575,plain,
% 0.71/0.89 (~(op(e1, e2) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[613, 3574])).
% 0.71/0.89 tff(3576,plain,
% 0.71/0.89 ((op(e3, e0) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3555])).
% 0.71/0.89 tff(3577,plain,
% 0.71/0.89 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.71/0.89 inference(transitivity,[status(thm)],[3576, 272])).
% 0.71/0.89 tff(3578,plain,
% 0.71/0.89 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3577])).
% 0.71/0.89 tff(3579,plain,
% 0.71/0.89 (~(op(e3, e2) = e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[572, 3578])).
% 0.71/0.89 tff(3580,plain,
% 0.71/0.89 (op(e3, e1) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[772, 663, 695, 1067])).
% 0.71/0.89 tff(3581,plain,
% 0.71/0.89 (op(e3, op(e1, e3)) = op(e1, e3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3580, 3522])).
% 0.71/0.89 tff(3582,plain,
% 0.71/0.89 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[756, 3581])).
% 0.71/0.89 tff(3583,plain,
% 0.71/0.89 (op(e3, op(e2, e3)) = op(e3, e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3493])).
% 0.71/0.89 tff(3584,plain,
% 0.71/0.89 ((op(e3, op(e2, e3)) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3583, 3493])).
% 0.71/0.89 tff(3585,plain,
% 0.71/0.89 ((op(e3, e2) = e2) <=> (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.89 inference(symmetry,[status(thm)],[3584])).
% 0.71/0.89 tff(3586,plain,
% 0.71/0.89 (op(e3, e2) = e2),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[736, 663, 861, 728])).
% 0.71/0.89 tff(3587,plain,
% 0.71/0.89 (op(e3, op(e2, e3)) = op(e2, e3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3586, 3585])).
% 0.71/0.89 tff(3588,plain,
% 0.71/0.89 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[776, 3587])).
% 0.71/0.89 tff(3589,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[798, 3588, 3582, 758, 3492])).
% 0.71/0.89 tff(3590,plain,((op(e3, e2) = e1) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))) | (~(op(e2, e3) = e2)) | (~(op(e1, e3) = e1)) | (op(e3, e2) = e3) | (op(e3, e2) = e0) | (op(e3, e3) = e1) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(3591,plain,
% 0.71/0.89 (op(e3, e2) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3590, 3579, 3492, 3493, 3503, 861, 758, 695, 1067])).
% 0.71/0.89 tff(3592,plain,
% 0.71/0.89 ((op(e3, e2) = e2) <=> (e1 = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3591])).
% 0.71/0.89 tff(3593,plain,
% 0.71/0.89 ((e1 = e2) <=> (op(e3, e2) = e2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[3592])).
% 0.71/0.89 tff(3594,plain,
% 0.71/0.89 ((~(e1 = e2)) <=> (~(op(e3, e2) = e2))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3593])).
% 0.71/0.89 tff(3595,plain,
% 0.71/0.89 (~(op(e3, e2) = e2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[353, 3594])).
% 0.71/0.89 tff(3596,plain,
% 0.71/0.89 (op(e0, e2) = e2),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[924, 3595, 1204, 3575])).
% 0.71/0.89 tff(3597,plain,
% 0.71/0.89 (op(e0, op(e1, e0)) = op(e1, e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3596, 3571])).
% 0.71/0.89 tff(3598,plain,
% 0.71/0.89 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[883, 3597])).
% 0.71/0.89 tff(3599,plain,
% 0.71/0.89 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3507])).
% 0.71/0.89 tff(3600,plain,
% 0.71/0.89 ((op(e0, op(e2, e0)) = op(e2, e0)) <=> (op(e0, e1) = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3599, 3507])).
% 0.71/0.89 tff(3601,plain,
% 0.71/0.89 ((op(e0, e1) = e1) <=> (op(e0, op(e2, e0)) = op(e2, e0))),
% 0.71/0.89 inference(symmetry,[status(thm)],[3600])).
% 0.71/0.89 tff(3602,plain,
% 0.71/0.89 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e1)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3591])).
% 0.71/0.89 tff(3603,plain,
% 0.71/0.89 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e1))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3602])).
% 0.71/0.89 tff(3604,plain,
% 0.71/0.89 (~(op(e0, e2) = e1)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1457, 3603])).
% 0.71/0.89 tff(3605,plain,
% 0.71/0.89 (op(e0, e1) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[2185, 3604, 421, 3502])).
% 0.71/0.89 tff(3606,plain,
% 0.71/0.89 (op(e0, op(e2, e0)) = op(e2, e0)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[3605, 3601])).
% 0.71/0.89 tff(3607,plain,
% 0.71/0.89 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[927, 3606])).
% 0.71/0.89 tff(3608,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[798, 3607, 3598, 758, 3492])).
% 0.71/0.89 tff(3609,plain,((op(e3, e0) = e1) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))) | (op(e0, e0) = e1) | (op(e0, e3) = e1) | (op(e2, e2) = e2) | (~(op(e2, e3) = e2)) | (op(e3, e2) = e3) | (op(e3, e3) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e0) | (op(e3, e3) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(3610,plain,
% 0.71/0.89 (op(e3, e0) = e1),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[3609, 2827, 3435, 3491, 3486, 3481, 3436, 3476, 3454, 3467, 1055, 3414, 3472])).
% 0.71/0.89 tff(3611,plain,
% 0.71/0.89 ((op(e3, e0) = e2) <=> (e1 = e2)),
% 0.71/0.89 inference(monotonicity,[status(thm)],[3610])).
% 0.71/0.89 tff(3612,plain,
% 0.71/0.89 ((e1 = e2) <=> (op(e3, e0) = e2)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3611])).
% 0.71/0.90 tff(3613,plain,
% 0.71/0.90 ((~(e1 = e2)) <=> (~(op(e3, e0) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3612])).
% 0.71/0.90 tff(3614,plain,
% 0.71/0.90 (~(op(e3, e0) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[353, 3613])).
% 0.71/0.90 tff(3615,plain,
% 0.71/0.90 (op(e1, e0) = e2),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[3567, 3614, 3467, 3443])).
% 0.71/0.90 tff(3616,plain,
% 0.71/0.90 ((op(e1, e0) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3615])).
% 0.71/0.90 tff(3617,plain,
% 0.71/0.90 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3616, 3440])).
% 0.71/0.90 tff(3618,plain,
% 0.71/0.90 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3617])).
% 0.71/0.90 tff(3619,plain,
% 0.71/0.90 (~(op(e1, e2) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[613, 3618])).
% 0.71/0.90 tff(3620,plain,
% 0.71/0.90 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3436])).
% 0.71/0.90 tff(3621,plain,
% 0.71/0.90 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3620, 1034])).
% 0.71/0.90 tff(3622,plain,
% 0.71/0.90 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3621])).
% 0.71/0.90 tff(3623,plain,
% 0.71/0.90 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3622])).
% 0.71/0.90 tff(3624,plain,
% 0.71/0.90 (~(op(e2, e3) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[353, 3623])).
% 0.71/0.90 tff(3625,plain,
% 0.71/0.90 (op(e1, e3) = e1),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[711, 3486, 3624, 3454])).
% 0.71/0.90 tff(3626,plain,
% 0.71/0.90 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3625])).
% 0.71/0.90 tff(3627,plain,
% 0.71/0.90 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3626])).
% 0.71/0.90 tff(3628,plain,
% 0.71/0.90 (~(op(e1, e2) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[691, 3627])).
% 0.71/0.90 tff(3629,plain,
% 0.71/0.90 ((e1 = e3) <=> (e1 = op(e2, e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3468])).
% 0.71/0.90 tff(3630,plain,
% 0.71/0.90 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3629, 91])).
% 0.71/0.90 tff(3631,plain,
% 0.71/0.90 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3630])).
% 0.71/0.90 tff(3632,plain,
% 0.71/0.90 (~(op(e2, e2) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[521, 3631])).
% 0.71/0.90 tff(3633,plain,
% 0.71/0.90 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3610])).
% 0.71/0.90 tff(3634,plain,
% 0.71/0.90 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3633, 2081])).
% 0.71/0.90 tff(3635,plain,
% 0.71/0.90 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3634])).
% 0.71/0.90 tff(3636,plain,
% 0.71/0.90 (~(op(e3, e2) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[572, 3635])).
% 0.71/0.90 tff(3637,plain,
% 0.71/0.90 (op(e0, e2) = e1),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[671, 3636, 3632, 3628])).
% 0.71/0.90 tff(3638,plain,
% 0.71/0.90 ((op(e0, e2) = e2) <=> (e1 = e2)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3637])).
% 0.71/0.90 tff(3639,plain,
% 0.71/0.90 ((e1 = e2) <=> (op(e0, e2) = e2)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3638])).
% 0.71/0.90 tff(3640,plain,
% 0.71/0.90 ((~(e1 = e2)) <=> (~(op(e0, e2) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3639])).
% 0.71/0.90 tff(3641,plain,
% 0.71/0.90 (~(op(e0, e2) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[353, 3640])).
% 0.71/0.90 tff(3642,plain,
% 0.71/0.90 (op(e3, e2) = e2),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[924, 3641, 3481, 3619])).
% 0.71/0.90 tff(3643,plain,
% 0.71/0.90 (op(e3, op(e2, e3)) = op(e2, e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[3642, 3439])).
% 0.71/0.90 tff(3644,plain,
% 0.71/0.90 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[776, 3643])).
% 0.71/0.90 tff(3645,plain,
% 0.71/0.90 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3409])).
% 0.71/0.90 tff(3646,plain,
% 0.71/0.90 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3645])).
% 0.71/0.90 tff(3647,plain,
% 0.71/0.90 (~(op(e1, e2) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[243, 3646])).
% 0.71/0.90 tff(3648,plain,
% 0.71/0.90 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3462])).
% 0.71/0.90 tff(3649,plain,
% 0.71/0.90 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3648, 256])).
% 0.71/0.90 tff(3650,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3649])).
% 0.71/0.90 tff(3651,plain,
% 0.71/0.90 (~(op(e1, e0) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[254, 3650])).
% 0.71/0.90 tff(3652,plain,
% 0.71/0.90 (op(e1, e1) = e3),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[530, 3651, 3647, 3457])).
% 0.71/0.90 tff(3653,plain,
% 0.71/0.90 ((op(e1, e1) = e0) <=> (e3 = e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3652])).
% 0.71/0.90 tff(3654,plain,
% 0.71/0.90 ((op(e1, e1) = e0) <=> (e0 = e3)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3653, 1])).
% 0.71/0.90 tff(3655,plain,
% 0.71/0.90 ((e0 = e3) <=> (op(e1, e1) = e0)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3654])).
% 0.71/0.90 tff(3656,plain,
% 0.71/0.90 ((~(e0 = e3)) <=> (~(op(e1, e1) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3655])).
% 0.71/0.90 tff(3657,plain,
% 0.71/0.90 (~(op(e1, e1) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[509, 3656])).
% 0.71/0.90 tff(3658,plain,
% 0.71/0.90 ((op(e0, e3) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3482])).
% 0.71/0.90 tff(3659,plain,
% 0.71/0.90 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3658, 2599])).
% 0.71/0.90 tff(3660,plain,
% 0.71/0.90 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3659])).
% 0.71/0.90 tff(3661,plain,
% 0.71/0.90 (~(op(e1, e3) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1762, 3660])).
% 0.71/0.90 tff(3662,plain,
% 0.71/0.90 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3615])).
% 0.71/0.90 tff(3663,plain,
% 0.71/0.90 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3662, 1213])).
% 0.71/0.90 tff(3664,plain,
% 0.71/0.90 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3663])).
% 0.71/0.90 tff(3665,plain,
% 0.71/0.90 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3664])).
% 0.71/0.90 tff(3666,plain,
% 0.71/0.90 (~(op(e1, e0) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[16, 3665])).
% 0.71/0.90 tff(3667,plain,
% 0.71/0.90 (op(e1, e2) = e0),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[548, 3666, 3661, 3657])).
% 0.71/0.90 tff(3668,plain,
% 0.71/0.90 (e0 = op(e1, e2)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3667])).
% 0.71/0.90 tff(3669,plain,
% 0.71/0.90 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3409])).
% 0.71/0.90 tff(3670,plain,
% 0.71/0.90 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3669])).
% 0.71/0.90 tff(3671,plain,
% 0.71/0.90 (~(op(e2, e0) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[85, 3670])).
% 0.71/0.90 tff(3672,plain,
% 0.71/0.90 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e1)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3610])).
% 0.71/0.90 tff(3673,plain,
% 0.71/0.90 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3672])).
% 0.71/0.90 tff(3674,plain,
% 0.71/0.90 (~(op(e2, e0) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[589, 3673])).
% 0.71/0.90 tff(3675,plain,
% 0.71/0.90 (op(e2, e0) = e0),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[121, 3674, 3671, 3443])).
% 0.71/0.90 tff(3676,plain,
% 0.71/0.90 (op(e2, op(e1, e2)) = op(e2, e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3667])).
% 0.71/0.90 tff(3677,plain,
% 0.71/0.90 (op(e2, op(e1, e2)) = op(e1, e2)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3676, 3675, 3668])).
% 0.71/0.90 tff(3678,plain,
% 0.71/0.90 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[961, 3677])).
% 0.71/0.90 tff(3679,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[798, 3678, 3644, 2827, 3435])).
% 0.71/0.90 tff(3680,plain,((op(e0, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3))) | (e0 = op(op(e2, e2), op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(3681,plain,
% 0.71/0.90 (op(e0, e0) = e0),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[3680, 1054, 1053])).
% 0.71/0.90 tff(3682,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3683,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3682, 820])).
% 0.71/0.90 tff(3684,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3683])).
% 0.71/0.90 tff(3685,plain,
% 0.71/0.90 (~(op(e0, e1) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[826, 3684])).
% 0.71/0.90 tff(3686,plain,
% 0.71/0.90 (e0 = op(e0, e0)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3681])).
% 0.71/0.90 tff(3687,plain,
% 0.71/0.90 ((e0 = e2) <=> (op(e0, e0) = e2)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3686])).
% 0.71/0.90 tff(3688,plain,
% 0.71/0.90 ((~(e0 = e2)) <=> (~(op(e0, e0) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3687])).
% 0.71/0.90 tff(3689,plain,
% 0.71/0.90 (~(op(e0, e0) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[16, 3688])).
% 0.71/0.90 tff(3690,plain,
% 0.71/0.90 (op(e0, op(e0, e0)) = op(e0, e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3691,plain,
% 0.71/0.90 ((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[650, 3690])).
% 0.71/0.90 tff(3692,plain,
% 0.71/0.90 ((op(e0, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3693,plain,
% 0.71/0.90 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3692, 261])).
% 0.71/0.90 tff(3694,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3693])).
% 0.71/0.90 tff(3695,plain,
% 0.71/0.90 (~(op(e3, e0) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[270, 3694])).
% 0.71/0.90 tff(3696,plain,
% 0.71/0.90 ((e0 = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 0.71/0.90 inference(commutativity,[status(thm)],[])).
% 0.71/0.90 tff(3697,plain,
% 0.71/0.90 ((op(e0, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3698,plain,
% 0.71/0.90 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3697, 3696])).
% 0.71/0.90 tff(3699,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3698])).
% 0.71/0.90 tff(3700,plain,
% 0.71/0.90 (~(op(e2, e0) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[162, 3699])).
% 0.71/0.90 tff(3701,plain,
% 0.71/0.90 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3702,plain,
% 0.71/0.90 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3701, 245])).
% 0.71/0.90 tff(3703,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3702])).
% 0.71/0.90 tff(3704,plain,
% 0.71/0.90 (~(op(e1, e0) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[254, 3703])).
% 0.71/0.90 tff(3705,plain,
% 0.71/0.90 ((e0 = e1) <=> (op(e0, e0) = e1)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3686])).
% 0.71/0.90 tff(3706,plain,
% 0.71/0.90 ((~(e0 = e1)) <=> (~(op(e0, e0) = e1))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3705])).
% 0.71/0.90 tff(3707,plain,
% 0.71/0.90 (~(op(e0, e0) = e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[40, 3706])).
% 0.71/0.90 tff(3708,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3709,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3708, 299])).
% 0.71/0.90 tff(3710,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3709])).
% 0.71/0.90 tff(3711,plain,
% 0.71/0.90 (~(op(e0, e3) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[305, 3710])).
% 0.71/0.90 tff(3712,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3681])).
% 0.71/0.90 tff(3713,plain,
% 0.71/0.90 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3712, 2615])).
% 0.71/0.90 tff(3714,plain,
% 0.71/0.90 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3713])).
% 0.71/0.90 tff(3715,plain,
% 0.71/0.90 (~(op(e0, e2) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1463, 3714])).
% 0.71/0.90 tff(3716,plain,
% 0.71/0.90 (op(op(e2, e2), op(e2, e2)) = op(e0, e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[257, 257])).
% 0.71/0.90 tff(3717,plain,
% 0.71/0.90 (op(e0, e0) = op(op(e2, e2), op(e2, e2))),
% 0.71/0.90 inference(symmetry,[status(thm)],[3716])).
% 0.71/0.90 tff(3718,assumption,(op(e0, e0) = e0), introduced(assumption)).
% 0.71/0.90 tff(3719,plain,
% 0.71/0.90 (e0 = op(e0, e0)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3718])).
% 0.71/0.90 tff(3720,plain,
% 0.71/0.90 (e0 = op(op(e2, e2), op(e2, e2))),
% 0.71/0.90 inference(transitivity,[status(thm)],[3719, 3717])).
% 0.71/0.90 tff(3721,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1054, 3720])).
% 0.71/0.90 tff(3722,plain,((~(op(e2, e2) = e0)) | (e0 = op(op(e2, e2), op(e2, e2))) | (~(op(e0, e0) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(3723,plain,
% 0.71/0.90 (~(op(e2, e2) = e0)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[3722, 1054, 3681])).
% 0.71/0.90 tff(3724,plain,
% 0.71/0.90 ((e1 = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.71/0.90 inference(commutativity,[status(thm)],[])).
% 0.71/0.90 tff(3725,plain,
% 0.71/0.90 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1074])).
% 0.71/0.90 tff(3726,plain,
% 0.71/0.90 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3725])).
% 0.71/0.90 tff(3727,plain,
% 0.71/0.90 (~(op(e3, e2) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1160, 3726])).
% 0.71/0.90 tff(3728,plain,
% 0.71/0.90 (op(e1, e2) = e0),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1678, 3727, 1211, 1789])).
% 0.71/0.90 tff(3729,plain,
% 0.71/0.90 ((op(e1, e2) = e3) <=> (e0 = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3728])).
% 0.71/0.90 tff(3730,plain,
% 0.71/0.90 ((e0 = e3) <=> (op(e1, e2) = e3)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3729])).
% 0.71/0.90 tff(3731,plain,
% 0.71/0.90 ((~(e0 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3730])).
% 0.71/0.90 tff(3732,plain,
% 0.71/0.90 (~(op(e1, e2) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[509, 3731])).
% 0.71/0.90 tff(3733,plain,
% 0.71/0.90 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1075])).
% 0.71/0.90 tff(3734,plain,
% 0.71/0.90 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3733])).
% 0.71/0.90 tff(3735,plain,
% 0.71/0.90 (~(op(e1, e0) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[564, 3734])).
% 0.71/0.90 tff(3736,plain,
% 0.71/0.90 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1075])).
% 0.71/0.90 tff(3737,plain,
% 0.71/0.90 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3736])).
% 0.71/0.90 tff(3738,plain,
% 0.71/0.90 (~(op(e2, e0) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[589, 3737])).
% 0.71/0.90 tff(3739,plain,
% 0.71/0.90 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1074])).
% 0.71/0.90 tff(3740,plain,
% 0.71/0.90 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3739])).
% 0.71/0.90 tff(3741,plain,
% 0.71/0.90 (~(op(e2, e3) = e0)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[196, 3740])).
% 0.71/0.90 tff(3742,plain,
% 0.71/0.90 (op(e2, e1) = e0),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1228, 3741, 1212, 1211])).
% 0.71/0.90 tff(3743,plain,
% 0.71/0.90 ((op(e2, e1) = e3) <=> (e0 = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3742])).
% 0.71/0.90 tff(3744,plain,
% 0.71/0.90 ((e0 = e3) <=> (op(e2, e1) = e3)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3743])).
% 0.71/0.90 tff(3745,plain,
% 0.71/0.90 ((~(e0 = e3)) <=> (~(op(e2, e1) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3744])).
% 0.71/0.90 tff(3746,plain,
% 0.71/0.90 (~(op(e2, e1) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[509, 3745])).
% 0.71/0.90 tff(3747,plain,
% 0.71/0.90 (op(e2, e3) = e3),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[189, 3746, 3738, 26])).
% 0.71/0.90 tff(3748,plain,
% 0.71/0.90 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3747])).
% 0.71/0.90 tff(3749,plain,
% 0.71/0.90 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3748])).
% 0.71/0.90 tff(3750,plain,
% 0.71/0.90 (~(op(e1, e3) = e3)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[894, 3749])).
% 0.71/0.90 tff(3751,plain,
% 0.71/0.90 (op(e1, e1) = e3),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[530, 3750, 3735, 3732])).
% 0.71/0.90 tff(3752,plain,
% 0.71/0.90 (op(op(e1, e1), op(e1, e1)) = op(e3, e3)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3751, 3751])).
% 0.71/0.90 tff(3753,plain,
% 0.71/0.90 (op(op(e1, e1), op(e1, e1)) = e0),
% 0.71/0.90 inference(transitivity,[status(thm)],[3752, 1074])).
% 0.71/0.90 tff(3754,plain,
% 0.71/0.90 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e0)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3753])).
% 0.71/0.90 tff(3755,plain,
% 0.71/0.90 (op(e1, e0) = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.90 inference(symmetry,[status(thm)],[3754])).
% 0.71/0.90 tff(3756,plain,
% 0.71/0.90 ((op(e3, e0) = e2) <=> (e3 = e2)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1075])).
% 0.71/0.90 tff(3757,plain,
% 0.71/0.90 ((op(e3, e0) = e2) <=> (e2 = e3)),
% 0.71/0.90 inference(transitivity,[status(thm)],[3756, 1178])).
% 0.71/0.90 tff(3758,plain,
% 0.71/0.90 ((e2 = e3) <=> (op(e3, e0) = e2)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3757])).
% 0.71/0.90 tff(3759,plain,
% 0.71/0.90 ((~(e2 = e3)) <=> (~(op(e3, e0) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3758])).
% 0.71/0.90 tff(3760,plain,
% 0.71/0.90 (~(op(e3, e0) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[170, 3759])).
% 0.71/0.90 tff(3761,plain,
% 0.71/0.90 ((op(e2, e1) = e2) <=> (e0 = e2)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3742])).
% 0.71/0.90 tff(3762,plain,
% 0.71/0.90 ((e0 = e2) <=> (op(e2, e1) = e2)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3761])).
% 0.71/0.90 tff(3763,plain,
% 0.71/0.90 ((~(e0 = e2)) <=> (~(op(e2, e1) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3762])).
% 0.71/0.90 tff(3764,plain,
% 0.71/0.90 (~(op(e2, e1) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[16, 3763])).
% 0.71/0.90 tff(3765,plain,
% 0.71/0.90 (~(op(e2, e2) = e1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[52, 3764])).
% 0.71/0.90 tff(3766,plain,
% 0.71/0.90 (op(e2, e2) = e2),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[226, 3765, 1211, 26])).
% 0.71/0.90 tff(3767,plain,
% 0.71/0.90 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e2)),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3766])).
% 0.71/0.90 tff(3768,plain,
% 0.71/0.90 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e2))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3767])).
% 0.71/0.90 tff(3769,plain,
% 0.71/0.90 (~(op(e2, e0) = e2)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[85, 3768])).
% 0.71/0.90 tff(3770,plain,
% 0.71/0.90 (op(e1, e0) = e2),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[3567, 3769, 3213, 3760])).
% 0.71/0.90 tff(3771,plain,
% 0.71/0.90 (e2 = op(e1, e0)),
% 0.71/0.90 inference(symmetry,[status(thm)],[3770])).
% 0.71/0.90 tff(3772,plain,
% 0.71/0.90 (e2 = op(e1, op(op(e1, e1), op(e1, e1)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[3771, 3755])).
% 0.71/0.90 tff(3773,plain,
% 0.71/0.90 ((op(e1, e1) = e3) <=> (e3 = op(e1, e1))),
% 0.71/0.90 inference(symmetry,[status(thm)],[1729])).
% 0.71/0.90 tff(3774,plain,
% 0.71/0.90 (e3 = op(e1, e1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[3751, 3773])).
% 0.71/0.90 tff(3775,plain,
% 0.71/0.90 (op(e3, e3) = op(op(e1, e1), op(e1, e1))),
% 0.71/0.90 inference(symmetry,[status(thm)],[3752])).
% 0.71/0.90 tff(3776,plain,
% 0.71/0.90 (e0 = op(e3, e3)),
% 0.71/0.90 inference(symmetry,[status(thm)],[1074])).
% 0.71/0.90 tff(3777,plain,
% 0.71/0.90 (e0 = op(op(e1, e1), op(e1, e1))),
% 0.71/0.90 inference(transitivity,[status(thm)],[3776, 3775])).
% 0.71/0.90 tff(3778,plain,
% 0.71/0.90 ((~(~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1)))))))) <=> ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(3779,plain,
% 0.71/0.90 (((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1)))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(3780,plain,
% 0.71/0.90 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[3779])).
% 0.71/0.90 tff(3781,plain,
% 0.71/0.90 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[3780, 3778])).
% 0.71/0.90 tff(3782,plain,
% 0.71/0.90 ((~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(3783,plain,
% 0.71/0.90 ((~(((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1))) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(3784,axiom,(~(((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1))) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax11')).
% 0.71/0.91 tff(3785,plain,
% 0.71/0.91 (~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 0.71/0.91 tff(3786,plain,
% 0.71/0.91 (~((e0 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[3785, 3782])).
% 0.71/0.91 tff(3787,plain,
% 0.71/0.91 ((~(e0 = op(op(e1, e1), op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[3786, 3781])).
% 0.71/0.91 tff(3788,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3787, 3777, 3774, 3772])).
% 0.71/0.91 tff(3789,plain,((~(op(e3, e3) = e0)) | (op(e0, e0) = e2) | (op(e2, e2) = e0) | (op(e2, e2) = e3) | (op(e0, e2) = e0) | (op(e2, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(3790,plain,
% 0.71/0.91 (~(op(e3, e3) = e0)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3789, 26, 1211, 3213, 1789, 1212])).
% 0.71/0.91 tff(3791,assumption,(op(e3, e3) = e2), introduced(assumption)).
% 0.71/0.91 tff(3792,plain,
% 0.71/0.91 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3791])).
% 0.71/0.91 tff(3793,plain,
% 0.71/0.91 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3792])).
% 0.71/0.91 tff(3794,plain,
% 0.71/0.91 (~(op(e3, e0) = e2)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1424, 3793])).
% 0.71/0.91 tff(3795,plain,
% 0.71/0.91 (op(e3, e2) = e3),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1127, 3791])).
% 0.71/0.91 tff(3796,plain,
% 0.71/0.91 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3795])).
% 0.71/0.91 tff(3797,plain,
% 0.71/0.91 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3796])).
% 0.71/0.91 tff(3798,plain,
% 0.71/0.91 (~(op(e3, e0) = e3)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[572, 3797])).
% 0.71/0.91 tff(3799,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1333, 3798, 3794, 2097, 1067])).
% 0.71/0.91 tff(3800,plain,((~(op(e3, e3) = e2)) | (op(e3, e0) = e0) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(3801,plain,
% 0.71/0.91 (~(op(e3, e3) = e2)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3800, 1067, 2097])).
% 0.71/0.91 tff(3802,plain,
% 0.71/0.91 (op(e3, e3) = e3),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1123, 280, 695, 3801])).
% 0.71/0.91 tff(3803,plain,
% 0.71/0.91 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3802])).
% 0.71/0.91 tff(3804,plain,
% 0.71/0.91 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3803])).
% 0.71/0.91 tff(3805,plain,
% 0.71/0.91 (~(op(e3, e0) = e3)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1424, 3804])).
% 0.71/0.91 tff(3806,plain,
% 0.71/0.91 (op(e3, e0) = e2),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1333, 3805, 2097, 1067])).
% 0.71/0.91 tff(3807,plain,
% 0.71/0.91 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3806])).
% 0.71/0.91 tff(3808,plain,
% 0.71/0.91 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3807, 1894])).
% 0.71/0.91 tff(3809,plain,
% 0.71/0.91 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3808])).
% 0.71/0.91 tff(3810,plain,
% 0.71/0.91 (~(op(e3, e1) = e2)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1320, 3809])).
% 0.71/0.91 tff(3811,plain,
% 0.71/0.91 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3802])).
% 0.71/0.91 tff(3812,plain,
% 0.71/0.91 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3811])).
% 0.71/0.91 tff(3813,plain,
% 0.71/0.91 (~(op(e3, e1) = e3)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1780, 3812])).
% 0.71/0.91 tff(3814,plain,
% 0.71/0.91 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3806])).
% 0.71/0.91 tff(3815,plain,
% 0.71/0.91 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3814])).
% 0.71/0.91 tff(3816,plain,
% 0.71/0.91 (~(op(e1, e0) = e2)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[564, 3815])).
% 0.71/0.91 tff(3817,plain,
% 0.71/0.91 (op(e3, op(e3, e3)) = op(e3, e3)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3432, 3802])).
% 0.71/0.91 tff(3818,plain,
% 0.71/0.91 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3434, 3817])).
% 0.71/0.91 tff(3819,assumption,(~(op(e3, e1) = e1)), introduced(assumption)).
% 0.71/0.91 tff(3820,plain,
% 0.71/0.91 (op(e3, e1) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[2875, 3819, 1833, 372])).
% 0.71/0.91 tff(3821,plain,
% 0.71/0.91 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3820])).
% 0.71/0.91 tff(3822,plain,
% 0.71/0.91 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3821])).
% 0.71/0.91 tff(3823,plain,
% 0.71/0.91 (~(op(e1, e1) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[338, 3822])).
% 0.71/0.91 tff(3824,plain,
% 0.71/0.91 (op(e3, e2) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[772, 3819, 695, 1067])).
% 0.71/0.91 tff(3825,plain,
% 0.71/0.91 ((op(e3, e2) = e0) <=> (e1 = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3824])).
% 0.71/0.91 tff(3826,plain,
% 0.71/0.91 ((op(e3, e2) = e0) <=> (e0 = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3825, 1203])).
% 0.71/0.91 tff(3827,plain,
% 0.71/0.91 ((e0 = e1) <=> (op(e3, e2) = e0)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3826])).
% 0.71/0.91 tff(3828,plain,
% 0.71/0.91 ((~(e0 = e1)) <=> (~(op(e3, e2) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3827])).
% 0.71/0.91 tff(3829,plain,
% 0.71/0.91 (~(op(e3, e2) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[40, 3828])).
% 0.71/0.91 tff(3830,plain,
% 0.71/0.91 (op(e1, e2) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1678, 3829, 1211, 1789])).
% 0.71/0.91 tff(3831,plain,
% 0.71/0.91 ((op(e1, e2) = e2) <=> (e0 = e2)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3830])).
% 0.71/0.91 tff(3832,plain,
% 0.71/0.91 ((e0 = e2) <=> (op(e1, e2) = e2)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3831])).
% 0.71/0.91 tff(3833,plain,
% 0.71/0.91 ((~(e0 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3832])).
% 0.71/0.91 tff(3834,plain,
% 0.71/0.91 (~(op(e1, e2) = e2)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[16, 3833])).
% 0.71/0.91 tff(3835,plain,
% 0.71/0.91 (op(e1, e3) = e2),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[751, 3834, 727, 379])).
% 0.71/0.91 tff(3836,plain,
% 0.71/0.91 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3835])).
% 0.71/0.91 tff(3837,plain,
% 0.71/0.91 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3836, 1034])).
% 0.71/0.91 tff(3838,plain,
% 0.71/0.91 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3837])).
% 0.71/0.91 tff(3839,plain,
% 0.71/0.91 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3838])).
% 0.71/0.91 tff(3840,plain,
% 0.71/0.91 (~(op(e1, e3) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[353, 3839])).
% 0.71/0.91 tff(3841,plain,
% 0.71/0.91 (~(op(e1, e1) = e3)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[332, 3840])).
% 0.71/0.91 tff(3842,plain,
% 0.71/0.91 (op(e1, e1) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[435, 3841, 3823, 379])).
% 0.71/0.91 tff(3843,plain,
% 0.71/0.91 (op(e1, op(e1, e1)) = op(e1, e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3842])).
% 0.71/0.91 tff(3844,plain,
% 0.71/0.91 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3824])).
% 0.71/0.91 tff(3845,plain,
% 0.71/0.91 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3844])).
% 0.71/0.91 tff(3846,plain,
% 0.71/0.91 (~(op(e2, e2) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[278, 3845])).
% 0.71/0.91 tff(3847,plain,
% 0.71/0.91 (op(e2, e2) = e2),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[226, 3846, 1211, 26])).
% 0.71/0.91 tff(3848,plain,
% 0.71/0.91 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3847])).
% 0.71/0.91 tff(3849,plain,
% 0.71/0.91 (((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))) | (~(op(e2, op(e2, e2)) = op(e2, e2)))),
% 0.71/0.91 inference(tautology,[status(thm)],[])).
% 0.71/0.91 tff(3850,plain,
% 0.71/0.91 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3849, 3848])).
% 0.71/0.91 tff(3851,plain,
% 0.71/0.91 (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[798, 3850, 758, 3492])).
% 0.71/0.91 tff(3852,plain,
% 0.71/0.91 (~(op(e1, op(e1, e1)) = op(e1, e1))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3222, 3851])).
% 0.71/0.91 tff(3853,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3852, 3843])).
% 0.71/0.91 tff(3854,plain,((op(e3, e1) = e1) | (op(e1, e1) = e2) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))) | (op(e1, e0) = e2) | (op(e2, e2) = e0) | (op(e2, e2) = e3) | (op(e0, e2) = e0) | (op(e3, e1) = e3) | (op(e3, e1) = e2) | (op(e3, e3) = e1) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(3855,plain,
% 0.71/0.91 (op(e3, e1) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3854, 379, 758, 3818, 3816, 1211, 26, 1789, 3813, 3810, 695, 1067])).
% 0.71/0.91 tff(3856,plain,
% 0.71/0.91 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3855])).
% 0.71/0.91 tff(3857,plain,
% 0.71/0.91 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3856])).
% 0.71/0.91 tff(3858,plain,
% 0.71/0.91 (~(op(e1, e1) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[338, 3857])).
% 0.71/0.91 tff(3859,plain,
% 0.71/0.91 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3855])).
% 0.71/0.91 tff(3860,plain,
% 0.71/0.91 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3859])).
% 0.71/0.91 tff(3861,plain,
% 0.71/0.91 (~(op(e2, e1) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1184, 3860])).
% 0.71/0.91 tff(3862,plain,
% 0.71/0.91 ((e1 = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.71/0.91 inference(commutativity,[status(thm)],[])).
% 0.71/0.91 tff(3863,plain,
% 0.71/0.91 ((op(e1, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3099])).
% 0.71/0.91 tff(3864,plain,
% 0.71/0.91 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3863, 3862])).
% 0.71/0.91 tff(3865,plain,
% 0.71/0.91 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3864])).
% 0.71/0.91 tff(3866,plain,
% 0.71/0.91 (~(op(e2, e0) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[638, 3865])).
% 0.71/0.91 tff(3867,assumption,(~(op(e2, e1) = e1)), introduced(assumption)).
% 0.71/0.91 tff(3868,plain,
% 0.71/0.91 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3087])).
% 0.71/0.91 tff(3869,plain,
% 0.71/0.91 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3868, 3241])).
% 0.71/0.91 tff(3870,plain,
% 0.71/0.91 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3869])).
% 0.71/0.91 tff(3871,plain,
% 0.71/0.91 (~(op(e2, e1) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1049, 3870])).
% 0.71/0.91 tff(3872,plain,
% 0.71/0.91 (op(e2, e3) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1228, 3871, 1212, 1211])).
% 0.71/0.91 tff(3873,plain,
% 0.71/0.91 ((op(e2, e3) = e1) <=> (e0 = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3872])).
% 0.71/0.91 tff(3874,plain,
% 0.71/0.91 ((e0 = e1) <=> (op(e2, e3) = e1)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3873])).
% 0.71/0.91 tff(3875,plain,
% 0.71/0.91 ((~(e0 = e1)) <=> (~(op(e2, e3) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3874])).
% 0.71/0.91 tff(3876,plain,
% 0.71/0.91 (~(op(e2, e3) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[40, 3875])).
% 0.71/0.91 tff(3877,plain,
% 0.71/0.91 (op(e2, e2) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[953, 3876, 3867, 3866])).
% 0.71/0.91 tff(3878,plain,
% 0.71/0.91 (op(op(e2, e2), op(e2, e2)) = op(e1, e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3877, 3877])).
% 0.71/0.91 tff(3879,plain,
% 0.71/0.91 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.71/0.91 inference(symmetry,[status(thm)],[3878])).
% 0.71/0.91 tff(3880,plain,
% 0.71/0.91 (e0 = op(e1, e1)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3087])).
% 0.71/0.91 tff(3881,plain,
% 0.71/0.91 (e0 = op(op(e2, e2), op(e2, e2))),
% 0.71/0.91 inference(transitivity,[status(thm)],[3880, 3879])).
% 0.71/0.91 tff(3882,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1054, 3881])).
% 0.71/0.91 tff(3883,plain,((~(op(e1, e1) = e0)) | (e0 = op(op(e2, e2), op(e2, e2))) | (op(e2, e1) = e1) | (op(e2, e0) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(3884,plain,
% 0.71/0.91 (~(op(e1, e1) = e0)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3883, 3861, 1054, 1212, 1211])).
% 0.71/0.91 tff(3885,plain,
% 0.71/0.91 (op(e1, e1) = e3),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[435, 3884, 3858, 379])).
% 0.71/0.91 tff(3886,plain,
% 0.71/0.91 (op(e1, e3) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[332, 3885])).
% 0.71/0.91 tff(3887,plain,
% 0.71/0.91 ((op(e3, e1) = e0) <=> (e1 = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3855])).
% 0.71/0.91 tff(3888,plain,
% 0.71/0.91 ((op(e3, e1) = e0) <=> (e0 = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3887, 1203])).
% 0.71/0.91 tff(3889,plain,
% 0.71/0.91 ((e0 = e1) <=> (op(e3, e1) = e0)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3888])).
% 0.71/0.91 tff(3890,plain,
% 0.71/0.91 ((~(e0 = e1)) <=> (~(op(e3, e1) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3889])).
% 0.71/0.91 tff(3891,plain,
% 0.71/0.91 (~(op(e3, e1) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[40, 3890])).
% 0.71/0.91 tff(3892,plain,
% 0.71/0.91 (op(e3, e2) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[288, 3891, 280, 2097])).
% 0.71/0.91 tff(3893,plain,
% 0.71/0.91 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3892])).
% 0.71/0.91 tff(3894,plain,
% 0.71/0.91 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3893])).
% 0.71/0.91 tff(3895,plain,
% 0.71/0.91 (~(op(e1, e2) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[742, 3894])).
% 0.71/0.91 tff(3896,plain,
% 0.71/0.91 (op(e1, e3) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[548, 3884, 1796, 3895])).
% 0.71/0.91 tff(3897,plain,
% 0.71/0.91 (e0 = op(e1, e3)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3896])).
% 0.71/0.91 tff(3898,plain,
% 0.71/0.91 (e0 = e1),
% 0.71/0.91 inference(transitivity,[status(thm)],[3897, 3886])).
% 0.71/0.91 tff(3899,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[40, 3898])).
% 0.71/0.91 tff(3900,plain,((op(e1, e1) = e2) | (op(e1, e0) = e0) | (e0 = op(op(e2, e2), op(e2, e2))) | (op(e2, e0) = e0) | (op(e2, e2) = e0) | (op(e3, e3) = e0) | (op(e3, e0) = e0) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e2, e2) = e3) | (op(e0, e2) = e0) | (op(e3, e3) = e1) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(3901,plain,
% 0.71/0.91 (op(e1, e1) = e2),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[3900, 3790, 1054, 1212, 1211, 1796, 2097, 758, 26, 1789, 695, 1067])).
% 0.71/0.91 tff(3902,plain,
% 0.71/0.91 (op(e1, e2) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[514, 3901])).
% 0.71/0.91 tff(3903,plain,
% 0.71/0.91 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3902])).
% 0.71/0.91 tff(3904,plain,
% 0.71/0.91 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3903])).
% 0.71/0.91 tff(3905,plain,
% 0.71/0.91 (~(op(e1, e0) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[613, 3904])).
% 0.71/0.91 tff(3906,plain,
% 0.71/0.91 (op(e2, e0) = e1),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[460, 3905, 421, 1067])).
% 0.71/0.91 tff(3907,plain,
% 0.71/0.91 ((op(e2, e0) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3906])).
% 0.71/0.91 tff(3908,plain,
% 0.71/0.91 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3907, 3724])).
% 0.71/0.91 tff(3909,plain,
% 0.71/0.91 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3908])).
% 0.71/0.91 tff(3910,plain,
% 0.71/0.91 (~(op(e2, e3) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[369, 3909])).
% 0.71/0.91 tff(3911,plain,
% 0.71/0.91 (op(e3, e3) = e3),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1123, 3790, 695, 3801])).
% 0.71/0.91 tff(3912,plain,
% 0.71/0.91 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3911])).
% 0.71/0.91 tff(3913,plain,
% 0.71/0.91 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3912])).
% 0.71/0.91 tff(3914,plain,
% 0.71/0.91 (~(op(e2, e3) = e3)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[196, 3913])).
% 0.71/0.91 tff(3915,plain,
% 0.71/0.91 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3902])).
% 0.71/0.91 tff(3916,plain,
% 0.71/0.91 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3915, 1203])).
% 0.71/0.91 tff(3917,plain,
% 0.71/0.91 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3916])).
% 0.71/0.91 tff(3918,plain,
% 0.71/0.91 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3917])).
% 0.71/0.91 tff(3919,plain,
% 0.71/0.91 (~(op(e1, e2) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[40, 3918])).
% 0.71/0.91 tff(3920,plain,
% 0.71/0.91 ((op(e1, e1) = e0) <=> (e2 = e0)),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3901])).
% 0.71/0.91 tff(3921,plain,
% 0.71/0.91 ((op(e1, e1) = e0) <=> (e0 = e2)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3920, 1213])).
% 0.71/0.91 tff(3922,plain,
% 0.71/0.91 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 0.71/0.91 inference(symmetry,[status(thm)],[3921])).
% 0.71/0.91 tff(3923,plain,
% 0.71/0.91 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3922])).
% 0.71/0.91 tff(3924,plain,
% 0.71/0.91 (~(op(e1, e1) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[16, 3923])).
% 0.71/0.91 tff(3925,plain,
% 0.71/0.91 (op(e1, e3) = e0),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[548, 3924, 1796, 3919])).
% 0.71/0.91 tff(3926,plain,
% 0.71/0.91 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3925])).
% 0.71/0.91 tff(3927,plain,
% 0.71/0.91 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3926, 307])).
% 0.71/0.91 tff(3928,plain,
% 0.71/0.91 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3927])).
% 0.71/0.91 tff(3929,plain,
% 0.71/0.91 (~(op(e2, e3) = e0)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[894, 3928])).
% 0.71/0.91 tff(3930,plain,
% 0.71/0.91 ((e2 = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.71/0.91 inference(commutativity,[status(thm)],[])).
% 0.71/0.91 tff(3931,plain,
% 0.71/0.91 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3902])).
% 0.71/0.91 tff(3932,plain,
% 0.71/0.91 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3931, 91])).
% 0.71/0.91 tff(3933,plain,
% 0.71/0.91 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3932])).
% 0.71/0.91 tff(3934,plain,
% 0.71/0.91 (~(op(e2, e2) = e1)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[243, 3933])).
% 0.71/0.91 tff(3935,plain,
% 0.71/0.91 (op(e2, e2) = e2),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[226, 3934, 1211, 26])).
% 0.71/0.91 tff(3936,plain,
% 0.71/0.91 ((op(e2, e2) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3935])).
% 0.71/0.91 tff(3937,plain,
% 0.71/0.91 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.71/0.91 inference(transitivity,[status(thm)],[3936, 3930])).
% 0.71/0.91 tff(3938,plain,
% 0.71/0.91 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3937])).
% 0.71/0.91 tff(3939,plain,
% 0.71/0.91 (~(op(e2, e3) = e2)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[313, 3938])).
% 0.71/0.91 tff(3940,plain,
% 0.71/0.91 (((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))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(3941,plain,
% 0.71/0.91 ((((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))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(3942,plain,
% 0.71/0.91 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(3943,plain,
% 0.71/0.91 (((((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))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[3942])).
% 0.71/0.91 tff(3944,plain,
% 0.71/0.91 (((((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))),
% 0.71/0.91 inference(transitivity,[status(thm)],[3943, 3941])).
% 0.71/0.91 tff(3945,plain,
% 0.71/0.91 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)),
% 0.71/0.91 inference(and_elim,[status(thm)],[115])).
% 0.71/0.91 tff(3946,plain,
% 0.71/0.91 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[3945, 3944])).
% 0.71/0.91 tff(3947,plain,
% 0.71/0.91 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[3946, 3940])).
% 0.71/0.92 tff(3948,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3947, 3939, 3929, 3914, 3910])).
% 0.71/0.92 tff(3949,plain,((op(e2, e2) = e3) | (op(e0, e0) = e1) | (op(e3, e0) = e1) | (op(e2, e2) = e0) | (op(e1, e0) = e0) | (e0 = op(op(e2, e2), op(e2, e2))) | (op(e2, e0) = e0) | (op(e3, e0) = e0) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e0, e2) = e0) | (op(e3, e3) = e1) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(3950,plain,
% 0.71/0.92 (op(e2, e2) = e3),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3949, 1067, 421, 1211, 1796, 1054, 1212, 2097, 758, 1789, 695, 3213])).
% 0.71/0.92 tff(3951,plain,
% 0.71/0.92 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3950, 3950])).
% 0.71/0.92 tff(3952,plain,
% 0.71/0.92 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (e0 = op(e3, e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3951])).
% 0.71/0.92 tff(3953,plain,
% 0.71/0.92 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e0)),
% 0.71/0.92 inference(transitivity,[status(thm)],[3952, 2])).
% 0.71/0.92 tff(3954,plain,
% 0.71/0.92 ((~(e0 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e0))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3953])).
% 0.71/0.92 tff(3955,plain,
% 0.71/0.92 (~(op(e3, e3) = e0)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1054, 3954])).
% 0.71/0.92 tff(3956,plain,
% 0.71/0.92 (op(e2, e3) = e2),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1004, 3950])).
% 0.71/0.92 tff(3957,plain,
% 0.71/0.92 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3956])).
% 0.71/0.92 tff(3958,plain,
% 0.71/0.92 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 0.71/0.92 inference(transitivity,[status(thm)],[3957, 1213])).
% 0.71/0.92 tff(3959,plain,
% 0.71/0.92 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 0.71/0.92 inference(symmetry,[status(thm)],[3958])).
% 0.71/0.92 tff(3960,plain,
% 0.71/0.92 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3959])).
% 0.71/0.92 tff(3961,plain,
% 0.71/0.92 (~(op(e2, e3) = e0)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[16, 3960])).
% 0.71/0.92 tff(3962,plain,
% 0.71/0.92 (op(e1, e3) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[322, 3961, 3319, 3955])).
% 0.71/0.92 tff(3963,plain,
% 0.71/0.92 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3962])).
% 0.71/0.92 tff(3964,plain,
% 0.71/0.92 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3963])).
% 0.71/0.92 tff(3965,plain,
% 0.71/0.92 (~(op(e1, e2) = e0)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[691, 3964])).
% 0.71/0.92 tff(3966,plain,
% 0.71/0.92 (op(e3, e2) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1678, 3965, 1211, 1789])).
% 0.71/0.92 tff(3967,plain,
% 0.71/0.92 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3966])).
% 0.71/0.92 tff(3968,plain,
% 0.71/0.92 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 0.71/0.92 inference(symmetry,[status(thm)],[3967])).
% 0.71/0.92 tff(3969,plain,
% 0.71/0.92 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3968])).
% 0.71/0.92 tff(3970,plain,
% 0.71/0.92 (~(op(e3, e2) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[40, 3969])).
% 0.71/0.92 tff(3971,plain,
% 0.71/0.92 ((e1 = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.71/0.92 inference(commutativity,[status(thm)],[])).
% 0.71/0.92 tff(3972,plain,
% 0.71/0.92 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3962])).
% 0.71/0.92 tff(3973,plain,
% 0.71/0.92 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3972])).
% 0.71/0.92 tff(3974,plain,
% 0.71/0.92 (~(op(e1, e1) = e0)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[2034, 3973])).
% 0.71/0.92 tff(3975,plain,
% 0.71/0.92 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3962])).
% 0.71/0.92 tff(3976,plain,
% 0.71/0.92 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 0.71/0.92 inference(symmetry,[status(thm)],[3975])).
% 0.71/0.92 tff(3977,plain,
% 0.71/0.92 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3976])).
% 0.71/0.92 tff(3978,plain,
% 0.71/0.92 (~(op(e1, e3) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[40, 3977])).
% 0.71/0.92 tff(3979,plain,
% 0.71/0.92 (~(op(e1, e1) = e3)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[332, 3978])).
% 0.71/0.92 tff(3980,plain,
% 0.71/0.92 ((op(e1, e3) = e3) <=> (e0 = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3962])).
% 0.71/0.92 tff(3981,plain,
% 0.71/0.92 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 0.71/0.92 inference(symmetry,[status(thm)],[3980])).
% 0.71/0.92 tff(3982,plain,
% 0.71/0.92 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3981])).
% 0.71/0.92 tff(3983,plain,
% 0.71/0.92 (~(op(e1, e3) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[509, 3982])).
% 0.71/0.92 tff(3984,plain,
% 0.71/0.92 (~(op(e1, e1) = e2)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3460, 3983, 3950])).
% 0.71/0.92 tff(3985,plain,
% 0.71/0.92 (op(e1, e1) = e1),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[435, 3984, 3979, 3974])).
% 0.71/0.92 tff(3986,plain,
% 0.71/0.92 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3985])).
% 0.71/0.92 tff(3987,plain,
% 0.71/0.92 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.71/0.92 inference(transitivity,[status(thm)],[3986, 3971])).
% 0.71/0.92 tff(3988,plain,
% 0.71/0.92 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3987])).
% 0.71/0.92 tff(3989,plain,
% 0.71/0.92 (~(op(e3, e1) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[338, 3988])).
% 0.71/0.92 tff(3990,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[772, 3989, 3970, 695, 1067])).
% 0.71/0.92 tff(3991,plain,((op(e3, e0) = e1) | (op(e3, e3) = e1) | (op(e2, e2) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0) | (e0 = op(op(e2, e2), op(e2, e2))) | (op(e0, e0) = e1) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(3992,plain,
% 0.71/0.92 (op(e3, e0) = e1),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3991, 695, 3723, 3715, 3711, 1054, 3707, 3704, 3700, 3695, 3691, 3689])).
% 0.71/0.92 tff(3993,plain,
% 0.71/0.92 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3992])).
% 0.71/0.92 tff(3994,plain,
% 0.71/0.92 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3993])).
% 0.71/0.92 tff(3995,plain,
% 0.71/0.92 (~(op(e2, e0) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[589, 3994])).
% 0.71/0.92 tff(3996,plain,
% 0.71/0.92 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3992])).
% 0.71/0.92 tff(3997,plain,
% 0.71/0.92 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.71/0.92 inference(transitivity,[status(thm)],[3996, 2081])).
% 0.71/0.92 tff(3998,plain,
% 0.71/0.92 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3997])).
% 0.71/0.92 tff(3999,plain,
% 0.71/0.92 (~(op(e3, e2) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[572, 3998])).
% 0.71/0.92 tff(4000,plain,
% 0.71/0.92 ((e0 = e3) <=> (op(e0, e0) = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3686])).
% 0.71/0.92 tff(4001,plain,
% 0.71/0.92 ((~(e0 = e3)) <=> (~(op(e0, e0) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4000])).
% 0.71/0.92 tff(4002,plain,
% 0.71/0.92 (~(op(e0, e0) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[509, 4001])).
% 0.71/0.92 tff(4003,plain,
% 0.71/0.92 ((op(e3, e0) = e3) <=> (e1 = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3992])).
% 0.71/0.92 tff(4004,plain,
% 0.71/0.92 ((e1 = e3) <=> (op(e3, e0) = e3)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4003])).
% 0.71/0.92 tff(4005,plain,
% 0.71/0.92 ((~(e1 = e3)) <=> (~(op(e3, e0) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4004])).
% 0.71/0.92 tff(4006,plain,
% 0.71/0.92 (~(op(e3, e0) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[521, 4005])).
% 0.71/0.92 tff(4007,plain,
% 0.71/0.92 (~(op(e3, e3) = e0)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[558, 4006])).
% 0.71/0.92 tff(4008,plain,
% 0.71/0.92 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3992])).
% 0.71/0.92 tff(4009,plain,
% 0.71/0.92 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4008])).
% 0.71/0.92 tff(4010,plain,
% 0.71/0.92 (~(op(e1, e0) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[564, 4009])).
% 0.71/0.92 tff(4011,plain,
% 0.71/0.92 (~(op(e1, e1) = e0)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[2026, 4010])).
% 0.71/0.92 tff(4012,plain,
% 0.71/0.92 ((op(e3, e0) = e2) <=> (e1 = e2)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3992])).
% 0.71/0.92 tff(4013,plain,
% 0.71/0.92 ((e1 = e2) <=> (op(e3, e0) = e2)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4012])).
% 0.71/0.92 tff(4014,plain,
% 0.71/0.92 ((~(e1 = e2)) <=> (~(op(e3, e0) = e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4013])).
% 0.71/0.92 tff(4015,plain,
% 0.71/0.92 (~(op(e3, e0) = e2)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[353, 4014])).
% 0.71/0.92 tff(4016,plain,
% 0.71/0.92 (e2 = op(e3, e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[3791, 360])).
% 0.71/0.92 tff(4017,plain,
% 0.71/0.92 (op(op(e3, e3), op(e3, e3)) = op(e2, e2)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3791, 3791])).
% 0.71/0.92 tff(4018,plain,
% 0.71/0.92 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (e1 = op(e2, e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4017])).
% 0.71/0.92 tff(4019,plain,
% 0.71/0.92 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e1)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4018, 91])).
% 0.71/0.92 tff(4020,plain,
% 0.71/0.92 ((op(e2, e2) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.71/0.92 inference(symmetry,[status(thm)],[4019])).
% 0.71/0.92 tff(4021,plain,
% 0.71/0.92 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (e2 = op(e2, e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4017])).
% 0.71/0.92 tff(4022,plain,
% 0.71/0.92 ((e2 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e2)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4021, 1137])).
% 0.71/0.92 tff(4023,plain,
% 0.71/0.92 ((~(e2 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4022])).
% 0.71/0.92 tff(4024,plain,
% 0.71/0.92 (~(op(e2, e2) = e2)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1053, 4023])).
% 0.71/0.92 tff(4025,plain,
% 0.71/0.92 (op(e2, e2) = e1),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[226, 4024, 1211, 26])).
% 0.71/0.92 tff(4026,plain,
% 0.71/0.92 (e1 = op(op(e3, e3), op(e3, e3))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[4025, 4020])).
% 0.71/0.92 tff(4027,plain,
% 0.71/0.92 (op(op(e3, e3), op(e3, e3)) = e1),
% 0.71/0.92 inference(transitivity,[status(thm)],[4017, 4025])).
% 0.71/0.92 tff(4028,plain,
% 0.71/0.92 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4027])).
% 0.71/0.92 tff(4029,plain,
% 0.71/0.92 (op(e3, e1) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.71/0.92 inference(symmetry,[status(thm)],[4028])).
% 0.71/0.92 tff(4030,plain,
% 0.71/0.92 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3795])).
% 0.71/0.92 tff(4031,plain,
% 0.71/0.92 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4030, 1])).
% 0.71/0.92 tff(4032,plain,
% 0.71/0.92 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4031])).
% 0.71/0.92 tff(4033,plain,
% 0.71/0.92 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4032])).
% 0.71/0.92 tff(4034,plain,
% 0.71/0.92 (~(op(e3, e2) = e0)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[509, 4033])).
% 0.71/0.92 tff(4035,plain,
% 0.71/0.92 (op(e3, e1) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[288, 4034, 280, 2097])).
% 0.71/0.92 tff(4036,plain,
% 0.71/0.92 (e0 = op(e3, e1)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4035])).
% 0.71/0.92 tff(4037,plain,
% 0.71/0.92 (e0 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[4036, 4029])).
% 0.71/0.92 tff(4038,plain,
% 0.71/0.92 ((~(~((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3)))))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(4039,plain,
% 0.71/0.92 (((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3)))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(4040,plain,
% 0.71/0.92 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4039])).
% 0.71/0.92 tff(4041,plain,
% 0.71/0.92 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.71/0.92 inference(transitivity,[status(thm)],[4040, 4038])).
% 0.71/0.92 tff(4042,plain,
% 0.71/0.92 ((~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(4043,plain,
% 0.71/0.92 ((~(((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(4044,axiom,(~(((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax14')).
% 0.71/0.92 tff(4045,plain,
% 0.71/0.92 (~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[4044, 4043])).
% 0.71/0.92 tff(4046,plain,
% 0.71/0.92 (~((e1 = op(op(e3, e3), op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[4045, 4042])).
% 0.71/0.92 tff(4047,plain,
% 0.71/0.92 ((~(e2 = op(e3, e3))) | (~(e1 = op(op(e3, e3), op(e3, e3)))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[4046, 4041])).
% 0.71/0.92 tff(4048,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[4047, 4037, 4026, 4016])).
% 0.71/0.92 tff(4049,plain,((~(op(e3, e3) = e2)) | (op(e2, e2) = e0) | (op(e2, e2) = e3) | (op(e3, e3) = e0) | (op(e3, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(4050,plain,
% 0.71/0.92 (~(op(e3, e3) = e2)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[4049, 26, 1211, 280, 2097, 1053])).
% 0.71/0.92 tff(4051,assumption,(~(op(e3, e0) = e2)), introduced(assumption)).
% 0.71/0.92 tff(4052,plain,
% 0.71/0.92 (op(e3, e3) = e3),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1123, 4050, 695, 280])).
% 0.71/0.92 tff(4053,plain,
% 0.71/0.92 (op(e3, op(e3, e3)) = op(e3, e3)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3432, 4052])).
% 0.71/0.92 tff(4054,plain,
% 0.71/0.92 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[3434, 4053])).
% 0.71/0.92 tff(4055,plain,
% 0.71/0.92 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4052])).
% 0.71/0.92 tff(4056,plain,
% 0.71/0.92 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4055])).
% 0.71/0.92 tff(4057,plain,
% 0.71/0.92 (~(op(e3, e2) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1160, 4056])).
% 0.71/0.92 tff(4058,assumption,(op(e1, e1) = e1), introduced(assumption)).
% 0.71/0.92 tff(4059,plain,
% 0.71/0.92 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4058])).
% 0.71/0.92 tff(4060,plain,
% 0.71/0.92 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4059])).
% 0.71/0.92 tff(4061,plain,
% 0.71/0.92 (~(op(e0, e1) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1402, 4060])).
% 0.71/0.92 tff(4062,plain,
% 0.71/0.92 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4058])).
% 0.71/0.92 tff(4063,plain,
% 0.71/0.92 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4062, 1938])).
% 0.71/0.92 tff(4064,plain,
% 0.71/0.92 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4063])).
% 0.71/0.92 tff(4065,plain,
% 0.71/0.92 (~(op(e2, e1) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1049, 4064])).
% 0.71/0.92 tff(4066,plain,
% 0.71/0.92 (op(e3, e2) = e2),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[736, 728, 663, 861])).
% 0.71/0.92 tff(4067,plain,
% 0.71/0.92 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4066])).
% 0.71/0.92 tff(4068,plain,
% 0.71/0.92 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4067])).
% 0.71/0.92 tff(4069,plain,
% 0.71/0.92 (~(op(e2, e2) = e2)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[278, 4068])).
% 0.71/0.92 tff(4070,plain,
% 0.71/0.92 (op(e1, e2) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1678, 728, 1211, 1789])).
% 0.71/0.92 tff(4071,plain,
% 0.71/0.92 ((op(e1, e2) = e3) <=> (e0 = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4070])).
% 0.71/0.92 tff(4072,plain,
% 0.71/0.92 ((e0 = e3) <=> (op(e1, e2) = e3)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4071])).
% 0.71/0.92 tff(4073,plain,
% 0.71/0.92 ((~(e0 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4072])).
% 0.71/0.92 tff(4074,plain,
% 0.71/0.92 (~(op(e1, e2) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[509, 4073])).
% 0.71/0.92 tff(4075,plain,
% 0.71/0.92 (op(e0, e2) = e3),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[684, 4074, 26, 861])).
% 0.71/0.92 tff(4076,plain,
% 0.71/0.92 ((e2 = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.71/0.92 inference(commutativity,[status(thm)],[])).
% 0.71/0.92 tff(4077,plain,
% 0.71/0.92 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3259])).
% 0.71/0.92 tff(4078,plain,
% 0.71/0.92 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4077])).
% 0.71/0.92 tff(4079,plain,
% 0.71/0.92 (~(op(e0, e1) = e3)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[867, 4078])).
% 0.71/0.92 tff(4080,plain,
% 0.71/0.92 (op(e0, e1) = e2),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[880, 4079, 2128, 854])).
% 0.71/0.92 tff(4081,plain,
% 0.71/0.92 ((op(e0, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4080])).
% 0.71/0.92 tff(4082,plain,
% 0.71/0.92 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4081, 4076])).
% 0.71/0.92 tff(4083,plain,
% 0.71/0.92 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4082])).
% 0.71/0.92 tff(4084,plain,
% 0.71/0.92 (~(op(e2, e1) = e2)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[2322, 4083])).
% 0.71/0.92 tff(4085,plain,
% 0.71/0.92 (~(op(e2, e2) = e1)),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[52, 4084])).
% 0.71/0.92 tff(4086,plain,
% 0.71/0.92 (op(e2, e2) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[226, 4085, 26, 1204])).
% 0.71/0.92 tff(4087,plain,
% 0.71/0.92 (op(e2, e0) = e2),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[230, 4086])).
% 0.71/0.92 tff(4088,plain,
% 0.71/0.92 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[3259])).
% 0.71/0.92 tff(4089,plain,
% 0.71/0.92 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4088, 601])).
% 0.71/0.92 tff(4090,plain,
% 0.71/0.92 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4089])).
% 0.71/0.92 tff(4091,plain,
% 0.71/0.92 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4090])).
% 0.71/0.92 tff(4092,plain,
% 0.71/0.92 (~(op(e0, e2) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[521, 4091])).
% 0.71/0.92 tff(4093,plain,
% 0.71/0.92 (op(e0, e3) = e1),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[2185, 4092, 421, 2128])).
% 0.71/0.92 tff(4094,plain,
% 0.71/0.92 ((op(e0, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4093])).
% 0.71/0.92 tff(4095,plain,
% 0.71/0.92 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.71/0.92 inference(transitivity,[status(thm)],[4094, 3724])).
% 0.71/0.92 tff(4096,plain,
% 0.71/0.92 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4095])).
% 0.71/0.92 tff(4097,plain,
% 0.71/0.92 (~(op(e2, e3) = e1)),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1275, 4096])).
% 0.71/0.92 tff(4098,plain,
% 0.71/0.92 (op(e2, e0) = e1),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[953, 4085, 3867, 4097])).
% 0.71/0.92 tff(4099,plain,
% 0.71/0.92 (e1 = op(e2, e0)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4098])).
% 0.71/0.92 tff(4100,plain,
% 0.71/0.92 (e1 = e2),
% 0.71/0.92 inference(transitivity,[status(thm)],[4099, 4087])).
% 0.71/0.92 tff(4101,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[353, 4100])).
% 0.71/0.92 tff(4102,plain,((~(op(e0, e2) = e3)) | (op(e2, e1) = e1) | (op(e2, e2) = e3) | (op(e2, e2) = e2) | (op(e0, e1) = e1) | (op(e0, e1) = e0) | (op(e0, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(4103,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[4102, 4075, 4069, 26, 3867, 2128, 854, 421])).
% 0.71/0.92 tff(4104,plain,((op(e3, e2) = e0) | (op(e2, e2) = e3) | (op(e2, e1) = e1) | (op(e0, e1) = e1) | (op(e0, e1) = e0) | (op(e0, e0) = e1) | (op(e3, e2) = e3) | (op(e3, e2) = e1) | (op(e2, e2) = e0) | (op(e0, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(4105,plain,
% 0.71/0.92 (op(e3, e2) = e0),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[4104, 4065, 26, 4061, 854, 421, 861, 663, 1211, 1789])).
% 0.71/0.92 tff(4106,plain,
% 0.71/0.92 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4105])).
% 0.71/0.92 tff(4107,plain,
% 0.71/0.92 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 0.71/0.92 inference(symmetry,[status(thm)],[4106])).
% 0.71/0.92 tff(4108,plain,
% 0.71/0.92 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[4107])).
% 0.71/0.93 tff(4109,plain,
% 0.71/0.93 (~(op(e3, e2) = e2)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[16, 4108])).
% 0.71/0.93 tff(4110,plain,
% 0.71/0.93 (op(e3, e1) = e2),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[818, 4109, 4051, 3169])).
% 0.71/0.93 tff(4111,plain,
% 0.71/0.93 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4110])).
% 0.71/0.93 tff(4112,plain,
% 0.71/0.93 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4111])).
% 0.71/0.93 tff(4113,plain,
% 0.71/0.93 (~(op(e2, e1) = e2)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1184, 4112])).
% 0.71/0.93 tff(4114,plain,
% 0.71/0.93 (~(op(e2, e2) = e1)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[52, 4113])).
% 0.71/0.93 tff(4115,plain,
% 0.71/0.93 (op(e2, e2) = e2),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[226, 4114, 1211, 26])).
% 0.71/0.93 tff(4116,plain,
% 0.71/0.93 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4115])).
% 0.71/0.93 tff(4117,plain,
% 0.71/0.93 (op(e1, op(e1, e1)) = op(e1, e1)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4058])).
% 0.71/0.93 tff(4118,plain,
% 0.71/0.93 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[3222, 4117])).
% 0.71/0.93 tff(4119,plain,
% 0.71/0.93 (~((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3)))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[798, 4118, 758, 3492])).
% 0.71/0.93 tff(4120,plain,
% 0.71/0.93 (~(op(e2, op(e2, e2)) = op(e2, e2))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[3849, 4119])).
% 0.71/0.93 tff(4121,plain,
% 0.71/0.93 ($false),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[4120, 4116])).
% 0.71/0.93 tff(4122,plain,((~(op(e1, e1) = e1)) | (op(e2, e2) = e0) | (op(e2, e2) = e3) | (op(e3, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e1) = e0) | (op(e0, e0) = e1) | (op(e3, e2) = e3) | (op(e3, e2) = e1) | (op(e0, e2) = e0) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.93 tff(4123,plain,
% 0.71/0.93 (~(op(e1, e1) = e1)),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[4122, 26, 1211, 4051, 4050, 854, 421, 4057, 663, 1789, 758, 4054])).
% 0.71/0.93 tff(4124,plain,
% 0.71/0.93 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4052])).
% 0.71/0.93 tff(4125,plain,
% 0.71/0.93 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4124])).
% 0.71/0.93 tff(4126,plain,
% 0.71/0.93 (~(op(e0, e3) = e3)),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[1578, 4125])).
% 0.71/0.93 tff(4127,plain,
% 0.71/0.93 (op(e1, e3) = e1),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[332, 2939])).
% 0.71/0.93 tff(4128,plain,
% 0.71/0.93 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4127])).
% 0.71/0.93 tff(4129,plain,
% 0.71/0.93 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[4128])).
% 0.71/0.93 tff(4130,plain,
% 0.79/0.93 (~(op(e1, e2) = e1)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[691, 4129])).
% 0.79/0.93 tff(4131,plain,
% 0.79/0.93 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[2939])).
% 0.79/0.93 tff(4132,plain,
% 0.79/0.93 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4131])).
% 0.79/0.93 tff(4133,plain,
% 0.79/0.93 (~(op(e0, e1) = e3)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1402, 4132])).
% 0.79/0.93 tff(4134,plain,
% 0.79/0.93 (op(e0, e2) = e3),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1090, 4133, 1590, 1587])).
% 0.79/0.93 tff(4135,plain,
% 0.79/0.93 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4134])).
% 0.79/0.93 tff(4136,plain,
% 0.79/0.93 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4135, 601])).
% 0.79/0.93 tff(4137,plain,
% 0.79/0.93 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4136])).
% 0.79/0.93 tff(4138,plain,
% 0.79/0.93 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4137])).
% 0.79/0.93 tff(4139,plain,
% 0.79/0.93 (~(op(e0, e2) = e1)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[521, 4138])).
% 0.79/0.93 tff(4140,plain,
% 0.79/0.93 (op(e2, e2) = e1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[671, 4139, 663, 4130])).
% 0.79/0.93 tff(4141,plain,
% 0.79/0.93 (op(op(e2, e2), op(e2, e2)) = op(e1, e1)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4140, 4140])).
% 0.79/0.93 tff(4142,plain,
% 0.79/0.93 (op(e1, e1) = op(op(e2, e2), op(e2, e2))),
% 0.79/0.93 inference(symmetry,[status(thm)],[4141])).
% 0.79/0.93 tff(4143,plain,
% 0.79/0.93 (e3 = op(e1, e1)),
% 0.79/0.93 inference(symmetry,[status(thm)],[2939])).
% 0.79/0.93 tff(4144,plain,
% 0.79/0.93 (e3 = op(op(e2, e2), op(e2, e2))),
% 0.79/0.93 inference(transitivity,[status(thm)],[4143, 4142])).
% 0.79/0.93 tff(4145,plain,
% 0.79/0.93 (e1 = op(e2, e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4140, 92])).
% 0.79/0.93 tff(4146,plain,
% 0.79/0.93 (op(op(e2, e2), op(e2, e2)) = e3),
% 0.79/0.93 inference(transitivity,[status(thm)],[4141, 2939])).
% 0.79/0.93 tff(4147,plain,
% 0.79/0.93 (op(e2, op(op(e2, e2), op(e2, e2))) = op(e2, e3)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4146])).
% 0.79/0.93 tff(4148,plain,
% 0.79/0.93 (op(e2, e3) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.79/0.93 inference(symmetry,[status(thm)],[4147])).
% 0.79/0.93 tff(4149,plain,
% 0.79/0.93 ((op(e1, e3) = e0) <=> (e1 = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4127])).
% 0.79/0.93 tff(4150,plain,
% 0.79/0.93 ((op(e1, e3) = e0) <=> (e0 = e1)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4149, 1203])).
% 0.79/0.93 tff(4151,plain,
% 0.79/0.93 ((e0 = e1) <=> (op(e1, e3) = e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4150])).
% 0.79/0.93 tff(4152,plain,
% 0.79/0.93 ((~(e0 = e1)) <=> (~(op(e1, e3) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4151])).
% 0.79/0.93 tff(4153,plain,
% 0.79/0.93 (~(op(e1, e3) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[40, 4152])).
% 0.79/0.93 tff(4154,plain,
% 0.79/0.93 (op(e2, e3) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[322, 4153, 3319, 280])).
% 0.79/0.93 tff(4155,plain,
% 0.79/0.93 (e0 = op(e2, e3)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4154])).
% 0.79/0.93 tff(4156,plain,
% 0.79/0.93 (e0 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[4155, 4148])).
% 0.79/0.93 tff(4157,plain,
% 0.79/0.93 ((~(~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2))))))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4158,plain,
% 0.79/0.93 (((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4159,plain,
% 0.79/0.93 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~(~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4158])).
% 0.79/0.93 tff(4160,plain,
% 0.79/0.93 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2)))))),
% 0.79/0.93 inference(transitivity,[status(thm)],[4159, 4157])).
% 0.79/0.93 tff(4161,plain,
% 0.79/0.93 ((~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4162,plain,
% 0.79/0.93 ((~(((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))) <=> (~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4163,axiom,(~(((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax26')).
% 0.79/0.93 tff(4164,plain,
% 0.79/0.93 (~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 0.79/0.93 tff(4165,plain,
% 0.79/0.93 (~((e3 = op(op(e2, e2), op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(op(e2, e2), op(e2, e2)))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4164, 4161])).
% 0.79/0.93 tff(4166,plain,
% 0.79/0.93 ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) | (~(e3 = op(op(e2, e2), op(e2, e2))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4165, 4160])).
% 0.79/0.93 tff(4167,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4166, 4156, 4145, 4144])).
% 0.79/0.93 tff(4168,plain,((~(op(e1, e1) = e3)) | (op(e3, e2) = e1) | (op(e0, e3) = e0) | (op(e3, e3) = e0) | (op(e0, e0) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(4169,plain,
% 0.79/0.93 (~(op(e1, e1) = e3)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4168, 4126, 3319, 280, 1590, 663])).
% 0.79/0.93 tff(4170,plain,
% 0.79/0.93 (op(e1, e1) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[435, 4169, 4123, 424])).
% 0.79/0.93 tff(4171,plain,
% 0.79/0.93 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4170])).
% 0.79/0.93 tff(4172,plain,
% 0.79/0.93 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4171, 1894])).
% 0.79/0.93 tff(4173,plain,
% 0.79/0.93 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4172])).
% 0.79/0.93 tff(4174,plain,
% 0.79/0.93 (~(op(e3, e1) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[338, 4173])).
% 0.79/0.93 tff(4175,plain,
% 0.79/0.93 (op(e3, e2) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[818, 4174, 4051, 4050])).
% 0.79/0.93 tff(4176,plain,
% 0.79/0.93 (op(e1, e2) = e1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[514, 4170])).
% 0.79/0.93 tff(4177,plain,
% 0.79/0.93 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4176])).
% 0.79/0.93 tff(4178,plain,
% 0.79/0.93 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4177, 1203])).
% 0.79/0.93 tff(4179,plain,
% 0.79/0.93 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4178])).
% 0.79/0.93 tff(4180,plain,
% 0.79/0.93 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4179])).
% 0.79/0.93 tff(4181,plain,
% 0.79/0.93 (~(op(e1, e2) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[40, 4180])).
% 0.79/0.93 tff(4182,plain,
% 0.79/0.93 (op(e3, e2) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1678, 4181, 1211, 1789])).
% 0.79/0.93 tff(4183,plain,
% 0.79/0.93 (e0 = op(e3, e2)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4182])).
% 0.79/0.93 tff(4184,plain,
% 0.79/0.93 (e0 = e2),
% 0.79/0.93 inference(transitivity,[status(thm)],[4183, 4175])).
% 0.79/0.93 tff(4185,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[16, 4184])).
% 0.79/0.93 tff(4186,plain,((op(e2, e2) = e3) | (op(e2, e2) = e0) | (op(e0, e2) = e0) | (op(e3, e0) = e2) | (op(e1, e1) = e0) | (op(e0, e3) = e0) | (op(e3, e3) = e0) | (op(e0, e0) = e3) | (op(e3, e2) = e1) | (op(e0, e1) = e0) | (op(e0, e0) = e1) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (op(e3, e3) = e1) | (op(e3, e0) = e0) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(4187,plain,
% 0.79/0.93 (op(e2, e2) = e3),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4186, 4015, 3715, 3723, 4011, 3711, 4007, 4002, 3999, 3685, 3707, 3691, 695, 3695, 1053])).
% 0.79/0.93 tff(4188,plain,
% 0.79/0.93 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4187])).
% 0.79/0.93 tff(4189,plain,
% 0.79/0.93 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4188])).
% 0.79/0.93 tff(4190,plain,
% 0.79/0.93 (~(op(e2, e0) = e3)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[85, 4189])).
% 0.79/0.93 tff(4191,plain,
% 0.79/0.93 (op(e2, e3) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1004, 4187])).
% 0.79/0.93 tff(4192,plain,
% 0.79/0.93 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4191])).
% 0.79/0.93 tff(4193,plain,
% 0.79/0.93 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4192])).
% 0.79/0.93 tff(4194,plain,
% 0.79/0.93 (~(op(e2, e0) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[369, 4193])).
% 0.79/0.93 tff(4195,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[121, 4194, 4190, 3700, 3995])).
% 0.79/0.93 tff(4196,plain,((op(e3, e3) = e1) | (e2 = op(op(e3, e3), op(e3, e3))) | (e0 = op(op(e2, e2), op(e2, e2)))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(4197,plain,
% 0.79/0.93 (op(e3, e3) = e1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4196, 1054, 1053])).
% 0.79/0.93 tff(4198,plain,
% 0.79/0.93 (op(e3, e1) = e3),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1150, 4197])).
% 0.79/0.93 tff(4199,plain,
% 0.79/0.93 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4198])).
% 0.79/0.93 tff(4200,plain,
% 0.79/0.93 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4199, 1])).
% 0.79/0.93 tff(4201,plain,
% 0.79/0.93 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4200])).
% 0.79/0.93 tff(4202,plain,
% 0.79/0.93 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4201])).
% 0.79/0.93 tff(4203,plain,
% 0.79/0.93 (~(op(e3, e1) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[509, 4202])).
% 0.79/0.93 tff(4204,plain,
% 0.79/0.93 ((op(e3, e3) = e0) <=> (e1 = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4197])).
% 0.79/0.93 tff(4205,plain,
% 0.79/0.93 ((op(e3, e3) = e0) <=> (e0 = e1)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4204, 1203])).
% 0.79/0.93 tff(4206,plain,
% 0.79/0.93 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4205])).
% 0.79/0.93 tff(4207,plain,
% 0.79/0.93 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4206])).
% 0.79/0.93 tff(4208,plain,
% 0.79/0.93 (~(op(e3, e3) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[40, 4207])).
% 0.79/0.93 tff(4209,plain,
% 0.79/0.93 (op(e3, e2) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[288, 4203, 4208, 3695])).
% 0.79/0.93 tff(4210,plain,
% 0.79/0.93 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4209])).
% 0.79/0.93 tff(4211,plain,
% 0.79/0.93 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4210])).
% 0.79/0.93 tff(4212,plain,
% 0.79/0.93 (~(op(e1, e2) = e0)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[742, 4211])).
% 0.79/0.93 tff(4213,plain,
% 0.79/0.93 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4197])).
% 0.79/0.93 tff(4214,plain,
% 0.79/0.93 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4213])).
% 0.79/0.93 tff(4215,plain,
% 0.79/0.93 (~(op(e3, e0) = e1)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1424, 4214])).
% 0.79/0.93 tff(4216,plain,
% 0.79/0.93 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4198])).
% 0.79/0.93 tff(4217,plain,
% 0.79/0.93 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4216])).
% 0.79/0.93 tff(4218,plain,
% 0.79/0.93 (~(op(e3, e0) = e3)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1320, 4217])).
% 0.79/0.93 tff(4219,plain,
% 0.79/0.93 (op(e3, e0) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1333, 4218, 3695, 4215])).
% 0.79/0.93 tff(4220,plain,
% 0.79/0.93 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4219])).
% 0.79/0.93 tff(4221,plain,
% 0.79/0.93 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4220])).
% 0.79/0.93 tff(4222,plain,
% 0.79/0.93 (~(op(e1, e0) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[564, 4221])).
% 0.79/0.93 tff(4223,plain,
% 0.79/0.93 (~(op(e1, e1) = e2)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[2399, 4197, 1053])).
% 0.79/0.93 tff(4224,plain,
% 0.79/0.93 ((op(e3, e3) = e1) <=> (e1 = op(e3, e3))),
% 0.79/0.93 inference(symmetry,[status(thm)],[1071])).
% 0.79/0.93 tff(4225,plain,
% 0.79/0.93 (e1 = op(e3, e3)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1155, 4224])).
% 0.79/0.93 tff(4226,plain,
% 0.79/0.93 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (e0 = op(e1, e1))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[2394])).
% 0.79/0.93 tff(4227,plain,
% 0.79/0.93 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e1) = e0)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4226, 1430])).
% 0.79/0.93 tff(4228,plain,
% 0.79/0.93 ((op(e1, e1) = e0) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.93 inference(symmetry,[status(thm)],[4227])).
% 0.79/0.93 tff(4229,plain,
% 0.79/0.93 (e0 = op(op(e3, e3), op(e3, e3))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[3087, 4228])).
% 0.79/0.93 tff(4230,plain,
% 0.79/0.93 (op(op(e3, e3), op(e3, e3)) = e0),
% 0.79/0.93 inference(transitivity,[status(thm)],[2394, 3087])).
% 0.79/0.93 tff(4231,plain,
% 0.79/0.93 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e0)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4230])).
% 0.79/0.93 tff(4232,plain,
% 0.79/0.93 (op(e3, e0) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.93 inference(symmetry,[status(thm)],[4231])).
% 0.79/0.93 tff(4233,assumption,(op(e3, e0) = e2), introduced(assumption)).
% 0.79/0.93 tff(4234,plain,
% 0.79/0.93 (e2 = op(e3, e0)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4233])).
% 0.79/0.93 tff(4235,plain,
% 0.79/0.93 (e2 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[4234, 4232])).
% 0.79/0.93 tff(4236,plain,
% 0.79/0.93 ((~(~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3)))))))) <=> ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4237,plain,
% 0.79/0.93 (((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3)))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4238,plain,
% 0.79/0.93 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4237])).
% 0.79/0.93 tff(4239,plain,
% 0.79/0.93 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.93 inference(transitivity,[status(thm)],[4238, 4236])).
% 0.79/0.93 tff(4240,plain,
% 0.79/0.93 ((~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4241,plain,
% 0.79/0.93 ((~(((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(4242,axiom,(~(((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax6')).
% 0.79/0.93 tff(4243,plain,
% 0.79/0.93 (~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 0.79/0.93 tff(4244,plain,
% 0.79/0.93 (~((e0 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4243, 4240])).
% 0.79/0.93 tff(4245,plain,
% 0.79/0.93 ((~(e0 = op(op(e3, e3), op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[4244, 4239])).
% 0.79/0.93 tff(4246,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4245, 4235, 4229, 4225])).
% 0.79/0.93 tff(4247,plain,((~(op(e1, e1) = e0)) | (~(op(e3, e0) = e2)) | (~(op(e3, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(4248,plain,
% 0.79/0.93 (~(op(e1, e1) = e0)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[4247, 4219, 4197])).
% 0.79/0.93 tff(4249,plain,
% 0.79/0.93 (op(e1, e3) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[548, 424, 1796, 837])).
% 0.79/0.93 tff(4250,plain,
% 0.79/0.93 ((op(e1, e3) = e2) <=> (e0 = e2)),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4249])).
% 0.79/0.93 tff(4251,plain,
% 0.79/0.93 ((e0 = e2) <=> (op(e1, e3) = e2)),
% 0.79/0.93 inference(symmetry,[status(thm)],[4250])).
% 0.79/0.93 tff(4252,plain,
% 0.79/0.93 ((~(e0 = e2)) <=> (~(op(e1, e3) = e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4251])).
% 0.79/0.93 tff(4253,plain,
% 0.79/0.93 (~(op(e1, e3) = e2)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[16, 4252])).
% 0.79/0.93 tff(4254,plain,
% 0.79/0.93 (op(e1, e2) = e2),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[751, 4253, 379, 727])).
% 0.79/0.93 tff(4255,plain,
% 0.79/0.93 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[4254])).
% 0.79/0.93 tff(4256,plain,
% 0.79/0.93 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.79/0.93 inference(transitivity,[status(thm)],[4255, 1137])).
% 0.79/0.93 tff(4257,plain,
% 0.79/0.93 ((op(e2, e2) = e2) <=> (op(e1, e2) = op(e2, e2))),
% 0.79/0.93 inference(symmetry,[status(thm)],[4256])).
% 0.79/0.93 tff(4258,plain,
% 0.79/0.93 (op(e2, e1) = e0),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1241, 424, 1233, 854])).
% 0.79/0.93 tff(4259,plain,
% 0.79/0.94 ((op(e2, e1) = e2) <=> (e0 = e2)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4258])).
% 0.79/0.94 tff(4260,plain,
% 0.79/0.94 ((e0 = e2) <=> (op(e2, e1) = e2)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4259])).
% 0.79/0.94 tff(4261,plain,
% 0.79/0.94 ((~(e0 = e2)) <=> (~(op(e2, e1) = e2))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4260])).
% 0.79/0.94 tff(4262,plain,
% 0.79/0.94 (~(op(e2, e1) = e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[16, 4261])).
% 0.79/0.94 tff(4263,plain,
% 0.79/0.94 (~(op(e2, e2) = e1)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[52, 4262])).
% 0.79/0.94 tff(4264,plain,
% 0.79/0.94 (op(e2, e2) = e2),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[226, 4263, 1211, 26])).
% 0.79/0.94 tff(4265,plain,
% 0.79/0.94 (op(e1, e2) = op(e2, e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4264, 4257])).
% 0.79/0.94 tff(4266,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[243, 4265])).
% 0.79/0.94 tff(4267,plain,((op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e2) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e1, e0) = e0) | (op(e1, e2) = e0) | (op(e3, e1) = e0) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(4268,plain,
% 0.79/0.94 (op(e2, e2) = e3),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4267, 4248, 3723, 4223, 4222, 3704, 4212, 4203, 3685])).
% 0.79/0.94 tff(4269,plain,
% 0.79/0.94 (e3 = op(e2, e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4268, 1016])).
% 0.79/0.94 tff(4270,plain,
% 0.79/0.94 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4268, 4268])).
% 0.79/0.94 tff(4271,plain,
% 0.79/0.94 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.79/0.94 inference(symmetry,[status(thm)],[4270])).
% 0.79/0.94 tff(4272,plain,
% 0.79/0.94 (e1 = op(e3, e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4197])).
% 0.79/0.94 tff(4273,plain,
% 0.79/0.94 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4272, 4271])).
% 0.79/0.94 tff(4274,plain,
% 0.79/0.94 (op(op(e2, e2), op(e2, e2)) = e1),
% 0.79/0.94 inference(transitivity,[status(thm)],[4270, 4197])).
% 0.79/0.94 tff(4275,plain,
% 0.79/0.94 (op(e2, op(op(e2, e2), op(e2, e2))) = op(e2, e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4274])).
% 0.79/0.94 tff(4276,plain,
% 0.79/0.94 (op(e2, e1) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.79/0.94 inference(symmetry,[status(thm)],[4275])).
% 0.79/0.94 tff(4277,plain,
% 0.79/0.94 (op(e2, e1) = e0),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1241, 4248, 4203, 3685])).
% 0.79/0.94 tff(4278,plain,
% 0.79/0.94 (e0 = op(e2, e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4277])).
% 0.79/0.94 tff(4279,plain,
% 0.79/0.94 (e0 = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4278, 4276])).
% 0.79/0.94 tff(4280,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1925, 4279, 4273, 4269])).
% 0.79/0.94 tff(4281,plain,((e0 = op(op(e2, e2), op(e2, e2))) | (e2 = op(op(e3, e3), op(e3, e3)))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(4282,plain,
% 0.79/0.94 (e2 = op(op(e3, e3), op(e3, e3))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4281, 1052])).
% 0.79/0.94 tff(4283,plain,
% 0.79/0.94 (op(op(e3, e3), op(e3, e3)) = e2),
% 0.79/0.94 inference(symmetry,[status(thm)],[4282])).
% 0.79/0.94 tff(4284,plain,
% 0.79/0.94 (op(e0, e0) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[3776, 3776])).
% 0.79/0.94 tff(4285,plain,
% 0.79/0.94 (op(e0, e0) = e2),
% 0.79/0.94 inference(transitivity,[status(thm)],[4284, 4283])).
% 0.79/0.94 tff(4286,plain,
% 0.79/0.94 ((op(e3, op(op(e3, e3), op(e3, e3))) = e1) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(commutativity,[status(thm)],[])).
% 0.79/0.94 tff(4287,plain,
% 0.79/0.94 (op(e3, op(op(e3, e3), op(e3, e3))) = op(e3, e2)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4283])).
% 0.79/0.94 tff(4288,plain,
% 0.79/0.94 (op(e3, e2) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(symmetry,[status(thm)],[4287])).
% 0.79/0.94 tff(4289,plain,
% 0.79/0.94 ((op(e3, e2) = e1) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4288])).
% 0.79/0.94 tff(4290,plain,
% 0.79/0.94 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4289, 4286])).
% 0.79/0.94 tff(4291,plain,
% 0.79/0.94 ((e1 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4290])).
% 0.79/0.94 tff(4292,plain,
% 0.79/0.94 ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4291])).
% 0.79/0.94 tff(4293,plain,
% 0.79/0.94 ((~(~((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3))))))) <=> ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4294,plain,
% 0.79/0.94 (((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4295,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4294])).
% 0.79/0.94 tff(4296,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4295, 4293])).
% 0.79/0.94 tff(4297,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4298,plain,
% 0.79/0.94 ((~(((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4299,axiom,(~(((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax18')).
% 0.79/0.94 tff(4300,plain,
% 0.79/0.94 (~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 0.79/0.94 tff(4301,plain,
% 0.79/0.94 (~((e2 = op(op(e3, e3), op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4300, 4297])).
% 0.79/0.94 tff(4302,plain,
% 0.79/0.94 ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4301, 4296])).
% 0.79/0.94 tff(4303,plain,
% 0.79/0.94 ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e0 = op(e3, e3)))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4302, 4282])).
% 0.79/0.94 tff(4304,plain,
% 0.79/0.94 (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4303, 2842])).
% 0.79/0.94 tff(4305,plain,
% 0.79/0.94 (~(op(e3, e2) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4304, 4292])).
% 0.79/0.94 tff(4306,plain,
% 0.79/0.94 (op(e0, e2) = e0),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1472, 4285])).
% 0.79/0.94 tff(4307,plain,
% 0.79/0.94 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4306])).
% 0.79/0.94 tff(4308,plain,
% 0.79/0.94 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4307])).
% 0.79/0.94 tff(4309,plain,
% 0.79/0.94 (~(op(e0, e1) = e0)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[867, 4308])).
% 0.79/0.94 tff(4310,plain,
% 0.79/0.94 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[3776])).
% 0.79/0.94 tff(4311,plain,
% 0.79/0.94 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4310])).
% 0.79/0.94 tff(4312,plain,
% 0.79/0.94 (~(op(e3, e3) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[40, 4311])).
% 0.79/0.94 tff(4313,plain,
% 0.79/0.94 ((op(e3, e0) = e1) <=> (e3 = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1075])).
% 0.79/0.94 tff(4314,plain,
% 0.79/0.94 ((op(e3, e0) = e1) <=> (e1 = e3)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4313, 601])).
% 0.79/0.94 tff(4315,plain,
% 0.79/0.94 ((e1 = e3) <=> (op(e3, e0) = e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4314])).
% 0.79/0.94 tff(4316,plain,
% 0.79/0.94 ((~(e1 = e3)) <=> (~(op(e3, e0) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4315])).
% 0.79/0.94 tff(4317,plain,
% 0.79/0.94 (~(op(e3, e0) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[521, 4316])).
% 0.79/0.94 tff(4318,plain,
% 0.79/0.94 (op(e3, e1) = e1),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[772, 4305, 4317, 4312])).
% 0.79/0.94 tff(4319,plain,
% 0.79/0.94 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4318])).
% 0.79/0.94 tff(4320,plain,
% 0.79/0.94 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4319])).
% 0.79/0.94 tff(4321,plain,
% 0.79/0.94 (~(op(e0, e1) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[859, 4320])).
% 0.79/0.94 tff(4322,plain,
% 0.79/0.94 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1075])).
% 0.79/0.94 tff(4323,plain,
% 0.79/0.94 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4322, 566])).
% 0.79/0.94 tff(4324,plain,
% 0.79/0.94 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4323])).
% 0.79/0.94 tff(4325,plain,
% 0.79/0.94 (~(op(e3, e2) = e3)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[572, 4324])).
% 0.79/0.94 tff(4326,plain,
% 0.79/0.94 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4306])).
% 0.79/0.94 tff(4327,plain,
% 0.79/0.94 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4326])).
% 0.79/0.94 tff(4328,plain,
% 0.79/0.94 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4327])).
% 0.79/0.94 tff(4329,plain,
% 0.79/0.94 (~(op(e0, e2) = e3)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[509, 4328])).
% 0.79/0.94 tff(4330,plain,
% 0.79/0.94 (op(e1, e2) = e3),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[684, 4329, 26, 4325])).
% 0.79/0.94 tff(4331,plain,
% 0.79/0.94 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4330])).
% 0.79/0.94 tff(4332,plain,
% 0.79/0.94 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4331, 601])).
% 0.79/0.94 tff(4333,plain,
% 0.79/0.94 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4332])).
% 0.79/0.94 tff(4334,plain,
% 0.79/0.94 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4333])).
% 0.79/0.94 tff(4335,plain,
% 0.79/0.94 (~(op(e1, e2) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[521, 4334])).
% 0.79/0.94 tff(4336,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[2147, 4335, 4321, 4309, 4305, 4285])).
% 0.79/0.94 tff(4337,plain,((~(op(e3, e3) = e0)) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(4338,plain,
% 0.79/0.94 (~(op(e3, e3) = e0)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4337, 26])).
% 0.79/0.94 tff(4339,plain,
% 0.79/0.94 (e3 = op(e3, e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[3428])).
% 0.79/0.94 tff(4340,plain,
% 0.79/0.94 (op(e3, e3) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4339, 4339])).
% 0.79/0.94 tff(4341,plain,
% 0.79/0.94 (op(op(e3, e3), op(e3, e3)) = op(e3, e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4340])).
% 0.79/0.94 tff(4342,plain,
% 0.79/0.94 (e2 = e3),
% 0.79/0.94 inference(transitivity,[status(thm)],[4282, 4341, 3428])).
% 0.79/0.94 tff(4343,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[170, 4342])).
% 0.79/0.94 tff(4344,plain,(~(op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(4345,plain,
% 0.79/0.94 (op(e3, e2) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4282])).
% 0.79/0.94 tff(4346,plain,
% 0.79/0.94 ((op(e3, e2) = e1) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4345])).
% 0.79/0.94 tff(4347,plain,
% 0.79/0.94 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4346, 4286])).
% 0.79/0.94 tff(4348,plain,
% 0.79/0.94 ((e1 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4347])).
% 0.79/0.94 tff(4349,plain,
% 0.79/0.94 (~(op(e3, e3) = e2)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1127, 861])).
% 0.79/0.94 tff(4350,plain,
% 0.79/0.94 (op(e3, e3) = e1),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1123, 4349, 4344, 280])).
% 0.79/0.94 tff(4351,plain,
% 0.79/0.94 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4345, 4350])).
% 0.79/0.94 tff(4352,plain,
% 0.79/0.94 ((op(e3, e2) = op(e3, e3)) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4351, 4286])).
% 0.79/0.94 tff(4353,plain,
% 0.79/0.94 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4352, 4348])).
% 0.79/0.94 tff(4354,plain,
% 0.79/0.94 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4353])).
% 0.79/0.94 tff(4355,plain,
% 0.79/0.94 (~(op(e3, e2) = e1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1160, 4354])).
% 0.79/0.94 tff(4356,plain,
% 0.79/0.94 ((op(e3, op(op(e3, e3), op(e3, e3))) = e0) <=> (e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(commutativity,[status(thm)],[])).
% 0.79/0.94 tff(4357,plain,
% 0.79/0.94 ((op(e3, e2) = e0) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e0)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4345])).
% 0.79/0.94 tff(4358,plain,
% 0.79/0.94 ((op(e3, e2) = e0) <=> (e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4357, 4356])).
% 0.79/0.94 tff(4359,plain,
% 0.79/0.94 ((e0 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e3, e2) = e0)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4358])).
% 0.79/0.94 tff(4360,plain,
% 0.79/0.94 ((~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e3, e2) = e0))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4359])).
% 0.79/0.94 tff(4361,plain,
% 0.79/0.94 (e1 = op(e3, e3)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4350, 4224])).
% 0.79/0.94 tff(4362,plain,
% 0.79/0.94 ((~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3))))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4363,plain,
% 0.79/0.94 (((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4364,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4363])).
% 0.79/0.94 tff(4365,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4364, 4362])).
% 0.79/0.94 tff(4366,plain,
% 0.79/0.94 ((~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4367,plain,
% 0.79/0.94 ((~(((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))) <=> (~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(4368,axiom,(~(((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax20')).
% 0.79/0.94 tff(4369,plain,
% 0.79/0.94 (~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4368, 4367])).
% 0.79/0.94 tff(4370,plain,
% 0.79/0.94 (~((e2 = op(op(e3, e3), op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4369, 4366])).
% 0.79/0.94 tff(4371,plain,
% 0.79/0.94 ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) | (~(e2 = op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4370, 4365])).
% 0.79/0.94 tff(4372,plain,
% 0.79/0.94 ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4371, 4282])).
% 0.79/0.94 tff(4373,plain,
% 0.79/0.94 (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4372, 4361])).
% 0.79/0.94 tff(4374,plain,
% 0.79/0.94 (~(op(e3, e2) = e0)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4373, 4360])).
% 0.79/0.94 tff(4375,plain,
% 0.79/0.94 ((op(e3, e2) = e2) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e2)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4345])).
% 0.79/0.94 tff(4376,plain,
% 0.79/0.94 ((op(e3, e2) = e2) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4375, 2834])).
% 0.79/0.94 tff(4377,plain,
% 0.79/0.94 ((e2 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e3, e2) = e2)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4376])).
% 0.79/0.94 tff(4378,plain,
% 0.79/0.94 (e1 = op(e3, e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4350])).
% 0.79/0.94 tff(4379,plain,
% 0.79/0.94 (op(e1, e1) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4378, 4378])).
% 0.79/0.94 tff(4380,plain,
% 0.79/0.94 (op(e1, e1) = e2),
% 0.79/0.94 inference(transitivity,[status(thm)],[4379, 4283])).
% 0.79/0.94 tff(4381,plain,
% 0.79/0.94 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4380])).
% 0.79/0.94 tff(4382,plain,
% 0.79/0.94 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4381, 4076])).
% 0.79/0.94 tff(4383,plain,
% 0.79/0.94 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4382])).
% 0.79/0.94 tff(4384,plain,
% 0.79/0.94 (~(op(e2, e1) = e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1049, 4383])).
% 0.79/0.94 tff(4385,plain,
% 0.79/0.94 (~(op(e2, e2) = e1)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[52, 4384])).
% 0.79/0.94 tff(4386,plain,
% 0.79/0.94 (op(e2, e2) = e2),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[226, 4385, 26, 1211])).
% 0.79/0.94 tff(4387,plain,
% 0.79/0.94 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4386, 4345])).
% 0.79/0.94 tff(4388,plain,
% 0.79/0.94 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.79/0.94 inference(transitivity,[status(thm)],[4387, 4377])).
% 0.79/0.94 tff(4389,plain,
% 0.79/0.94 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4388])).
% 0.79/0.94 tff(4390,plain,
% 0.79/0.94 (~(op(e3, e2) = e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[278, 4389])).
% 0.79/0.94 tff(4391,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[736, 4390, 4374, 861, 4355])).
% 0.79/0.94 tff(4392,plain,((op(e3, e2) = e3) | (op(e2, e2) = e3) | (op(e2, e2) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(4393,plain,
% 0.79/0.94 (op(e2, e2) = e0),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4392, 861, 4338, 26])).
% 0.79/0.94 tff(4394,plain,
% 0.79/0.94 ((~(op(e2, e2) = e0)) | (~(op(e0, e0) = e0))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[3722, 1052])).
% 0.79/0.94 tff(4395,plain,
% 0.79/0.94 (~(op(e0, e0) = e0)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[4394, 4393])).
% 0.79/0.94 tff(4396,plain,
% 0.79/0.94 ((op(e2, e2) = e2) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4393, 4282])).
% 0.79/0.94 tff(4397,plain,
% 0.79/0.94 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e2)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4396])).
% 0.79/0.94 tff(4398,plain,
% 0.79/0.94 ((~(e0 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e2))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4397])).
% 0.79/0.94 tff(4399,plain,
% 0.79/0.94 ((e0 = e2) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4282])).
% 0.79/0.94 tff(4400,plain,
% 0.79/0.94 ((~(e0 = e2)) <=> (~(e0 = op(op(e3, e3), op(e3, e3))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4399])).
% 0.79/0.94 tff(4401,plain,
% 0.79/0.94 (~(e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[16, 4400])).
% 0.79/0.94 tff(4402,plain,
% 0.79/0.94 (~(op(e2, e2) = e2)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[4401, 4398])).
% 0.79/0.94 tff(4403,plain,
% 0.79/0.94 ((op(op(e3, e3), op(e3, e3)) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(commutativity,[status(thm)],[])).
% 0.79/0.94 tff(4404,plain,
% 0.79/0.94 (op(e3, e3) = e1),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1123, 4349, 4344, 4338])).
% 0.79/0.94 tff(4405,plain,
% 0.79/0.94 (e1 = op(e3, e3)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4404])).
% 0.79/0.94 tff(4406,plain,
% 0.79/0.94 (op(e1, e1) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4405, 4405])).
% 0.79/0.94 tff(4407,plain,
% 0.79/0.94 ((op(e1, e1) = e1) <=> (op(op(e3, e3), op(e3, e3)) = e1)),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4406])).
% 0.79/0.94 tff(4408,plain,
% 0.79/0.94 ((op(e1, e1) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[4407, 4403])).
% 0.79/0.94 tff(4409,plain,
% 0.79/0.94 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e1) = e1)),
% 0.79/0.94 inference(symmetry,[status(thm)],[4408])).
% 0.79/0.94 tff(4410,plain,
% 0.79/0.94 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e1, e1) = e1))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4409])).
% 0.79/0.94 tff(4411,plain,
% 0.79/0.94 ((e1 = e2) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[4282])).
% 0.79/0.95 tff(4412,plain,
% 0.79/0.95 ((~(e1 = e2)) <=> (~(e1 = op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4411])).
% 0.79/0.95 tff(4413,plain,
% 0.79/0.95 (~(e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[353, 4412])).
% 0.79/0.95 tff(4414,plain,
% 0.79/0.95 (~(op(e1, e1) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4413, 4410])).
% 0.79/0.95 tff(4415,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[215, 4414, 4402, 4344, 4395])).
% 0.79/0.95 tff(4416,plain,((op(e3, e2) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(4417,plain,
% 0.79/0.95 (op(e3, e2) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4416, 26])).
% 0.79/0.95 tff(4418,plain,
% 0.79/0.95 (e3 = op(e3, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4417])).
% 0.79/0.95 tff(4419,plain,
% 0.79/0.95 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4418])).
% 0.79/0.95 tff(4420,plain,
% 0.79/0.95 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4419])).
% 0.79/0.95 tff(4421,plain,
% 0.79/0.95 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4420])).
% 0.79/0.95 tff(4422,plain,
% 0.79/0.95 (~(op(e3, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[974, 4421])).
% 0.79/0.95 tff(4423,plain,
% 0.79/0.95 (~(op(e3, e3) = e1)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1150, 4422])).
% 0.79/0.95 tff(4424,plain,
% 0.79/0.95 (op(e3, e3) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1123, 4423, 4344, 4338])).
% 0.79/0.95 tff(4425,plain,
% 0.79/0.95 (e2 = op(e3, e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4424])).
% 0.79/0.95 tff(4426,plain,
% 0.79/0.95 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4425, 4425])).
% 0.79/0.95 tff(4427,plain,
% 0.79/0.95 (op(e2, e2) = e2),
% 0.79/0.95 inference(transitivity,[status(thm)],[4426, 4283])).
% 0.79/0.95 tff(4428,plain,
% 0.79/0.95 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4427])).
% 0.79/0.95 tff(4429,plain,
% 0.79/0.95 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4428])).
% 0.79/0.95 tff(4430,plain,
% 0.79/0.95 (~(op(e1, e2) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[243, 4429])).
% 0.79/0.95 tff(4431,plain,
% 0.79/0.95 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4424])).
% 0.79/0.95 tff(4432,plain,
% 0.79/0.95 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4431])).
% 0.79/0.95 tff(4433,plain,
% 0.79/0.95 (~(op(e1, e3) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[539, 4432])).
% 0.79/0.95 tff(4434,plain,
% 0.79/0.95 ((op(op(e3, e3), op(e3, e3)) = e0) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(commutativity,[status(thm)],[])).
% 0.79/0.95 tff(4435,plain,
% 0.79/0.95 ((op(e2, e2) = e0) <=> (op(op(e3, e3), op(e3, e3)) = e0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4426])).
% 0.79/0.95 tff(4436,plain,
% 0.79/0.95 ((op(e2, e2) = e0) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4435, 4434])).
% 0.79/0.95 tff(4437,plain,
% 0.79/0.95 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e0)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4436])).
% 0.79/0.95 tff(4438,plain,
% 0.79/0.95 ((~(e0 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4437])).
% 0.79/0.95 tff(4439,plain,
% 0.79/0.95 (~(op(e2, e2) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4401, 4438])).
% 0.79/0.95 tff(4440,plain,
% 0.79/0.95 (op(e3, e2) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4392, 280, 1211, 26])).
% 0.79/0.95 tff(4441,plain,
% 0.79/0.95 (e3 = op(e3, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4440])).
% 0.79/0.95 tff(4442,plain,
% 0.79/0.95 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4441])).
% 0.79/0.95 tff(4443,plain,
% 0.79/0.95 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4442])).
% 0.79/0.95 tff(4444,plain,
% 0.79/0.95 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4443])).
% 0.79/0.95 tff(4445,plain,
% 0.79/0.95 (~(op(e3, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[974, 4444])).
% 0.79/0.95 tff(4446,plain,
% 0.79/0.95 (~(op(e3, e3) = e1)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1150, 4445])).
% 0.79/0.95 tff(4447,plain,
% 0.79/0.95 (op(e3, e3) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1123, 4446, 4344, 280])).
% 0.79/0.95 tff(4448,assumption,(op(e3, e2) = e3), introduced(assumption)).
% 0.79/0.95 tff(4449,plain,
% 0.79/0.95 (e3 = op(e3, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4448])).
% 0.79/0.95 tff(4450,plain,
% 0.79/0.95 (op(e2, e3) = op(e2, op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4449])).
% 0.79/0.95 tff(4451,plain,
% 0.79/0.95 ((op(e2, e3) = e3) <=> (op(e2, op(e3, e2)) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4450, 4449])).
% 0.79/0.95 tff(4452,plain,
% 0.79/0.95 (e3 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4449, 4345])).
% 0.79/0.95 tff(4453,plain,
% 0.79/0.95 ((e1 = e3) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4452])).
% 0.79/0.95 tff(4454,plain,
% 0.79/0.95 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4453, 4348])).
% 0.79/0.95 tff(4455,plain,
% 0.79/0.95 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4454])).
% 0.79/0.95 tff(4456,plain,
% 0.79/0.95 (~(op(e3, e2) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[521, 4455])).
% 0.79/0.95 tff(4457,plain,
% 0.79/0.95 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4449])).
% 0.79/0.95 tff(4458,plain,
% 0.79/0.95 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4457])).
% 0.79/0.95 tff(4459,plain,
% 0.79/0.95 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4458])).
% 0.79/0.95 tff(4460,plain,
% 0.79/0.95 (~(op(e3, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[974, 4459])).
% 0.79/0.95 tff(4461,plain,
% 0.79/0.95 (~(op(e3, e3) = e1)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1150, 4460])).
% 0.79/0.95 tff(4462,plain,
% 0.79/0.95 (op(e3, e3) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1123, 4461, 4344, 280])).
% 0.79/0.95 tff(4463,plain,
% 0.79/0.95 (e2 = op(e3, e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[3791])).
% 0.79/0.95 tff(4464,plain,
% 0.79/0.95 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4463, 4463])).
% 0.79/0.95 tff(4465,plain,
% 0.79/0.95 (op(e2, e2) = e2),
% 0.79/0.95 inference(transitivity,[status(thm)],[4464, 4283])).
% 0.79/0.95 tff(4466,plain,
% 0.79/0.95 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4465])).
% 0.79/0.95 tff(4467,plain,
% 0.79/0.95 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4466])).
% 0.79/0.95 tff(4468,plain,
% 0.79/0.95 (~(op(e0, e2) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1396, 4467])).
% 0.79/0.95 tff(4469,plain,
% 0.79/0.95 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4345, 3791])).
% 0.79/0.95 tff(4470,plain,
% 0.79/0.95 ((op(e3, e2) = op(e3, e3)) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4469, 2834])).
% 0.79/0.95 tff(4471,plain,
% 0.79/0.95 ((~(op(e3, e2) = op(e3, e3))) <=> (~(e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4470])).
% 0.79/0.95 tff(4472,plain,
% 0.79/0.95 (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1160, 4471])).
% 0.79/0.95 tff(4473,plain,
% 0.79/0.95 (e3 = op(e3, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[3795])).
% 0.79/0.95 tff(4474,plain,
% 0.79/0.95 (e3 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4473, 4345])).
% 0.79/0.95 tff(4475,plain,
% 0.79/0.95 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4465])).
% 0.79/0.95 tff(4476,plain,
% 0.79/0.95 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4475])).
% 0.79/0.95 tff(4477,plain,
% 0.79/0.95 (~(op(e1, e2) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[243, 4476])).
% 0.79/0.95 tff(4478,plain,
% 0.79/0.95 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[3791])).
% 0.79/0.95 tff(4479,plain,
% 0.79/0.95 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4478])).
% 0.79/0.95 tff(4480,plain,
% 0.79/0.95 (~(op(e1, e3) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[539, 4479])).
% 0.79/0.95 tff(4481,plain,
% 0.79/0.95 (op(e1, e0) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[751, 379, 4480, 4477])).
% 0.79/0.95 tff(4482,plain,
% 0.79/0.95 ((op(e1, e0) = e3) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4481, 4474])).
% 0.79/0.95 tff(4483,plain,
% 0.79/0.95 ((e2 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e1, e0) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4482])).
% 0.79/0.95 tff(4484,plain,
% 0.79/0.95 ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e1, e0) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4483])).
% 0.79/0.95 tff(4485,plain,
% 0.79/0.95 (~(op(e1, e0) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4472, 4484])).
% 0.79/0.95 tff(4486,plain,
% 0.79/0.95 ((op(e2, e2) = e1) <=> (op(op(e3, e3), op(e3, e3)) = e1)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4464])).
% 0.79/0.95 tff(4487,plain,
% 0.79/0.95 ((op(e2, e2) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4486, 4403])).
% 0.79/0.95 tff(4488,plain,
% 0.79/0.95 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e1)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4487])).
% 0.79/0.95 tff(4489,plain,
% 0.79/0.95 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4488])).
% 0.79/0.95 tff(4490,plain,
% 0.79/0.95 (~(op(e2, e2) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4413, 4489])).
% 0.79/0.95 tff(4491,plain,
% 0.79/0.95 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[436])).
% 0.79/0.95 tff(4492,plain,
% 0.79/0.95 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4491, 591])).
% 0.79/0.95 tff(4493,plain,
% 0.79/0.95 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4492])).
% 0.79/0.95 tff(4494,plain,
% 0.79/0.95 (~(op(e1, e2) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1604, 4493])).
% 0.79/0.95 tff(4495,plain,
% 0.79/0.95 (op(e0, e2) = e1),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[671, 4494, 663, 4490])).
% 0.79/0.95 tff(4496,assumption,(op(e0, e2) = e1), introduced(assumption)).
% 0.79/0.95 tff(4497,plain,
% 0.79/0.95 ((op(e0, e2) = e3) <=> (e1 = e3)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4496])).
% 0.79/0.95 tff(4498,plain,
% 0.79/0.95 ((e1 = e3) <=> (op(e0, e2) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4497])).
% 0.79/0.95 tff(4499,plain,
% 0.79/0.95 ((~(e1 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4498])).
% 0.79/0.95 tff(4500,plain,
% 0.79/0.95 (~(op(e0, e2) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[521, 4499])).
% 0.79/0.95 tff(4501,plain,
% 0.79/0.95 ((op(e0, e2) = e0) <=> (e1 = e0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4496])).
% 0.79/0.95 tff(4502,plain,
% 0.79/0.95 ((op(e0, e2) = e0) <=> (e0 = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4501, 1203])).
% 0.79/0.95 tff(4503,plain,
% 0.79/0.95 ((e0 = e1) <=> (op(e0, e2) = e0)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4502])).
% 0.79/0.95 tff(4504,plain,
% 0.79/0.95 ((~(e0 = e1)) <=> (~(op(e0, e2) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4503])).
% 0.79/0.95 tff(4505,plain,
% 0.79/0.95 (~(op(e0, e2) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[40, 4504])).
% 0.79/0.95 tff(4506,plain,
% 0.79/0.95 (~(op(e0, e0) = e2)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1472, 4505])).
% 0.79/0.95 tff(4507,plain,
% 0.79/0.95 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[3791])).
% 0.79/0.95 tff(4508,plain,
% 0.79/0.95 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4507])).
% 0.79/0.95 tff(4509,plain,
% 0.79/0.95 (~(op(e0, e3) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1578, 4508])).
% 0.79/0.95 tff(4510,plain,
% 0.79/0.95 (op(e0, e1) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1346, 4509, 3283, 4506])).
% 0.79/0.95 tff(4511,plain,
% 0.79/0.95 ((op(e0, e1) = e3) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4510, 4474])).
% 0.79/0.95 tff(4512,plain,
% 0.79/0.95 ((e2 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e0, e1) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4511])).
% 0.79/0.95 tff(4513,plain,
% 0.79/0.95 ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e0, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4512])).
% 0.79/0.95 tff(4514,assumption,(~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))), introduced(assumption)).
% 0.79/0.95 tff(4515,plain,
% 0.79/0.95 (~(op(e0, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 0.79/0.95 tff(4516,plain,
% 0.79/0.95 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4473])).
% 0.79/0.95 tff(4517,plain,
% 0.79/0.95 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4516])).
% 0.79/0.95 tff(4518,plain,
% 0.79/0.95 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4517])).
% 0.79/0.95 tff(4519,plain,
% 0.79/0.95 (~(op(e1, e2) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[742, 4518])).
% 0.79/0.95 tff(4520,plain,
% 0.79/0.95 (op(e1, e3) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[530, 4519, 423, 887])).
% 0.79/0.95 tff(4521,plain,
% 0.79/0.95 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4520])).
% 0.79/0.95 tff(4522,plain,
% 0.79/0.95 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4521])).
% 0.79/0.95 tff(4523,plain,
% 0.79/0.95 (~(op(e0, e3) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1762, 4522])).
% 0.79/0.95 tff(4524,plain,
% 0.79/0.95 (op(e0, e0) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1090, 4523, 4515, 4500])).
% 0.79/0.95 tff(4525,plain,
% 0.79/0.95 (e3 = op(e0, e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4524, 1299])).
% 0.79/0.95 tff(4526,plain,
% 0.79/0.95 (op(op(e0, e0), op(e0, e0)) = op(e3, e3)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4524, 4524])).
% 0.79/0.95 tff(4527,plain,
% 0.79/0.95 (op(e3, e3) = op(op(e0, e0), op(e0, e0))),
% 0.79/0.95 inference(symmetry,[status(thm)],[4526])).
% 0.79/0.95 tff(4528,plain,
% 0.79/0.95 (e2 = op(op(e0, e0), op(e0, e0))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4463, 4527])).
% 0.79/0.95 tff(4529,plain,
% 0.79/0.95 (op(op(e0, e0), op(e0, e0)) = e2),
% 0.79/0.95 inference(transitivity,[status(thm)],[4526, 3791])).
% 0.79/0.95 tff(4530,plain,
% 0.79/0.95 (op(e0, op(op(e0, e0), op(e0, e0))) = op(e0, e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4529])).
% 0.79/0.95 tff(4531,plain,
% 0.79/0.95 (op(e0, e2) = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.79/0.95 inference(symmetry,[status(thm)],[4530])).
% 0.79/0.95 tff(4532,plain,
% 0.79/0.95 (e1 = op(e0, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4496])).
% 0.79/0.95 tff(4533,plain,
% 0.79/0.95 (e1 = op(e0, op(op(e0, e0), op(e0, e0)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4532, 4531])).
% 0.79/0.95 tff(4534,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2169, 4533, 4528, 4525])).
% 0.79/0.95 tff(4535,plain,((~(op(e3, e3) = e2)) | (~(op(e0, e2) = e1)) | (e2 = op(e3, op(op(e3, e3), op(e3, e3)))) | (op(e1, e1) = e3) | (op(e1, e0) = e3) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(4536,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4535, 4495, 4485, 3791, 423, 4472, 4468])).
% 0.79/0.95 tff(4537,plain,((op(e1, e1) = e2) | (~(op(e3, e3) = e2)) | (op(e1, e1) = e3) | (op(e3, e2) = e1) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(4538,plain,
% 0.79/0.95 (op(e1, e1) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4537, 423, 4462, 4456, 424])).
% 0.79/0.95 tff(4539,plain,
% 0.79/0.95 (op(e1, e2) = e1),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[514, 4538])).
% 0.79/0.95 tff(4540,plain,
% 0.79/0.95 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4539])).
% 0.79/0.95 tff(4541,plain,
% 0.79/0.95 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4540])).
% 0.79/0.95 tff(4542,plain,
% 0.79/0.95 (~(op(e1, e0) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[613, 4541])).
% 0.79/0.95 tff(4543,plain,
% 0.79/0.95 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4538])).
% 0.79/0.95 tff(4544,plain,
% 0.79/0.95 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4543])).
% 0.79/0.95 tff(4545,plain,
% 0.79/0.95 (~(op(e1, e0) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[441, 4544])).
% 0.79/0.95 tff(4546,plain,
% 0.79/0.95 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2708, 4345])).
% 0.79/0.95 tff(4547,plain,
% 0.79/0.95 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4546, 4348])).
% 0.79/0.95 tff(4548,plain,
% 0.79/0.95 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4547])).
% 0.79/0.95 tff(4549,plain,
% 0.79/0.95 (~(op(e3, e2) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[572, 4548])).
% 0.79/0.95 tff(4550,plain,
% 0.79/0.95 ((op(e3, e0) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2708])).
% 0.79/0.95 tff(4551,plain,
% 0.79/0.95 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4550, 1071])).
% 0.79/0.95 tff(4552,plain,
% 0.79/0.95 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4551])).
% 0.79/0.95 tff(4553,plain,
% 0.79/0.95 (~(op(e3, e3) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1424, 4552])).
% 0.79/0.95 tff(4554,plain,
% 0.79/0.95 (op(e3, e3) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1123, 4553, 4344, 280])).
% 0.79/0.95 tff(4555,plain,
% 0.79/0.95 (op(e1, e1) = e2),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4537, 4554, 423, 4549, 424])).
% 0.79/0.95 tff(4556,plain,
% 0.79/0.95 (op(e1, e2) = e1),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[514, 4555])).
% 0.79/0.95 tff(4557,plain,
% 0.79/0.95 (op(e2, op(e1, e2)) = op(e2, e1)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4556])).
% 0.79/0.95 tff(4558,plain,
% 0.79/0.95 ((op(e2, op(e1, e2)) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4557, 4556])).
% 0.79/0.95 tff(4559,plain,
% 0.79/0.95 ((op(e2, e1) = e1) <=> (op(e2, op(e1, e2)) = op(e1, e2))),
% 0.79/0.95 inference(symmetry,[status(thm)],[4558])).
% 0.79/0.95 tff(4560,plain,
% 0.79/0.95 (e2 = op(e3, e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4554])).
% 0.79/0.95 tff(4561,plain,
% 0.79/0.95 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4560, 4560])).
% 0.79/0.95 tff(4562,plain,
% 0.79/0.95 ((op(e2, e2) = e1) <=> (op(op(e3, e3), op(e3, e3)) = e1)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4561])).
% 0.79/0.95 tff(4563,plain,
% 0.79/0.95 ((op(e2, e2) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4562, 4403])).
% 0.79/0.95 tff(4564,plain,
% 0.79/0.95 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e2, e2) = e1)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4563])).
% 0.79/0.95 tff(4565,plain,
% 0.79/0.95 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e2, e2) = e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4564])).
% 0.79/0.95 tff(4566,plain,
% 0.79/0.95 (~(op(e2, e2) = e1)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[4413, 4565])).
% 0.79/0.95 tff(4567,plain,
% 0.79/0.95 (op(e3, e2) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1127, 4554])).
% 0.79/0.95 tff(4568,plain,
% 0.79/0.95 (e3 = op(e3, e2)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4567])).
% 0.79/0.95 tff(4569,plain,
% 0.79/0.95 (e3 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[4568, 4345])).
% 0.79/0.95 tff(4570,plain,
% 0.79/0.95 ((e0 = e3) <=> (e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4569])).
% 0.79/0.95 tff(4571,plain,
% 0.79/0.95 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4570, 4359])).
% 0.79/0.95 tff(4572,plain,
% 0.79/0.95 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4571])).
% 0.79/0.95 tff(4573,plain,
% 0.79/0.95 (~(op(e3, e2) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[509, 4572])).
% 0.79/0.95 tff(4574,plain,
% 0.79/0.95 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4556])).
% 0.79/0.95 tff(4575,plain,
% 0.79/0.95 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4574, 1203])).
% 0.79/0.95 tff(4576,plain,
% 0.79/0.95 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4575])).
% 0.79/0.95 tff(4577,plain,
% 0.79/0.95 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4576])).
% 0.79/0.95 tff(4578,plain,
% 0.79/0.95 (~(op(e1, e2) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[40, 4577])).
% 0.79/0.95 tff(4579,plain,
% 0.79/0.95 (op(e0, e2) = e0),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1678, 4578, 1211, 4573])).
% 0.79/0.95 tff(4580,plain,
% 0.79/0.95 ((op(e0, e2) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4579])).
% 0.79/0.95 tff(4581,plain,
% 0.79/0.95 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4580, 299])).
% 0.79/0.95 tff(4582,plain,
% 0.79/0.95 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4581])).
% 0.79/0.95 tff(4583,plain,
% 0.79/0.95 (~(op(e0, e3) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[702, 4582])).
% 0.79/0.95 tff(4584,plain,
% 0.79/0.95 (op(e2, e2) = e2),
% 0.79/0.95 inference(transitivity,[status(thm)],[4561, 4283])).
% 0.79/0.95 tff(4585,plain,
% 0.79/0.95 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4584])).
% 0.79/0.95 tff(4586,plain,
% 0.79/0.95 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[3849, 4585])).
% 0.79/0.95 tff(4587,plain,
% 0.79/0.95 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4584])).
% 0.79/0.95 tff(4588,plain,
% 0.79/0.95 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4587])).
% 0.79/0.95 tff(4589,plain,
% 0.79/0.95 (~(op(e2, e0) = e2)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[85, 4588])).
% 0.79/0.95 tff(4590,plain,
% 0.79/0.95 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4568])).
% 0.79/0.95 tff(4591,plain,
% 0.79/0.95 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4590])).
% 0.79/0.95 tff(4592,plain,
% 0.79/0.95 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4591])).
% 0.79/0.95 tff(4593,plain,
% 0.79/0.95 (~(op(e1, e2) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[742, 4592])).
% 0.79/0.95 tff(4594,plain,
% 0.79/0.95 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4568])).
% 0.79/0.95 tff(4595,plain,
% 0.79/0.95 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4594])).
% 0.79/0.95 tff(4596,plain,
% 0.79/0.95 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4595])).
% 0.79/0.95 tff(4597,plain,
% 0.79/0.95 (~(op(e3, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[974, 4596])).
% 0.79/0.95 tff(4598,plain,
% 0.79/0.95 ((e3 = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.79/0.95 inference(commutativity,[status(thm)],[])).
% 0.79/0.95 tff(4599,assumption,(~(op(e2, e0) = e2)), introduced(assumption)).
% 0.79/0.95 tff(4600,assumption,(op(e0, e2) = e0), introduced(assumption)).
% 0.79/0.95 tff(4601,plain,
% 0.79/0.95 (op(e2, op(e0, e2)) = op(e2, e0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4600])).
% 0.79/0.95 tff(4602,plain,
% 0.79/0.95 ((op(e2, op(e0, e2)) = op(e0, e2)) <=> (op(e2, e0) = e0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4601, 4600])).
% 0.79/0.95 tff(4603,plain,
% 0.79/0.95 ((~(op(e2, op(e0, e2)) = op(e0, e2))) <=> (~(op(e2, e0) = e0))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4602])).
% 0.79/0.95 tff(4604,plain,
% 0.79/0.95 (~(op(e2, e0) = e0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1058, 4603])).
% 0.79/0.95 tff(4605,plain,
% 0.79/0.95 (op(e2, e0) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[121, 4604, 422, 4599])).
% 0.79/0.95 tff(4606,plain,
% 0.79/0.95 ((op(e2, e0) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4605])).
% 0.79/0.95 tff(4607,plain,
% 0.79/0.95 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4606, 4598])).
% 0.79/0.95 tff(4608,plain,
% 0.79/0.95 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4607])).
% 0.79/0.95 tff(4609,plain,
% 0.79/0.95 (~(op(e2, e1) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[70, 4608])).
% 0.79/0.95 tff(4610,plain,
% 0.79/0.95 (op(e0, e1) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1841, 4609, 423, 1833])).
% 0.79/0.95 tff(4611,plain,
% 0.79/0.95 (e3 = op(e0, e1)),
% 0.79/0.95 inference(symmetry,[status(thm)],[4610])).
% 0.79/0.95 tff(4612,plain,
% 0.79/0.95 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e3)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4605])).
% 0.79/0.95 tff(4613,plain,
% 0.79/0.95 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e3))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4612])).
% 0.79/0.95 tff(4614,plain,
% 0.79/0.95 (~(op(e1, e0) = e3)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[638, 4613])).
% 0.79/0.95 tff(4615,plain,
% 0.79/0.95 (op(e1, e3) = e3),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[530, 4614, 423, 838])).
% 0.79/0.95 tff(4616,plain,
% 0.79/0.95 (op(e1, op(e0, e1)) = op(e1, e3)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4610])).
% 0.79/0.95 tff(4617,plain,
% 0.79/0.95 (op(e1, op(e0, e1)) = op(e0, e1)),
% 0.79/0.95 inference(transitivity,[status(thm)],[4616, 4615, 4611])).
% 0.79/0.95 tff(4618,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1060, 4617])).
% 0.79/0.95 tff(4619,plain,(((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))) | (op(e1, e1) = e3) | (op(e3, e1) = e3) | (op(e1, e2) = e3) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (~(op(e0, e2) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(4620,plain,
% 0.79/0.95 ((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[4619, 4597, 423, 4593, 2711, 4589, 4579])).
% 0.79/0.95 tff(4621,plain,
% 0.79/0.95 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4554])).
% 0.79/0.95 tff(4622,plain,
% 0.79/0.95 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[4621])).
% 0.79/0.96 tff(4623,plain,
% 0.79/0.96 (~(op(e0, e3) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1578, 4622])).
% 0.79/0.96 tff(4624,plain,
% 0.79/0.96 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4584])).
% 0.79/0.96 tff(4625,plain,
% 0.79/0.96 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4624])).
% 0.79/0.96 tff(4626,plain,
% 0.79/0.96 (~(op(e0, e2) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1396, 4625])).
% 0.79/0.96 tff(4627,plain,
% 0.79/0.96 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4555])).
% 0.79/0.96 tff(4628,plain,
% 0.79/0.96 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4627])).
% 0.79/0.96 tff(4629,plain,
% 0.79/0.96 (~(op(e0, e1) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1402, 4628])).
% 0.79/0.96 tff(4630,plain,
% 0.79/0.96 (op(e0, e0) = e2),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1346, 4629, 4626, 4623])).
% 0.79/0.96 tff(4631,plain,
% 0.79/0.96 ((op(e0, e0) = e3) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4630, 4569])).
% 0.79/0.96 tff(4632,plain,
% 0.79/0.96 ((e2 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e0, e0) = e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4631])).
% 0.79/0.96 tff(4633,plain,
% 0.79/0.96 ((~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e0, e0) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4632])).
% 0.79/0.96 tff(4634,plain,
% 0.79/0.96 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4345, 4554])).
% 0.79/0.96 tff(4635,plain,
% 0.79/0.96 ((op(e3, e2) = op(e3, e3)) <=> (e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4634, 2834])).
% 0.79/0.96 tff(4636,plain,
% 0.79/0.96 ((~(op(e3, e2) = op(e3, e3))) <=> (~(e2 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4635])).
% 0.79/0.96 tff(4637,plain,
% 0.79/0.96 (~(e2 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1160, 4636])).
% 0.79/0.96 tff(4638,plain,
% 0.79/0.96 (~(op(e0, e0) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4637, 4633])).
% 0.79/0.96 tff(4639,plain,
% 0.79/0.96 (op(e1, e1) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4555, 4282])).
% 0.79/0.96 tff(4640,plain,
% 0.79/0.96 ((op(e1, e1) = e1) <=> (op(op(e3, e3), op(e3, e3)) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4639])).
% 0.79/0.96 tff(4641,plain,
% 0.79/0.96 ((op(e1, e1) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4640, 4403])).
% 0.79/0.96 tff(4642,plain,
% 0.79/0.96 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e1) = e1)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4641])).
% 0.79/0.96 tff(4643,plain,
% 0.79/0.96 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e1, e1) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4642])).
% 0.79/0.96 tff(4644,plain,
% 0.79/0.96 (~(op(e1, e1) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4413, 4643])).
% 0.79/0.96 tff(4645,plain,
% 0.79/0.96 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e3, e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4449])).
% 0.79/0.96 tff(4646,plain,
% 0.79/0.96 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4645])).
% 0.79/0.96 tff(4647,plain,
% 0.79/0.96 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4646])).
% 0.79/0.96 tff(4648,plain,
% 0.79/0.96 (~(op(e0, e2) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1457, 4647])).
% 0.79/0.96 tff(4649,plain,
% 0.79/0.96 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4449])).
% 0.79/0.96 tff(4650,plain,
% 0.79/0.96 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4649])).
% 0.79/0.96 tff(4651,plain,
% 0.79/0.96 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4650])).
% 0.79/0.96 tff(4652,plain,
% 0.79/0.96 (~(op(e1, e2) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[742, 4651])).
% 0.79/0.96 tff(4653,plain,
% 0.79/0.96 (op(e1, e0) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[530, 933, 423, 4652])).
% 0.79/0.96 tff(4654,plain,
% 0.79/0.96 (op(e0, op(e1, e0)) = op(e0, e3)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4653])).
% 0.79/0.96 tff(4655,plain,
% 0.79/0.96 ((op(e0, op(e1, e0)) = op(e1, e0)) <=> (op(e0, e3) = e3)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4654, 4653])).
% 0.79/0.96 tff(4656,plain,
% 0.79/0.96 ((~(op(e0, op(e1, e0)) = op(e1, e0))) <=> (~(op(e0, e3) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4655])).
% 0.79/0.96 tff(4657,assumption,((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))), introduced(assumption)).
% 0.79/0.96 tff(4658,assumption,(op(e1, e2) = e1), introduced(assumption)).
% 0.79/0.96 tff(4659,plain,
% 0.79/0.96 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4658])).
% 0.79/0.96 tff(4660,plain,
% 0.79/0.96 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4659])).
% 0.79/0.96 tff(4661,plain,
% 0.79/0.96 (~(op(e0, e2) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1740, 4660])).
% 0.79/0.96 tff(4662,plain,
% 0.79/0.96 ((op(e2, op(e3, e2)) = op(e3, e2)) <=> (op(e2, e3) = e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4451])).
% 0.79/0.96 tff(4663,plain,
% 0.79/0.96 ((~(op(e2, op(e3, e2)) = op(e3, e2))) <=> (~(op(e2, e3) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4662])).
% 0.79/0.96 tff(4664,plain,
% 0.79/0.96 (~(op(e2, e3) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[944, 4663])).
% 0.79/0.96 tff(4665,plain,
% 0.79/0.96 (op(e0, e3) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[724, 4664, 4344, 933])).
% 0.79/0.96 tff(4666,plain,
% 0.79/0.96 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2708])).
% 0.79/0.96 tff(4667,plain,
% 0.79/0.96 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4666])).
% 0.79/0.96 tff(4668,plain,
% 0.79/0.96 (~(op(e0, e0) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[270, 4667])).
% 0.79/0.96 tff(4669,plain,
% 0.79/0.96 (op(e0, op(e3, e0)) = op(e0, e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2708])).
% 0.79/0.96 tff(4670,plain,
% 0.79/0.96 ((op(e0, op(e3, e0)) = op(e3, e0)) <=> (op(e0, e1) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4669, 2708])).
% 0.79/0.96 tff(4671,plain,
% 0.79/0.96 ((~(op(e0, op(e3, e0)) = op(e3, e0))) <=> (~(op(e0, e1) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4670])).
% 0.79/0.96 tff(4672,plain,
% 0.79/0.96 (~(op(e0, e1) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[936, 4671])).
% 0.79/0.96 tff(4673,plain,
% 0.79/0.96 (op(e0, e3) = e1),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2185, 4672, 4668, 1808])).
% 0.79/0.96 tff(4674,plain,
% 0.79/0.96 (e1 = op(e0, e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4673])).
% 0.79/0.96 tff(4675,plain,
% 0.79/0.96 (e1 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4674, 4665, 4449, 4288])).
% 0.79/0.96 tff(4676,plain,
% 0.79/0.96 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2708, 4288])).
% 0.79/0.96 tff(4677,plain,
% 0.79/0.96 ((~(op(e3, e0) = op(e3, e2))) <=> (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4676])).
% 0.79/0.96 tff(4678,plain,
% 0.79/0.96 (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[572, 4677])).
% 0.79/0.96 tff(4679,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4678, 4675])).
% 0.79/0.96 tff(4680,plain,(((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))) | (~(op(e3, e2) = e3)) | (op(e1, e3) = e3) | (op(e0, e2) = e1) | (~(op(e3, e0) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(4681,plain,
% 0.79/0.96 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4680, 933, 4448, 4661, 2708])).
% 0.79/0.96 tff(4682,plain,
% 0.79/0.96 (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[798, 4681, 758, 4657])).
% 0.79/0.96 tff(4683,plain,
% 0.79/0.96 (~(op(e0, op(e1, e0)) = op(e1, e0))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[883, 4682])).
% 0.79/0.96 tff(4684,plain,
% 0.79/0.96 (~(op(e0, e3) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4683, 4656])).
% 0.79/0.96 tff(4685,plain,
% 0.79/0.96 (op(e0, e1) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1090, 4684, 1590, 4648])).
% 0.79/0.96 tff(4686,assumption,(~(op(e1, e1) = e1)), introduced(assumption)).
% 0.79/0.96 tff(4687,plain,
% 0.79/0.96 ((op(e3, e0) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2708])).
% 0.79/0.96 tff(4688,plain,
% 0.79/0.96 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.79/0.96 inference(transitivity,[status(thm)],[4687, 3971])).
% 0.79/0.96 tff(4689,plain,
% 0.79/0.96 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4688])).
% 0.79/0.96 tff(4690,plain,
% 0.79/0.96 (~(op(e3, e1) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1320, 4689])).
% 0.79/0.96 tff(4691,plain,
% 0.79/0.96 (op(e2, op(e1, e2)) = op(e2, e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4658])).
% 0.79/0.96 tff(4692,plain,
% 0.79/0.96 ((op(e2, op(e1, e2)) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4691, 4658])).
% 0.79/0.96 tff(4693,plain,
% 0.79/0.96 ((~(op(e2, op(e1, e2)) = op(e1, e2))) <=> (~(op(e2, e1) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4692])).
% 0.79/0.96 tff(4694,plain,
% 0.79/0.96 (~(op(e2, op(e1, e2)) = op(e1, e2))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[961, 4682])).
% 0.79/0.96 tff(4695,plain,
% 0.79/0.96 (~(op(e2, e1) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4694, 4693])).
% 0.79/0.96 tff(4696,plain,
% 0.79/0.96 (op(e0, e1) = e1),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[988, 4695, 4690, 4686])).
% 0.79/0.96 tff(4697,plain,
% 0.79/0.96 (e1 = op(e0, e1)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4696])).
% 0.79/0.96 tff(4698,plain,
% 0.79/0.96 (e1 = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4697, 4685, 4449, 4345])).
% 0.79/0.96 tff(4699,plain,
% 0.79/0.96 ((~(op(e3, e0) = op(e3, e2))) <=> (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4546])).
% 0.79/0.96 tff(4700,plain,
% 0.79/0.96 (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[572, 4699])).
% 0.79/0.96 tff(4701,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4700, 4698])).
% 0.79/0.96 tff(4702,plain,((op(e1, e3) = e3) | (~(op(e3, e2) = e3)) | (op(e1, e1) = e1) | (op(e0, e0) = e3) | (~(op(e1, e2) = e1)) | (~((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3)))) | (~((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3)))) | (~(op(e3, e0) = e1)) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(4703,plain,
% 0.79/0.96 (op(e1, e3) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4702, 4567, 4644, 4638, 4556, 4620, 4586, 2708, 423])).
% 0.79/0.96 tff(4704,plain,
% 0.79/0.96 (op(e1, e3) = op(e3, op(op(e3, e3), op(e3, e3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4703, 4568, 4345])).
% 0.79/0.96 tff(4705,plain,
% 0.79/0.96 ((op(e1, e3) = e0) <=> (op(e3, op(op(e3, e3), op(e3, e3))) = e0)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4704])).
% 0.79/0.96 tff(4706,plain,
% 0.79/0.96 ((op(e1, e3) = e0) <=> (e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4705, 4356])).
% 0.79/0.96 tff(4707,plain,
% 0.79/0.96 ((e0 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e1, e3) = e0)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4706])).
% 0.79/0.96 tff(4708,plain,
% 0.79/0.96 ((~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e1, e3) = e0))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4707])).
% 0.79/0.96 tff(4709,plain,
% 0.79/0.96 ((~(e0 = e3)) <=> (~(e0 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4570])).
% 0.79/0.96 tff(4710,plain,
% 0.79/0.96 (~(e0 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[509, 4709])).
% 0.79/0.96 tff(4711,plain,
% 0.79/0.96 (~(op(e1, e3) = e0)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4710, 4708])).
% 0.79/0.96 tff(4712,plain,
% 0.79/0.96 (op(e2, e3) = e0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[322, 4711, 280, 4583])).
% 0.79/0.96 tff(4713,plain,
% 0.79/0.96 ((op(e2, e3) = e1) <=> (e0 = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4712])).
% 0.79/0.96 tff(4714,plain,
% 0.79/0.96 ((e0 = e1) <=> (op(e2, e3) = e1)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4713])).
% 0.79/0.96 tff(4715,plain,
% 0.79/0.96 ((~(e0 = e1)) <=> (~(op(e2, e3) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4714])).
% 0.79/0.96 tff(4716,plain,
% 0.79/0.96 (~(op(e2, e3) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[40, 4715])).
% 0.79/0.96 tff(4717,plain,
% 0.79/0.96 (op(e2, e1) = e1),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[953, 4716, 2711, 4566])).
% 0.79/0.96 tff(4718,plain,
% 0.79/0.96 (op(e2, op(e1, e2)) = op(e1, e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4717, 4559])).
% 0.79/0.96 tff(4719,plain,
% 0.79/0.96 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4554])).
% 0.79/0.96 tff(4720,plain,
% 0.79/0.96 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4719])).
% 0.79/0.96 tff(4721,plain,
% 0.79/0.96 (~(op(e3, e1) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1780, 4720])).
% 0.79/0.96 tff(4722,plain,
% 0.79/0.96 (op(e3, e1) = e0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2875, 4721, 4690, 4597])).
% 0.79/0.96 tff(4723,plain,
% 0.79/0.96 (op(e1, op(e3, e1)) = op(e1, e0)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4722])).
% 0.79/0.96 tff(4724,plain,
% 0.79/0.96 ((op(e1, op(e3, e1)) = op(e3, e1)) <=> (op(e1, e0) = e0)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4723, 4722])).
% 0.79/0.96 tff(4725,plain,
% 0.79/0.96 ((op(e1, e0) = e0) <=> (op(e1, op(e3, e1)) = op(e3, e1))),
% 0.79/0.96 inference(symmetry,[status(thm)],[4724])).
% 0.79/0.96 tff(4726,plain,
% 0.79/0.96 (op(e1, e0) = e0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[548, 4711, 424, 4578])).
% 0.79/0.96 tff(4727,plain,
% 0.79/0.96 (op(e1, op(e3, e1)) = op(e3, e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4726, 4725])).
% 0.79/0.96 tff(4728,plain,
% 0.79/0.96 ((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[849, 4727])).
% 0.79/0.96 tff(4729,plain,
% 0.79/0.96 (~((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3)))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[798, 4728, 4620, 4586])).
% 0.79/0.96 tff(4730,plain,
% 0.79/0.96 (~(op(e2, op(e1, e2)) = op(e1, e2))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[961, 4729])).
% 0.79/0.96 tff(4731,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4730, 4718])).
% 0.79/0.96 tff(4732,plain,((~(op(e3, e0) = e1)) | (op(e1, e1) = e0) | (op(e3, e3) = e0) | (op(e1, e1) = e3) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(4733,plain,
% 0.79/0.96 (~(op(e3, e0) = e1)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[4732, 423, 280, 424, 1211])).
% 0.79/0.96 tff(4734,plain,
% 0.79/0.96 (op(e3, e0) = e0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[3800, 4733, 4462])).
% 0.79/0.96 tff(4735,plain,
% 0.79/0.96 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4734])).
% 0.79/0.96 tff(4736,plain,
% 0.79/0.96 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4735])).
% 0.79/0.96 tff(4737,plain,
% 0.79/0.96 (~(op(e1, e0) = e0)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[564, 4736])).
% 0.79/0.96 tff(4738,plain,
% 0.79/0.96 (op(e1, e0) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1548, 4737, 4545, 4542])).
% 0.79/0.96 tff(4739,plain,
% 0.79/0.96 ((op(e1, e0) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4738])).
% 0.79/0.96 tff(4740,plain,
% 0.79/0.96 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.79/0.96 inference(transitivity,[status(thm)],[4739, 656])).
% 0.79/0.96 tff(4741,plain,
% 0.79/0.96 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4740])).
% 0.79/0.96 tff(4742,plain,
% 0.79/0.96 (~(op(e1, e3) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[625, 4741])).
% 0.79/0.96 tff(4743,plain,
% 0.79/0.96 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4539])).
% 0.79/0.96 tff(4744,plain,
% 0.79/0.96 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4743])).
% 0.79/0.96 tff(4745,plain,
% 0.79/0.96 (~(op(e0, e2) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1740, 4744])).
% 0.79/0.96 tff(4746,plain,
% 0.79/0.96 (op(e3, e1) = e1),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[772, 4733, 4456, 4461])).
% 0.79/0.96 tff(4747,plain,
% 0.79/0.96 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4746])).
% 0.79/0.96 tff(4748,plain,
% 0.79/0.96 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4747])).
% 0.79/0.96 tff(4749,plain,
% 0.79/0.96 (~(op(e0, e1) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[859, 4748])).
% 0.79/0.96 tff(4750,plain,
% 0.79/0.96 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4462])).
% 0.79/0.96 tff(4751,plain,
% 0.79/0.96 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4750])).
% 0.79/0.96 tff(4752,plain,
% 0.79/0.96 (~(op(e0, e3) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1578, 4751])).
% 0.79/0.96 tff(4753,plain,
% 0.79/0.96 (e2 = op(e3, e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4462])).
% 0.79/0.96 tff(4754,plain,
% 0.79/0.96 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4753, 4753])).
% 0.79/0.96 tff(4755,plain,
% 0.79/0.96 (op(e2, e2) = e2),
% 0.79/0.96 inference(transitivity,[status(thm)],[4754, 4283])).
% 0.79/0.96 tff(4756,plain,
% 0.79/0.96 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4755])).
% 0.79/0.96 tff(4757,plain,
% 0.79/0.96 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4756])).
% 0.79/0.96 tff(4758,plain,
% 0.79/0.96 (~(op(e0, e2) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1396, 4757])).
% 0.79/0.96 tff(4759,plain,
% 0.79/0.96 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4538])).
% 0.79/0.96 tff(4760,plain,
% 0.79/0.96 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4759])).
% 0.79/0.96 tff(4761,plain,
% 0.79/0.96 (~(op(e0, e1) = e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1402, 4760])).
% 0.79/0.96 tff(4762,plain,
% 0.79/0.96 (op(e0, e0) = e2),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1346, 4761, 4758, 4752])).
% 0.79/0.96 tff(4763,plain,
% 0.79/0.96 (op(e0, e0) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4762, 4282])).
% 0.79/0.96 tff(4764,plain,
% 0.79/0.96 ((op(e0, e0) = e1) <=> (op(op(e3, e3), op(e3, e3)) = e1)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4763])).
% 0.79/0.96 tff(4765,plain,
% 0.79/0.96 ((op(e0, e0) = e1) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[4764, 4403])).
% 0.79/0.96 tff(4766,plain,
% 0.79/0.96 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e0, e0) = e1)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4765])).
% 0.79/0.96 tff(4767,plain,
% 0.79/0.96 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e0, e0) = e1))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4766])).
% 0.79/0.96 tff(4768,plain,
% 0.79/0.96 (~(op(e0, e0) = e1)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4413, 4767])).
% 0.79/0.96 tff(4769,plain,
% 0.79/0.96 (op(e0, e3) = e1),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2185, 4768, 4749, 4745])).
% 0.79/0.96 tff(4770,plain,
% 0.79/0.96 ((op(e0, e3) = e3) <=> (e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4769, 4452])).
% 0.79/0.96 tff(4771,plain,
% 0.79/0.96 ((e1 = op(e3, op(op(e3, e3), op(e3, e3)))) <=> (op(e0, e3) = e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4770])).
% 0.79/0.96 tff(4772,plain,
% 0.79/0.96 ((~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))) <=> (~(op(e0, e3) = e3))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4771])).
% 0.79/0.96 tff(4773,plain,
% 0.79/0.96 ((~(e1 = e3)) <=> (~(e1 = op(e3, op(op(e3, e3), op(e3, e3)))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4453])).
% 0.79/0.96 tff(4774,plain,
% 0.79/0.96 (~(e1 = op(e3, op(op(e3, e3), op(e3, e3))))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[521, 4773])).
% 0.79/0.96 tff(4775,plain,
% 0.79/0.96 (~(op(e0, e3) = e3)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4774, 4772])).
% 0.79/0.96 tff(4776,plain,
% 0.79/0.96 (op(e2, e3) = e3),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[724, 4775, 4344, 4742])).
% 0.79/0.96 tff(4777,plain,
% 0.79/0.96 (op(e2, op(e3, e2)) = op(e3, e2)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[4776, 4451])).
% 0.79/0.96 tff(4778,plain,
% 0.79/0.96 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4755])).
% 0.79/0.96 tff(4779,plain,
% 0.79/0.96 ((op(e0, op(e2, e0)) = op(e2, e0)) | (op(e1, op(e2, e1)) = op(e2, e1)) | (op(e2, op(e2, e2)) = op(e2, e2)) | (op(e3, op(e2, e3)) = op(e2, e3))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[3849, 4778])).
% 0.79/0.96 tff(4780,plain,
% 0.79/0.96 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4539])).
% 0.79/0.96 tff(4781,plain,
% 0.79/0.96 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.79/0.96 inference(transitivity,[status(thm)],[4780, 1203])).
% 0.79/0.96 tff(4782,plain,
% 0.79/0.96 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4781])).
% 0.79/0.96 tff(4783,plain,
% 0.79/0.96 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[4782])).
% 0.79/0.96 tff(4784,plain,
% 0.79/0.96 (~(op(e1, e2) = e0)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[40, 4783])).
% 0.79/0.96 tff(4785,plain,
% 0.79/0.96 (op(e1, e3) = e0),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[548, 4737, 424, 4784])).
% 0.79/0.96 tff(4786,plain,
% 0.79/0.96 (e0 = op(e1, e3)),
% 0.79/0.96 inference(symmetry,[status(thm)],[4785])).
% 0.79/0.97 tff(4787,plain,
% 0.79/0.97 (op(e3, op(e1, e3)) = op(e3, e0)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4785])).
% 0.79/0.97 tff(4788,plain,
% 0.79/0.97 (op(e3, op(e1, e3)) = op(e1, e3)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4787, 4734, 4786])).
% 0.79/0.97 tff(4789,plain,
% 0.79/0.97 ((op(e0, op(e1, e0)) = op(e1, e0)) | (op(e1, op(e1, e1)) = op(e1, e1)) | (op(e2, op(e1, e2)) = op(e1, e2)) | (op(e3, op(e1, e3)) = op(e1, e3))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[756, 4788])).
% 0.79/0.97 tff(4790,plain,
% 0.79/0.97 (e1 = op(e0, e3)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4769])).
% 0.79/0.97 tff(4791,plain,
% 0.79/0.97 (op(e3, op(e0, e3)) = op(e3, e1)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4769])).
% 0.79/0.97 tff(4792,plain,
% 0.79/0.97 (op(e3, op(e0, e3)) = op(e0, e3)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4791, 4746, 4790])).
% 0.79/0.97 tff(4793,plain,
% 0.79/0.97 ((op(e0, op(e0, e0)) = op(e0, e0)) | (op(e1, op(e0, e1)) = op(e0, e1)) | (op(e2, op(e0, e2)) = op(e0, e2)) | (op(e3, op(e0, e3)) = op(e0, e3))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1061, 4792])).
% 0.79/0.97 tff(4794,plain,
% 0.79/0.97 (~((op(e0, op(e3, e0)) = op(e3, e0)) | (op(e1, op(e3, e1)) = op(e3, e1)) | (op(e2, op(e3, e2)) = op(e3, e2)) | (op(e3, op(e3, e3)) = op(e3, e3)))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[798, 4793, 4789, 4779])).
% 0.79/0.97 tff(4795,plain,
% 0.79/0.97 (~(op(e2, op(e3, e2)) = op(e3, e2))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[943, 4794])).
% 0.79/0.97 tff(4796,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[4795, 4777])).
% 0.79/0.97 tff(4797,plain,((op(e1, e1) = e3) | (~(op(e3, e2) = e3)) | (op(e1, e1) = e0) | (op(e3, e3) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(4798,plain,
% 0.79/0.97 (op(e1, e1) = e3),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[4797, 4440, 424, 280, 1211])).
% 0.79/0.97 tff(4799,plain,
% 0.79/0.97 (op(op(e1, e1), op(e1, e1)) = op(e3, e3)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4798, 4798])).
% 0.79/0.97 tff(4800,plain,
% 0.79/0.97 (op(op(e1, e1), op(e1, e1)) = e2),
% 0.79/0.97 inference(transitivity,[status(thm)],[4799, 4447])).
% 0.79/0.97 tff(4801,plain,
% 0.79/0.97 (op(e1, op(op(e1, e1), op(e1, e1))) = op(e1, e2)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4800])).
% 0.79/0.97 tff(4802,plain,
% 0.79/0.97 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4801])).
% 0.79/0.97 tff(4803,plain,
% 0.79/0.97 ((e0 = op(e1, op(op(e1, e1), op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4802, 2541])).
% 0.79/0.97 tff(4804,plain,
% 0.79/0.97 ((~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4803])).
% 0.79/0.97 tff(4805,plain,
% 0.79/0.97 (e3 = op(e1, e1)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4798, 3773])).
% 0.79/0.97 tff(4806,plain,
% 0.79/0.97 (op(e3, e3) = op(op(e1, e1), op(e1, e1))),
% 0.79/0.97 inference(symmetry,[status(thm)],[4799])).
% 0.79/0.97 tff(4807,plain,
% 0.79/0.97 (e2 = op(e3, e3)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4447])).
% 0.79/0.97 tff(4808,plain,
% 0.79/0.97 (e2 = op(op(e1, e1), op(e1, e1))),
% 0.79/0.97 inference(transitivity,[status(thm)],[4807, 4806])).
% 0.79/0.97 tff(4809,plain,
% 0.79/0.97 ((~(~((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1)))))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(4810,plain,
% 0.79/0.97 (((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))) <=> (~((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1)))))))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(4811,plain,
% 0.79/0.97 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~(~((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4810])).
% 0.79/0.97 tff(4812,plain,
% 0.79/0.97 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.79/0.97 inference(transitivity,[status(thm)],[4811, 4809])).
% 0.79/0.97 tff(4813,plain,
% 0.79/0.97 ((~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(4814,plain,
% 0.79/0.97 ((~(((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1))) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))) <=> (~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1))))))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(4815,axiom,(~(((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1))) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax22')).
% 0.79/0.97 tff(4816,plain,
% 0.79/0.97 (~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 0.79/0.97 tff(4817,plain,
% 0.79/0.97 (~((e2 = op(op(e1, e1), op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4816, 4813])).
% 0.79/0.97 tff(4818,plain,
% 0.79/0.97 ((~(e3 = op(e1, e1))) | (~(e2 = op(op(e1, e1), op(e1, e1)))) | (~(e0 = op(e1, op(op(e1, e1), op(e1, e1)))))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4817, 4812])).
% 0.79/0.97 tff(4819,plain,
% 0.79/0.97 (~(e0 = op(e1, op(op(e1, e1), op(e1, e1))))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[4818, 4808, 4805])).
% 0.79/0.97 tff(4820,plain,
% 0.79/0.97 (~(op(e1, e2) = e0)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4819, 4804])).
% 0.79/0.97 tff(4821,plain,
% 0.79/0.97 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4441])).
% 0.79/0.97 tff(4822,plain,
% 0.79/0.97 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4821])).
% 0.79/0.97 tff(4823,plain,
% 0.79/0.97 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4822])).
% 0.79/0.97 tff(4824,plain,
% 0.79/0.97 (~(op(e1, e2) = e3)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[742, 4823])).
% 0.79/0.97 tff(4825,plain,
% 0.79/0.97 (op(e2, e2) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4807, 4807])).
% 0.79/0.97 tff(4826,plain,
% 0.79/0.97 (op(e2, e2) = e2),
% 0.79/0.97 inference(transitivity,[status(thm)],[4825, 4283])).
% 0.79/0.97 tff(4827,plain,
% 0.79/0.97 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4826])).
% 0.79/0.97 tff(4828,plain,
% 0.79/0.97 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4827])).
% 0.79/0.97 tff(4829,plain,
% 0.79/0.97 (~(op(e1, e2) = e2)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[243, 4828])).
% 0.79/0.97 tff(4830,plain,
% 0.79/0.97 (op(e1, e3) = e1),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[332, 4798])).
% 0.79/0.97 tff(4831,plain,
% 0.79/0.97 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4830])).
% 0.79/0.97 tff(4832,plain,
% 0.79/0.97 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4831])).
% 0.79/0.97 tff(4833,plain,
% 0.79/0.97 (~(op(e1, e2) = e1)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[691, 4832])).
% 0.79/0.97 tff(4834,plain,
% 0.79/0.97 (op(e1, e2) = e0),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[846, 4833, 4829, 4824])).
% 0.79/0.97 tff(4835,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[4834, 4820])).
% 0.79/0.97 tff(4836,plain,((op(e3, e3) = e0) | (op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(4837,plain,
% 0.79/0.97 (op(e1, e1) = e0),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[4836, 4439, 4338, 26])).
% 0.79/0.97 tff(4838,plain,
% 0.79/0.97 ((op(e1, e1) = e2) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4837, 4282])).
% 0.79/0.97 tff(4839,plain,
% 0.79/0.97 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e1) = e2)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4838])).
% 0.79/0.97 tff(4840,plain,
% 0.79/0.97 ((~(e0 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e1, e1) = e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4839])).
% 0.79/0.97 tff(4841,plain,
% 0.79/0.97 (~(op(e1, e1) = e2)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4401, 4840])).
% 0.79/0.97 tff(4842,plain,
% 0.79/0.97 (op(e1, e0) = e1),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2026, 4837])).
% 0.79/0.97 tff(4843,plain,
% 0.79/0.97 ((op(e1, e0) = e2) <=> (e1 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4842, 4282])).
% 0.79/0.97 tff(4844,plain,
% 0.79/0.97 ((e1 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e0) = e2)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4843])).
% 0.79/0.97 tff(4845,plain,
% 0.79/0.97 ((~(e1 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e1, e0) = e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4844])).
% 0.79/0.97 tff(4846,plain,
% 0.79/0.97 (~(op(e1, e0) = e2)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4413, 4845])).
% 0.79/0.97 tff(4847,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[751, 4846, 4841, 4433, 4430])).
% 0.79/0.97 tff(4848,plain,(op(e2, e2) = e3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(4849,plain,
% 0.79/0.97 (op(op(e2, e2), op(e2, e2)) = op(e3, e3)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4848, 4848])).
% 0.79/0.97 tff(4850,plain,
% 0.79/0.97 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (e0 = op(e3, e3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4849])).
% 0.79/0.97 tff(4851,plain,
% 0.79/0.97 ((e0 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e0)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4850, 2])).
% 0.79/0.97 tff(4852,plain,
% 0.79/0.97 ((~(e0 = op(op(e2, e2), op(e2, e2)))) <=> (~(op(e3, e3) = e0))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4851])).
% 0.79/0.97 tff(4853,plain,
% 0.79/0.97 (~(op(e3, e3) = e0)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1052, 4852])).
% 0.79/0.97 tff(4854,plain,
% 0.79/0.97 (op(e2, e3) = e2),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1004, 4848])).
% 0.79/0.97 tff(4855,plain,
% 0.79/0.97 ((op(e2, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4854])).
% 0.79/0.97 tff(4856,plain,
% 0.79/0.97 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4855, 359])).
% 0.79/0.97 tff(4857,plain,
% 0.79/0.97 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4856])).
% 0.79/0.97 tff(4858,plain,
% 0.79/0.97 (~(op(e3, e3) = e2)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[196, 4857])).
% 0.79/0.97 tff(4859,plain,
% 0.79/0.97 (op(e3, e3) = e1),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1123, 4858, 4344, 4853])).
% 0.79/0.97 tff(4860,plain,
% 0.79/0.97 (op(e3, e1) = e3),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1150, 4859])).
% 0.79/0.97 tff(4861,plain,
% 0.79/0.97 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4860])).
% 0.79/0.97 tff(4862,plain,
% 0.79/0.97 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.79/0.97 inference(transitivity,[status(thm)],[4861, 1])).
% 0.79/0.97 tff(4863,plain,
% 0.79/0.97 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4862])).
% 0.79/0.97 tff(4864,plain,
% 0.79/0.97 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4863])).
% 0.79/0.97 tff(4865,plain,
% 0.79/0.97 (~(op(e3, e1) = e0)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[509, 4864])).
% 0.79/0.97 tff(4866,plain,
% 0.79/0.97 (e1 = op(e3, e3)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4859])).
% 0.79/0.97 tff(4867,plain,
% 0.79/0.97 (op(e1, e1) = op(op(e3, e3), op(e3, e3))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4866, 4866])).
% 0.79/0.97 tff(4868,plain,
% 0.79/0.97 ((op(e1, e1) = e0) <=> (op(op(e3, e3), op(e3, e3)) = e0)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4867])).
% 0.79/0.97 tff(4869,plain,
% 0.79/0.97 ((op(e1, e1) = e0) <=> (e0 = op(op(e3, e3), op(e3, e3)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[4868, 4434])).
% 0.79/0.97 tff(4870,plain,
% 0.79/0.97 ((e0 = op(op(e3, e3), op(e3, e3))) <=> (op(e1, e1) = e0)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4869])).
% 0.79/0.97 tff(4871,plain,
% 0.79/0.97 ((~(e0 = op(op(e3, e3), op(e3, e3)))) <=> (~(op(e1, e1) = e0))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4870])).
% 0.79/0.97 tff(4872,plain,
% 0.79/0.97 (~(op(e1, e1) = e0)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[4401, 4871])).
% 0.79/0.97 tff(4873,plain,
% 0.79/0.97 (op(e3, e3) = op(op(e2, e2), op(e2, e2))),
% 0.79/0.97 inference(symmetry,[status(thm)],[4849])).
% 0.79/0.97 tff(4874,plain,
% 0.79/0.97 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.79/0.97 inference(transitivity,[status(thm)],[4866, 4873])).
% 0.79/0.97 tff(4875,plain,
% 0.79/0.97 (op(e2, e1) = op(e2, op(op(e2, e2), op(e2, e2)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4874])).
% 0.79/0.97 tff(4876,plain,
% 0.79/0.97 ((op(e2, e1) = e0) <=> (op(e2, op(op(e2, e2), op(e2, e2))) = e0)),
% 0.79/0.97 inference(monotonicity,[status(thm)],[4875])).
% 0.79/0.97 tff(4877,plain,
% 0.79/0.97 ((op(e2, e1) = e0) <=> (e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.79/0.97 inference(transitivity,[status(thm)],[4876, 293])).
% 0.79/0.97 tff(4878,plain,
% 0.79/0.97 ((e0 = op(e2, op(op(e2, e2), op(e2, e2)))) <=> (op(e2, e1) = e0)),
% 0.79/0.97 inference(symmetry,[status(thm)],[4877])).
% 0.79/0.98 tff(4879,plain,
% 0.79/0.98 ((~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))) <=> (~(op(e2, e1) = e0))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4878])).
% 0.79/0.98 tff(4880,plain,
% 0.79/0.98 (e3 = op(e2, e2)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[4848, 1016])).
% 0.79/0.98 tff(4881,plain,
% 0.79/0.98 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (e1 = op(e3, e3))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4849])).
% 0.79/0.98 tff(4882,plain,
% 0.79/0.98 ((e1 = op(op(e2, e2), op(e2, e2))) <=> (op(e3, e3) = e1)),
% 0.79/0.98 inference(transitivity,[status(thm)],[4881, 1071])).
% 0.79/0.98 tff(4883,plain,
% 0.79/0.98 ((op(e3, e3) = e1) <=> (e1 = op(op(e2, e2), op(e2, e2)))),
% 0.79/0.98 inference(symmetry,[status(thm)],[4882])).
% 0.79/0.98 tff(4884,plain,
% 0.79/0.98 (e1 = op(op(e2, e2), op(e2, e2))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[4859, 4883])).
% 0.79/0.98 tff(4885,plain,
% 0.79/0.98 (~(e0 = op(e2, op(op(e2, e2), op(e2, e2))))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1925, 4884, 4880])).
% 0.79/0.98 tff(4886,plain,
% 0.79/0.98 (~(op(e2, e1) = e0)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[4885, 4879])).
% 0.79/0.98 tff(4887,plain,
% 0.79/0.98 ((op(e2, e2) = e2) <=> (e3 = e2)),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4848])).
% 0.79/0.98 tff(4888,plain,
% 0.79/0.98 ((op(e2, e2) = e2) <=> (e2 = e3)),
% 0.79/0.98 inference(transitivity,[status(thm)],[4887, 1178])).
% 0.79/0.98 tff(4889,plain,
% 0.79/0.98 ((e2 = e3) <=> (op(e2, e2) = e2)),
% 0.79/0.98 inference(symmetry,[status(thm)],[4888])).
% 0.79/0.98 tff(4890,plain,
% 0.79/0.98 ((~(e2 = e3)) <=> (~(op(e2, e2) = e2))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4889])).
% 0.79/0.98 tff(4891,plain,
% 0.79/0.98 (~(op(e2, e2) = e2)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[170, 4890])).
% 0.79/0.98 tff(4892,plain,
% 0.79/0.98 (op(e1, e1) = e2),
% 0.79/0.98 inference(transitivity,[status(thm)],[4867, 4283])).
% 0.79/0.98 tff(4893,plain,
% 0.79/0.98 ((op(e1, e1) = e1) <=> (e2 = op(e3, e3))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4892, 4866])).
% 0.79/0.98 tff(4894,plain,
% 0.79/0.98 ((op(e1, e1) = e1) <=> (op(e3, e3) = e2)),
% 0.79/0.98 inference(transitivity,[status(thm)],[4893, 359])).
% 0.79/0.98 tff(4895,plain,
% 0.79/0.98 ((op(e3, e3) = e2) <=> (op(e1, e1) = e1)),
% 0.79/0.98 inference(symmetry,[status(thm)],[4894])).
% 0.79/0.98 tff(4896,plain,
% 0.79/0.98 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e1) = e1))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4895])).
% 0.79/0.98 tff(4897,plain,
% 0.79/0.98 (~(op(e1, e1) = e1)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[4858, 4896])).
% 0.79/0.98 tff(4898,plain,
% 0.79/0.98 (op(e0, e0) = e0),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[215, 4897, 4344, 4891])).
% 0.79/0.98 tff(4899,plain,
% 0.79/0.98 ((op(e0, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4898])).
% 0.79/0.98 tff(4900,plain,
% 0.79/0.98 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 0.79/0.98 inference(transitivity,[status(thm)],[4899, 820])).
% 0.79/0.98 tff(4901,plain,
% 0.79/0.98 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e0))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[4900])).
% 0.79/0.98 tff(4902,plain,
% 0.79/0.98 (~(op(e0, e1) = e0)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[826, 4901])).
% 0.79/0.98 tff(4903,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1241, 4902, 4886, 4872, 4865])).
% 0.79/0.98 % SZS output end Proof
%------------------------------------------------------------------------------