TSTP Solution File: ALG157+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG157+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:08:39 EDT 2022
% Result : Unsatisfiable 0.46s 0.61s
% Output : Proof 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ALG157+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.37 % Computer : n015.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Aug 29 13:51:04 EDT 2022
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.37 Usage: tptp [options] [-file:]file
% 0.13/0.37 -h, -? prints this message.
% 0.13/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.37 -m, -model generate model.
% 0.13/0.37 -p, -proof generate proof.
% 0.13/0.37 -c, -core generate unsat core of named formulas.
% 0.13/0.37 -st, -statistics display statistics.
% 0.13/0.37 -t:timeout set timeout (in second).
% 0.13/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.37 -<param>:<value> configuration parameter and value.
% 0.13/0.37 -o:<output-file> file to place output in.
% 0.46/0.61 % SZS status Unsatisfiable
% 0.46/0.61 % SZS output start Proof
% 0.46/0.61 tff(e3_type, type, (
% 0.46/0.61 e3: $i)).
% 0.46/0.61 tff(e2_type, type, (
% 0.46/0.61 e2: $i)).
% 0.46/0.61 tff(op_type, type, (
% 0.46/0.61 op: ( $i * $i ) > $i)).
% 0.46/0.61 tff(e0_type, type, (
% 0.46/0.61 e0: $i)).
% 0.46/0.61 tff(e1_type, type, (
% 0.46/0.61 e1: $i)).
% 0.46/0.61 tff(1,plain,
% 0.46/0.61 ((e2 = e0) <=> (e0 = e2)),
% 0.46/0.61 inference(commutativity,[status(thm)],[])).
% 0.46/0.61 tff(2,assumption,(op(e0, e3) = e2), introduced(assumption)).
% 0.46/0.61 tff(3,plain,
% 0.46/0.61 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[2])).
% 0.46/0.61 tff(4,plain,
% 0.46/0.61 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.46/0.61 inference(transitivity,[status(thm)],[3, 1])).
% 0.46/0.61 tff(5,plain,
% 0.46/0.61 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.46/0.61 inference(symmetry,[status(thm)],[4])).
% 0.46/0.61 tff(6,plain,
% 0.46/0.61 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[5])).
% 0.46/0.61 tff(7,plain,
% 0.46/0.61 ((~(e0 = e2)) <=> (~(e0 = e2))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(8,axiom,((((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))) & (~(e2 = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.46/0.61 tff(9,plain,
% 0.46/0.61 (((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))),
% 0.46/0.61 inference(and_elim,[status(thm)],[8])).
% 0.46/0.61 tff(10,plain,
% 0.46/0.61 ((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))),
% 0.46/0.61 inference(and_elim,[status(thm)],[9])).
% 0.46/0.61 tff(11,plain,
% 0.46/0.61 (((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))),
% 0.46/0.61 inference(and_elim,[status(thm)],[10])).
% 0.46/0.61 tff(12,plain,
% 0.46/0.61 ((~(e0 = e1)) & (~(e0 = e2))),
% 0.46/0.61 inference(and_elim,[status(thm)],[11])).
% 0.46/0.61 tff(13,plain,
% 0.46/0.61 (~(e0 = e2)),
% 0.46/0.61 inference(and_elim,[status(thm)],[12])).
% 0.46/0.61 tff(14,plain,
% 0.46/0.61 (~(e0 = e2)),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.46/0.61 tff(15,plain,
% 0.46/0.61 (~(op(e0, e3) = e0)),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.46/0.61 tff(16,plain,
% 0.46/0.61 ((e1 = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.46/0.61 inference(commutativity,[status(thm)],[])).
% 0.46/0.61 tff(17,assumption,(~(op(e2, e2) = e0)), introduced(assumption)).
% 0.46/0.61 tff(18,plain,
% 0.46/0.61 ((e1 = e0) <=> (e0 = e1)),
% 0.46/0.61 inference(commutativity,[status(thm)],[])).
% 0.46/0.61 tff(19,assumption,(op(e0, e3) = e1), introduced(assumption)).
% 0.46/0.61 tff(20,plain,
% 0.46/0.61 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[19])).
% 0.46/0.61 tff(21,plain,
% 0.46/0.61 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 0.46/0.61 inference(transitivity,[status(thm)],[20, 18])).
% 0.46/0.61 tff(22,plain,
% 0.46/0.61 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 0.46/0.61 inference(symmetry,[status(thm)],[21])).
% 0.46/0.61 tff(23,plain,
% 0.46/0.61 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[22])).
% 0.46/0.61 tff(24,plain,
% 0.46/0.61 ((~(e0 = e1)) <=> (~(e0 = e1))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(25,plain,
% 0.46/0.61 (~(e0 = e1)),
% 0.46/0.61 inference(and_elim,[status(thm)],[12])).
% 0.46/0.61 tff(26,plain,
% 0.46/0.61 (~(e0 = e1)),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.46/0.61 tff(27,plain,
% 0.46/0.61 (~(op(e0, e3) = e0)),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.46/0.61 tff(28,plain,
% 0.46/0.61 ((e1 = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.46/0.61 inference(commutativity,[status(thm)],[])).
% 0.46/0.61 tff(29,plain,
% 0.46/0.61 ((op(e0, e3) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[19])).
% 0.46/0.62 tff(30,plain,
% 0.46/0.62 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.46/0.62 inference(transitivity,[status(thm)],[29, 28])).
% 0.46/0.62 tff(31,plain,
% 0.46/0.62 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[30])).
% 0.46/0.62 tff(32,plain,
% 0.46/0.62 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = op(e1, e3)))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(33,axiom,((((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))) & (~(op(e3, e1) = op(e3, e3)))) & (~(op(e3, e2) = op(e3, e3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.46/0.62 tff(34,plain,
% 0.46/0.62 (((((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.46/0.62 inference(and_elim,[status(thm)],[33])).
% 0.46/0.62 tff(35,plain,
% 0.46/0.62 ((((((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[34])).
% 0.46/0.63 tff(36,plain,
% 0.46/0.63 (((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(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)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[35])).
% 0.46/0.63 tff(37,plain,
% 0.46/0.63 ((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(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)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[36])).
% 0.46/0.63 tff(38,plain,
% 0.46/0.63 (((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[37])).
% 0.46/0.63 tff(39,plain,
% 0.46/0.63 ((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(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)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[38])).
% 0.46/0.63 tff(40,plain,
% 0.46/0.63 (((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(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)))),
% 0.46/0.63 inference(and_elim,[status(thm)],[39])).
% 0.46/0.63 tff(41,plain,
% 0.46/0.63 ((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[40])).
% 0.54/0.64 tff(42,plain,
% 0.54/0.64 (((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[41])).
% 0.54/0.64 tff(43,plain,
% 0.54/0.64 ((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[42])).
% 0.54/0.64 tff(44,plain,
% 0.54/0.64 (((((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[43])).
% 0.54/0.64 tff(45,plain,
% 0.54/0.64 ((((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[44])).
% 0.54/0.64 tff(46,plain,
% 0.54/0.64 (((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.64 inference(and_elim,[status(thm)],[45])).
% 0.54/0.64 tff(47,plain,
% 0.54/0.64 ((((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[46])).
% 0.54/0.65 tff(48,plain,
% 0.54/0.65 (((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[47])).
% 0.54/0.65 tff(49,plain,
% 0.54/0.65 ((((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[48])).
% 0.54/0.65 tff(50,plain,
% 0.54/0.65 (((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[49])).
% 0.54/0.65 tff(51,plain,
% 0.54/0.65 ((((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[50])).
% 0.54/0.65 tff(52,plain,
% 0.54/0.65 (((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[51])).
% 0.54/0.65 tff(53,plain,
% 0.54/0.65 ((((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[52])).
% 0.54/0.65 tff(54,plain,
% 0.54/0.65 (((((((((((((((((((((((((((~(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)))),
% 0.54/0.65 inference(and_elim,[status(thm)],[53])).
% 0.54/0.65 tff(55,plain,
% 0.54/0.65 ((((((((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[54])).
% 0.54/0.66 tff(56,plain,
% 0.54/0.66 (((((((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[55])).
% 0.54/0.66 tff(57,plain,
% 0.54/0.66 ((((((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[56])).
% 0.54/0.66 tff(58,plain,
% 0.54/0.66 (((((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[57])).
% 0.54/0.66 tff(59,plain,
% 0.54/0.66 ((((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[58])).
% 0.54/0.66 tff(60,plain,
% 0.54/0.66 (((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[59])).
% 0.54/0.66 tff(61,plain,
% 0.54/0.66 ((((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[60])).
% 0.54/0.66 tff(62,plain,
% 0.54/0.66 (((((((((((((((((((~(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)))),
% 0.54/0.66 inference(and_elim,[status(thm)],[61])).
% 0.54/0.66 tff(63,plain,
% 0.54/0.66 (~(op(e0, e3) = op(e1, e3))),
% 0.54/0.66 inference(and_elim,[status(thm)],[62])).
% 0.54/0.66 tff(64,plain,
% 0.54/0.66 (~(op(e0, e3) = op(e1, e3))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[63, 32])).
% 0.54/0.66 tff(65,plain,
% 0.54/0.66 (~(op(e1, e3) = e1)),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[64, 31])).
% 0.54/0.66 tff(66,plain,
% 0.54/0.66 ((e2 = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(67,plain,
% 0.54/0.66 ((e0 = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(68,assumption,(~(op(e1, e1) = e2)), introduced(assumption)).
% 0.54/0.66 tff(69,plain,
% 0.54/0.66 ((e2 = e1) <=> (e1 = e2)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(70,plain,
% 0.54/0.66 ((e3 = op(e0, e0)) <=> (op(e0, e0) = e3)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(71,plain,
% 0.54/0.66 ((op(e0, e0) = e3) <=> (e3 = op(e0, e0))),
% 0.54/0.66 inference(symmetry,[status(thm)],[70])).
% 0.54/0.66 tff(72,assumption,(~(op(e1, e3) = e2)), introduced(assumption)).
% 0.54/0.66 tff(73,plain,
% 0.54/0.66 ((e1 = op(e0, e0)) <=> (op(e0, e0) = e1)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(74,plain,
% 0.54/0.66 ((op(e0, e0) = e1) <=> (e1 = op(e0, e0))),
% 0.54/0.66 inference(symmetry,[status(thm)],[73])).
% 0.54/0.66 tff(75,assumption,(~(op(e1, e2) = e3)), introduced(assumption)).
% 0.54/0.66 tff(76,assumption,(~(op(e2, e3) = e1)), introduced(assumption)).
% 0.54/0.66 tff(77,plain,
% 0.54/0.66 ((e2 = op(e0, e0)) <=> (op(e0, e0) = e2)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(78,plain,
% 0.54/0.66 ((op(e0, e0) = e2) <=> (e2 = op(e0, e0))),
% 0.54/0.66 inference(symmetry,[status(thm)],[77])).
% 0.54/0.66 tff(79,assumption,(~(op(e0, e3) = e2)), introduced(assumption)).
% 0.54/0.66 tff(80,assumption,(~(op(e1, e3) = e0)), introduced(assumption)).
% 0.54/0.66 tff(81,plain,
% 0.54/0.66 ((e2 = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(82,assumption,(~(op(e3, e1) = e2)), introduced(assumption)).
% 0.54/0.66 tff(83,plain,
% 0.54/0.66 ((e0 = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(84,assumption,(~(op(e1, e1) = e0)), introduced(assumption)).
% 0.54/0.66 tff(85,assumption,(~(op(e3, e2) = e0)), introduced(assumption)).
% 0.54/0.66 tff(86,plain,
% 0.54/0.66 ((e0 = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.54/0.66 inference(commutativity,[status(thm)],[])).
% 0.54/0.66 tff(87,assumption,(~(op(e1, e3) = e1)), introduced(assumption)).
% 0.54/0.66 tff(88,plain,
% 0.54/0.66 (((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))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(89,plain,
% 0.54/0.66 ((((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))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(90,plain,
% 0.54/0.66 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(91,plain,
% 0.54/0.66 (((((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))),
% 0.54/0.66 inference(monotonicity,[status(thm)],[90])).
% 0.54/0.66 tff(92,plain,
% 0.54/0.66 (((((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))),
% 0.54/0.66 inference(transitivity,[status(thm)],[91, 89])).
% 0.54/0.66 tff(93,axiom,(((((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))) & ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))) & ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 0.54/0.66 tff(94,plain,
% 0.54/0.66 ((((((((((((((((((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))),
% 0.54/0.66 inference(and_elim,[status(thm)],[93])).
% 0.54/0.66 tff(95,plain,
% 0.54/0.66 (((((((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[94])).
% 0.54/0.67 tff(96,plain,
% 0.54/0.67 ((((((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[95])).
% 0.54/0.67 tff(97,plain,
% 0.54/0.67 (((((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[96])).
% 0.54/0.67 tff(98,plain,
% 0.54/0.67 ((((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[97])).
% 0.54/0.67 tff(99,plain,
% 0.54/0.67 (((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[98])).
% 0.54/0.67 tff(100,plain,
% 0.54/0.67 ((((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[99])).
% 0.54/0.67 tff(101,plain,
% 0.54/0.67 (((((((((((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))),
% 0.54/0.67 inference(and_elim,[status(thm)],[100])).
% 0.54/0.67 tff(102,plain,
% 0.54/0.67 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)),
% 0.54/0.67 inference(and_elim,[status(thm)],[101])).
% 0.54/0.67 tff(103,plain,
% 0.54/0.67 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.54/0.67 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.54/0.67 tff(104,plain,
% 0.54/0.67 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.54/0.67 inference(modus_ponens,[status(thm)],[103, 88])).
% 0.54/0.67 tff(105,plain,
% 0.54/0.67 (op(e1, e3) = e3),
% 0.54/0.67 inference(unit_resolution,[status(thm)],[104, 87, 72, 80])).
% 0.54/0.67 tff(106,plain,
% 0.54/0.67 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 0.54/0.67 inference(monotonicity,[status(thm)],[105])).
% 0.54/0.67 tff(107,plain,
% 0.54/0.67 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 0.54/0.67 inference(monotonicity,[status(thm)],[106])).
% 0.54/0.67 tff(108,plain,
% 0.54/0.67 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e1, e3)))),
% 0.54/0.67 inference(rewrite,[status(thm)],[])).
% 0.54/0.67 tff(109,plain,
% 0.54/0.67 (~(op(e1, e0) = op(e1, e3))),
% 0.54/0.67 inference(and_elim,[status(thm)],[48])).
% 0.54/0.67 tff(110,plain,
% 0.54/0.67 (~(op(e1, e0) = op(e1, e3))),
% 0.54/0.67 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.54/0.67 tff(111,plain,
% 0.54/0.67 (~(op(e1, e0) = e3)),
% 0.54/0.67 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.54/0.67 tff(112,plain,
% 0.54/0.67 ((e3 = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.54/0.67 inference(commutativity,[status(thm)],[])).
% 0.54/0.67 tff(113,plain,
% 0.54/0.67 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[105])).
% 0.58/0.68 tff(114,plain,
% 0.58/0.68 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.58/0.68 inference(transitivity,[status(thm)],[113, 112])).
% 0.58/0.68 tff(115,plain,
% 0.58/0.68 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[114])).
% 0.58/0.68 tff(116,plain,
% 0.58/0.68 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = op(e2, e3)))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(117,plain,
% 0.58/0.68 (~(op(e1, e3) = op(e2, e3))),
% 0.58/0.68 inference(and_elim,[status(thm)],[59])).
% 0.58/0.68 tff(118,plain,
% 0.58/0.68 (~(op(e1, e3) = op(e2, e3))),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.58/0.68 tff(119,plain,
% 0.58/0.68 (~(op(e2, e3) = e3)),
% 0.58/0.68 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.58/0.68 tff(120,plain,
% 0.58/0.68 ((e2 = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.58/0.68 inference(commutativity,[status(thm)],[])).
% 0.58/0.68 tff(121,assumption,(~(op(e0, e3) = e1)), introduced(assumption)).
% 0.58/0.68 tff(122,plain,
% 0.58/0.68 ((e0 = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.58/0.68 inference(commutativity,[status(thm)],[])).
% 0.58/0.68 tff(123,plain,
% 0.58/0.68 ((op(e1, e1) = e0) <=> (e0 = op(e1, e1))),
% 0.58/0.68 inference(symmetry,[status(thm)],[122])).
% 0.58/0.68 tff(124,assumption,(~(op(e2, e3) = e3)), introduced(assumption)).
% 0.58/0.68 tff(125,plain,
% 0.58/0.68 ((op(e1, e3) = op(e1, e2)) <=> (op(e1, e2) = op(e1, e3))),
% 0.58/0.68 inference(commutativity,[status(thm)],[])).
% 0.58/0.68 tff(126,assumption,(~(op(e3, e3) = e2)), introduced(assumption)).
% 0.58/0.68 tff(127,plain,
% 0.58/0.68 ((e3 = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 0.58/0.68 inference(commutativity,[status(thm)],[])).
% 0.58/0.68 tff(128,plain,
% 0.58/0.68 ((e3 = e1) <=> (e1 = e3)),
% 0.58/0.68 inference(commutativity,[status(thm)],[])).
% 0.58/0.68 tff(129,assumption,(~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))), introduced(assumption)).
% 0.58/0.68 tff(130,plain,
% 0.58/0.68 (((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (~(op(op(e1, e3), e3) = e1))),
% 0.58/0.68 inference(tautology,[status(thm)],[])).
% 0.58/0.68 tff(131,plain,
% 0.58/0.68 (~(op(op(e1, e3), e3) = e1)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.58/0.68 tff(132,assumption,(op(e1, e3) = e1), introduced(assumption)).
% 0.58/0.68 tff(133,plain,
% 0.58/0.68 (op(op(e1, e3), e3) = op(e1, e3)),
% 0.58/0.68 inference(monotonicity,[status(thm)],[132])).
% 0.58/0.68 tff(134,plain,
% 0.58/0.68 (op(op(e1, e3), e3) = e1),
% 0.58/0.68 inference(transitivity,[status(thm)],[133, 132])).
% 0.58/0.68 tff(135,assumption,(~(op(op(e1, e3), e3) = e1)), introduced(assumption)).
% 0.58/0.68 tff(136,plain,
% 0.58/0.68 ($false),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.58/0.68 tff(137,plain,((~(op(e1, e3) = e1)) | (op(op(e1, e3), e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.68 tff(138,plain,
% 0.58/0.68 (~(op(e1, e3) = e1)),
% 0.58/0.68 inference(unit_resolution,[status(thm)],[137, 131])).
% 0.58/0.68 tff(139,plain,
% 0.58/0.68 (((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))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(140,plain,
% 0.58/0.68 ((((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))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(141,plain,
% 0.58/0.68 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(142,plain,
% 0.58/0.68 (((((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))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[141])).
% 0.58/0.68 tff(143,plain,
% 0.58/0.68 (((((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))),
% 0.58/0.68 inference(transitivity,[status(thm)],[142, 140])).
% 0.58/0.68 tff(144,axiom,(((((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))) & ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))) & ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))) & ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax2')).
% 0.58/0.68 tff(145,plain,
% 0.58/0.68 ((((((((((((((((((((((((((((((((((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))),
% 0.58/0.69 inference(and_elim,[status(thm)],[144])).
% 0.58/0.69 tff(146,plain,
% 0.58/0.69 (((((((((((((((((((((((((((((((((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))),
% 0.58/0.69 inference(and_elim,[status(thm)],[145])).
% 0.58/0.69 tff(147,plain,
% 0.58/0.69 ((((((((((((((((((((((((((((((((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))),
% 0.58/0.69 inference(and_elim,[status(thm)],[146])).
% 0.58/0.69 tff(148,plain,
% 0.58/0.69 (((((((((((((((((((((((((((((((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))),
% 0.58/0.70 inference(and_elim,[status(thm)],[147])).
% 0.58/0.70 tff(149,plain,
% 0.58/0.70 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)),
% 0.58/0.70 inference(and_elim,[status(thm)],[148])).
% 0.58/0.70 tff(150,plain,
% 0.58/0.70 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[149, 143])).
% 0.58/0.70 tff(151,plain,
% 0.58/0.70 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[150, 139])).
% 0.58/0.70 tff(152,plain,
% 0.58/0.70 (op(e3, e3) = e1),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[151, 138, 121, 76])).
% 0.58/0.70 tff(153,plain,
% 0.58/0.70 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[152])).
% 0.58/0.70 tff(154,plain,
% 0.58/0.70 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[153])).
% 0.58/0.70 tff(155,plain,
% 0.58/0.70 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = op(e3, e3)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(156,plain,
% 0.58/0.70 (~(op(e3, e0) = op(e3, e3))),
% 0.58/0.70 inference(and_elim,[status(thm)],[36])).
% 0.58/0.70 tff(157,plain,
% 0.58/0.70 (~(op(e3, e0) = op(e3, e3))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.58/0.70 tff(158,plain,
% 0.58/0.70 (~(op(e3, e0) = e1)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[157, 154])).
% 0.58/0.70 tff(159,plain,
% 0.58/0.70 ((e3 = e0) <=> (e0 = e3)),
% 0.58/0.70 inference(commutativity,[status(thm)],[])).
% 0.58/0.70 tff(160,plain,
% 0.58/0.70 (((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(op(e1, e3), e1) = e3)),
% 0.58/0.70 inference(tautology,[status(thm)],[])).
% 0.58/0.70 tff(161,plain,
% 0.58/0.70 (op(op(e1, e3), e1) = e3),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[160, 129])).
% 0.58/0.70 tff(162,plain,
% 0.58/0.70 (((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (~(op(e1, op(e1, e3)) = e3))),
% 0.58/0.70 inference(tautology,[status(thm)],[])).
% 0.58/0.70 tff(163,plain,
% 0.58/0.70 (~(op(e1, op(e1, e3)) = e3)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[162, 129])).
% 0.58/0.70 tff(164,assumption,(op(e1, e3) = e3), introduced(assumption)).
% 0.58/0.70 tff(165,plain,
% 0.58/0.70 (op(e1, op(e1, e3)) = op(e1, e3)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[164])).
% 0.58/0.70 tff(166,plain,
% 0.58/0.70 (op(e1, op(e1, e3)) = e3),
% 0.58/0.70 inference(transitivity,[status(thm)],[165, 164])).
% 0.58/0.70 tff(167,assumption,(~(op(e1, op(e1, e3)) = e3)), introduced(assumption)).
% 0.58/0.70 tff(168,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.58/0.70 tff(169,plain,((~(op(e1, e3) = e3)) | (op(e1, op(e1, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.70 tff(170,plain,
% 0.58/0.70 (~(op(e1, e3) = e3)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[169, 163])).
% 0.58/0.70 tff(171,plain,
% 0.58/0.70 (op(e1, e3) = e2),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[104, 170, 80, 138])).
% 0.58/0.70 tff(172,plain,
% 0.58/0.70 (e2 = op(e1, e3)),
% 0.58/0.70 inference(symmetry,[status(thm)],[171])).
% 0.58/0.70 tff(173,plain,
% 0.58/0.70 (op(e2, e1) = op(op(e1, e3), e1)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[172])).
% 0.58/0.70 tff(174,plain,
% 0.58/0.70 (op(e2, e1) = e3),
% 0.58/0.70 inference(transitivity,[status(thm)],[173, 161])).
% 0.58/0.70 tff(175,plain,
% 0.58/0.70 ((op(e2, e1) = e0) <=> (e3 = e0)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[174])).
% 0.58/0.70 tff(176,plain,
% 0.58/0.70 ((op(e2, e1) = e0) <=> (e0 = e3)),
% 0.58/0.70 inference(transitivity,[status(thm)],[175, 159])).
% 0.58/0.70 tff(177,plain,
% 0.58/0.70 ((e0 = e3) <=> (op(e2, e1) = e0)),
% 0.58/0.70 inference(symmetry,[status(thm)],[176])).
% 0.58/0.70 tff(178,plain,
% 0.58/0.70 ((~(e0 = e3)) <=> (~(op(e2, e1) = e0))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[177])).
% 0.58/0.70 tff(179,plain,
% 0.58/0.70 ((~(e0 = e3)) <=> (~(e0 = e3))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(180,plain,
% 0.58/0.70 (~(e0 = e3)),
% 0.58/0.70 inference(and_elim,[status(thm)],[11])).
% 0.58/0.70 tff(181,plain,
% 0.58/0.70 (~(e0 = e3)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.58/0.70 tff(182,plain,
% 0.58/0.70 (~(op(e2, e1) = e0)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.58/0.70 tff(183,assumption,(~(op(e3, e1) = e0)), introduced(assumption)).
% 0.58/0.70 tff(184,plain,
% 0.58/0.70 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[171])).
% 0.58/0.70 tff(185,plain,
% 0.58/0.70 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.58/0.70 inference(transitivity,[status(thm)],[184, 120])).
% 0.58/0.70 tff(186,plain,
% 0.58/0.70 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[185])).
% 0.58/0.70 tff(187,plain,
% 0.58/0.70 (~(op(e2, e3) = e2)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[118, 186])).
% 0.58/0.70 tff(188,plain,
% 0.58/0.70 (op(op(e1, e3), e3) = op(e2, e3)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[171])).
% 0.58/0.70 tff(189,plain,
% 0.58/0.70 ((op(op(e1, e3), e3) = e1) <=> (op(e2, e3) = e1)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[188])).
% 0.58/0.70 tff(190,plain,
% 0.58/0.70 ((~(op(op(e1, e3), e3) = e1)) <=> (~(op(e2, e3) = e1))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[189])).
% 0.58/0.70 tff(191,plain,
% 0.58/0.70 (~(op(e2, e3) = e1)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[131, 190])).
% 0.58/0.70 tff(192,plain,
% 0.58/0.70 ((op(e2, e1) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[174])).
% 0.58/0.70 tff(193,plain,
% 0.58/0.70 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.58/0.70 inference(transitivity,[status(thm)],[192, 112])).
% 0.58/0.70 tff(194,plain,
% 0.58/0.70 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[193])).
% 0.58/0.70 tff(195,plain,
% 0.58/0.70 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e2, e3)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(196,plain,
% 0.58/0.70 (~(op(e2, e1) = op(e2, e3))),
% 0.58/0.70 inference(and_elim,[status(thm)],[40])).
% 0.58/0.70 tff(197,plain,
% 0.58/0.70 (~(op(e2, e1) = op(e2, e3))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.58/0.70 tff(198,plain,
% 0.58/0.70 (~(op(e2, e3) = e3)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[197, 194])).
% 0.58/0.70 tff(199,plain,
% 0.58/0.70 (((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(200,plain,
% 0.58/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(201,plain,
% 0.58/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(202,plain,
% 0.58/0.70 (((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> (((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[201])).
% 0.58/0.70 tff(203,plain,
% 0.58/0.70 (((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3))),
% 0.58/0.70 inference(transitivity,[status(thm)],[202, 200])).
% 0.58/0.70 tff(204,plain,
% 0.58/0.70 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)),
% 0.58/0.70 inference(and_elim,[status(thm)],[97])).
% 0.58/0.70 tff(205,plain,
% 0.58/0.70 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.58/0.70 tff(206,plain,
% 0.58/0.70 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[205, 199])).
% 0.58/0.70 tff(207,plain,
% 0.58/0.70 (op(e2, e3) = e0),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[206, 198, 191, 187])).
% 0.58/0.70 tff(208,plain,
% 0.58/0.70 (op(e1, op(e1, e3)) = op(e1, e2)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[171])).
% 0.58/0.70 tff(209,plain,
% 0.58/0.70 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e2) = e3)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[208])).
% 0.58/0.70 tff(210,plain,
% 0.58/0.70 ((~(op(e1, op(e1, e3)) = e3)) <=> (~(op(e1, e2) = e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[209])).
% 0.58/0.70 tff(211,plain,
% 0.58/0.70 (~(op(e1, e2) = e3)),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[163, 210])).
% 0.58/0.70 tff(212,plain,
% 0.58/0.70 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 0.58/0.70 inference(monotonicity,[status(thm)],[174])).
% 0.58/0.70 tff(213,plain,
% 0.58/0.70 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 0.58/0.70 inference(monotonicity,[status(thm)],[212])).
% 0.58/0.70 tff(214,plain,
% 0.58/0.70 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = op(e2, e1)))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(215,plain,
% 0.58/0.70 ((((((((((((((((((~(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)))),
% 0.58/0.70 inference(and_elim,[status(thm)],[62])).
% 0.58/0.70 tff(216,plain,
% 0.58/0.70 (((((((((((((((((~(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)))),
% 0.58/0.70 inference(and_elim,[status(thm)],[215])).
% 0.58/0.70 tff(217,plain,
% 0.58/0.70 ((((((((((((((((~(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)))),
% 0.58/0.70 inference(and_elim,[status(thm)],[216])).
% 0.58/0.70 tff(218,plain,
% 0.58/0.70 (((((((((((((((~(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)))),
% 0.58/0.70 inference(and_elim,[status(thm)],[217])).
% 0.58/0.70 tff(219,plain,
% 0.58/0.70 ((((((((((((((~(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)))),
% 0.58/0.70 inference(and_elim,[status(thm)],[218])).
% 0.58/0.70 tff(220,plain,
% 0.58/0.70 (((((((((((((~(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)))),
% 0.58/0.71 inference(and_elim,[status(thm)],[219])).
% 0.58/0.71 tff(221,plain,
% 0.58/0.71 ((((((((((((~(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)))),
% 0.58/0.71 inference(and_elim,[status(thm)],[220])).
% 0.58/0.71 tff(222,plain,
% 0.58/0.71 (((((((((((~(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)))),
% 0.58/0.71 inference(and_elim,[status(thm)],[221])).
% 0.58/0.71 tff(223,plain,
% 0.58/0.71 ((((((((((~(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)))),
% 0.58/0.71 inference(and_elim,[status(thm)],[222])).
% 0.58/0.71 tff(224,plain,
% 0.58/0.71 (~(op(e1, e1) = op(e2, e1))),
% 0.58/0.71 inference(and_elim,[status(thm)],[223])).
% 0.58/0.71 tff(225,plain,
% 0.58/0.71 (~(op(e1, e1) = op(e2, e1))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[224, 214])).
% 0.58/0.71 tff(226,plain,
% 0.58/0.71 (~(op(e1, e1) = e3)),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[225, 213])).
% 0.58/0.71 tff(227,plain,
% 0.58/0.71 (((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))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(228,plain,
% 0.58/0.71 ((((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))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(229,plain,
% 0.58/0.71 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3))),
% 0.58/0.71 inference(rewrite,[status(thm)],[])).
% 0.58/0.71 tff(230,plain,
% 0.58/0.71 (((((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))),
% 0.58/0.71 inference(monotonicity,[status(thm)],[229])).
% 0.58/0.71 tff(231,plain,
% 0.58/0.71 (((((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))),
% 0.58/0.71 inference(transitivity,[status(thm)],[230, 228])).
% 0.58/0.71 tff(232,plain,
% 0.58/0.71 ((((((((((((((((((((((((((((((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))),
% 0.58/0.71 inference(and_elim,[status(thm)],[148])).
% 0.58/0.71 tff(233,plain,
% 0.58/0.71 (((((((((((((((((((((((((((((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))),
% 0.58/0.71 inference(and_elim,[status(thm)],[232])).
% 0.58/0.71 tff(234,plain,
% 0.58/0.71 ((((((((((((((((((((((((((((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))),
% 0.58/0.72 inference(and_elim,[status(thm)],[233])).
% 0.58/0.72 tff(235,plain,
% 0.58/0.72 (((((((((((((((((((((((((((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))),
% 0.58/0.72 inference(and_elim,[status(thm)],[234])).
% 0.58/0.72 tff(236,plain,
% 0.58/0.72 ((((((((((((((((((((((((((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))),
% 0.58/0.73 inference(and_elim,[status(thm)],[235])).
% 0.58/0.73 tff(237,plain,
% 0.58/0.73 (((((((((((((((((((((((((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))),
% 0.58/0.73 inference(and_elim,[status(thm)],[236])).
% 0.58/0.73 tff(238,plain,
% 0.58/0.73 ((((((((((((((((((((((((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))),
% 0.58/0.73 inference(and_elim,[status(thm)],[237])).
% 0.58/0.73 tff(239,plain,
% 0.58/0.73 (((((((((((((((((((((((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))),
% 0.58/0.73 inference(and_elim,[status(thm)],[238])).
% 0.58/0.73 tff(240,plain,
% 0.58/0.73 ((((((((((((((((((((((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))),
% 0.58/0.74 inference(and_elim,[status(thm)],[239])).
% 0.58/0.74 tff(241,plain,
% 0.58/0.74 (((((((((((((((((((((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))),
% 0.58/0.74 inference(and_elim,[status(thm)],[240])).
% 0.58/0.74 tff(242,plain,
% 0.58/0.74 ((((((((((((((((((((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))),
% 0.64/0.74 inference(and_elim,[status(thm)],[241])).
% 0.64/0.74 tff(243,plain,
% 0.64/0.74 (((((((((((((((((((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))),
% 0.64/0.74 inference(and_elim,[status(thm)],[242])).
% 0.64/0.74 tff(244,plain,
% 0.64/0.74 ((((((((((((((((((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))),
% 0.64/0.74 inference(and_elim,[status(thm)],[243])).
% 0.64/0.74 tff(245,plain,
% 0.64/0.74 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)),
% 0.64/0.74 inference(and_elim,[status(thm)],[244])).
% 0.64/0.74 tff(246,plain,
% 0.64/0.74 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[245, 231])).
% 0.64/0.74 tff(247,plain,
% 0.64/0.74 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[246, 227])).
% 0.64/0.74 tff(248,plain,
% 0.64/0.74 (op(e1, e0) = e3),
% 0.64/0.74 inference(unit_resolution,[status(thm)],[247, 226, 211, 170])).
% 0.64/0.74 tff(249,assumption,(op(e1, e1) = e0), introduced(assumption)).
% 0.64/0.74 tff(250,plain,
% 0.64/0.74 (e0 = op(e1, e1)),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[249, 123])).
% 0.64/0.74 tff(251,assumption,(op(e2, e3) = e0), introduced(assumption)).
% 0.64/0.74 tff(252,plain,
% 0.64/0.74 (e0 = op(e2, e3)),
% 0.64/0.74 inference(symmetry,[status(thm)],[251])).
% 0.64/0.74 tff(253,plain,
% 0.64/0.74 (op(e1, e1) = op(e2, e3)),
% 0.64/0.74 inference(transitivity,[status(thm)],[249, 252])).
% 0.64/0.74 tff(254,plain,
% 0.64/0.74 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 0.64/0.74 inference(monotonicity,[status(thm)],[253])).
% 0.64/0.74 tff(255,plain,
% 0.64/0.74 (op(e1, op(e2, e3)) = op(e1, op(e1, e1))),
% 0.64/0.74 inference(symmetry,[status(thm)],[254])).
% 0.64/0.74 tff(256,plain,
% 0.64/0.74 (op(e1, op(e2, e3)) = op(e1, e0)),
% 0.64/0.74 inference(monotonicity,[status(thm)],[251])).
% 0.64/0.74 tff(257,plain,
% 0.64/0.74 (op(e1, e0) = op(e1, op(e2, e3))),
% 0.64/0.74 inference(symmetry,[status(thm)],[256])).
% 0.64/0.74 tff(258,assumption,(op(e1, e0) = e3), introduced(assumption)).
% 0.64/0.74 tff(259,plain,
% 0.64/0.74 (e3 = op(e1, e0)),
% 0.64/0.74 inference(symmetry,[status(thm)],[258])).
% 0.64/0.74 tff(260,plain,
% 0.64/0.74 (e3 = op(e1, op(e1, e1))),
% 0.64/0.74 inference(transitivity,[status(thm)],[259, 257, 255])).
% 0.64/0.74 tff(261,plain,
% 0.64/0.74 (op(e1, op(e1, e1)) = e3),
% 0.64/0.74 inference(transitivity,[status(thm)],[254, 256, 258])).
% 0.64/0.74 tff(262,plain,
% 0.64/0.74 (op(e1, op(e1, op(e1, e1))) = op(e1, e3)),
% 0.64/0.74 inference(monotonicity,[status(thm)],[261])).
% 0.64/0.74 tff(263,plain,
% 0.64/0.74 (op(e1, e3) = op(e1, op(e1, op(e1, e1)))),
% 0.64/0.74 inference(symmetry,[status(thm)],[262])).
% 0.64/0.74 tff(264,assumption,(op(e1, e3) = e2), introduced(assumption)).
% 0.64/0.74 tff(265,plain,
% 0.64/0.74 (e2 = op(e1, e3)),
% 0.64/0.74 inference(symmetry,[status(thm)],[264])).
% 0.64/0.74 tff(266,plain,
% 0.64/0.74 (e2 = op(e1, op(e1, op(e1, e1)))),
% 0.64/0.74 inference(transitivity,[status(thm)],[265, 263])).
% 0.64/0.74 tff(267,plain,
% 0.64/0.74 ((~(~((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1))))))) <=> ((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.64/0.74 inference(rewrite,[status(thm)],[])).
% 0.64/0.74 tff(268,plain,
% 0.64/0.74 (((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1))))))),
% 0.64/0.74 inference(rewrite,[status(thm)],[])).
% 0.64/0.74 tff(269,plain,
% 0.64/0.74 ((~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1)))))))),
% 0.64/0.74 inference(monotonicity,[status(thm)],[268])).
% 0.64/0.74 tff(270,plain,
% 0.64/0.74 ((~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.64/0.74 inference(transitivity,[status(thm)],[269, 267])).
% 0.64/0.74 tff(271,plain,
% 0.64/0.74 ((~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.64/0.74 inference(rewrite,[status(thm)],[])).
% 0.64/0.74 tff(272,plain,
% 0.64/0.74 ((~(((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1))) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.64/0.74 inference(rewrite,[status(thm)],[])).
% 0.64/0.74 tff(273,axiom,(~(((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1))) & (e2 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax16')).
% 0.64/0.74 tff(274,plain,
% 0.64/0.74 (~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.64/0.74 tff(275,plain,
% 0.64/0.74 (~((e3 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[274, 271])).
% 0.64/0.74 tff(276,plain,
% 0.64/0.74 ((~(e2 = op(e1, op(e1, op(e1, e1))))) | (~(e0 = op(e1, e1))) | (~(e3 = op(e1, op(e1, e1))))),
% 0.64/0.74 inference(modus_ponens,[status(thm)],[275, 270])).
% 0.64/0.74 tff(277,plain,
% 0.64/0.74 ($false),
% 0.64/0.74 inference(unit_resolution,[status(thm)],[276, 266, 260, 250])).
% 0.64/0.74 tff(278,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e3) = e2)) | (~(op(e1, e0) = e3)) | (~(op(e2, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.74 tff(279,plain,
% 0.64/0.74 (~(op(e1, e1) = e0)),
% 0.64/0.74 inference(unit_resolution,[status(thm)],[278, 171, 248, 207])).
% 0.64/0.74 tff(280,plain,
% 0.64/0.74 (((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))),
% 0.64/0.74 inference(rewrite,[status(thm)],[])).
% 0.64/0.74 tff(281,plain,
% 0.64/0.74 ((((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))),
% 0.64/0.75 inference(rewrite,[status(thm)],[])).
% 0.64/0.75 tff(282,plain,
% 0.64/0.75 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0))),
% 0.64/0.75 inference(rewrite,[status(thm)],[])).
% 0.64/0.75 tff(283,plain,
% 0.64/0.75 (((((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))),
% 0.64/0.75 inference(monotonicity,[status(thm)],[282])).
% 0.64/0.75 tff(284,plain,
% 0.64/0.75 (((((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))),
% 0.64/0.75 inference(transitivity,[status(thm)],[283, 281])).
% 0.64/0.75 tff(285,plain,
% 0.64/0.75 (((((((((((((((((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))),
% 0.64/0.75 inference(and_elim,[status(thm)],[244])).
% 0.64/0.75 tff(286,plain,
% 0.64/0.75 ((((((((((((((((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))),
% 0.64/0.75 inference(and_elim,[status(thm)],[285])).
% 0.64/0.75 tff(287,plain,
% 0.64/0.75 (((((((((((((((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))),
% 0.64/0.75 inference(and_elim,[status(thm)],[286])).
% 0.64/0.75 tff(288,plain,
% 0.64/0.75 ((((((((((((((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))),
% 0.64/0.75 inference(and_elim,[status(thm)],[287])).
% 0.64/0.75 tff(289,plain,
% 0.64/0.75 (((((((((((((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))),
% 0.64/0.75 inference(and_elim,[status(thm)],[288])).
% 0.64/0.75 tff(290,plain,
% 0.64/0.75 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)),
% 0.64/0.75 inference(and_elim,[status(thm)],[289])).
% 0.64/0.75 tff(291,plain,
% 0.64/0.75 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.64/0.75 inference(modus_ponens,[status(thm)],[290, 284])).
% 0.64/0.75 tff(292,plain,
% 0.64/0.75 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.64/0.75 inference(modus_ponens,[status(thm)],[291, 280])).
% 0.64/0.75 tff(293,plain,
% 0.64/0.75 (op(e0, e1) = e0),
% 0.64/0.75 inference(unit_resolution,[status(thm)],[292, 279, 183, 182])).
% 0.64/0.75 tff(294,plain,
% 0.64/0.75 (op(e3, e3) = e1),
% 0.64/0.75 inference(unit_resolution,[status(thm)],[151, 191, 121, 138])).
% 0.64/0.75 tff(295,plain,
% 0.64/0.75 (op(e0, op(e3, e3)) = op(e0, e1)),
% 0.64/0.75 inference(monotonicity,[status(thm)],[294])).
% 0.64/0.75 tff(296,plain,
% 0.64/0.75 (e1 = op(e3, e3)),
% 0.64/0.75 inference(symmetry,[status(thm)],[294])).
% 0.64/0.75 tff(297,plain,
% 0.64/0.75 ((op(e2, e1) = e1) <=> (e3 = e1)),
% 0.64/0.75 inference(monotonicity,[status(thm)],[174])).
% 0.64/0.75 tff(298,plain,
% 0.64/0.75 ((op(e2, e1) = e1) <=> (e1 = e3)),
% 0.64/0.75 inference(transitivity,[status(thm)],[297, 128])).
% 0.64/0.75 tff(299,plain,
% 0.64/0.75 ((e1 = e3) <=> (op(e2, e1) = e1)),
% 0.64/0.75 inference(symmetry,[status(thm)],[298])).
% 0.64/0.75 tff(300,plain,
% 0.64/0.75 ((~(e1 = e3)) <=> (~(op(e2, e1) = e1))),
% 0.64/0.75 inference(monotonicity,[status(thm)],[299])).
% 0.64/0.75 tff(301,plain,
% 0.64/0.75 ((~(e1 = e3)) <=> (~(e1 = e3))),
% 0.64/0.75 inference(rewrite,[status(thm)],[])).
% 0.64/0.75 tff(302,plain,
% 0.64/0.75 (~(e1 = e3)),
% 0.64/0.75 inference(and_elim,[status(thm)],[9])).
% 0.64/0.75 tff(303,plain,
% 0.64/0.75 (~(e1 = e3)),
% 0.64/0.75 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.64/0.75 tff(304,plain,
% 0.64/0.75 (~(op(e2, e1) = e1)),
% 0.64/0.75 inference(modus_ponens,[status(thm)],[303, 300])).
% 0.64/0.75 tff(305,assumption,(op(e3, e3) = e1), introduced(assumption)).
% 0.64/0.75 tff(306,plain,
% 0.64/0.75 (e1 = op(e3, e3)),
% 0.64/0.75 inference(symmetry,[status(thm)],[305])).
% 0.64/0.75 tff(307,assumption,(op(e2, e2) = e1), introduced(assumption)).
% 0.64/0.75 tff(308,plain,
% 0.66/0.76 (op(e2, e2) = op(e3, e3)),
% 0.66/0.76 inference(transitivity,[status(thm)],[307, 306])).
% 0.66/0.76 tff(309,plain,
% 0.66/0.76 (op(e2, op(e2, e2)) = op(e2, op(e3, e3))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[308])).
% 0.66/0.76 tff(310,plain,
% 0.66/0.76 (op(e2, op(e3, e3)) = op(e2, op(e2, e2))),
% 0.66/0.76 inference(symmetry,[status(thm)],[309])).
% 0.66/0.76 tff(311,plain,
% 0.66/0.76 (op(e2, op(e3, e3)) = op(op(e1, e3), e1)),
% 0.66/0.76 inference(monotonicity,[status(thm)],[265, 305])).
% 0.66/0.76 tff(312,plain,
% 0.66/0.76 (op(op(e1, e3), e1) = op(e2, op(e3, e3))),
% 0.66/0.76 inference(symmetry,[status(thm)],[311])).
% 0.66/0.76 tff(313,assumption,(op(op(e1, e3), e1) = e3), introduced(assumption)).
% 0.66/0.76 tff(314,plain,
% 0.66/0.76 (e3 = op(op(e1, e3), e1)),
% 0.66/0.76 inference(symmetry,[status(thm)],[313])).
% 0.66/0.76 tff(315,plain,
% 0.66/0.76 (e3 = op(e2, op(e2, e2))),
% 0.66/0.76 inference(transitivity,[status(thm)],[314, 312, 310])).
% 0.66/0.76 tff(316,plain,
% 0.66/0.76 ((e1 = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.66/0.76 inference(commutativity,[status(thm)],[])).
% 0.66/0.76 tff(317,plain,
% 0.66/0.76 ((op(e2, e2) = e1) <=> (e1 = op(e2, e2))),
% 0.66/0.76 inference(symmetry,[status(thm)],[316])).
% 0.66/0.76 tff(318,plain,
% 0.66/0.76 (e1 = op(e2, e2)),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[307, 317])).
% 0.66/0.76 tff(319,plain,
% 0.66/0.76 (op(e2, op(e2, e2)) = e3),
% 0.66/0.76 inference(transitivity,[status(thm)],[309, 311, 313])).
% 0.66/0.76 tff(320,plain,
% 0.66/0.76 (op(e2, op(e2, op(e2, e2))) = op(op(e1, e3), e3)),
% 0.66/0.76 inference(monotonicity,[status(thm)],[265, 319])).
% 0.66/0.76 tff(321,plain,
% 0.66/0.76 (op(op(e1, e3), e3) = op(e2, op(e2, op(e2, e2)))),
% 0.66/0.76 inference(symmetry,[status(thm)],[320])).
% 0.66/0.76 tff(322,plain,
% 0.66/0.76 (op(op(e1, e3), e3) = op(e2, e3)),
% 0.66/0.76 inference(monotonicity,[status(thm)],[264])).
% 0.66/0.76 tff(323,plain,
% 0.66/0.76 (op(e2, e3) = op(op(e1, e3), e3)),
% 0.66/0.76 inference(symmetry,[status(thm)],[322])).
% 0.66/0.76 tff(324,plain,
% 0.66/0.76 (e0 = op(e2, op(e2, op(e2, e2)))),
% 0.66/0.76 inference(transitivity,[status(thm)],[252, 323, 321])).
% 0.66/0.76 tff(325,plain,
% 0.66/0.76 ((~(~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2))))))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(326,plain,
% 0.66/0.76 (((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2))))))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(327,plain,
% 0.66/0.76 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2)))))))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[326])).
% 0.66/0.76 tff(328,plain,
% 0.66/0.76 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.66/0.76 inference(transitivity,[status(thm)],[327, 325])).
% 0.66/0.76 tff(329,plain,
% 0.66/0.76 ((~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(330,plain,
% 0.66/0.76 ((~(((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(331,axiom,(~(((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e0 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax23')).
% 0.66/0.76 tff(332,plain,
% 0.66/0.76 (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.66/0.76 tff(333,plain,
% 0.66/0.76 (~((e3 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[332, 329])).
% 0.66/0.76 tff(334,plain,
% 0.66/0.76 ((~(e1 = op(e2, e2))) | (~(e0 = op(e2, op(e2, op(e2, e2))))) | (~(e3 = op(e2, op(e2, e2))))),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[333, 328])).
% 0.66/0.76 tff(335,plain,
% 0.66/0.76 ($false),
% 0.66/0.76 inference(unit_resolution,[status(thm)],[334, 324, 318, 315])).
% 0.66/0.76 tff(336,plain,((~(op(e2, e2) = e1)) | (~(op(e2, e3) = e0)) | (~(op(op(e1, e3), e1) = e3)) | (~(op(e3, e3) = e1)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.76 tff(337,plain,
% 0.66/0.76 (~(op(e2, e2) = e1)),
% 0.66/0.76 inference(unit_resolution,[status(thm)],[336, 207, 161, 294, 171])).
% 0.66/0.76 tff(338,plain,
% 0.66/0.76 (((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))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(339,plain,
% 0.66/0.76 ((((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))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(340,plain,
% 0.66/0.76 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(341,plain,
% 0.66/0.76 (((((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))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[340])).
% 0.66/0.76 tff(342,plain,
% 0.66/0.76 (((((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))),
% 0.66/0.76 inference(transitivity,[status(thm)],[341, 339])).
% 0.66/0.76 tff(343,plain,
% 0.66/0.76 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)),
% 0.66/0.76 inference(and_elim,[status(thm)],[240])).
% 0.66/0.76 tff(344,plain,
% 0.66/0.76 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.66/0.76 tff(345,plain,
% 0.66/0.76 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[344, 338])).
% 0.66/0.76 tff(346,plain,
% 0.66/0.76 (op(e2, e0) = e1),
% 0.66/0.76 inference(unit_resolution,[status(thm)],[345, 337, 191, 304])).
% 0.66/0.76 tff(347,plain,
% 0.66/0.76 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e1)),
% 0.66/0.76 inference(monotonicity,[status(thm)],[346])).
% 0.66/0.76 tff(348,plain,
% 0.66/0.76 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e1))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[347])).
% 0.66/0.76 tff(349,plain,
% 0.66/0.76 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = op(e2, e0)))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(350,plain,
% 0.66/0.76 (((((((((~(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)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[223])).
% 0.66/0.76 tff(351,plain,
% 0.66/0.76 ((((((((~(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)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[350])).
% 0.66/0.76 tff(352,plain,
% 0.66/0.76 (((((((~(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)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[351])).
% 0.66/0.76 tff(353,plain,
% 0.66/0.76 ((((((~(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)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[352])).
% 0.66/0.76 tff(354,plain,
% 0.66/0.76 (((((~(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)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[353])).
% 0.66/0.76 tff(355,plain,
% 0.66/0.76 ((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[354])).
% 0.66/0.76 tff(356,plain,
% 0.66/0.76 (((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[355])).
% 0.66/0.76 tff(357,plain,
% 0.66/0.76 ((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))),
% 0.66/0.76 inference(and_elim,[status(thm)],[356])).
% 0.66/0.76 tff(358,plain,
% 0.66/0.76 (~(op(e0, e0) = op(e2, e0))),
% 0.66/0.76 inference(and_elim,[status(thm)],[357])).
% 0.66/0.76 tff(359,plain,
% 0.66/0.76 (~(op(e0, e0) = op(e2, e0))),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[358, 349])).
% 0.66/0.76 tff(360,plain,
% 0.66/0.76 (~(op(e0, e0) = e1)),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[359, 348])).
% 0.66/0.76 tff(361,plain,
% 0.66/0.76 (e0 = op(e2, e3)),
% 0.66/0.76 inference(symmetry,[status(thm)],[207])).
% 0.66/0.76 tff(362,plain,
% 0.66/0.76 (op(e0, e1) = op(e2, e3)),
% 0.66/0.76 inference(transitivity,[status(thm)],[293, 361])).
% 0.66/0.76 tff(363,plain,
% 0.66/0.76 ((op(e0, e1) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[362, 296])).
% 0.66/0.76 tff(364,plain,
% 0.66/0.76 ((op(e2, e3) = op(e3, e3)) <=> (op(e0, e1) = e1)),
% 0.66/0.76 inference(symmetry,[status(thm)],[363])).
% 0.66/0.76 tff(365,plain,
% 0.66/0.76 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e0, e1) = e1))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[364])).
% 0.66/0.76 tff(366,plain,
% 0.66/0.76 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = op(e3, e3)))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(367,plain,
% 0.66/0.76 (~(op(e2, e3) = op(e3, e3))),
% 0.66/0.76 inference(and_elim,[status(thm)],[57])).
% 0.66/0.76 tff(368,plain,
% 0.66/0.76 (~(op(e2, e3) = op(e3, e3))),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.66/0.76 tff(369,plain,
% 0.66/0.76 (~(op(e0, e1) = e1)),
% 0.66/0.76 inference(modus_ponens,[status(thm)],[368, 365])).
% 0.66/0.76 tff(370,plain,
% 0.66/0.76 (((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))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(371,plain,
% 0.66/0.76 ((((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))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(372,plain,
% 0.66/0.76 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1))),
% 0.66/0.76 inference(rewrite,[status(thm)],[])).
% 0.66/0.76 tff(373,plain,
% 0.66/0.76 (((((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))),
% 0.66/0.76 inference(monotonicity,[status(thm)],[372])).
% 0.66/0.76 tff(374,plain,
% 0.66/0.76 (((((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))),
% 0.66/0.76 inference(transitivity,[status(thm)],[373, 371])).
% 0.66/0.76 tff(375,plain,
% 0.66/0.76 ((((((((((((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))),
% 0.66/0.76 inference(and_elim,[status(thm)],[289])).
% 0.66/0.76 tff(376,plain,
% 0.66/0.76 (((((((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[375])).
% 0.66/0.77 tff(377,plain,
% 0.66/0.77 ((((((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[376])).
% 0.66/0.77 tff(378,plain,
% 0.66/0.77 (((((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[377])).
% 0.66/0.77 tff(379,plain,
% 0.66/0.77 ((((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[378])).
% 0.66/0.77 tff(380,plain,
% 0.66/0.77 (((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[379])).
% 0.66/0.77 tff(381,plain,
% 0.66/0.77 ((((((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))),
% 0.66/0.77 inference(and_elim,[status(thm)],[380])).
% 0.66/0.77 tff(382,plain,
% 0.66/0.77 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)),
% 0.66/0.77 inference(and_elim,[status(thm)],[381])).
% 0.66/0.77 tff(383,plain,
% 0.66/0.77 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[382, 374])).
% 0.66/0.77 tff(384,plain,
% 0.66/0.77 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[383, 370])).
% 0.66/0.77 tff(385,plain,
% 0.66/0.77 (op(e0, e2) = e1),
% 0.66/0.77 inference(unit_resolution,[status(thm)],[384, 369, 121, 360])).
% 0.66/0.77 tff(386,plain,
% 0.66/0.77 (op(e0, e2) = op(e3, e3)),
% 0.66/0.77 inference(transitivity,[status(thm)],[385, 296])).
% 0.66/0.77 tff(387,plain,
% 0.66/0.77 (op(e0, op(e0, e2)) = op(e0, op(e3, e3))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[386])).
% 0.66/0.77 tff(388,plain,
% 0.66/0.77 (op(e0, op(e0, e2)) = e0),
% 0.66/0.77 inference(transitivity,[status(thm)],[387, 295, 293])).
% 0.66/0.77 tff(389,plain,
% 0.66/0.77 (op(e0, e1) = op(e0, op(e3, e3))),
% 0.66/0.77 inference(symmetry,[status(thm)],[295])).
% 0.66/0.77 tff(390,plain,
% 0.66/0.77 ((op(e0, e1) = e0) <=> (op(e0, op(e3, e3)) = e0)),
% 0.66/0.77 inference(monotonicity,[status(thm)],[389])).
% 0.66/0.77 tff(391,plain,
% 0.66/0.77 (op(e0, op(e3, e3)) = e0),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[293, 390])).
% 0.66/0.77 tff(392,plain,
% 0.66/0.77 (((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)) | (~(op(e0, op(e3, e3)) = e0))),
% 0.66/0.77 inference(tautology,[status(thm)],[])).
% 0.66/0.77 tff(393,plain,
% 0.66/0.77 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 0.66/0.77 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.66/0.77 tff(394,plain,
% 0.66/0.77 ((op(e2, e3) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 0.66/0.77 inference(commutativity,[status(thm)],[])).
% 0.66/0.77 tff(395,plain,
% 0.66/0.77 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = op(e3, e2))),
% 0.66/0.77 inference(symmetry,[status(thm)],[394])).
% 0.66/0.77 tff(396,plain,
% 0.66/0.77 ((e3 = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.66/0.77 inference(commutativity,[status(thm)],[])).
% 0.66/0.77 tff(397,plain,
% 0.66/0.77 ((op(e2, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[174])).
% 0.66/0.77 tff(398,plain,
% 0.66/0.77 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.66/0.77 inference(transitivity,[status(thm)],[397, 396])).
% 0.66/0.77 tff(399,plain,
% 0.66/0.77 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[398])).
% 0.66/0.77 tff(400,plain,
% 0.66/0.77 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e3, e1)))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(401,plain,
% 0.66/0.77 (~(op(e2, e1) = op(e3, e1))),
% 0.66/0.77 inference(and_elim,[status(thm)],[221])).
% 0.66/0.77 tff(402,plain,
% 0.66/0.77 (~(op(e2, e1) = op(e3, e1))),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.66/0.77 tff(403,plain,
% 0.66/0.77 (~(op(e3, e1) = e3)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[402, 399])).
% 0.66/0.77 tff(404,plain,
% 0.66/0.77 ((e3 = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.66/0.77 inference(commutativity,[status(thm)],[])).
% 0.66/0.77 tff(405,plain,
% 0.66/0.77 ((op(e1, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[248])).
% 0.66/0.77 tff(406,plain,
% 0.66/0.77 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.66/0.77 inference(transitivity,[status(thm)],[405, 404])).
% 0.66/0.77 tff(407,plain,
% 0.66/0.77 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[406])).
% 0.66/0.77 tff(408,plain,
% 0.66/0.77 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e3, e0)))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(409,plain,
% 0.66/0.77 (~(op(e1, e0) = op(e3, e0))),
% 0.66/0.77 inference(and_elim,[status(thm)],[354])).
% 0.66/0.77 tff(410,plain,
% 0.66/0.77 (~(op(e1, e0) = op(e3, e0))),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.66/0.77 tff(411,plain,
% 0.66/0.77 (~(op(e3, e0) = e3)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.66/0.77 tff(412,plain,
% 0.66/0.77 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 0.66/0.77 inference(monotonicity,[status(thm)],[296])).
% 0.66/0.77 tff(413,plain,
% 0.66/0.77 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[412])).
% 0.66/0.77 tff(414,plain,
% 0.66/0.77 (~(op(e3, e3) = e3)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[303, 413])).
% 0.66/0.77 tff(415,plain,
% 0.66/0.77 (((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(416,plain,
% 0.66/0.77 ((((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(417,plain,
% 0.66/0.77 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3))),
% 0.66/0.77 inference(rewrite,[status(thm)],[])).
% 0.66/0.77 tff(418,plain,
% 0.66/0.77 (((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> (((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))),
% 0.66/0.77 inference(monotonicity,[status(thm)],[417])).
% 0.66/0.77 tff(419,plain,
% 0.66/0.77 (((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3))),
% 0.66/0.77 inference(transitivity,[status(thm)],[418, 416])).
% 0.66/0.77 tff(420,plain,
% 0.66/0.77 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)),
% 0.66/0.77 inference(and_elim,[status(thm)],[145])).
% 0.66/0.77 tff(421,plain,
% 0.66/0.77 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.66/0.77 tff(422,plain,
% 0.66/0.77 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.66/0.77 inference(modus_ponens,[status(thm)],[421, 415])).
% 0.66/0.77 tff(423,plain,
% 0.66/0.78 (op(e3, e2) = e3),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[422, 414, 411, 403])).
% 0.66/0.78 tff(424,plain,
% 0.66/0.78 ((op(e3, e2) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[423])).
% 0.66/0.78 tff(425,plain,
% 0.66/0.78 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.66/0.78 inference(transitivity,[status(thm)],[424, 112])).
% 0.66/0.78 tff(426,plain,
% 0.66/0.78 ((op(e2, e3) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 0.66/0.78 inference(symmetry,[status(thm)],[425])).
% 0.66/0.78 tff(427,plain,
% 0.66/0.78 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e3, e2))),
% 0.66/0.78 inference(transitivity,[status(thm)],[426, 395])).
% 0.66/0.78 tff(428,plain,
% 0.66/0.78 ((~(op(e2, e3) = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[427])).
% 0.66/0.78 tff(429,plain,
% 0.66/0.78 (~(op(e2, e3) = op(e3, e2))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[198, 428])).
% 0.66/0.78 tff(430,plain,
% 0.66/0.78 (((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)) | (op(e2, e3) = op(e3, e2))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(431,plain,
% 0.66/0.78 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[430, 429])).
% 0.66/0.78 tff(432,plain,
% 0.66/0.78 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[296])).
% 0.66/0.78 tff(433,plain,
% 0.66/0.78 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 0.66/0.78 inference(symmetry,[status(thm)],[432])).
% 0.66/0.78 tff(434,plain,
% 0.66/0.78 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[433])).
% 0.66/0.78 tff(435,plain,
% 0.66/0.78 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = op(e3, e3)))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(436,plain,
% 0.66/0.78 (~(op(e3, e1) = op(e3, e3))),
% 0.66/0.78 inference(and_elim,[status(thm)],[34])).
% 0.66/0.78 tff(437,plain,
% 0.66/0.78 (~(op(e3, e1) = op(e3, e3))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.66/0.78 tff(438,plain,
% 0.66/0.78 (~(op(e3, e1) = e1)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.66/0.78 tff(439,plain,
% 0.66/0.78 (((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(440,plain,
% 0.66/0.78 ((((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(441,plain,
% 0.66/0.78 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(442,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[441])).
% 0.66/0.78 tff(443,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(transitivity,[status(thm)],[442, 440])).
% 0.66/0.78 tff(444,plain,
% 0.66/0.78 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)),
% 0.66/0.78 inference(and_elim,[status(thm)],[95])).
% 0.66/0.78 tff(445,plain,
% 0.66/0.78 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.66/0.78 tff(446,plain,
% 0.66/0.78 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[445, 439])).
% 0.66/0.78 tff(447,plain,
% 0.66/0.78 (op(e3, e1) = e2),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[446, 438, 183, 403])).
% 0.66/0.78 tff(448,plain,
% 0.66/0.78 (op(e3, op(e3, e1)) = op(e3, e2)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[447])).
% 0.66/0.78 tff(449,plain,
% 0.66/0.78 (op(e3, op(e3, e1)) = e3),
% 0.66/0.78 inference(transitivity,[status(thm)],[448, 423])).
% 0.66/0.78 tff(450,plain,
% 0.66/0.78 (((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)) | (~(op(e3, op(e3, e1)) = e3))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(451,plain,
% 0.66/0.78 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[450, 449])).
% 0.66/0.78 tff(452,plain,
% 0.66/0.78 ((op(e0, e3) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 0.66/0.78 inference(commutativity,[status(thm)],[])).
% 0.66/0.78 tff(453,plain,
% 0.66/0.78 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = op(e3, e0))),
% 0.66/0.78 inference(symmetry,[status(thm)],[452])).
% 0.66/0.78 tff(454,plain,
% 0.66/0.78 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[453])).
% 0.66/0.78 tff(455,plain,
% 0.66/0.78 (~(op(e1, e3) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.66/0.78 tff(456,plain,
% 0.66/0.78 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e0)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[251])).
% 0.66/0.78 tff(457,plain,
% 0.66/0.78 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e0))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[456])).
% 0.66/0.78 tff(458,plain,
% 0.66/0.78 (~(op(e1, e3) = e0)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[118, 457])).
% 0.66/0.78 tff(459,plain,
% 0.66/0.78 (op(e1, e3) = e2),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[104, 458, 87, 455])).
% 0.66/0.78 tff(460,plain,
% 0.66/0.78 (e2 = op(e1, e3)),
% 0.66/0.78 inference(symmetry,[status(thm)],[459])).
% 0.66/0.78 tff(461,plain,
% 0.66/0.78 (op(e2, e1) = op(op(e1, e3), e1)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[460])).
% 0.66/0.78 tff(462,plain,
% 0.66/0.78 (op(e2, e1) = e3),
% 0.66/0.78 inference(transitivity,[status(thm)],[461, 313])).
% 0.66/0.78 tff(463,plain,
% 0.66/0.78 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[462])).
% 0.66/0.78 tff(464,plain,
% 0.66/0.78 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[463])).
% 0.66/0.78 tff(465,plain,
% 0.66/0.78 (~(op(e1, e1) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[225, 464])).
% 0.66/0.78 tff(466,assumption,(op(e3, e0) = op(e0, e3)), introduced(assumption)).
% 0.66/0.78 tff(467,plain,
% 0.66/0.78 (op(e0, e3) = op(e3, e0)),
% 0.66/0.78 inference(symmetry,[status(thm)],[466])).
% 0.66/0.78 tff(468,assumption,(~(op(e3, e3) = e3)), introduced(assumption)).
% 0.66/0.78 tff(469,plain,
% 0.66/0.78 ((op(e2, e3) = e3) <=> (e0 = e3)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[251])).
% 0.66/0.78 tff(470,plain,
% 0.66/0.78 ((e0 = e3) <=> (op(e2, e3) = e3)),
% 0.66/0.78 inference(symmetry,[status(thm)],[469])).
% 0.66/0.78 tff(471,plain,
% 0.66/0.78 ((~(e0 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[470])).
% 0.66/0.78 tff(472,plain,
% 0.66/0.78 (~(op(e2, e3) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[181, 471])).
% 0.66/0.78 tff(473,plain,
% 0.66/0.78 (((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(474,plain,
% 0.66/0.78 ((((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(475,plain,
% 0.66/0.78 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(476,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[475])).
% 0.66/0.78 tff(477,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(transitivity,[status(thm)],[476, 474])).
% 0.66/0.78 tff(478,plain,
% 0.66/0.78 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)),
% 0.66/0.78 inference(and_elim,[status(thm)],[144])).
% 0.66/0.78 tff(479,plain,
% 0.66/0.78 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.66/0.78 tff(480,plain,
% 0.66/0.78 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[479, 473])).
% 0.66/0.78 tff(481,plain,
% 0.66/0.78 (op(e0, e3) = e3),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[480, 472, 455, 468])).
% 0.66/0.78 tff(482,plain,
% 0.66/0.78 (e3 = op(e0, e3)),
% 0.66/0.78 inference(symmetry,[status(thm)],[481])).
% 0.66/0.78 tff(483,plain,
% 0.66/0.78 (e3 = op(e3, e0)),
% 0.66/0.78 inference(transitivity,[status(thm)],[482, 467])).
% 0.66/0.78 tff(484,plain,
% 0.66/0.78 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[483])).
% 0.66/0.78 tff(485,plain,
% 0.66/0.78 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 0.66/0.78 inference(symmetry,[status(thm)],[484])).
% 0.66/0.78 tff(486,plain,
% 0.66/0.78 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[485])).
% 0.66/0.78 tff(487,plain,
% 0.66/0.78 (~(op(e1, e0) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[410, 486])).
% 0.66/0.78 tff(488,plain,
% 0.66/0.78 (op(e1, op(e1, e3)) = op(e1, e2)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[459])).
% 0.66/0.78 tff(489,plain,
% 0.66/0.78 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e2) = e3)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[488])).
% 0.66/0.78 tff(490,plain,
% 0.66/0.78 ((~(op(e1, op(e1, e3)) = e3)) <=> (~(op(e1, e2) = e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[489])).
% 0.66/0.78 tff(491,plain,
% 0.66/0.78 (~(op(e1, e2) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[167, 490])).
% 0.66/0.78 tff(492,plain,
% 0.66/0.78 ($false),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[247, 491, 487, 465, 455])).
% 0.66/0.78 tff(493,plain,((~(op(e2, e3) = e0)) | (~(op(op(e1, e3), e1) = e3)) | (op(e1, op(e1, e3)) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e3) = e1) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.66/0.78 tff(494,plain,
% 0.66/0.78 (~(op(e3, e0) = op(e0, e3))),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[493, 414, 161, 163, 138, 207])).
% 0.66/0.78 tff(495,plain,
% 0.66/0.78 (~(op(e0, e3) = op(e3, e0))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[494, 454])).
% 0.66/0.78 tff(496,plain,
% 0.66/0.78 (((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)) | (op(e0, e3) = op(e3, e0))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(497,plain,
% 0.66/0.78 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[496, 495])).
% 0.66/0.78 tff(498,plain,
% 0.66/0.78 ((~(op(e2, e3) = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[426])).
% 0.66/0.78 tff(499,plain,
% 0.66/0.78 (~(op(e3, e2) = op(e2, e3))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[198, 498])).
% 0.66/0.78 tff(500,plain,
% 0.66/0.78 (((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)) | (op(e3, e2) = op(e2, e3))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(501,plain,
% 0.66/0.78 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[500, 499])).
% 0.66/0.78 tff(502,plain,
% 0.66/0.78 ((e3 = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.66/0.78 inference(commutativity,[status(thm)],[])).
% 0.66/0.78 tff(503,plain,
% 0.66/0.78 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[174])).
% 0.66/0.78 tff(504,plain,
% 0.66/0.78 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.66/0.78 inference(transitivity,[status(thm)],[503, 502])).
% 0.66/0.78 tff(505,plain,
% 0.66/0.78 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[504])).
% 0.66/0.78 tff(506,plain,
% 0.66/0.78 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = op(e2, e2)))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(507,plain,
% 0.66/0.78 (~(op(e2, e1) = op(e2, e2))),
% 0.66/0.78 inference(and_elim,[status(thm)],[41])).
% 0.66/0.78 tff(508,plain,
% 0.66/0.78 (~(op(e2, e1) = op(e2, e2))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.66/0.78 tff(509,plain,
% 0.66/0.78 (~(op(e2, e2) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[508, 505])).
% 0.66/0.78 tff(510,plain,
% 0.66/0.78 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[361])).
% 0.66/0.78 tff(511,plain,
% 0.66/0.78 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 0.66/0.78 inference(symmetry,[status(thm)],[510])).
% 0.66/0.78 tff(512,plain,
% 0.66/0.78 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[511])).
% 0.66/0.78 tff(513,plain,
% 0.66/0.78 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = op(e2, e3)))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(514,plain,
% 0.66/0.78 (~(op(e2, e2) = op(e2, e3))),
% 0.66/0.78 inference(and_elim,[status(thm)],[39])).
% 0.66/0.78 tff(515,plain,
% 0.66/0.78 (~(op(e2, e2) = op(e2, e3))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.66/0.78 tff(516,plain,
% 0.66/0.78 (~(op(e2, e2) = e0)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[515, 512])).
% 0.66/0.78 tff(517,plain,
% 0.66/0.78 (((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(518,plain,
% 0.66/0.78 ((((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))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(519,plain,
% 0.66/0.78 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2))),
% 0.66/0.78 inference(rewrite,[status(thm)],[])).
% 0.66/0.78 tff(520,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[519])).
% 0.66/0.78 tff(521,plain,
% 0.66/0.78 (((((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))),
% 0.66/0.78 inference(transitivity,[status(thm)],[520, 518])).
% 0.66/0.78 tff(522,plain,
% 0.66/0.78 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)),
% 0.66/0.78 inference(and_elim,[status(thm)],[98])).
% 0.66/0.78 tff(523,plain,
% 0.66/0.78 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.66/0.78 tff(524,plain,
% 0.66/0.78 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[523, 517])).
% 0.66/0.78 tff(525,plain,
% 0.66/0.78 (op(e2, e2) = e2),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[524, 516, 509, 337])).
% 0.66/0.78 tff(526,plain,
% 0.66/0.78 (op(e2, op(e2, e2)) = op(e2, e2)),
% 0.66/0.78 inference(monotonicity,[status(thm)],[525])).
% 0.66/0.78 tff(527,plain,
% 0.66/0.78 (op(e2, op(e2, e2)) = e2),
% 0.66/0.78 inference(transitivity,[status(thm)],[526, 525])).
% 0.66/0.78 tff(528,plain,
% 0.66/0.78 (((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)) | (~(op(e2, op(e2, e2)) = e2))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(529,plain,
% 0.66/0.78 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 0.66/0.78 inference(unit_resolution,[status(thm)],[528, 527])).
% 0.66/0.78 tff(530,plain,
% 0.66/0.78 ((op(e1, e2) = op(e2, e1)) <=> (op(e2, e1) = op(e1, e2))),
% 0.66/0.78 inference(commutativity,[status(thm)],[])).
% 0.66/0.78 tff(531,plain,
% 0.66/0.78 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 0.66/0.78 inference(symmetry,[status(thm)],[530])).
% 0.66/0.78 tff(532,plain,
% 0.66/0.78 ((e3 = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.66/0.78 inference(commutativity,[status(thm)],[])).
% 0.66/0.78 tff(533,plain,
% 0.66/0.78 ((op(e2, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[174])).
% 0.66/0.78 tff(534,plain,
% 0.66/0.78 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.66/0.78 inference(transitivity,[status(thm)],[533, 532])).
% 0.66/0.78 tff(535,plain,
% 0.66/0.78 ((op(e1, e2) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 0.66/0.78 inference(symmetry,[status(thm)],[534])).
% 0.66/0.78 tff(536,plain,
% 0.66/0.78 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e1))),
% 0.66/0.78 inference(transitivity,[status(thm)],[535, 531])).
% 0.66/0.78 tff(537,plain,
% 0.66/0.78 ((~(op(e1, e2) = e3)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 0.66/0.78 inference(monotonicity,[status(thm)],[536])).
% 0.66/0.78 tff(538,plain,
% 0.66/0.78 (~(op(e1, e2) = op(e2, e1))),
% 0.66/0.78 inference(modus_ponens,[status(thm)],[211, 537])).
% 0.66/0.78 tff(539,plain,
% 0.66/0.78 (((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)) | (op(e1, e2) = op(e2, e1))),
% 0.66/0.78 inference(tautology,[status(thm)],[])).
% 0.66/0.78 tff(540,plain,
% 0.66/0.79 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[539, 538])).
% 0.66/0.79 tff(541,plain,
% 0.66/0.79 (op(e2, e0) = op(e3, e3)),
% 0.66/0.79 inference(transitivity,[status(thm)],[346, 296])).
% 0.66/0.79 tff(542,plain,
% 0.66/0.79 (op(e0, op(e2, e0)) = op(e0, op(e3, e3))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[541])).
% 0.66/0.79 tff(543,plain,
% 0.66/0.79 ((op(e0, op(e2, e0)) = e0) <=> (op(e0, op(e3, e3)) = e0)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[542])).
% 0.66/0.79 tff(544,plain,
% 0.66/0.79 ((op(e0, op(e3, e3)) = e0) <=> (op(e0, op(e2, e0)) = e0)),
% 0.66/0.79 inference(symmetry,[status(thm)],[543])).
% 0.66/0.79 tff(545,plain,
% 0.66/0.79 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e0)) = e0)),
% 0.66/0.79 inference(transitivity,[status(thm)],[390, 544])).
% 0.66/0.79 tff(546,plain,
% 0.66/0.79 (op(e0, op(e2, e0)) = e0),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[293, 545])).
% 0.66/0.79 tff(547,plain,
% 0.66/0.79 (((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)) | (~(op(e0, op(e2, e0)) = e0))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(548,plain,
% 0.66/0.79 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[547, 546])).
% 0.66/0.79 tff(549,plain,
% 0.66/0.79 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[171])).
% 0.66/0.79 tff(550,plain,
% 0.66/0.79 ((op(e3, op(e1, e3)) = e3) <=> (op(e3, e2) = e3)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[549])).
% 0.66/0.79 tff(551,plain,
% 0.66/0.79 ((op(e3, e2) = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.66/0.79 inference(symmetry,[status(thm)],[550])).
% 0.66/0.79 tff(552,plain,
% 0.66/0.79 (op(e3, op(e1, e3)) = e3),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[423, 551])).
% 0.66/0.79 tff(553,plain,
% 0.66/0.79 (((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(554,plain,
% 0.66/0.79 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[553, 552])).
% 0.66/0.79 tff(555,plain,
% 0.66/0.79 ((~(op(e1, e2) = e3)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[535])).
% 0.66/0.79 tff(556,plain,
% 0.66/0.79 (~(op(e2, e1) = op(e1, e2))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[211, 555])).
% 0.66/0.79 tff(557,plain,
% 0.66/0.79 (((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)) | (op(e2, e1) = op(e1, e2))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(558,plain,
% 0.66/0.79 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[557, 556])).
% 0.66/0.79 tff(559,plain,
% 0.66/0.79 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[171])).
% 0.66/0.79 tff(560,plain,
% 0.66/0.79 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[559])).
% 0.66/0.79 tff(561,plain,
% 0.66/0.79 (~(op(e1, e0) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[110, 560])).
% 0.66/0.79 tff(562,plain,
% 0.66/0.79 ((op(e2, e0) = e2) <=> (op(e3, e3) = e2)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[541])).
% 0.66/0.79 tff(563,plain,
% 0.66/0.79 ((op(e3, e3) = e2) <=> (op(e2, e0) = e2)),
% 0.66/0.79 inference(symmetry,[status(thm)],[562])).
% 0.66/0.79 tff(564,plain,
% 0.66/0.79 ((~(op(e3, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[563])).
% 0.66/0.79 tff(565,plain,
% 0.66/0.79 ((e2 = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.66/0.79 inference(commutativity,[status(thm)],[])).
% 0.66/0.79 tff(566,plain,
% 0.66/0.79 ((op(e1, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[171])).
% 0.66/0.79 tff(567,plain,
% 0.66/0.79 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.66/0.79 inference(transitivity,[status(thm)],[566, 565])).
% 0.66/0.79 tff(568,plain,
% 0.66/0.79 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[567])).
% 0.66/0.79 tff(569,plain,
% 0.66/0.79 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = op(e3, e3)))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(570,plain,
% 0.66/0.79 (~(op(e1, e3) = op(e3, e3))),
% 0.66/0.79 inference(and_elim,[status(thm)],[58])).
% 0.66/0.79 tff(571,plain,
% 0.66/0.79 (~(op(e1, e3) = op(e3, e3))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.66/0.79 tff(572,plain,
% 0.66/0.79 (~(op(e3, e3) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[571, 568])).
% 0.66/0.79 tff(573,plain,
% 0.66/0.79 (~(op(e2, e0) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[572, 564])).
% 0.66/0.79 tff(574,plain,
% 0.66/0.79 (e2 = op(e3, e1)),
% 0.66/0.79 inference(symmetry,[status(thm)],[447])).
% 0.66/0.79 tff(575,plain,
% 0.66/0.79 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e3, e1))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[574])).
% 0.66/0.79 tff(576,plain,
% 0.66/0.79 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.66/0.79 inference(symmetry,[status(thm)],[575])).
% 0.66/0.79 tff(577,plain,
% 0.66/0.79 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[576])).
% 0.66/0.79 tff(578,plain,
% 0.66/0.79 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = op(e3, e1)))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(579,plain,
% 0.66/0.79 (~(op(e3, e0) = op(e3, e1))),
% 0.66/0.79 inference(and_elim,[status(thm)],[38])).
% 0.66/0.79 tff(580,plain,
% 0.66/0.79 (~(op(e3, e0) = op(e3, e1))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.66/0.79 tff(581,plain,
% 0.66/0.79 (~(op(e3, e0) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[580, 577])).
% 0.66/0.79 tff(582,plain,
% 0.66/0.79 (((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))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(583,plain,
% 0.66/0.79 ((((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))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(584,plain,
% 0.66/0.79 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(585,plain,
% 0.66/0.79 (((((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))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[584])).
% 0.66/0.79 tff(586,plain,
% 0.66/0.79 (((((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))),
% 0.66/0.79 inference(transitivity,[status(thm)],[585, 583])).
% 0.66/0.79 tff(587,plain,
% 0.66/0.79 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)),
% 0.66/0.79 inference(and_elim,[status(thm)],[378])).
% 0.66/0.79 tff(588,plain,
% 0.66/0.79 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.66/0.79 tff(589,plain,
% 0.66/0.79 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[588, 582])).
% 0.66/0.79 tff(590,plain,
% 0.66/0.79 (op(e0, e0) = e2),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[589, 581, 573, 561])).
% 0.66/0.79 tff(591,plain,
% 0.66/0.79 (op(e2, op(e0, e0)) = op(e2, e2)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[590])).
% 0.66/0.79 tff(592,plain,
% 0.66/0.79 (op(e2, op(e0, e0)) = e2),
% 0.66/0.79 inference(transitivity,[status(thm)],[591, 525])).
% 0.66/0.79 tff(593,plain,
% 0.66/0.79 (((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)) | (~(op(e2, op(e0, e0)) = e2))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(594,plain,
% 0.66/0.79 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[593, 592])).
% 0.66/0.79 tff(595,plain,
% 0.66/0.79 ((op(e0, e1) = op(e1, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 0.66/0.79 inference(commutativity,[status(thm)],[])).
% 0.66/0.79 tff(596,plain,
% 0.66/0.79 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e1, e0))),
% 0.66/0.79 inference(symmetry,[status(thm)],[595])).
% 0.66/0.79 tff(597,plain,
% 0.66/0.79 ((op(e1, e0) = op(e0, e1)) <=> (e3 = op(e0, e1))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[248])).
% 0.66/0.79 tff(598,plain,
% 0.66/0.79 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 0.66/0.79 inference(transitivity,[status(thm)],[597, 127])).
% 0.66/0.79 tff(599,plain,
% 0.66/0.79 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 0.66/0.79 inference(symmetry,[status(thm)],[598])).
% 0.66/0.79 tff(600,plain,
% 0.66/0.79 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 0.66/0.79 inference(transitivity,[status(thm)],[599, 596])).
% 0.66/0.79 tff(601,plain,
% 0.66/0.79 ((~(op(e0, e1) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[600])).
% 0.66/0.79 tff(602,plain,
% 0.66/0.79 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[174])).
% 0.66/0.79 tff(603,plain,
% 0.66/0.79 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e3))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[602])).
% 0.66/0.79 tff(604,plain,
% 0.66/0.79 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = op(e2, e1)))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(605,plain,
% 0.66/0.79 (~(op(e0, e1) = op(e2, e1))),
% 0.66/0.79 inference(and_elim,[status(thm)],[351])).
% 0.66/0.79 tff(606,plain,
% 0.66/0.79 (~(op(e0, e1) = op(e2, e1))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.66/0.79 tff(607,plain,
% 0.66/0.79 (~(op(e0, e1) = e3)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[606, 603])).
% 0.66/0.79 tff(608,plain,
% 0.66/0.79 (~(op(e0, e1) = op(e1, e0))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[607, 601])).
% 0.66/0.79 tff(609,plain,
% 0.66/0.79 (((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)) | (op(e0, e1) = op(e1, e0))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(610,plain,
% 0.66/0.79 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[609, 608])).
% 0.66/0.79 tff(611,plain,
% 0.66/0.79 ((~(op(e0, e1) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[599])).
% 0.66/0.79 tff(612,plain,
% 0.66/0.79 (~(op(e1, e0) = op(e0, e1))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[607, 611])).
% 0.66/0.79 tff(613,plain,
% 0.66/0.79 (((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)) | (op(e1, e0) = op(e0, e1))),
% 0.66/0.79 inference(tautology,[status(thm)],[])).
% 0.66/0.79 tff(614,plain,
% 0.66/0.79 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 0.66/0.79 inference(unit_resolution,[status(thm)],[613, 612])).
% 0.66/0.79 tff(615,plain,
% 0.66/0.79 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 0.66/0.79 inference(monotonicity,[status(thm)],[171])).
% 0.66/0.79 tff(616,plain,
% 0.66/0.79 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[615])).
% 0.66/0.79 tff(617,plain,
% 0.66/0.79 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = op(e1, e3)))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(618,plain,
% 0.66/0.79 (~(op(e1, e1) = op(e1, e3))),
% 0.66/0.79 inference(and_elim,[status(thm)],[46])).
% 0.66/0.79 tff(619,plain,
% 0.66/0.79 (~(op(e1, e1) = op(e1, e3))),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.66/0.79 tff(620,plain,
% 0.66/0.79 (~(op(e1, e1) = e2)),
% 0.66/0.79 inference(modus_ponens,[status(thm)],[619, 616])).
% 0.66/0.79 tff(621,plain,
% 0.66/0.79 (((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))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(622,plain,
% 0.66/0.79 ((((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))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(623,plain,
% 0.66/0.79 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2))),
% 0.66/0.79 inference(rewrite,[status(thm)],[])).
% 0.66/0.79 tff(624,plain,
% 0.66/0.79 (((((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))),
% 0.66/0.79 inference(monotonicity,[status(thm)],[623])).
% 0.66/0.79 tff(625,plain,
% 0.66/0.79 (((((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))),
% 0.66/0.80 inference(transitivity,[status(thm)],[624, 622])).
% 0.66/0.80 tff(626,plain,
% 0.66/0.80 ((((((((((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))),
% 0.66/0.80 inference(and_elim,[status(thm)],[101])).
% 0.66/0.80 tff(627,plain,
% 0.66/0.80 (((((((((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))),
% 0.66/0.80 inference(and_elim,[status(thm)],[626])).
% 0.66/0.80 tff(628,plain,
% 0.66/0.80 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)),
% 0.66/0.80 inference(and_elim,[status(thm)],[627])).
% 0.66/0.80 tff(629,plain,
% 0.66/0.80 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.66/0.80 tff(630,plain,
% 0.66/0.80 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[629, 621])).
% 0.66/0.80 tff(631,plain,
% 0.66/0.80 (op(e1, e1) = e1),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[630, 279, 620, 226])).
% 0.66/0.80 tff(632,plain,
% 0.66/0.80 (op(e1, e1) = op(e3, e3)),
% 0.66/0.80 inference(transitivity,[status(thm)],[631, 296])).
% 0.66/0.80 tff(633,plain,
% 0.66/0.80 (op(e0, op(e1, e1)) = op(e0, op(e3, e3))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[632])).
% 0.66/0.80 tff(634,plain,
% 0.66/0.80 (op(e0, op(e1, e1)) = e0),
% 0.66/0.80 inference(transitivity,[status(thm)],[633, 295, 293])).
% 0.66/0.80 tff(635,plain,
% 0.66/0.80 (((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)) | (~(op(e0, op(e1, e1)) = e0))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(636,plain,
% 0.66/0.80 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[635, 634])).
% 0.66/0.80 tff(637,plain,
% 0.66/0.80 ((e2 = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(638,assumption,(~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))), introduced(assumption)).
% 0.66/0.80 tff(639,plain,
% 0.66/0.80 (((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(640,plain,
% 0.66/0.80 (~(op(e3, op(e0, e3)) = e3)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[639, 638])).
% 0.66/0.80 tff(641,plain,
% 0.66/0.80 (((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)) | (~(op(e0, op(e0, e3)) = e0))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(642,plain,
% 0.66/0.80 (~(op(e0, op(e0, e3)) = e0)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[641, 638])).
% 0.66/0.80 tff(643,plain,
% 0.66/0.80 (((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)) | (~(op(e1, op(e0, e3)) = e1))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(644,plain,
% 0.66/0.80 (~(op(e1, op(e0, e3)) = e1)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[643, 638])).
% 0.66/0.80 tff(645,plain,
% 0.66/0.80 (((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)) | (~(op(e2, op(e0, e3)) = e2))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(646,plain,
% 0.66/0.80 (~(op(e2, op(e0, e3)) = e2)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[645, 638])).
% 0.66/0.80 tff(647,plain,
% 0.66/0.80 (((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)) | (op(e3, e0) = op(e0, e3))),
% 0.66/0.80 inference(tautology,[status(thm)],[])).
% 0.66/0.80 tff(648,plain,
% 0.66/0.80 (op(e3, e0) = op(e0, e3)),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[647, 638])).
% 0.66/0.80 tff(649,assumption,(~(op(e0, op(e0, e3)) = e0)), introduced(assumption)).
% 0.66/0.80 tff(650,assumption,(~(op(e3, op(e0, e3)) = e3)), introduced(assumption)).
% 0.66/0.80 tff(651,assumption,(~(op(e2, op(e0, e3)) = e2)), introduced(assumption)).
% 0.66/0.80 tff(652,assumption,(~(op(e1, op(e0, e3)) = e1)), introduced(assumption)).
% 0.66/0.80 tff(653,plain,
% 0.66/0.80 ((e0 = op(e0, op(e1, e3))) <=> (op(e0, op(e1, e3)) = e0)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(654,plain,
% 0.66/0.80 ((op(e1, e3) = op(e0, e3)) <=> (op(e0, e3) = op(e1, e3))),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(655,assumption,(~(op(op(e1, e3), e1) = e3)), introduced(assumption)).
% 0.66/0.80 tff(656,assumption,(~(op(e3, e3) = e0)), introduced(assumption)).
% 0.66/0.80 tff(657,plain,
% 0.66/0.80 ((e1 = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(658,plain,
% 0.66/0.80 ((op(e3, e3) = e1) <=> (e1 = op(e3, e3))),
% 0.66/0.80 inference(symmetry,[status(thm)],[657])).
% 0.66/0.80 tff(659,plain,
% 0.66/0.80 ((op(e3, e3) = op(e0, e3)) <=> (op(e0, e3) = op(e3, e3))),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(660,plain,
% 0.66/0.80 ((e3 = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(661,assumption,(~(op(e0, e3) = e3)), introduced(assumption)).
% 0.66/0.80 tff(662,plain,
% 0.66/0.80 ((op(e3, e0) = e3) <=> (op(e0, e3) = e3)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[466])).
% 0.66/0.80 tff(663,plain,
% 0.66/0.80 ((op(e0, e3) = e3) <=> (op(e3, e0) = e3)),
% 0.66/0.80 inference(symmetry,[status(thm)],[662])).
% 0.66/0.80 tff(664,plain,
% 0.66/0.80 ((~(op(e0, e3) = e3)) <=> (~(op(e3, e0) = e3))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[663])).
% 0.66/0.80 tff(665,plain,
% 0.66/0.80 (~(op(e3, e0) = e3)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[661, 664])).
% 0.66/0.80 tff(666,plain,
% 0.66/0.80 ((e3 = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(667,plain,
% 0.66/0.80 ((op(e3, e0) = e2) <=> (op(e0, e3) = e2)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[466])).
% 0.66/0.80 tff(668,plain,
% 0.66/0.80 ((op(e0, e3) = e2) <=> (op(e3, e0) = e2)),
% 0.66/0.80 inference(symmetry,[status(thm)],[667])).
% 0.66/0.80 tff(669,plain,
% 0.66/0.80 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e2)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[264])).
% 0.66/0.80 tff(670,plain,
% 0.66/0.80 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e0) = e2)),
% 0.66/0.80 inference(transitivity,[status(thm)],[669, 668])).
% 0.66/0.80 tff(671,plain,
% 0.66/0.80 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e0) = e2))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[670])).
% 0.66/0.80 tff(672,plain,
% 0.66/0.80 (~(op(e3, e0) = e2)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[64, 671])).
% 0.66/0.80 tff(673,plain,
% 0.66/0.80 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[264])).
% 0.66/0.80 tff(674,plain,
% 0.66/0.80 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[673])).
% 0.66/0.80 tff(675,plain,
% 0.66/0.80 (~(op(e1, e0) = e2)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[110, 674])).
% 0.66/0.80 tff(676,plain,
% 0.66/0.80 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e2))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[669])).
% 0.66/0.80 tff(677,plain,
% 0.66/0.80 (~(op(e0, e3) = e2)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[64, 676])).
% 0.66/0.80 tff(678,plain,
% 0.66/0.80 (((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))),
% 0.66/0.80 inference(rewrite,[status(thm)],[])).
% 0.66/0.80 tff(679,plain,
% 0.66/0.80 ((((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))),
% 0.66/0.80 inference(rewrite,[status(thm)],[])).
% 0.66/0.80 tff(680,plain,
% 0.66/0.80 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) <=> ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2))),
% 0.66/0.80 inference(rewrite,[status(thm)],[])).
% 0.66/0.80 tff(681,plain,
% 0.66/0.80 (((((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))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[680])).
% 0.66/0.80 tff(682,plain,
% 0.66/0.80 (((((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))),
% 0.66/0.80 inference(transitivity,[status(thm)],[681, 679])).
% 0.66/0.80 tff(683,plain,
% 0.66/0.80 ((((((((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))),
% 0.66/0.80 inference(and_elim,[status(thm)],[627])).
% 0.66/0.80 tff(684,plain,
% 0.66/0.80 (((((((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))),
% 0.66/0.80 inference(and_elim,[status(thm)],[683])).
% 0.66/0.80 tff(685,plain,
% 0.66/0.80 ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3)),
% 0.66/0.80 inference(and_elim,[status(thm)],[684])).
% 0.66/0.80 tff(686,plain,
% 0.66/0.80 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[685, 682])).
% 0.66/0.80 tff(687,plain,
% 0.66/0.80 ((op(e0, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e3)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[686, 678])).
% 0.66/0.80 tff(688,plain,
% 0.66/0.80 (op(e0, e3) = e0),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[687, 677, 121, 661])).
% 0.66/0.80 tff(689,plain,
% 0.66/0.80 (e0 = op(e0, e3)),
% 0.66/0.80 inference(symmetry,[status(thm)],[688])).
% 0.66/0.80 tff(690,plain,
% 0.66/0.80 (op(e2, e0) = op(e2, op(e0, e3))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[689])).
% 0.66/0.80 tff(691,plain,
% 0.66/0.80 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[690])).
% 0.66/0.80 tff(692,plain,
% 0.66/0.80 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 0.66/0.80 inference(symmetry,[status(thm)],[691])).
% 0.66/0.80 tff(693,plain,
% 0.66/0.80 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e0) = e2))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[692])).
% 0.66/0.80 tff(694,plain,
% 0.66/0.80 (~(op(e2, e0) = e2)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[651, 693])).
% 0.66/0.80 tff(695,plain,
% 0.66/0.80 (op(e0, e0) = e2),
% 0.66/0.80 inference(unit_resolution,[status(thm)],[589, 694, 675, 672])).
% 0.66/0.80 tff(696,plain,
% 0.66/0.80 (e2 = op(e0, e0)),
% 0.66/0.80 inference(modus_ponens,[status(thm)],[695, 78])).
% 0.66/0.80 tff(697,plain,
% 0.66/0.80 ((e1 = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.66/0.80 inference(commutativity,[status(thm)],[])).
% 0.66/0.80 tff(698,plain,
% 0.66/0.80 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.66/0.80 inference(monotonicity,[status(thm)],[695])).
% 0.66/0.80 tff(699,plain,
% 0.66/0.80 ((e1 = op(e0, op(e0, e0))) <=> (e1 = op(e0, e2))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[698])).
% 0.66/0.80 tff(700,plain,
% 0.66/0.80 ((e1 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e1)),
% 0.66/0.80 inference(transitivity,[status(thm)],[699, 697])).
% 0.66/0.80 tff(701,plain,
% 0.66/0.80 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.66/0.80 inference(symmetry,[status(thm)],[700])).
% 0.66/0.80 tff(702,plain,
% 0.66/0.80 (e2 = op(e0, e0)),
% 0.66/0.80 inference(symmetry,[status(thm)],[695])).
% 0.66/0.80 tff(703,plain,
% 0.66/0.80 ((e1 = e2) <=> (e1 = op(e0, e0))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[702])).
% 0.66/0.80 tff(704,plain,
% 0.66/0.80 ((e1 = e2) <=> (op(e0, e0) = e1)),
% 0.66/0.80 inference(transitivity,[status(thm)],[703, 73])).
% 0.66/0.80 tff(705,plain,
% 0.66/0.80 ((~(e1 = e2)) <=> (~(op(e0, e0) = e1))),
% 0.66/0.80 inference(monotonicity,[status(thm)],[704])).
% 0.66/0.80 tff(706,plain,
% 0.66/0.80 ((~(e1 = e2)) <=> (~(e1 = e2))),
% 0.66/0.80 inference(rewrite,[status(thm)],[])).
% 0.66/0.80 tff(707,plain,
% 0.66/0.80 (~(e1 = e2)),
% 0.66/0.80 inference(and_elim,[status(thm)],[10])).
% 0.66/0.81 tff(708,plain,
% 0.66/0.81 (~(e1 = e2)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.66/0.81 tff(709,plain,
% 0.66/0.81 (~(op(e0, e0) = e1)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[708, 705])).
% 0.66/0.81 tff(710,plain,
% 0.66/0.81 ((op(e1, e1) = op(e1, e0)) <=> (op(e1, e0) = op(e1, e1))),
% 0.66/0.81 inference(commutativity,[status(thm)],[])).
% 0.66/0.81 tff(711,plain,
% 0.66/0.81 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[689])).
% 0.66/0.81 tff(712,plain,
% 0.66/0.81 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[711])).
% 0.66/0.81 tff(713,plain,
% 0.66/0.81 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 0.66/0.81 inference(symmetry,[status(thm)],[712])).
% 0.66/0.81 tff(714,plain,
% 0.66/0.81 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[713])).
% 0.66/0.81 tff(715,plain,
% 0.66/0.81 (~(op(e1, e0) = e1)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[652, 714])).
% 0.66/0.81 tff(716,plain,
% 0.66/0.81 (e0 = op(e3, e0)),
% 0.66/0.81 inference(transitivity,[status(thm)],[689, 467])).
% 0.66/0.81 tff(717,plain,
% 0.66/0.81 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[716])).
% 0.66/0.81 tff(718,plain,
% 0.66/0.81 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[717])).
% 0.66/0.81 tff(719,plain,
% 0.66/0.81 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[718])).
% 0.66/0.81 tff(720,plain,
% 0.66/0.81 (~(op(e1, e0) = e0)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[410, 719])).
% 0.66/0.81 tff(721,plain,
% 0.66/0.81 (((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))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(722,plain,
% 0.66/0.81 ((((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))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(723,plain,
% 0.66/0.81 ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) <=> ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(724,plain,
% 0.66/0.81 (((((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))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[723])).
% 0.66/0.81 tff(725,plain,
% 0.66/0.81 (((((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))),
% 0.66/0.81 inference(transitivity,[status(thm)],[724, 722])).
% 0.66/0.81 tff(726,plain,
% 0.66/0.81 ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3)),
% 0.66/0.81 inference(and_elim,[status(thm)],[683])).
% 0.66/0.81 tff(727,plain,
% 0.66/0.81 ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.66/0.81 tff(728,plain,
% 0.66/0.81 ((op(e1, e0) = e0) | (op(e1, e0) = e1) | (op(e1, e0) = e2) | (op(e1, e0) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[727, 721])).
% 0.66/0.81 tff(729,plain,
% 0.66/0.81 (op(e1, e0) = e3),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[728, 720, 675, 715])).
% 0.66/0.81 tff(730,plain,
% 0.66/0.81 (e3 = op(e1, e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[729])).
% 0.66/0.81 tff(731,plain,
% 0.66/0.81 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[730])).
% 0.66/0.81 tff(732,plain,
% 0.66/0.81 ((op(e1, e1) = e3) <=> (op(e1, e0) = op(e1, e1))),
% 0.66/0.81 inference(transitivity,[status(thm)],[731, 710])).
% 0.66/0.81 tff(733,plain,
% 0.66/0.81 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.66/0.81 inference(symmetry,[status(thm)],[732])).
% 0.66/0.81 tff(734,plain,
% 0.66/0.81 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[733])).
% 0.66/0.81 tff(735,plain,
% 0.66/0.81 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = op(e1, e1)))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(736,plain,
% 0.66/0.81 (~(op(e1, e0) = op(e1, e1))),
% 0.66/0.81 inference(and_elim,[status(thm)],[50])).
% 0.66/0.81 tff(737,plain,
% 0.66/0.81 (~(op(e1, e0) = op(e1, e1))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.66/0.81 tff(738,plain,
% 0.66/0.81 (~(op(e1, e1) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[737, 734])).
% 0.66/0.81 tff(739,plain,
% 0.66/0.81 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[264])).
% 0.66/0.81 tff(740,plain,
% 0.66/0.81 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[739])).
% 0.66/0.81 tff(741,plain,
% 0.66/0.81 (~(op(e1, e1) = e2)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[619, 740])).
% 0.66/0.81 tff(742,plain,
% 0.66/0.81 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[716])).
% 0.66/0.81 tff(743,plain,
% 0.66/0.81 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[742])).
% 0.66/0.81 tff(744,plain,
% 0.66/0.81 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[743])).
% 0.66/0.81 tff(745,plain,
% 0.66/0.81 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = op(e3, e0)))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(746,plain,
% 0.66/0.81 (~(op(e2, e0) = op(e3, e0))),
% 0.66/0.81 inference(and_elim,[status(thm)],[353])).
% 0.66/0.81 tff(747,plain,
% 0.66/0.81 (~(op(e2, e0) = op(e3, e0))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.66/0.81 tff(748,plain,
% 0.66/0.81 (~(op(e2, e0) = e0)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[747, 744])).
% 0.66/0.81 tff(749,plain,
% 0.66/0.81 ((op(e2, e0) = op(e1, e0)) <=> (op(e1, e0) = op(e2, e0))),
% 0.66/0.81 inference(commutativity,[status(thm)],[])).
% 0.66/0.81 tff(750,plain,
% 0.66/0.81 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[730])).
% 0.66/0.81 tff(751,plain,
% 0.66/0.81 ((op(e2, e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 0.66/0.81 inference(transitivity,[status(thm)],[750, 749])).
% 0.66/0.81 tff(752,plain,
% 0.66/0.81 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.66/0.81 inference(symmetry,[status(thm)],[751])).
% 0.66/0.81 tff(753,plain,
% 0.66/0.81 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[752])).
% 0.66/0.81 tff(754,plain,
% 0.66/0.81 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = op(e2, e0)))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(755,plain,
% 0.66/0.81 (~(op(e1, e0) = op(e2, e0))),
% 0.66/0.81 inference(and_elim,[status(thm)],[355])).
% 0.66/0.81 tff(756,plain,
% 0.66/0.81 (~(op(e1, e0) = op(e2, e0))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.66/0.81 tff(757,plain,
% 0.66/0.81 (~(op(e2, e0) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[756, 753])).
% 0.66/0.81 tff(758,plain,
% 0.66/0.81 (((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))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(759,plain,
% 0.66/0.81 ((((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))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(760,plain,
% 0.66/0.81 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(761,plain,
% 0.66/0.81 (((((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))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[760])).
% 0.66/0.81 tff(762,plain,
% 0.66/0.81 (((((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))),
% 0.66/0.81 inference(transitivity,[status(thm)],[761, 759])).
% 0.66/0.81 tff(763,plain,
% 0.66/0.81 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)),
% 0.66/0.81 inference(and_elim,[status(thm)],[100])).
% 0.66/0.81 tff(764,plain,
% 0.66/0.81 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.66/0.81 tff(765,plain,
% 0.66/0.81 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[764, 758])).
% 0.66/0.81 tff(766,plain,
% 0.66/0.81 (op(e2, e0) = e1),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[765, 757, 748, 694])).
% 0.66/0.81 tff(767,assumption,(op(e2, e0) = e1), introduced(assumption)).
% 0.66/0.81 tff(768,plain,
% 0.66/0.81 (e1 = op(e2, e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[767])).
% 0.66/0.81 tff(769,plain,
% 0.66/0.81 (op(e1, op(e1, e1)) = op(op(e2, e0), e0)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[768, 249])).
% 0.66/0.81 tff(770,plain,
% 0.66/0.81 (op(op(e2, e0), e0) = op(e1, op(e1, e1))),
% 0.66/0.81 inference(symmetry,[status(thm)],[769])).
% 0.66/0.81 tff(771,assumption,(op(e0, e3) = e0), introduced(assumption)).
% 0.66/0.81 tff(772,plain,
% 0.66/0.81 (e0 = op(e0, e3)),
% 0.66/0.81 inference(symmetry,[status(thm)],[771])).
% 0.66/0.81 tff(773,plain,
% 0.66/0.81 (op(op(e2, e0), e0) = op(e1, op(e0, e3))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[767, 772])).
% 0.66/0.81 tff(774,plain,
% 0.66/0.81 (op(e1, op(e0, e3)) = op(op(e2, e0), e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[773])).
% 0.66/0.81 tff(775,plain,
% 0.66/0.81 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[772])).
% 0.66/0.81 tff(776,plain,
% 0.66/0.81 (e3 = op(e1, op(e1, e1))),
% 0.66/0.81 inference(transitivity,[status(thm)],[259, 775, 774, 770])).
% 0.66/0.81 tff(777,plain,
% 0.66/0.81 (op(e1, op(e0, e3)) = op(e1, e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[775])).
% 0.66/0.81 tff(778,plain,
% 0.66/0.81 (op(e1, op(e1, e1)) = op(e1, e0)),
% 0.66/0.81 inference(transitivity,[status(thm)],[769, 773, 777])).
% 0.66/0.81 tff(779,plain,
% 0.66/0.81 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[778])).
% 0.66/0.81 tff(780,plain,
% 0.66/0.81 (op(e1, op(e1, e0)) = op(e1, op(e1, op(e1, e1)))),
% 0.66/0.81 inference(symmetry,[status(thm)],[779])).
% 0.66/0.81 tff(781,plain,
% 0.66/0.81 (op(e1, op(e1, e0)) = op(e1, e3)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[258])).
% 0.66/0.81 tff(782,plain,
% 0.66/0.81 (op(e1, e3) = op(e1, op(e1, e0))),
% 0.66/0.81 inference(symmetry,[status(thm)],[781])).
% 0.66/0.81 tff(783,plain,
% 0.66/0.81 (e2 = op(e1, op(e1, op(e1, e1)))),
% 0.66/0.81 inference(transitivity,[status(thm)],[265, 782, 780])).
% 0.66/0.81 tff(784,plain,
% 0.66/0.81 ($false),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[276, 783, 250, 776])).
% 0.66/0.81 tff(785,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e3) = e2)) | (~(op(e1, e0) = e3)) | (~(op(e2, e0) = e1)) | (~(op(e0, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.81 tff(786,plain,
% 0.66/0.81 (~(op(e1, e1) = e0)),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[785, 264, 729, 766, 688])).
% 0.66/0.81 tff(787,plain,
% 0.66/0.81 (op(e1, e1) = e1),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[630, 786, 741, 738])).
% 0.66/0.81 tff(788,plain,
% 0.66/0.81 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[787])).
% 0.66/0.81 tff(789,plain,
% 0.66/0.81 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[788])).
% 0.66/0.81 tff(790,plain,
% 0.66/0.81 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = op(e1, e1)))),
% 0.66/0.81 inference(rewrite,[status(thm)],[])).
% 0.66/0.81 tff(791,plain,
% 0.66/0.81 (~(op(e0, e1) = op(e1, e1))),
% 0.66/0.81 inference(and_elim,[status(thm)],[352])).
% 0.66/0.81 tff(792,plain,
% 0.66/0.81 (~(op(e0, e1) = op(e1, e1))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.66/0.81 tff(793,plain,
% 0.66/0.81 (~(op(e0, e1) = e1)),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[792, 789])).
% 0.66/0.81 tff(794,plain,
% 0.66/0.81 (op(e0, e2) = e1),
% 0.66/0.81 inference(unit_resolution,[status(thm)],[384, 793, 121, 709])).
% 0.66/0.81 tff(795,plain,
% 0.66/0.81 (e1 = op(e0, op(e0, e0))),
% 0.66/0.81 inference(modus_ponens,[status(thm)],[794, 701])).
% 0.66/0.81 tff(796,plain,
% 0.66/0.81 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e2))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[698])).
% 0.66/0.81 tff(797,plain,
% 0.66/0.81 (op(e0, op(e0, e2)) = op(e0, op(e0, op(e0, e0)))),
% 0.66/0.81 inference(symmetry,[status(thm)],[796])).
% 0.66/0.81 tff(798,plain,
% 0.66/0.81 (e1 = op(e2, e0)),
% 0.66/0.81 inference(symmetry,[status(thm)],[766])).
% 0.66/0.81 tff(799,plain,
% 0.66/0.81 (op(e0, e2) = op(e2, e0)),
% 0.66/0.81 inference(transitivity,[status(thm)],[794, 798])).
% 0.66/0.81 tff(800,plain,
% 0.66/0.81 (op(e0, op(e0, e2)) = op(e0, op(e2, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[799])).
% 0.66/0.81 tff(801,plain,
% 0.66/0.81 (op(e0, op(e2, e0)) = op(e0, op(e0, e2))),
% 0.66/0.81 inference(symmetry,[status(thm)],[800])).
% 0.66/0.81 tff(802,plain,
% 0.66/0.81 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.66/0.81 inference(monotonicity,[status(thm)],[766])).
% 0.66/0.81 tff(803,plain,
% 0.66/0.81 (op(e0, e1) = op(e0, op(e2, e0))),
% 0.66/0.81 inference(symmetry,[status(thm)],[802])).
% 0.66/0.81 tff(804,plain,
% 0.66/0.81 ((op(e0, e1) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e1))),
% 0.66/0.81 inference(commutativity,[status(thm)],[])).
% 0.66/0.81 tff(805,plain,
% 0.66/0.81 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e0))),
% 0.66/0.81 inference(monotonicity,[status(thm)],[702])).
% 0.66/0.81 tff(806,plain,
% 0.66/0.81 ((op(e0, e1) = e2) <=> (op(e0, e0) = op(e0, e1))),
% 0.66/0.81 inference(transitivity,[status(thm)],[805, 804])).
% 0.66/0.81 tff(807,plain,
% 0.72/0.82 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 0.72/0.82 inference(symmetry,[status(thm)],[806])).
% 0.72/0.82 tff(808,plain,
% 0.72/0.82 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[807])).
% 0.72/0.82 tff(809,plain,
% 0.72/0.82 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = op(e0, e1)))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(810,plain,
% 0.72/0.82 (~(op(e0, e0) = op(e0, e1))),
% 0.72/0.82 inference(and_elim,[status(thm)],[56])).
% 0.72/0.82 tff(811,plain,
% 0.72/0.82 (~(op(e0, e0) = op(e0, e1))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.72/0.82 tff(812,plain,
% 0.72/0.82 (~(op(e0, e1) = e2)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[811, 808])).
% 0.72/0.82 tff(813,plain,
% 0.72/0.82 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[689])).
% 0.72/0.82 tff(814,plain,
% 0.72/0.82 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[813])).
% 0.72/0.82 tff(815,plain,
% 0.72/0.82 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[814])).
% 0.72/0.82 tff(816,plain,
% 0.72/0.82 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e0, e3)))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(817,plain,
% 0.72/0.82 (~(op(e0, e1) = op(e0, e3))),
% 0.72/0.82 inference(and_elim,[status(thm)],[52])).
% 0.72/0.82 tff(818,plain,
% 0.72/0.82 (~(op(e0, e1) = op(e0, e3))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.72/0.82 tff(819,plain,
% 0.72/0.82 (~(op(e0, e1) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[818, 815])).
% 0.72/0.82 tff(820,plain,
% 0.72/0.82 (((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))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(821,plain,
% 0.72/0.82 ((((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))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(822,plain,
% 0.72/0.82 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(823,plain,
% 0.72/0.82 (((((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))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[822])).
% 0.72/0.82 tff(824,plain,
% 0.72/0.82 (((((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))),
% 0.72/0.82 inference(transitivity,[status(thm)],[823, 821])).
% 0.72/0.82 tff(825,plain,
% 0.72/0.82 ((((((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))),
% 0.72/0.82 inference(and_elim,[status(thm)],[684])).
% 0.72/0.82 tff(826,plain,
% 0.72/0.82 (((((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))),
% 0.72/0.82 inference(and_elim,[status(thm)],[825])).
% 0.72/0.82 tff(827,plain,
% 0.72/0.82 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)),
% 0.72/0.82 inference(and_elim,[status(thm)],[826])).
% 0.72/0.82 tff(828,plain,
% 0.72/0.82 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[827, 824])).
% 0.72/0.82 tff(829,plain,
% 0.72/0.82 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[828, 820])).
% 0.72/0.82 tff(830,plain,
% 0.72/0.82 (op(e0, e1) = e3),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[829, 793, 819, 812])).
% 0.72/0.82 tff(831,plain,
% 0.72/0.82 (e3 = op(e0, e1)),
% 0.72/0.82 inference(symmetry,[status(thm)],[830])).
% 0.72/0.82 tff(832,plain,
% 0.72/0.82 (e3 = op(e0, op(e0, op(e0, e0)))),
% 0.72/0.82 inference(transitivity,[status(thm)],[831, 803, 801, 797])).
% 0.72/0.82 tff(833,plain,
% 0.72/0.82 ((~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0)))))))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(834,plain,
% 0.72/0.82 (((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0)))))))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(835,plain,
% 0.72/0.82 ((~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0))))))))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[834])).
% 0.72/0.82 tff(836,plain,
% 0.72/0.82 ((~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.72/0.82 inference(transitivity,[status(thm)],[835, 833])).
% 0.72/0.82 tff(837,plain,
% 0.72/0.82 ((~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(838,plain,
% 0.72/0.82 ((~(((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0))) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(839,axiom,(~(((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0))) & (e3 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax6')).
% 0.72/0.82 tff(840,plain,
% 0.72/0.82 (~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.72/0.82 tff(841,plain,
% 0.72/0.82 (~((e1 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[840, 837])).
% 0.72/0.82 tff(842,plain,
% 0.72/0.82 ((~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(e0, e0))) | (~(e3 = op(e0, op(e0, op(e0, e0)))))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[841, 836])).
% 0.72/0.82 tff(843,plain,
% 0.72/0.82 ($false),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[842, 832, 795, 696])).
% 0.72/0.82 tff(844,plain,((~(op(e1, e3) = e2)) | (op(e0, e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e0, e3)) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.82 tff(845,plain,
% 0.72/0.82 (~(op(e1, e3) = e2)),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[844, 661, 651, 652, 466, 121])).
% 0.72/0.82 tff(846,plain,
% 0.72/0.82 (op(e1, e3) = e3),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[104, 845, 80, 87])).
% 0.72/0.82 tff(847,plain,
% 0.72/0.82 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[846])).
% 0.72/0.82 tff(848,plain,
% 0.72/0.82 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.72/0.82 inference(transitivity,[status(thm)],[847, 666])).
% 0.72/0.82 tff(849,plain,
% 0.72/0.82 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[848])).
% 0.72/0.82 tff(850,plain,
% 0.72/0.82 (~(op(e3, e3) = e3)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[571, 849])).
% 0.72/0.82 tff(851,plain,
% 0.72/0.82 (op(op(e1, e3), e1) = op(e3, e1)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[846])).
% 0.72/0.82 tff(852,plain,
% 0.72/0.82 ((op(op(e1, e3), e1) = e3) <=> (op(e3, e1) = e3)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[851])).
% 0.72/0.82 tff(853,plain,
% 0.72/0.82 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e3, e1) = e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[852])).
% 0.72/0.82 tff(854,plain,
% 0.72/0.82 (~(op(e3, e1) = e3)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[655, 853])).
% 0.72/0.82 tff(855,plain,
% 0.72/0.82 (op(e3, e2) = e3),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[422, 854, 850, 665])).
% 0.72/0.82 tff(856,assumption,(op(e3, e2) = e3), introduced(assumption)).
% 0.72/0.82 tff(857,plain,
% 0.72/0.82 (op(e3, op(e0, e3)) = op(e3, e2)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[2])).
% 0.72/0.82 tff(858,plain,
% 0.72/0.82 (op(e3, op(e0, e3)) = e3),
% 0.72/0.82 inference(transitivity,[status(thm)],[857, 856])).
% 0.72/0.82 tff(859,plain,
% 0.72/0.82 ($false),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[650, 858])).
% 0.72/0.82 tff(860,plain,((~(op(e0, e3) = e2)) | (op(e3, op(e0, e3)) = e3) | (~(op(e3, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.82 tff(861,plain,
% 0.72/0.82 (~(op(e0, e3) = e2)),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[860, 855, 650])).
% 0.72/0.82 tff(862,plain,
% 0.72/0.82 (op(e0, e3) = e0),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[687, 861, 121, 661])).
% 0.72/0.82 tff(863,plain,
% 0.72/0.82 (e0 = op(e0, e3)),
% 0.72/0.82 inference(symmetry,[status(thm)],[862])).
% 0.72/0.82 tff(864,plain,
% 0.72/0.82 (op(e2, e0) = op(e2, op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[863])).
% 0.72/0.82 tff(865,plain,
% 0.72/0.82 (op(e2, op(e0, e3)) = op(e2, e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[864])).
% 0.72/0.82 tff(866,plain,
% 0.72/0.82 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[863])).
% 0.72/0.82 tff(867,plain,
% 0.72/0.82 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[866])).
% 0.72/0.82 tff(868,plain,
% 0.72/0.82 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 0.72/0.82 inference(symmetry,[status(thm)],[867])).
% 0.72/0.82 tff(869,plain,
% 0.72/0.82 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[868])).
% 0.72/0.82 tff(870,plain,
% 0.72/0.82 (~(op(e1, e0) = e1)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[652, 869])).
% 0.72/0.82 tff(871,plain,
% 0.72/0.82 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[846])).
% 0.72/0.82 tff(872,plain,
% 0.72/0.82 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[871])).
% 0.72/0.82 tff(873,plain,
% 0.72/0.82 (~(op(e1, e0) = e3)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[110, 872])).
% 0.72/0.82 tff(874,plain,
% 0.72/0.82 (e0 = op(e3, e0)),
% 0.72/0.82 inference(transitivity,[status(thm)],[863, 467])).
% 0.72/0.82 tff(875,plain,
% 0.72/0.82 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[874])).
% 0.72/0.82 tff(876,plain,
% 0.72/0.82 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[875])).
% 0.72/0.82 tff(877,plain,
% 0.72/0.82 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[876])).
% 0.72/0.82 tff(878,plain,
% 0.72/0.82 (~(op(e1, e0) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[410, 877])).
% 0.72/0.82 tff(879,plain,
% 0.72/0.82 (op(e1, e0) = e2),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[728, 878, 873, 870])).
% 0.72/0.82 tff(880,plain,
% 0.72/0.82 (op(op(e1, e0), e0) = op(e2, op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[879, 863])).
% 0.72/0.82 tff(881,plain,
% 0.72/0.82 ((op(e3, e1) = op(e3, e0)) <=> (op(e3, e0) = op(e3, e1))),
% 0.72/0.82 inference(commutativity,[status(thm)],[])).
% 0.72/0.82 tff(882,plain,
% 0.72/0.82 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[874])).
% 0.72/0.82 tff(883,plain,
% 0.72/0.82 ((op(e3, e1) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 0.72/0.82 inference(transitivity,[status(thm)],[882, 881])).
% 0.72/0.82 tff(884,plain,
% 0.72/0.82 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[883])).
% 0.72/0.82 tff(885,plain,
% 0.72/0.82 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[884])).
% 0.72/0.82 tff(886,plain,
% 0.72/0.82 (~(op(e3, e1) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[580, 885])).
% 0.72/0.82 tff(887,plain,
% 0.72/0.82 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[863])).
% 0.72/0.82 tff(888,plain,
% 0.72/0.82 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[887])).
% 0.72/0.82 tff(889,plain,
% 0.72/0.82 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[888])).
% 0.72/0.82 tff(890,plain,
% 0.72/0.82 (~(op(e0, e1) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[818, 889])).
% 0.72/0.82 tff(891,plain,
% 0.72/0.82 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[855])).
% 0.72/0.82 tff(892,plain,
% 0.72/0.82 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 0.72/0.82 inference(transitivity,[status(thm)],[891, 128])).
% 0.72/0.82 tff(893,plain,
% 0.72/0.82 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 0.72/0.82 inference(symmetry,[status(thm)],[892])).
% 0.72/0.82 tff(894,plain,
% 0.72/0.82 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[893])).
% 0.72/0.82 tff(895,plain,
% 0.72/0.82 (~(op(e3, e2) = e1)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[303, 894])).
% 0.72/0.82 tff(896,plain,
% 0.72/0.82 ((op(e3, e0) = e1) <=> (op(e0, e3) = e1)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[466])).
% 0.72/0.82 tff(897,plain,
% 0.72/0.82 ((op(e0, e3) = e1) <=> (op(e3, e0) = e1)),
% 0.72/0.82 inference(symmetry,[status(thm)],[896])).
% 0.72/0.82 tff(898,plain,
% 0.72/0.82 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e0) = e1))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[897])).
% 0.72/0.82 tff(899,plain,
% 0.72/0.82 (~(op(e3, e0) = e1)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[121, 898])).
% 0.72/0.82 tff(900,plain,
% 0.72/0.82 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[864])).
% 0.72/0.82 tff(901,plain,
% 0.72/0.82 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 0.72/0.82 inference(symmetry,[status(thm)],[900])).
% 0.72/0.82 tff(902,plain,
% 0.72/0.82 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e0) = e2))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[901])).
% 0.72/0.82 tff(903,plain,
% 0.72/0.82 (~(op(e2, e0) = e2)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[651, 902])).
% 0.72/0.82 tff(904,plain,
% 0.72/0.82 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[874])).
% 0.72/0.82 tff(905,plain,
% 0.72/0.82 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[904])).
% 0.72/0.82 tff(906,plain,
% 0.72/0.82 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[905])).
% 0.72/0.82 tff(907,plain,
% 0.72/0.82 (~(op(e2, e0) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[747, 906])).
% 0.72/0.82 tff(908,plain,
% 0.72/0.82 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[855])).
% 0.72/0.82 tff(909,plain,
% 0.72/0.82 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.72/0.82 inference(transitivity,[status(thm)],[908, 159])).
% 0.72/0.82 tff(910,plain,
% 0.72/0.82 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[909])).
% 0.72/0.82 tff(911,plain,
% 0.72/0.82 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[910])).
% 0.72/0.82 tff(912,plain,
% 0.72/0.82 (~(op(e3, e2) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[181, 911])).
% 0.72/0.82 tff(913,plain,
% 0.72/0.82 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e0, e3))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[772])).
% 0.72/0.82 tff(914,plain,
% 0.72/0.82 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[913])).
% 0.72/0.82 tff(915,plain,
% 0.72/0.82 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 0.72/0.82 inference(monotonicity,[status(thm)],[914])).
% 0.72/0.82 tff(916,plain,
% 0.72/0.82 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e0, e3)))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(917,plain,
% 0.72/0.82 (~(op(e0, e2) = op(e0, e3))),
% 0.72/0.82 inference(and_elim,[status(thm)],[51])).
% 0.72/0.82 tff(918,plain,
% 0.72/0.82 (~(op(e0, e2) = op(e0, e3))),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.72/0.82 tff(919,plain,
% 0.72/0.82 (~(op(e0, e2) = e0)),
% 0.72/0.82 inference(modus_ponens,[status(thm)],[918, 915])).
% 0.72/0.82 tff(920,assumption,(op(e1, e0) = e2), introduced(assumption)).
% 0.72/0.82 tff(921,plain,
% 0.72/0.82 (op(e1, op(e1, e0)) = op(e1, e2)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[920])).
% 0.72/0.82 tff(922,plain,
% 0.72/0.82 (op(e1, e2) = op(e1, op(e1, e0))),
% 0.72/0.82 inference(symmetry,[status(thm)],[921])).
% 0.72/0.82 tff(923,plain,
% 0.72/0.82 ((op(e1, e2) = e0) <=> (op(e1, op(e1, e0)) = e0)),
% 0.72/0.82 inference(monotonicity,[status(thm)],[922])).
% 0.72/0.82 tff(924,plain,
% 0.72/0.82 ((op(e1, op(e1, e0)) = e0) <=> (op(e1, e2) = e0)),
% 0.72/0.82 inference(symmetry,[status(thm)],[923])).
% 0.72/0.82 tff(925,plain,
% 0.72/0.82 ((op(e2, e3) = op(e0, e3)) <=> (op(e0, e3) = op(e2, e3))),
% 0.72/0.82 inference(commutativity,[status(thm)],[])).
% 0.72/0.82 tff(926,assumption,(~(op(e3, e3) = e1)), introduced(assumption)).
% 0.72/0.82 tff(927,plain,
% 0.72/0.82 (op(e2, e3) = e1),
% 0.72/0.82 inference(unit_resolution,[status(thm)],[151, 926, 121, 87])).
% 0.72/0.82 tff(928,plain,
% 0.72/0.82 (e1 = op(e2, e3)),
% 0.72/0.82 inference(symmetry,[status(thm)],[927])).
% 0.72/0.82 tff(929,assumption,(~(op(e1, e0) = e1)), introduced(assumption)).
% 0.72/0.82 tff(930,assumption,(~(op(e3, e2) = e1)), introduced(assumption)).
% 0.72/0.82 tff(931,assumption,(~(op(e3, e0) = e1)), introduced(assumption)).
% 0.72/0.82 tff(932,plain,
% 0.72/0.82 (((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))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(933,plain,
% 0.72/0.82 ((((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))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(934,plain,
% 0.72/0.82 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1))),
% 0.72/0.82 inference(rewrite,[status(thm)],[])).
% 0.72/0.82 tff(935,plain,
% 0.72/0.82 (((((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))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[934])).
% 0.72/0.83 tff(936,plain,
% 0.72/0.83 (((((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))),
% 0.72/0.83 inference(transitivity,[status(thm)],[935, 933])).
% 0.72/0.83 tff(937,plain,
% 0.72/0.83 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)),
% 0.72/0.83 inference(and_elim,[status(thm)],[232])).
% 0.72/0.83 tff(938,plain,
% 0.72/0.83 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.72/0.83 tff(939,plain,
% 0.72/0.83 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[938, 932])).
% 0.72/0.83 tff(940,plain,
% 0.72/0.83 (op(e3, e1) = e1),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[939, 926, 931, 930])).
% 0.72/0.83 tff(941,plain,
% 0.72/0.83 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.72/0.83 inference(monotonicity,[status(thm)],[940])).
% 0.72/0.83 tff(942,plain,
% 0.72/0.83 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[941])).
% 0.72/0.83 tff(943,plain,
% 0.72/0.83 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = op(e3, e1)))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(944,plain,
% 0.72/0.83 (~(op(e1, e1) = op(e3, e1))),
% 0.72/0.83 inference(and_elim,[status(thm)],[222])).
% 0.72/0.83 tff(945,plain,
% 0.72/0.83 (~(op(e1, e1) = op(e3, e1))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[944, 943])).
% 0.72/0.83 tff(946,plain,
% 0.72/0.83 (~(op(e1, e1) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[945, 942])).
% 0.72/0.83 tff(947,plain,
% 0.72/0.83 (((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(948,plain,
% 0.72/0.83 ((((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(949,plain,
% 0.72/0.83 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(950,plain,
% 0.72/0.83 (((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> (((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[949])).
% 0.72/0.83 tff(951,plain,
% 0.72/0.83 (((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1))),
% 0.72/0.83 inference(transitivity,[status(thm)],[950, 948])).
% 0.72/0.83 tff(952,plain,
% 0.72/0.83 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)),
% 0.72/0.83 inference(and_elim,[status(thm)],[288])).
% 0.72/0.83 tff(953,plain,
% 0.72/0.83 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.72/0.83 tff(954,plain,
% 0.72/0.83 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[953, 947])).
% 0.72/0.83 tff(955,plain,
% 0.72/0.83 (op(e1, e2) = e1),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[954, 946, 929, 87])).
% 0.72/0.83 tff(956,plain,
% 0.72/0.83 (op(e1, op(e1, e0)) = op(e2, e3)),
% 0.72/0.83 inference(transitivity,[status(thm)],[921, 955, 928])).
% 0.72/0.83 tff(957,plain,
% 0.72/0.83 ((op(e1, op(e1, e0)) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[956, 772])).
% 0.72/0.83 tff(958,plain,
% 0.72/0.83 ((op(e1, op(e1, e0)) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.72/0.83 inference(transitivity,[status(thm)],[957, 925])).
% 0.72/0.83 tff(959,plain,
% 0.72/0.83 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, op(e1, e0)) = e0)),
% 0.72/0.83 inference(symmetry,[status(thm)],[958])).
% 0.72/0.83 tff(960,plain,
% 0.72/0.83 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e2) = e0)),
% 0.72/0.83 inference(transitivity,[status(thm)],[959, 924])).
% 0.72/0.83 tff(961,plain,
% 0.72/0.83 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e2) = e0))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[960])).
% 0.72/0.83 tff(962,plain,
% 0.72/0.83 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = op(e2, e3)))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(963,plain,
% 0.72/0.83 (~(op(e0, e3) = op(e2, e3))),
% 0.72/0.83 inference(and_elim,[status(thm)],[61])).
% 0.72/0.83 tff(964,plain,
% 0.72/0.83 (~(op(e0, e3) = op(e2, e3))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.72/0.83 tff(965,plain,
% 0.72/0.83 (~(op(e1, e2) = e0)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[964, 961])).
% 0.72/0.83 tff(966,plain,
% 0.72/0.83 (((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))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(967,plain,
% 0.72/0.83 ((((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))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(968,plain,
% 0.72/0.83 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(969,plain,
% 0.72/0.83 (((((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))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[968])).
% 0.72/0.83 tff(970,plain,
% 0.72/0.83 (((((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))),
% 0.72/0.83 inference(transitivity,[status(thm)],[969, 967])).
% 0.72/0.83 tff(971,plain,
% 0.72/0.83 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)),
% 0.72/0.83 inference(and_elim,[status(thm)],[241])).
% 0.72/0.83 tff(972,plain,
% 0.72/0.83 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.72/0.83 tff(973,plain,
% 0.72/0.83 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[972, 966])).
% 0.72/0.83 tff(974,plain,
% 0.72/0.83 (op(e2, e2) = e0),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[973, 965, 919, 85])).
% 0.72/0.83 tff(975,plain,
% 0.72/0.83 (e2 = op(e1, e0)),
% 0.72/0.83 inference(symmetry,[status(thm)],[920])).
% 0.72/0.83 tff(976,plain,
% 0.72/0.83 (op(e2, op(e2, e2)) = op(op(e1, e0), e0)),
% 0.72/0.83 inference(monotonicity,[status(thm)],[975, 974])).
% 0.72/0.83 tff(977,plain,
% 0.72/0.83 (op(op(e1, e0), e0) = op(e2, op(e2, e2))),
% 0.72/0.83 inference(symmetry,[status(thm)],[976])).
% 0.72/0.83 tff(978,plain,
% 0.72/0.83 (op(op(e1, e0), e0) = op(e2, op(e0, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[920, 772])).
% 0.72/0.83 tff(979,plain,
% 0.72/0.83 (op(e2, op(e0, e3)) = op(op(e1, e0), e0)),
% 0.72/0.83 inference(symmetry,[status(thm)],[978])).
% 0.72/0.83 tff(980,plain,
% 0.72/0.83 (op(e2, op(e0, e3)) = op(e2, e0)),
% 0.72/0.83 inference(monotonicity,[status(thm)],[771])).
% 0.72/0.83 tff(981,plain,
% 0.72/0.83 (op(e2, e0) = op(e2, op(e0, e3))),
% 0.72/0.83 inference(symmetry,[status(thm)],[980])).
% 0.72/0.83 tff(982,assumption,(~(op(e2, e0) = e2)), introduced(assumption)).
% 0.72/0.83 tff(983,assumption,(~(op(e2, e0) = e0)), introduced(assumption)).
% 0.72/0.83 tff(984,plain,
% 0.72/0.83 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e2, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[928])).
% 0.72/0.83 tff(985,plain,
% 0.72/0.83 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 0.72/0.83 inference(symmetry,[status(thm)],[984])).
% 0.72/0.83 tff(986,plain,
% 0.72/0.83 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[985])).
% 0.72/0.83 tff(987,plain,
% 0.72/0.83 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = op(e2, e3)))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(988,plain,
% 0.72/0.83 (~(op(e2, e0) = op(e2, e3))),
% 0.72/0.83 inference(and_elim,[status(thm)],[42])).
% 0.72/0.83 tff(989,plain,
% 0.72/0.83 (~(op(e2, e0) = op(e2, e3))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.72/0.83 tff(990,plain,
% 0.72/0.83 (~(op(e2, e0) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[989, 986])).
% 0.72/0.83 tff(991,plain,
% 0.72/0.83 (op(e2, e0) = e3),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[765, 990, 983, 982])).
% 0.72/0.83 tff(992,plain,
% 0.72/0.83 (e3 = op(e2, e0)),
% 0.72/0.83 inference(symmetry,[status(thm)],[991])).
% 0.72/0.83 tff(993,plain,
% 0.72/0.83 (e3 = op(e2, op(e2, e2))),
% 0.72/0.83 inference(transitivity,[status(thm)],[992, 981, 979, 977])).
% 0.72/0.83 tff(994,plain,
% 0.72/0.83 ((e0 = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.72/0.83 inference(commutativity,[status(thm)],[])).
% 0.72/0.83 tff(995,plain,
% 0.72/0.83 ((op(e2, e2) = e0) <=> (e0 = op(e2, e2))),
% 0.72/0.83 inference(symmetry,[status(thm)],[994])).
% 0.72/0.83 tff(996,plain,
% 0.72/0.83 (e0 = op(e2, e2)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[974, 995])).
% 0.72/0.83 tff(997,plain,
% 0.72/0.83 (op(e2, op(e2, e2)) = e3),
% 0.72/0.83 inference(transitivity,[status(thm)],[976, 978, 980, 991])).
% 0.72/0.83 tff(998,plain,
% 0.72/0.83 (op(e2, op(e2, op(e2, e2))) = op(e2, e3)),
% 0.72/0.83 inference(monotonicity,[status(thm)],[997])).
% 0.72/0.83 tff(999,plain,
% 0.72/0.83 (op(e2, e3) = op(e2, op(e2, op(e2, e2)))),
% 0.72/0.83 inference(symmetry,[status(thm)],[998])).
% 0.72/0.83 tff(1000,plain,
% 0.72/0.83 (e1 = op(e2, op(e2, op(e2, e2)))),
% 0.72/0.83 inference(transitivity,[status(thm)],[928, 999])).
% 0.72/0.83 tff(1001,plain,
% 0.72/0.83 ((~(~((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2))))))) <=> ((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(1002,plain,
% 0.72/0.83 (((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2))))))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(1003,plain,
% 0.72/0.83 ((~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2)))))))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1002])).
% 0.72/0.83 tff(1004,plain,
% 0.72/0.83 ((~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2)))))),
% 0.72/0.83 inference(transitivity,[status(thm)],[1003, 1001])).
% 0.72/0.83 tff(1005,plain,
% 0.72/0.83 ((~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(1006,plain,
% 0.72/0.83 ((~(((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2))) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.72/0.83 inference(rewrite,[status(thm)],[])).
% 0.72/0.83 tff(1007,axiom,(~(((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2))) & (e1 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax22')).
% 0.72/0.83 tff(1008,plain,
% 0.72/0.83 (~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.72/0.83 tff(1009,plain,
% 0.72/0.83 (~((e3 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[1008, 1005])).
% 0.72/0.83 tff(1010,plain,
% 0.72/0.83 ((~(e1 = op(e2, op(e2, op(e2, e2))))) | (~(e0 = op(e2, e2))) | (~(e3 = op(e2, op(e2, e2))))),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[1009, 1004])).
% 0.72/0.83 tff(1011,plain,
% 0.72/0.83 ($false),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[1010, 1000, 996, 993])).
% 0.72/0.83 tff(1012,plain,((op(e3, e3) = e1) | (~(op(e0, e3) = e0)) | (~(op(e1, e0) = e2)) | (op(e3, e2) = e0) | (op(e1, e0) = e1) | (op(e1, e3) = e1) | (op(e2, e0) = e0) | (op(e2, e0) = e2) | (op(e3, e0) = e1) | (op(e3, e2) = e1) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.83 tff(1013,plain,
% 0.72/0.83 (op(e3, e3) = e1),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[1012, 862, 879, 912, 870, 87, 907, 903, 899, 895, 121])).
% 0.72/0.83 tff(1014,plain,
% 0.72/0.83 (e1 = op(e3, e3)),
% 0.72/0.83 inference(symmetry,[status(thm)],[1013])).
% 0.72/0.83 tff(1015,plain,
% 0.72/0.83 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 0.72/0.83 inference(monotonicity,[status(thm)],[846])).
% 0.72/0.83 tff(1016,plain,
% 0.72/0.83 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1015])).
% 0.72/0.83 tff(1017,plain,
% 0.72/0.83 (~(op(e1, e1) = e3)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[619, 1016])).
% 0.72/0.83 tff(1018,plain,
% 0.72/0.83 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[863])).
% 0.72/0.83 tff(1019,plain,
% 0.72/0.83 ((op(e2, e3) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.72/0.83 inference(transitivity,[status(thm)],[1018, 925])).
% 0.72/0.83 tff(1020,plain,
% 0.72/0.83 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.72/0.83 inference(symmetry,[status(thm)],[1019])).
% 0.72/0.83 tff(1021,plain,
% 0.72/0.83 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1020])).
% 0.72/0.83 tff(1022,plain,
% 0.72/0.83 (~(op(e2, e3) = e0)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[964, 1021])).
% 0.72/0.83 tff(1023,plain,
% 0.72/0.83 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[846])).
% 0.72/0.83 tff(1024,plain,
% 0.72/0.83 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.72/0.83 inference(transitivity,[status(thm)],[1023, 112])).
% 0.72/0.83 tff(1025,plain,
% 0.72/0.83 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1024])).
% 0.72/0.83 tff(1026,plain,
% 0.72/0.83 (~(op(e2, e3) = e3)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[118, 1025])).
% 0.72/0.83 tff(1027,plain,
% 0.72/0.83 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1014])).
% 0.72/0.83 tff(1028,plain,
% 0.72/0.83 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e1)),
% 0.72/0.83 inference(symmetry,[status(thm)],[1027])).
% 0.72/0.83 tff(1029,plain,
% 0.72/0.83 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e1))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1028])).
% 0.72/0.83 tff(1030,plain,
% 0.72/0.83 (~(op(e2, e3) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[368, 1029])).
% 0.72/0.83 tff(1031,plain,
% 0.72/0.83 (op(e2, e3) = e2),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[206, 1030, 1026, 1022])).
% 0.72/0.83 tff(1032,plain,
% 0.72/0.83 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1014])).
% 0.72/0.83 tff(1033,plain,
% 0.72/0.83 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 0.72/0.83 inference(symmetry,[status(thm)],[1032])).
% 0.72/0.83 tff(1034,plain,
% 0.72/0.83 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 0.72/0.83 inference(monotonicity,[status(thm)],[1033])).
% 0.72/0.83 tff(1035,plain,
% 0.72/0.83 (~(op(e3, e1) = e1)),
% 0.72/0.83 inference(modus_ponens,[status(thm)],[437, 1034])).
% 0.72/0.83 tff(1036,plain,
% 0.72/0.83 (op(e3, e1) = e2),
% 0.72/0.83 inference(unit_resolution,[status(thm)],[446, 1035, 854, 886])).
% 0.72/0.84 tff(1037,plain,
% 0.72/0.84 (op(op(e3, e1), e3) = op(e2, e3)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1036])).
% 0.72/0.84 tff(1038,plain,
% 0.72/0.84 (op(op(e3, e1), e3) = e2),
% 0.72/0.84 inference(transitivity,[status(thm)],[1037, 1031])).
% 0.72/0.84 tff(1039,plain,
% 0.72/0.84 ((op(op(e3, e1), e3) = e1) <=> (e2 = op(e3, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1038, 1014])).
% 0.72/0.84 tff(1040,plain,
% 0.72/0.84 ((op(op(e3, e1), e3) = e1) <=> (op(e3, e3) = e2)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1039, 565])).
% 0.72/0.84 tff(1041,plain,
% 0.72/0.84 ((op(e3, e3) = e2) <=> (op(op(e3, e1), e3) = e1)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1040])).
% 0.72/0.84 tff(1042,plain,
% 0.72/0.84 ((~(op(e3, e3) = e2)) <=> (~(op(op(e3, e1), e3) = e1))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1041])).
% 0.72/0.84 tff(1043,plain,
% 0.72/0.84 (op(e1, op(e0, e3)) = op(e1, e0)),
% 0.72/0.84 inference(symmetry,[status(thm)],[866])).
% 0.72/0.84 tff(1044,plain,
% 0.72/0.84 (op(e1, op(e0, e3)) = e2),
% 0.72/0.84 inference(transitivity,[status(thm)],[1043, 879])).
% 0.72/0.84 tff(1045,plain,
% 0.72/0.84 ((op(e1, op(e0, e3)) = e1) <=> (e2 = op(e3, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1044, 1014])).
% 0.72/0.84 tff(1046,plain,
% 0.72/0.84 ((op(e1, op(e0, e3)) = e1) <=> (op(e3, e3) = e2)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1045, 565])).
% 0.72/0.84 tff(1047,plain,
% 0.72/0.84 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e3, e3) = e2))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1046])).
% 0.72/0.84 tff(1048,plain,
% 0.72/0.84 (~(op(e3, e3) = e2)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[652, 1047])).
% 0.72/0.84 tff(1049,plain,
% 0.72/0.84 (~(op(op(e3, e1), e3) = e1)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1048, 1042])).
% 0.72/0.84 tff(1050,plain,
% 0.72/0.84 (((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))) | (op(op(e3, e1), e3) = e1)),
% 0.72/0.84 inference(tautology,[status(thm)],[])).
% 0.72/0.84 tff(1051,plain,
% 0.72/0.84 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[1050, 1049])).
% 0.72/0.84 tff(1052,plain,
% 0.72/0.84 (~(op(e1, e3) = e1)),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.72/0.84 tff(1053,plain,
% 0.72/0.84 (op(e2, e3) = e1),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[151, 926, 1052, 121])).
% 0.72/0.84 tff(1054,plain,
% 0.72/0.84 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1053])).
% 0.72/0.84 tff(1055,plain,
% 0.72/0.84 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1054, 18])).
% 0.72/0.84 tff(1056,plain,
% 0.72/0.84 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1055])).
% 0.72/0.84 tff(1057,plain,
% 0.72/0.84 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1056])).
% 0.72/0.84 tff(1058,plain,
% 0.72/0.84 (~(op(e2, e3) = e0)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[26, 1057])).
% 0.72/0.84 tff(1059,plain,
% 0.72/0.84 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1053])).
% 0.72/0.84 tff(1060,plain,
% 0.72/0.84 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1059])).
% 0.72/0.84 tff(1061,plain,
% 0.72/0.84 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1060])).
% 0.72/0.84 tff(1062,plain,
% 0.72/0.84 (~(op(e2, e3) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[303, 1061])).
% 0.72/0.84 tff(1063,assumption,(~(op(e2, e3) = e0)), introduced(assumption)).
% 0.72/0.84 tff(1064,plain,
% 0.72/0.84 (((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1065,plain,
% 0.72/0.84 ((((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1066,plain,
% 0.72/0.84 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1067,plain,
% 0.72/0.84 (((((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))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1066])).
% 0.72/0.84 tff(1068,plain,
% 0.72/0.84 (((((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))),
% 0.72/0.84 inference(transitivity,[status(thm)],[1067, 1065])).
% 0.72/0.84 tff(1069,plain,
% 0.72/0.84 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)),
% 0.72/0.84 inference(and_elim,[status(thm)],[93])).
% 0.72/0.84 tff(1070,plain,
% 0.72/0.84 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.72/0.84 tff(1071,plain,
% 0.72/0.84 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1070, 1064])).
% 0.72/0.84 tff(1072,plain,
% 0.72/0.84 (op(e3, e3) = e2),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[1071, 468, 656, 926])).
% 0.72/0.84 tff(1073,plain,
% 0.72/0.84 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1072])).
% 0.72/0.84 tff(1074,plain,
% 0.72/0.84 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1073])).
% 0.72/0.84 tff(1075,plain,
% 0.72/0.84 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = op(e3, e3)))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1076,plain,
% 0.72/0.84 (~(op(e0, e3) = op(e3, e3))),
% 0.72/0.84 inference(and_elim,[status(thm)],[60])).
% 0.72/0.84 tff(1077,plain,
% 0.72/0.84 (~(op(e0, e3) = op(e3, e3))),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.72/0.84 tff(1078,plain,
% 0.72/0.84 (~(op(e0, e3) = e2)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1077, 1074])).
% 0.72/0.84 tff(1079,plain,
% 0.72/0.84 ((e0 = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.72/0.84 inference(commutativity,[status(thm)],[])).
% 0.72/0.84 tff(1080,assumption,(~(op(e1, e3) = e3)), introduced(assumption)).
% 0.72/0.84 tff(1081,plain,
% 0.72/0.84 (op(e0, e3) = e3),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[480, 468, 1080, 124])).
% 0.72/0.84 tff(1082,plain,
% 0.72/0.84 (e3 = op(e0, e3)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1081])).
% 0.72/0.84 tff(1083,plain,
% 0.72/0.84 ((e0 = e3) <=> (e0 = op(e0, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1082])).
% 0.72/0.84 tff(1084,plain,
% 0.72/0.84 ((e0 = e3) <=> (op(e0, e3) = e0)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1083, 1079])).
% 0.72/0.84 tff(1085,plain,
% 0.72/0.84 ((~(e0 = e3)) <=> (~(op(e0, e3) = e0))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1084])).
% 0.72/0.84 tff(1086,plain,
% 0.72/0.84 (~(op(e0, e3) = e0)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[181, 1085])).
% 0.72/0.84 tff(1087,assumption,(~(op(e0, e3) = e0)), introduced(assumption)).
% 0.72/0.84 tff(1088,plain,
% 0.72/0.84 (op(e0, e3) = e3),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[687, 1087, 121, 79])).
% 0.72/0.84 tff(1089,plain,
% 0.72/0.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1088])).
% 0.72/0.84 tff(1090,plain,
% 0.72/0.84 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 0.72/0.84 inference(symmetry,[status(thm)],[1089])).
% 0.72/0.84 tff(1091,plain,
% 0.72/0.84 (((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1092,plain,
% 0.72/0.84 ((((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1093,plain,
% 0.72/0.84 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1094,plain,
% 0.72/0.84 (((((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))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1093])).
% 0.72/0.84 tff(1095,plain,
% 0.72/0.84 (((((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))),
% 0.72/0.84 inference(transitivity,[status(thm)],[1094, 1092])).
% 0.72/0.84 tff(1096,plain,
% 0.72/0.84 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)),
% 0.72/0.84 inference(and_elim,[status(thm)],[233])).
% 0.72/0.84 tff(1097,plain,
% 0.72/0.84 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.72/0.84 tff(1098,plain,
% 0.72/0.84 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1097, 1091])).
% 0.72/0.84 tff(1099,plain,
% 0.72/0.84 (op(e1, e3) = e0),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[1098, 1087, 656, 1063])).
% 0.72/0.84 tff(1100,plain,
% 0.72/0.84 (e0 = op(e1, e3)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1099])).
% 0.72/0.84 tff(1101,plain,
% 0.72/0.84 (op(e0, e1) = op(op(e1, e3), e1)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1100])).
% 0.72/0.84 tff(1102,plain,
% 0.72/0.84 (op(e0, e1) = e3),
% 0.72/0.84 inference(transitivity,[status(thm)],[1101, 313])).
% 0.72/0.84 tff(1103,plain,
% 0.72/0.84 (op(e0, e1) = op(e0, e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1102, 1090])).
% 0.72/0.84 tff(1104,plain,
% 0.72/0.84 ($false),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[818, 1103])).
% 0.72/0.84 tff(1105,plain,((op(e0, e3) = e0) | (~(op(op(e1, e3), e1) = e3)) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e3, e3) = e0) | (op(e2, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.84 tff(1106,plain,
% 0.72/0.84 ($false),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[1105, 1086, 1078, 121, 313, 656, 1063])).
% 0.72/0.84 tff(1107,plain,((op(e3, e3) = e3) | (op(e0, e3) = e1) | (~(op(op(e1, e3), e1) = e3)) | (op(e3, e3) = e0) | (op(e2, e3) = e0) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.84 tff(1108,plain,
% 0.72/0.84 (op(e3, e3) = e3),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[1107, 1058, 313, 656, 121, 455, 1062, 926])).
% 0.72/0.84 tff(1109,plain,
% 0.72/0.84 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1108])).
% 0.72/0.84 tff(1110,plain,
% 0.72/0.84 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1109])).
% 0.72/0.84 tff(1111,plain,
% 0.72/0.84 (~(op(e0, e3) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1077, 1110])).
% 0.72/0.84 tff(1112,plain,
% 0.72/0.84 ((e3 = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.72/0.84 inference(commutativity,[status(thm)],[])).
% 0.72/0.84 tff(1113,plain,
% 0.72/0.84 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1102])).
% 0.72/0.84 tff(1114,plain,
% 0.72/0.84 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1113, 1112])).
% 0.72/0.84 tff(1115,plain,
% 0.72/0.84 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1114])).
% 0.72/0.84 tff(1116,plain,
% 0.72/0.84 (~(op(e1, e1) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[792, 1115])).
% 0.72/0.84 tff(1117,plain,
% 0.72/0.84 (op(e1, e0) = op(e1, op(e1, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1100])).
% 0.72/0.84 tff(1118,plain,
% 0.72/0.84 (op(e1, op(e1, e3)) = op(e1, e0)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1117])).
% 0.72/0.84 tff(1119,plain,
% 0.72/0.84 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e0) = e3)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1118])).
% 0.72/0.84 tff(1120,plain,
% 0.72/0.84 ((~(op(e1, op(e1, e3)) = e3)) <=> (~(op(e1, e0) = e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1119])).
% 0.72/0.84 tff(1121,plain,
% 0.72/0.84 (~(op(e1, e0) = e3)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[167, 1120])).
% 0.72/0.84 tff(1122,plain,
% 0.72/0.84 (op(e1, e2) = e3),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[247, 1121, 1116, 455])).
% 0.72/0.84 tff(1123,plain,
% 0.72/0.84 ((op(e3, e2) = op(e3, e0)) <=> (op(e3, e0) = op(e3, e2))),
% 0.72/0.84 inference(commutativity,[status(thm)],[])).
% 0.72/0.84 tff(1124,plain,
% 0.72/0.84 (op(e0, e3) = e2),
% 0.72/0.84 inference(unit_resolution,[status(thm)],[687, 1087, 121, 661])).
% 0.72/0.84 tff(1125,plain,
% 0.72/0.84 (e2 = op(e0, e3)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1124])).
% 0.72/0.84 tff(1126,plain,
% 0.72/0.84 (e2 = op(e3, e0)),
% 0.72/0.84 inference(transitivity,[status(thm)],[1125, 467])).
% 0.72/0.84 tff(1127,plain,
% 0.72/0.84 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e0))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1126])).
% 0.72/0.84 tff(1128,plain,
% 0.72/0.84 ((op(e3, e2) = e2) <=> (op(e3, e0) = op(e3, e2))),
% 0.72/0.84 inference(transitivity,[status(thm)],[1127, 1123])).
% 0.72/0.84 tff(1129,plain,
% 0.72/0.84 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1128])).
% 0.72/0.84 tff(1130,plain,
% 0.72/0.84 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1129])).
% 0.72/0.84 tff(1131,plain,
% 0.72/0.84 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = op(e3, e2)))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1132,plain,
% 0.72/0.84 (~(op(e3, e0) = op(e3, e2))),
% 0.72/0.84 inference(and_elim,[status(thm)],[37])).
% 0.72/0.84 tff(1133,plain,
% 0.72/0.84 (~(op(e3, e0) = op(e3, e2))),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.72/0.84 tff(1134,plain,
% 0.72/0.84 (~(op(e3, e2) = e2)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[1133, 1130])).
% 0.72/0.84 tff(1135,plain,
% 0.72/0.84 (op(e2, e2) = op(e2, op(e0, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1125])).
% 0.72/0.84 tff(1136,plain,
% 0.72/0.84 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1135])).
% 0.72/0.84 tff(1137,plain,
% 0.72/0.84 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1136])).
% 0.72/0.84 tff(1138,plain,
% 0.72/0.84 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e2) = e2))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1137])).
% 0.72/0.84 tff(1139,plain,
% 0.72/0.84 (~(op(e2, e2) = e2)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[651, 1138])).
% 0.72/0.84 tff(1140,plain,
% 0.72/0.84 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1125])).
% 0.72/0.84 tff(1141,plain,
% 0.72/0.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 0.72/0.84 inference(symmetry,[status(thm)],[1140])).
% 0.72/0.84 tff(1142,plain,
% 0.72/0.84 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 0.72/0.84 inference(monotonicity,[status(thm)],[1141])).
% 0.72/0.84 tff(1143,plain,
% 0.72/0.84 (~(op(e0, e2) = e2)),
% 0.72/0.84 inference(modus_ponens,[status(thm)],[918, 1142])).
% 0.72/0.84 tff(1144,plain,
% 0.72/0.84 (((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1145,plain,
% 0.72/0.84 ((((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))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1146,plain,
% 0.72/0.84 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2))),
% 0.72/0.84 inference(rewrite,[status(thm)],[])).
% 0.72/0.84 tff(1147,plain,
% 0.72/0.84 (((((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))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1146])).
% 0.72/0.85 tff(1148,plain,
% 0.72/0.85 (((((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))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1147, 1145])).
% 0.72/0.85 tff(1149,plain,
% 0.72/0.85 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)),
% 0.72/0.85 inference(and_elim,[status(thm)],[237])).
% 0.72/0.85 tff(1150,plain,
% 0.72/0.85 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.72/0.85 tff(1151,plain,
% 0.72/0.85 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1150, 1144])).
% 0.72/0.85 tff(1152,plain,
% 0.72/0.85 (op(e1, e2) = e2),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1151, 1143, 1139, 1134])).
% 0.72/0.85 tff(1153,plain,
% 0.72/0.85 (e2 = op(e1, e2)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1152])).
% 0.72/0.85 tff(1154,plain,
% 0.72/0.85 (op(e0, e3) = e3),
% 0.72/0.85 inference(transitivity,[status(thm)],[1124, 1153, 1122])).
% 0.72/0.85 tff(1155,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[661, 1154])).
% 0.72/0.85 tff(1156,plain,((op(e0, e3) = e0) | (op(e0, e3) = e3) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e1, e3)) = e3) | (~(op(op(e1, e3), e1) = e3)) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e1) | (op(e3, e3) = e0) | (op(e2, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1157,plain,
% 0.72/0.85 (op(e0, e3) = e0),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1156, 1111, 651, 167, 313, 466, 121, 656, 1058])).
% 0.72/0.85 tff(1158,plain,
% 0.72/0.85 (e0 = op(e0, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1157])).
% 0.72/0.85 tff(1159,plain,
% 0.72/0.85 ((op(e1, e3) = e0) <=> (op(e1, e3) = op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1158])).
% 0.72/0.85 tff(1160,plain,
% 0.72/0.85 ((op(e1, e3) = e0) <=> (op(e0, e3) = op(e1, e3))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1159, 654])).
% 0.72/0.85 tff(1161,plain,
% 0.72/0.85 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1160])).
% 0.72/0.85 tff(1162,plain,
% 0.72/0.85 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1161])).
% 0.72/0.85 tff(1163,plain,
% 0.72/0.85 (~(op(e1, e3) = e0)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[64, 1162])).
% 0.72/0.85 tff(1164,plain,
% 0.72/0.85 (op(e1, e3) = e2),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[104, 1163, 1052, 455])).
% 0.72/0.85 tff(1165,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = op(e2, e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1164])).
% 0.72/0.85 tff(1166,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = e1),
% 0.72/0.85 inference(transitivity,[status(thm)],[1165, 1053])).
% 0.72/0.85 tff(1167,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[135, 1166])).
% 0.72/0.85 tff(1168,plain,((op(e3, e3) = e1) | (op(op(e1, e3), e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e1, e3)) = e3) | (~(op(op(e1, e3), e1) = e3)) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e1) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1169,plain,
% 0.72/0.85 (op(e3, e3) = e1),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1168, 656, 651, 167, 313, 466, 121, 135])).
% 0.72/0.85 tff(1170,plain,
% 0.72/0.85 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1169])).
% 0.72/0.85 tff(1171,plain,
% 0.72/0.85 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1170])).
% 0.72/0.85 tff(1172,plain,
% 0.72/0.85 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1171])).
% 0.72/0.85 tff(1173,plain,
% 0.72/0.85 (~(op(e3, e3) = e3)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[303, 1172])).
% 0.72/0.85 tff(1174,plain,
% 0.72/0.85 (~(op(e2, e3) = e0)),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[493, 1173, 167, 466, 1052, 313])).
% 0.72/0.85 tff(1175,plain,
% 0.72/0.85 (op(e0, e3) = e3),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1156, 1063, 651, 167, 313, 466, 121, 656, 1087])).
% 0.72/0.85 tff(1176,plain,
% 0.72/0.85 (e3 = op(e0, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1175])).
% 0.72/0.85 tff(1177,plain,
% 0.72/0.85 (op(e1, e3) = e0),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1098, 1063, 656, 1087])).
% 0.72/0.85 tff(1178,plain,
% 0.72/0.85 (e0 = op(e1, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1177])).
% 0.72/0.85 tff(1179,plain,
% 0.72/0.85 (op(e0, e1) = op(op(e1, e3), e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1178])).
% 0.72/0.85 tff(1180,plain,
% 0.72/0.85 (op(e0, e1) = op(e0, e3)),
% 0.72/0.85 inference(transitivity,[status(thm)],[1179, 313, 1176])).
% 0.72/0.85 tff(1181,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[818, 1180])).
% 0.72/0.85 tff(1182,plain,((op(e2, e3) = e0) | (~(op(op(e1, e3), e1) = e3)) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e1, e3)) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e1) | (op(e3, e3) = e0) | (op(e0, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1183,plain,
% 0.72/0.85 (op(e0, e3) = e0),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1182, 1174, 651, 167, 466, 121, 656, 313])).
% 0.72/0.85 tff(1184,plain,
% 0.72/0.85 (e0 = op(e0, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1183])).
% 0.72/0.85 tff(1185,plain,
% 0.72/0.85 ((e0 = e3) <=> (op(e0, e3) = e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1184])).
% 0.72/0.85 tff(1186,plain,
% 0.72/0.85 ((~(e0 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1185])).
% 0.72/0.85 tff(1187,plain,
% 0.72/0.85 (~(op(e0, e3) = e3)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[181, 1186])).
% 0.72/0.85 tff(1188,plain,
% 0.72/0.85 (op(e2, e3) = e3),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[480, 1187, 455, 1173])).
% 0.72/0.85 tff(1189,plain,
% 0.72/0.85 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1188])).
% 0.72/0.85 tff(1190,plain,
% 0.72/0.85 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 0.72/0.85 inference(symmetry,[status(thm)],[1189])).
% 0.72/0.85 tff(1191,plain,
% 0.72/0.85 ((op(e1, e3) = e0) <=> (op(e1, e3) = op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1184])).
% 0.72/0.85 tff(1192,plain,
% 0.72/0.85 ((op(e1, e3) = e0) <=> (op(e0, e3) = op(e1, e3))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1191, 654])).
% 0.72/0.85 tff(1193,plain,
% 0.72/0.85 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1192])).
% 0.72/0.85 tff(1194,plain,
% 0.72/0.85 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1193])).
% 0.72/0.85 tff(1195,plain,
% 0.72/0.85 (~(op(e1, e3) = e0)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[64, 1194])).
% 0.72/0.85 tff(1196,plain,
% 0.72/0.85 (op(e1, e3) = e2),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[104, 1195, 1052, 455])).
% 0.72/0.85 tff(1197,plain,
% 0.72/0.85 (e2 = op(e1, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1196])).
% 0.72/0.85 tff(1198,plain,
% 0.72/0.85 (op(e2, e1) = op(op(e1, e3), e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1197])).
% 0.72/0.85 tff(1199,plain,
% 0.72/0.85 (op(e2, e1) = e3),
% 0.72/0.85 inference(transitivity,[status(thm)],[1198, 313])).
% 0.72/0.85 tff(1200,plain,
% 0.72/0.85 (op(e2, e1) = op(e2, e3)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1199, 1190])).
% 0.72/0.85 tff(1201,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[197, 1200])).
% 0.72/0.85 tff(1202,plain,((op(e3, e3) = e0) | (~(op(op(e1, e3), e1) = e3)) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e1, e3)) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e1) | (op(op(e1, e3), e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1203,plain,
% 0.72/0.85 (op(e3, e3) = e0),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1202, 121, 651, 167, 466, 313, 135])).
% 0.72/0.85 tff(1204,plain,
% 0.72/0.85 (e0 = op(e3, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1203])).
% 0.72/0.85 tff(1205,plain,
% 0.72/0.85 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1204])).
% 0.72/0.85 tff(1206,plain,
% 0.72/0.85 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1205])).
% 0.72/0.85 tff(1207,plain,
% 0.72/0.85 (~(op(e3, e3) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[26, 1206])).
% 0.72/0.85 tff(1208,plain,
% 0.72/0.85 (op(e2, e3) = e1),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[151, 1207, 1052, 121])).
% 0.72/0.85 tff(1209,plain,
% 0.72/0.85 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1203])).
% 0.72/0.85 tff(1210,plain,
% 0.72/0.85 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1209])).
% 0.72/0.85 tff(1211,plain,
% 0.72/0.85 (~(op(e1, e3) = e0)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[571, 1210])).
% 0.72/0.85 tff(1212,plain,
% 0.72/0.85 (op(e1, e3) = e2),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[104, 1211, 1052, 455])).
% 0.72/0.85 tff(1213,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = op(e2, e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1212])).
% 0.72/0.85 tff(1214,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = e1),
% 0.72/0.85 inference(transitivity,[status(thm)],[1213, 1208])).
% 0.72/0.85 tff(1215,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[135, 1214])).
% 0.72/0.85 tff(1216,plain,((op(e0, e3) = e1) | (op(op(e1, e3), e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e1, e3)) = e3) | (~(op(e3, e0) = op(e0, e3))) | (~(op(op(e1, e3), e1) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1217,plain,
% 0.72/0.85 (op(e0, e3) = e1),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1216, 131, 651, 163, 466, 161])).
% 0.72/0.85 tff(1218,plain,
% 0.72/0.85 (e1 = op(e0, e3)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1217])).
% 0.72/0.85 tff(1219,assumption,(op(e1, e3) = e0), introduced(assumption)).
% 0.72/0.85 tff(1220,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = op(e0, e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1219])).
% 0.72/0.85 tff(1221,plain,
% 0.72/0.85 (op(op(e1, e3), e3) = e1),
% 0.72/0.85 inference(transitivity,[status(thm)],[1220, 19])).
% 0.72/0.85 tff(1222,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[135, 1221])).
% 0.72/0.85 tff(1223,plain,((~(op(e1, e3) = e0)) | (op(op(e1, e3), e3) = e1) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1224,plain,
% 0.72/0.85 (~(op(e1, e3) = e0)),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1223, 131, 1217])).
% 0.72/0.85 tff(1225,plain,
% 0.72/0.85 (op(e1, e3) = e2),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[104, 1224, 138, 170])).
% 0.72/0.85 tff(1226,plain,
% 0.72/0.85 (op(op(e1, e3), e1) = op(e2, op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1225, 1218])).
% 0.72/0.85 tff(1227,plain,
% 0.72/0.85 (op(e2, op(e0, e3)) = op(op(e1, e3), e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1226])).
% 0.72/0.85 tff(1228,plain,
% 0.72/0.85 (op(e2, op(e0, e3)) = op(e2, e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1217])).
% 0.72/0.85 tff(1229,plain,
% 0.72/0.85 (op(e2, e1) = op(e2, op(e0, e3))),
% 0.72/0.85 inference(symmetry,[status(thm)],[1228])).
% 0.72/0.85 tff(1230,plain,
% 0.72/0.85 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1218])).
% 0.72/0.85 tff(1231,plain,
% 0.72/0.85 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1230])).
% 0.72/0.85 tff(1232,plain,
% 0.72/0.85 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1231])).
% 0.72/0.85 tff(1233,plain,
% 0.72/0.85 (~(op(e0, e1) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[818, 1232])).
% 0.72/0.85 tff(1234,plain,
% 0.72/0.85 (e1 = op(e3, e0)),
% 0.72/0.85 inference(transitivity,[status(thm)],[1218, 467])).
% 0.72/0.85 tff(1235,plain,
% 0.72/0.85 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e0))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1234])).
% 0.72/0.85 tff(1236,plain,
% 0.72/0.85 ((op(e3, e1) = e1) <=> (op(e3, e0) = op(e3, e1))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1235, 881])).
% 0.72/0.85 tff(1237,plain,
% 0.72/0.85 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1236])).
% 0.72/0.85 tff(1238,plain,
% 0.72/0.85 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1237])).
% 0.72/0.85 tff(1239,plain,
% 0.72/0.85 (~(op(e3, e1) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[580, 1238])).
% 0.72/0.85 tff(1240,plain,
% 0.72/0.85 (op(e1, e1) = op(e1, op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1218])).
% 0.72/0.85 tff(1241,plain,
% 0.72/0.85 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1240])).
% 0.72/0.85 tff(1242,plain,
% 0.72/0.85 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e1) = e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1241])).
% 0.72/0.85 tff(1243,plain,
% 0.72/0.85 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e1) = e1))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1242])).
% 0.72/0.85 tff(1244,plain,
% 0.72/0.85 (~(op(e1, e1) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[652, 1243])).
% 0.72/0.85 tff(1245,plain,
% 0.72/0.85 (((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))),
% 0.72/0.85 inference(rewrite,[status(thm)],[])).
% 0.72/0.85 tff(1246,plain,
% 0.72/0.85 ((((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))),
% 0.72/0.85 inference(rewrite,[status(thm)],[])).
% 0.72/0.85 tff(1247,plain,
% 0.72/0.85 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1))),
% 0.72/0.85 inference(rewrite,[status(thm)],[])).
% 0.72/0.85 tff(1248,plain,
% 0.72/0.85 (((((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))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1247])).
% 0.72/0.85 tff(1249,plain,
% 0.72/0.85 (((((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))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.72/0.85 tff(1250,plain,
% 0.72/0.85 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)),
% 0.72/0.85 inference(and_elim,[status(thm)],[287])).
% 0.72/0.85 tff(1251,plain,
% 0.72/0.85 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.72/0.85 tff(1252,plain,
% 0.72/0.85 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1251, 1245])).
% 0.72/0.85 tff(1253,plain,
% 0.72/0.85 (op(e2, e1) = e1),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1252, 1244, 1239, 1233])).
% 0.72/0.85 tff(1254,plain,
% 0.72/0.85 (e1 = op(e2, e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1253])).
% 0.72/0.85 tff(1255,plain,
% 0.72/0.85 (op(e0, e3) = e3),
% 0.72/0.85 inference(transitivity,[status(thm)],[1217, 1254, 1229, 1227, 161])).
% 0.72/0.85 tff(1256,plain,
% 0.72/0.85 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1218])).
% 0.72/0.85 tff(1257,plain,
% 0.72/0.85 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1256])).
% 0.72/0.85 tff(1258,plain,
% 0.72/0.85 (~(op(e0, e3) = e3)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[303, 1257])).
% 0.72/0.85 tff(1259,plain,
% 0.72/0.85 ($false),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1258, 1255])).
% 0.72/0.85 tff(1260,plain,(((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e1, op(e0, e3)) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e2, op(e0, e3)) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.85 tff(1261,plain,
% 0.72/0.85 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[1260, 652, 466, 651])).
% 0.72/0.85 tff(1262,plain,
% 0.72/0.85 ((e3 = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.72/0.85 inference(commutativity,[status(thm)],[])).
% 0.72/0.85 tff(1263,plain,
% 0.72/0.85 (op(e2, e1) = op(op(e1, e0), e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[975])).
% 0.72/0.85 tff(1264,plain,
% 0.72/0.85 (op(op(e1, e0), e1) = op(e2, e1)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1263])).
% 0.72/0.85 tff(1265,plain,
% 0.72/0.85 (op(e2, op(e3, e3)) = op(op(e1, e0), e1)),
% 0.72/0.85 inference(monotonicity,[status(thm)],[975, 305])).
% 0.72/0.85 tff(1266,assumption,(~(op(e1, e1) = e1)), introduced(assumption)).
% 0.72/0.85 tff(1267,plain,
% 0.72/0.85 (op(e1, e2) = e1),
% 0.72/0.85 inference(unit_resolution,[status(thm)],[954, 1266, 929, 87])).
% 0.72/0.85 tff(1268,plain,
% 0.72/0.85 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1267])).
% 0.72/0.85 tff(1269,plain,
% 0.72/0.85 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.72/0.85 inference(transitivity,[status(thm)],[1268, 316])).
% 0.72/0.85 tff(1270,plain,
% 0.72/0.85 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1269])).
% 0.72/0.85 tff(1271,plain,
% 0.72/0.85 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = op(e2, e2)))),
% 0.72/0.85 inference(rewrite,[status(thm)],[])).
% 0.72/0.85 tff(1272,plain,
% 0.72/0.85 (~(op(e1, e2) = op(e2, e2))),
% 0.72/0.85 inference(and_elim,[status(thm)],[217])).
% 0.72/0.85 tff(1273,plain,
% 0.72/0.85 (~(op(e1, e2) = op(e2, e2))),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.72/0.85 tff(1274,plain,
% 0.72/0.85 (~(op(e2, e2) = e1)),
% 0.72/0.85 inference(modus_ponens,[status(thm)],[1273, 1270])).
% 0.72/0.85 tff(1275,assumption,((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))), introduced(assumption)).
% 0.72/0.85 tff(1276,plain,
% 0.72/0.85 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[772])).
% 0.72/0.85 tff(1277,plain,
% 0.72/0.85 ((op(e2, e3) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.72/0.85 inference(transitivity,[status(thm)],[1276, 925])).
% 0.72/0.85 tff(1278,plain,
% 0.72/0.85 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.72/0.85 inference(symmetry,[status(thm)],[1277])).
% 0.72/0.85 tff(1279,plain,
% 0.72/0.85 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.72/0.85 inference(monotonicity,[status(thm)],[1278])).
% 0.72/0.85 tff(1280,plain,
% 0.72/0.85 (~(op(e2, e3) = e0)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[964, 1279])).
% 0.76/0.86 tff(1281,plain,
% 0.76/0.86 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[306])).
% 0.76/0.86 tff(1282,plain,
% 0.76/0.86 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e1)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1281])).
% 0.76/0.86 tff(1283,plain,
% 0.76/0.86 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e1))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1282])).
% 0.76/0.86 tff(1284,plain,
% 0.76/0.86 (~(op(e2, e3) = e1)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[368, 1283])).
% 0.76/0.86 tff(1285,plain,
% 0.76/0.86 (op(e2, e3) = e2),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[206, 1284, 124, 1280])).
% 0.76/0.86 tff(1286,plain,
% 0.76/0.86 (op(op(e2, e3), e3) = op(e2, e3)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1285])).
% 0.76/0.86 tff(1287,plain,
% 0.76/0.86 (op(op(e2, e3), e3) = e2),
% 0.76/0.86 inference(transitivity,[status(thm)],[1286, 1285])).
% 0.76/0.86 tff(1288,plain,
% 0.76/0.86 (((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))) | (~(op(op(e2, e3), e3) = e2))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1289,plain,
% 0.76/0.86 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1288, 1287])).
% 0.76/0.86 tff(1290,plain,
% 0.76/0.86 ((e0 = op(op(e1, e0), e1)) <=> (op(op(e1, e0), e1) = e0)),
% 0.76/0.86 inference(commutativity,[status(thm)],[])).
% 0.76/0.86 tff(1291,assumption,(~(op(e1, e1) = e3)), introduced(assumption)).
% 0.76/0.86 tff(1292,plain,
% 0.76/0.86 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[975])).
% 0.76/0.86 tff(1293,plain,
% 0.76/0.86 ((op(e1, e1) = e2) <=> (op(e1, e0) = op(e1, e1))),
% 0.76/0.86 inference(transitivity,[status(thm)],[1292, 710])).
% 0.76/0.86 tff(1294,plain,
% 0.76/0.86 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1293])).
% 0.76/0.86 tff(1295,plain,
% 0.76/0.86 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1294])).
% 0.76/0.86 tff(1296,plain,
% 0.76/0.86 (~(op(e1, e1) = e2)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[737, 1295])).
% 0.76/0.86 tff(1297,plain,
% 0.76/0.86 (op(e1, e1) = e0),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[630, 1266, 1296, 1291])).
% 0.76/0.86 tff(1298,plain,
% 0.76/0.86 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(op(e1, e0), e1))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1297, 1263])).
% 0.76/0.86 tff(1299,plain,
% 0.76/0.86 ((op(e1, e1) = op(e2, e1)) <=> (op(op(e1, e0), e1) = e0)),
% 0.76/0.86 inference(transitivity,[status(thm)],[1298, 1290])).
% 0.76/0.86 tff(1300,plain,
% 0.76/0.86 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(op(e1, e0), e1) = e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1299])).
% 0.76/0.86 tff(1301,plain,
% 0.76/0.86 (~(op(op(e1, e0), e1) = e0)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[225, 1300])).
% 0.76/0.86 tff(1302,plain,
% 0.76/0.86 (((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))) | (op(op(e1, e0), e1) = e0)),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1303,plain,
% 0.76/0.86 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1302, 1301])).
% 0.76/0.86 tff(1304,assumption,((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))), introduced(assumption)).
% 0.76/0.86 tff(1305,plain,
% 0.76/0.86 ((op(e1, e2) = op(e1, e0)) <=> (op(e1, e0) = op(e1, e2))),
% 0.76/0.86 inference(commutativity,[status(thm)],[])).
% 0.76/0.86 tff(1306,plain,
% 0.76/0.86 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[975])).
% 0.76/0.86 tff(1307,plain,
% 0.76/0.86 ((op(e1, e2) = e2) <=> (op(e1, e0) = op(e1, e2))),
% 0.76/0.86 inference(transitivity,[status(thm)],[1306, 1305])).
% 0.76/0.86 tff(1308,plain,
% 0.76/0.86 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1307])).
% 0.76/0.86 tff(1309,plain,
% 0.76/0.86 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1308])).
% 0.76/0.86 tff(1310,plain,
% 0.76/0.86 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = op(e1, e2)))),
% 0.76/0.86 inference(rewrite,[status(thm)],[])).
% 0.76/0.86 tff(1311,plain,
% 0.76/0.86 (~(op(e1, e0) = op(e1, e2))),
% 0.76/0.86 inference(and_elim,[status(thm)],[49])).
% 0.76/0.86 tff(1312,plain,
% 0.76/0.86 (~(op(e1, e0) = op(e1, e2))),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 0.76/0.86 tff(1313,plain,
% 0.76/0.86 (~(op(e1, e2) = e2)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[1312, 1309])).
% 0.76/0.86 tff(1314,plain,
% 0.76/0.86 ((e3 = e2) <=> (e2 = e3)),
% 0.76/0.86 inference(commutativity,[status(thm)],[])).
% 0.76/0.86 tff(1315,plain,
% 0.76/0.86 ((op(e3, e2) = e2) <=> (e3 = e2)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[856])).
% 0.76/0.86 tff(1316,plain,
% 0.76/0.86 ((op(e3, e2) = e2) <=> (e2 = e3)),
% 0.76/0.86 inference(transitivity,[status(thm)],[1315, 1314])).
% 0.76/0.86 tff(1317,plain,
% 0.76/0.86 ((e2 = e3) <=> (op(e3, e2) = e2)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1316])).
% 0.76/0.86 tff(1318,plain,
% 0.76/0.86 ((~(e2 = e3)) <=> (~(op(e3, e2) = e2))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1317])).
% 0.76/0.86 tff(1319,plain,
% 0.76/0.86 ((~(e2 = e3)) <=> (~(e2 = e3))),
% 0.76/0.86 inference(rewrite,[status(thm)],[])).
% 0.76/0.86 tff(1320,plain,
% 0.76/0.86 (~(e2 = e3)),
% 0.76/0.86 inference(and_elim,[status(thm)],[8])).
% 0.76/0.86 tff(1321,plain,
% 0.76/0.86 (~(e2 = e3)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.76/0.86 tff(1322,plain,
% 0.76/0.86 (~(op(e3, e2) = e2)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[1321, 1318])).
% 0.76/0.86 tff(1323,plain,
% 0.76/0.86 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1285])).
% 0.76/0.86 tff(1324,plain,
% 0.76/0.86 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1323])).
% 0.76/0.86 tff(1325,plain,
% 0.76/0.86 (~(op(e2, e2) = e2)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[515, 1324])).
% 0.76/0.86 tff(1326,plain,
% 0.76/0.86 (op(e0, e2) = e2),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1151, 1325, 1322, 1313])).
% 0.76/0.86 tff(1327,plain,
% 0.76/0.86 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[920])).
% 0.76/0.86 tff(1328,plain,
% 0.76/0.86 (op(e0, e2) = op(e1, e0)),
% 0.76/0.86 inference(transitivity,[status(thm)],[1326, 975])).
% 0.76/0.86 tff(1329,plain,
% 0.76/0.86 (op(e0, op(e0, e2)) = op(e0, op(e1, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1328])).
% 0.76/0.86 tff(1330,plain,
% 0.76/0.86 (op(e0, op(e0, e2)) = e2),
% 0.76/0.86 inference(transitivity,[status(thm)],[1329, 1327, 1326])).
% 0.76/0.86 tff(1331,plain,
% 0.76/0.86 (((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))) | (~(op(e0, op(e0, e2)) = e2))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1332,plain,
% 0.76/0.86 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1331, 1330])).
% 0.76/0.86 tff(1333,plain,
% 0.76/0.86 (op(op(e1, e2), e2) = op(e1, op(e1, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1267, 975])).
% 0.76/0.86 tff(1334,plain,
% 0.76/0.86 (op(op(e1, e2), e2) = e1),
% 0.76/0.86 inference(transitivity,[status(thm)],[1333, 921, 1267])).
% 0.76/0.86 tff(1335,plain,
% 0.76/0.86 (((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))) | (~(op(op(e1, e2), e2) = e1))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1336,plain,
% 0.76/0.86 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1335, 1334])).
% 0.76/0.86 tff(1337,plain,
% 0.76/0.86 (op(op(e3, e2), e2) = op(e3, e2)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[856])).
% 0.76/0.86 tff(1338,plain,
% 0.76/0.86 (op(op(e3, e2), e2) = e3),
% 0.76/0.86 inference(transitivity,[status(thm)],[1337, 856])).
% 0.76/0.86 tff(1339,plain,
% 0.76/0.86 (((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))) | (~(op(op(e3, e2), e2) = e3))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1340,plain,
% 0.76/0.86 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1339, 1338])).
% 0.76/0.86 tff(1341,plain,
% 0.76/0.86 (op(e3, e0) = op(e3, op(e0, e3))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[772])).
% 0.76/0.86 tff(1342,plain,
% 0.76/0.86 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1341])).
% 0.76/0.86 tff(1343,plain,
% 0.76/0.86 (op(e3, op(e3, e0)) = op(e3, op(e0, e3))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[466])).
% 0.76/0.86 tff(1344,plain,
% 0.76/0.86 (op(e3, op(e3, e0)) = e0),
% 0.76/0.86 inference(transitivity,[status(thm)],[1343, 1342, 466, 771])).
% 0.76/0.86 tff(1345,plain,
% 0.76/0.86 (((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))) | (~(op(e3, op(e3, e0)) = e0))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1346,plain,
% 0.76/0.86 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1345, 1344])).
% 0.76/0.86 tff(1347,assumption,((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))), introduced(assumption)).
% 0.76/0.86 tff(1348,assumption,(~(op(e2, e2) = e1)), introduced(assumption)).
% 0.76/0.86 tff(1349,assumption,(~(op(e2, e0) = e1)), introduced(assumption)).
% 0.76/0.86 tff(1350,plain,
% 0.76/0.86 (op(e2, e1) = e1),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[345, 1349, 1284, 1348])).
% 0.76/0.86 tff(1351,plain,
% 0.76/0.86 (op(op(e1, e0), e1) = op(e2, e1)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[920])).
% 0.76/0.86 tff(1352,plain,
% 0.76/0.86 (op(e2, e1) = op(e3, e3)),
% 0.76/0.86 inference(transitivity,[status(thm)],[1350, 306])).
% 0.76/0.86 tff(1353,plain,
% 0.76/0.86 (op(e2, op(e2, e1)) = op(e2, op(e3, e3))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1352])).
% 0.76/0.86 tff(1354,plain,
% 0.76/0.86 (op(e2, op(e2, e1)) = e1),
% 0.76/0.86 inference(transitivity,[status(thm)],[1353, 1265, 1351, 1350])).
% 0.76/0.86 tff(1355,plain,
% 0.76/0.86 (((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))) | (~(op(e2, op(e2, e1)) = e1))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1356,plain,
% 0.76/0.86 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1355, 1354])).
% 0.76/0.86 tff(1357,assumption,((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))), introduced(assumption)).
% 0.76/0.86 tff(1358,assumption,((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))), introduced(assumption)).
% 0.76/0.86 tff(1359,plain,
% 0.76/0.86 (op(op(e0, e3), e3) = op(e0, e3)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[771])).
% 0.76/0.86 tff(1360,plain,
% 0.76/0.86 (op(op(e0, e3), e3) = e0),
% 0.76/0.86 inference(transitivity,[status(thm)],[1359, 771])).
% 0.76/0.86 tff(1361,plain,
% 0.76/0.86 (((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))) | (~(op(op(e0, e3), e3) = e0))),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1362,plain,
% 0.76/0.86 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[1361, 1360])).
% 0.76/0.86 tff(1363,assumption,((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))), introduced(assumption)).
% 0.76/0.86 tff(1364,plain,
% 0.76/0.86 ((e3 = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 0.76/0.86 inference(commutativity,[status(thm)],[])).
% 0.76/0.86 tff(1365,plain,
% 0.76/0.86 (op(e3, op(e1, e0)) = op(e3, e2)),
% 0.76/0.86 inference(monotonicity,[status(thm)],[920])).
% 0.76/0.86 tff(1366,plain,
% 0.76/0.86 (e0 = op(e3, e0)),
% 0.76/0.86 inference(transitivity,[status(thm)],[772, 467])).
% 0.76/0.86 tff(1367,plain,
% 0.76/0.86 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1366])).
% 0.76/0.86 tff(1368,plain,
% 0.76/0.86 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1367])).
% 0.76/0.86 tff(1369,plain,
% 0.76/0.86 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1368])).
% 0.76/0.86 tff(1370,plain,
% 0.76/0.86 (~(op(e2, e0) = e0)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[747, 1369])).
% 0.76/0.86 tff(1371,plain,
% 0.76/0.86 (op(e2, e0) = e3),
% 0.76/0.86 inference(unit_resolution,[status(thm)],[765, 1349, 1370, 982])).
% 0.76/0.86 tff(1372,plain,
% 0.76/0.86 (op(op(e2, e0), e2) = op(e3, op(e1, e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1371, 975])).
% 0.76/0.86 tff(1373,plain,
% 0.76/0.86 (op(op(e2, e0), e2) = e3),
% 0.76/0.86 inference(transitivity,[status(thm)],[1372, 1365, 856])).
% 0.76/0.86 tff(1374,plain,
% 0.76/0.86 ((op(op(e2, e0), e2) = e0) <=> (e3 = op(e0, e3))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1373, 772])).
% 0.76/0.86 tff(1375,plain,
% 0.76/0.86 ((op(op(e2, e0), e2) = e0) <=> (op(e0, e3) = e3)),
% 0.76/0.86 inference(transitivity,[status(thm)],[1374, 1364])).
% 0.76/0.86 tff(1376,plain,
% 0.76/0.86 ((op(e0, e3) = e3) <=> (op(op(e2, e0), e2) = e0)),
% 0.76/0.86 inference(symmetry,[status(thm)],[1375])).
% 0.76/0.86 tff(1377,plain,
% 0.76/0.86 ((~(op(e0, e3) = e3)) <=> (~(op(op(e2, e0), e2) = e0))),
% 0.76/0.86 inference(monotonicity,[status(thm)],[1376])).
% 0.76/0.86 tff(1378,plain,
% 0.76/0.86 (~(op(op(e2, e0), e2) = e0)),
% 0.76/0.86 inference(modus_ponens,[status(thm)],[661, 1377])).
% 0.76/0.86 tff(1379,plain,
% 0.76/0.86 (((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))) | (op(op(e2, e0), e2) = e0)),
% 0.76/0.86 inference(tautology,[status(thm)],[])).
% 0.76/0.86 tff(1380,plain,
% 0.76/0.86 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.76/0.87 inference(unit_resolution,[status(thm)],[1379, 1378])).
% 0.76/0.87 tff(1381,plain,
% 0.76/0.87 (((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))))) <=> ((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1382,plain,
% 0.76/0.87 (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))) <=> (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1383,plain,
% 0.76/0.87 (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) <=> (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1384,plain,
% 0.76/0.87 (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) <=> (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1385,plain,
% 0.76/0.87 (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) <=> (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1386,plain,
% 0.76/0.87 (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) <=> (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1387,plain,
% 0.76/0.87 (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) <=> (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1388,plain,
% 0.76/0.87 (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) <=> (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1389,plain,
% 0.76/0.87 (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) <=> (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1390,plain,
% 0.76/0.87 (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) <=> (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1391,plain,
% 0.76/0.87 (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) <=> (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1392,plain,
% 0.76/0.87 (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) <=> (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1393,plain,
% 0.76/0.87 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) <=> (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.87 tff(1394,plain,
% 0.76/0.87 ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) <=> ((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))))),
% 0.76/0.87 inference(monotonicity,[status(thm)],[1393, 1392, 1391, 1390, 1389, 1388, 1387, 1386, 1385, 1384, 1383, 1382])).
% 0.76/0.87 tff(1395,plain,
% 0.76/0.87 ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) <=> ((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))))),
% 0.76/0.87 inference(transitivity,[status(thm)],[1394, 1381])).
% 0.76/0.87 tff(1396,plain,
% 0.76/0.87 ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.76/0.87 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1397,plain,
% 0.76/0.88 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) | $false) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1398,plain,
% 0.76/0.88 ((((~(op(e3, op(e3, e3)) = e3)) & (op(op(e3, e3), e3) = e3)) & (~(op(op(e3, e3), e3) = e3))) <=> $false),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1399,plain,
% 0.76/0.88 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3)))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1400,plain,
% 0.76/0.88 ((((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3))) <=> ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1401,plain,
% 0.76/0.88 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3)))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))))),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1402,plain,
% 0.76/0.88 ((((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3))) <=> ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3)))),
% 0.76/0.88 inference(rewrite,[status(thm)],[])).
% 0.76/0.88 tff(1403,plain,
% 0.76/0.88 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2)))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1404,plain,
% 0.76/0.89 ((((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3))) <=> ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3)))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1405,plain,
% 0.76/0.89 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1406,plain,
% 0.76/0.89 ((((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2))) <=> ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2)))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1407,plain,
% 0.76/0.89 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))) | $false) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1408,plain,
% 0.76/0.89 ((((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2))) <=> $false),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1409,plain,
% 0.76/0.89 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2)))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1410,plain,
% 0.76/0.89 ((((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2))) <=> ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1411,plain,
% 0.76/0.89 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1)))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))))),
% 0.76/0.89 inference(rewrite,[status(thm)],[])).
% 0.76/0.89 tff(1412,plain,
% 0.76/0.89 ((((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2))) <=> ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2)))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1413,plain,
% 0.76/0.90 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1)))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1414,plain,
% 0.76/0.90 ((((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1))) <=> ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1)))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1415,plain,
% 0.76/0.90 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1416,plain,
% 0.76/0.90 ((((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1))) <=> ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1)))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1417,plain,
% 0.76/0.90 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | $false) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1418,plain,
% 0.76/0.90 ((((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1))) <=> $false),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1419,plain,
% 0.76/0.90 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1420,plain,
% 0.76/0.90 ((((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1))) <=> ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1)))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1421,plain,
% 0.76/0.90 (((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0)))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1422,plain,
% 0.76/0.90 ((((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0))) <=> ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1423,plain,
% 0.76/0.90 ((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))))),
% 0.76/0.90 inference(rewrite,[status(thm)],[])).
% 0.76/0.90 tff(1424,plain,
% 0.76/0.90 (((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0)))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(monotonicity,[status(thm)],[1423, 1422])).
% 0.76/0.90 tff(1425,plain,
% 0.76/0.90 (((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(transitivity,[status(thm)],[1424, 1421])).
% 0.76/0.90 tff(1426,plain,
% 0.76/0.90 ((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))))),
% 0.76/0.90 inference(monotonicity,[status(thm)],[1425, 1420])).
% 0.76/0.90 tff(1427,plain,
% 0.76/0.90 ((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(transitivity,[status(thm)],[1426, 1419])).
% 0.76/0.90 tff(1428,plain,
% 0.76/0.90 (((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | $false)),
% 0.76/0.90 inference(monotonicity,[status(thm)],[1427, 1418])).
% 0.76/0.90 tff(1429,plain,
% 0.76/0.90 (((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))))),
% 0.76/0.90 inference(transitivity,[status(thm)],[1428, 1417])).
% 0.76/0.90 tff(1430,plain,
% 0.76/0.90 ((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0)))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))))),
% 0.76/0.91 inference(monotonicity,[status(thm)],[1429, 1416])).
% 0.76/0.91 tff(1431,plain,
% 0.76/0.91 ((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))))),
% 0.76/0.91 inference(transitivity,[status(thm)],[1430, 1415])).
% 0.76/0.91 tff(1432,plain,
% 0.76/0.91 (((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1)))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))))),
% 0.76/0.91 inference(monotonicity,[status(thm)],[1431, 1414])).
% 0.76/0.91 tff(1433,plain,
% 0.76/0.91 (((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))))),
% 0.76/0.91 inference(transitivity,[status(thm)],[1432, 1413])).
% 0.76/0.91 tff(1434,plain,
% 0.76/0.91 ((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1)))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))))),
% 0.76/0.91 inference(monotonicity,[status(thm)],[1433, 1412])).
% 0.76/0.91 tff(1435,plain,
% 0.76/0.91 ((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))))),
% 0.76/0.91 inference(transitivity,[status(thm)],[1434, 1411])).
% 0.76/0.91 tff(1436,plain,
% 0.76/0.91 (((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2)))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))))),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1435, 1410])).
% 0.76/0.92 tff(1437,plain,
% 0.76/0.92 (((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1436, 1409])).
% 0.76/0.92 tff(1438,plain,
% 0.76/0.92 ((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))) | $false)),
% 0.76/0.92 inference(monotonicity,[status(thm)],[1437, 1408])).
% 0.76/0.92 tff(1439,plain,
% 0.76/0.92 ((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))))),
% 0.76/0.92 inference(transitivity,[status(thm)],[1438, 1407])).
% 0.76/0.92 tff(1440,plain,
% 0.76/0.92 (((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2)))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1439, 1406])).
% 0.76/0.93 tff(1441,plain,
% 0.76/0.93 (((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1440, 1405])).
% 0.76/0.93 tff(1442,plain,
% 0.76/0.93 ((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2)))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[1441, 1404])).
% 0.76/0.93 tff(1443,plain,
% 0.76/0.93 ((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))))),
% 0.76/0.93 inference(transitivity,[status(thm)],[1442, 1403])).
% 0.76/0.93 tff(1444,plain,
% 0.76/0.93 (((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3)))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))))),
% 0.84/0.94 inference(monotonicity,[status(thm)],[1443, 1402])).
% 0.84/0.94 tff(1445,plain,
% 0.84/0.94 (((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))))),
% 0.84/0.94 inference(transitivity,[status(thm)],[1444, 1401])).
% 0.84/0.94 tff(1446,plain,
% 0.84/0.94 ((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3)))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.84/0.94 inference(monotonicity,[status(thm)],[1445, 1400])).
% 0.84/0.94 tff(1447,plain,
% 0.84/0.94 ((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.84/0.94 inference(transitivity,[status(thm)],[1446, 1399])).
% 0.84/0.94 tff(1448,plain,
% 0.84/0.94 (((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) | (((~(op(e3, op(e3, e3)) = e3)) & (op(op(e3, e3), e3) = e3)) & (~(op(op(e3, e3), e3) = e3)))) <=> ((((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))) | $false)),
% 0.84/0.94 inference(monotonicity,[status(thm)],[1447, 1398])).
% 0.84/0.94 tff(1449,plain,
% 0.84/0.94 (((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) | (((~(op(e3, op(e3, e3)) = e3)) & (op(op(e3, e3), e3) = e3)) & (~(op(op(e3, e3), e3) = e3)))) <=> (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3))))),
% 0.84/0.95 inference(transitivity,[status(thm)],[1448, 1397])).
% 0.84/0.95 tff(1450,axiom,(((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) | (((~(op(e3, op(e3, e3)) = e3)) & (op(op(e3, e3), e3) = e3)) & (~(op(op(e3, e3), e3) = e3)))) & ((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) | (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax5')).
% 0.84/0.95 tff(1451,plain,
% 0.84/0.95 ((((((((((((((((((~(op(e0, op(e0, e0)) = e0)) & (op(op(e0, e0), e0) = e0)) & (~(op(op(e0, e0), e0) = e0))) | (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1)) & (~(op(op(e0, e1), e1) = e0)))) | (((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2)) & (~(op(op(e0, e2), e2) = e0)))) | (((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3)) & (~(op(op(e0, e3), e3) = e0)))) | (((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0)) & (~(op(op(e1, e0), e0) = e1)))) | (((~(op(e1, op(e1, e1)) = e1)) & (op(op(e1, e1), e1) = e1)) & (~(op(op(e1, e1), e1) = e1)))) | (((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2)) & (~(op(op(e1, e2), e2) = e1)))) | (((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3)) & (~(op(op(e1, e3), e3) = e1)))) | (((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0)) & (~(op(op(e2, e0), e0) = e2)))) | (((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1)) & (~(op(op(e2, e1), e1) = e2)))) | (((~(op(e2, op(e2, e2)) = e2)) & (op(op(e2, e2), e2) = e2)) & (~(op(op(e2, e2), e2) = e2)))) | (((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3)) & (~(op(op(e2, e3), e3) = e2)))) | (((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0)) & (~(op(op(e3, e0), e0) = e3)))) | (((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1)) & (~(op(op(e3, e1), e1) = e3)))) | (((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2)) & (~(op(op(e3, e2), e2) = e3)))) | (((~(op(e3, op(e3, e3)) = e3)) & (op(op(e3, e3), e3) = e3)) & (~(op(op(e3, e3), e3) = e3)))),
% 0.84/0.96 inference(and_elim,[status(thm)],[1450])).
% 0.84/0.96 tff(1452,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1451, 1449])).
% 0.84/0.96 tff(1453,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1452, 1396])).
% 0.84/0.96 tff(1454,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1453, 1396])).
% 0.84/0.96 tff(1455,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1454, 1396])).
% 0.84/0.96 tff(1456,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1455, 1396])).
% 0.84/0.96 tff(1457,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.96 inference(modus_ponens,[status(thm)],[1456, 1396])).
% 0.84/0.96 tff(1458,plain,
% 0.84/0.96 (((~(op(e0, op(e0, e1)) = e1)) & (op(op(e0, e1), e0) = e1) & (~(op(op(e0, e1), e1) = e0))) | ((~(op(e1, op(e1, e0)) = e0)) & (op(op(e1, e0), e1) = e0) & (~(op(op(e1, e0), e0) = e1))) | ((~(op(e0, op(e0, e2)) = e2)) & (op(op(e0, e2), e0) = e2) & (~(op(op(e0, e2), e2) = e0))) | ((~(op(e0, op(e0, e3)) = e3)) & (op(op(e0, e3), e0) = e3) & (~(op(op(e0, e3), e3) = e0))) | ((~(op(e1, op(e1, e2)) = e2)) & (op(op(e1, e2), e1) = e2) & (~(op(op(e1, e2), e2) = e1))) | ((~(op(e1, op(e1, e3)) = e3)) & (op(op(e1, e3), e1) = e3) & (~(op(op(e1, e3), e3) = e1))) | ((~(op(e2, op(e2, e0)) = e0)) & (op(op(e2, e0), e2) = e0) & (~(op(op(e2, e0), e0) = e2))) | ((~(op(e2, op(e2, e1)) = e1)) & (op(op(e2, e1), e2) = e1) & (~(op(op(e2, e1), e1) = e2))) | ((~(op(e2, op(e2, e3)) = e3)) & (op(op(e2, e3), e2) = e3) & (~(op(op(e2, e3), e3) = e2))) | ((~(op(e3, op(e3, e0)) = e0)) & (op(op(e3, e0), e3) = e0) & (~(op(op(e3, e0), e0) = e3))) | ((~(op(e3, op(e3, e1)) = e1)) & (op(op(e3, e1), e3) = e1) & (~(op(op(e3, e1), e1) = e3))) | ((~(op(e3, op(e3, e2)) = e2)) & (op(op(e3, e2), e3) = e2) & (~(op(op(e3, e2), e2) = e3)))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1457, 1396])).
% 0.84/0.97 tff(1459,plain,
% 0.84/0.97 ((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1458, 1395])).
% 0.84/0.97 tff(1460,plain,
% 0.84/0.97 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1459, 1380, 1363, 1362, 1358, 1304, 1357, 1356, 1347, 1346, 1275, 1340])).
% 0.84/0.97 tff(1461,plain,
% 0.84/0.97 (((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))) | (op(op(e0, e1), e0) = e1)),
% 0.84/0.97 inference(tautology,[status(thm)],[])).
% 0.84/0.97 tff(1462,plain,
% 0.84/0.97 (op(op(e0, e1), e0) = e1),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1461, 1460])).
% 0.84/0.97 tff(1463,plain,
% 0.84/0.97 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[856])).
% 0.84/0.97 tff(1464,plain,
% 0.84/0.97 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1463])).
% 0.84/0.97 tff(1465,plain,
% 0.84/0.97 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = op(e3, e2)))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1466,plain,
% 0.84/0.97 (~(op(e0, e2) = op(e3, e2))),
% 0.84/0.97 inference(and_elim,[status(thm)],[218])).
% 0.84/0.97 tff(1467,plain,
% 0.84/0.97 (~(op(e0, e2) = op(e3, e2))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 0.84/0.97 tff(1468,plain,
% 0.84/0.97 (~(op(e0, e2) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1467, 1464])).
% 0.84/0.97 tff(1469,plain,
% 0.84/0.97 (op(e0, op(e0, e3)) = op(e0, e0)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[771])).
% 0.84/0.97 tff(1470,plain,
% 0.84/0.97 (op(e0, e0) = op(e0, op(e0, e3))),
% 0.84/0.97 inference(symmetry,[status(thm)],[1469])).
% 0.84/0.97 tff(1471,plain,
% 0.84/0.97 ((op(e0, e0) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1470])).
% 0.84/0.97 tff(1472,plain,
% 0.84/0.97 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e0) = e3)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1471])).
% 0.84/0.97 tff(1473,plain,
% 0.84/0.97 (((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1474,plain,
% 0.84/0.97 ((((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1475,plain,
% 0.84/0.97 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1476,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1475])).
% 0.84/0.97 tff(1477,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.97 inference(transitivity,[status(thm)],[1476, 1474])).
% 0.84/0.97 tff(1478,plain,
% 0.84/0.97 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)),
% 0.84/0.97 inference(and_elim,[status(thm)],[380])).
% 0.84/0.97 tff(1479,plain,
% 0.84/0.97 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.84/0.97 tff(1480,plain,
% 0.84/0.97 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1479, 1473])).
% 0.84/0.97 tff(1481,plain,
% 0.84/0.97 (op(e0, e0) = e1),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1480, 1349, 931, 929])).
% 0.84/0.97 tff(1482,plain,
% 0.84/0.97 (op(e0, op(e0, e3)) = op(e3, e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1469, 1481, 306])).
% 0.84/0.97 tff(1483,plain,
% 0.84/0.97 ((op(e0, op(e0, e3)) = e3) <=> (op(e3, e3) = e3)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1482])).
% 0.84/0.97 tff(1484,plain,
% 0.84/0.97 ((op(e3, e3) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1483])).
% 0.84/0.97 tff(1485,plain,
% 0.84/0.97 ((op(e3, e3) = e3) <=> (op(e0, e0) = e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1484, 1472])).
% 0.84/0.97 tff(1486,plain,
% 0.84/0.97 ((~(op(e3, e3) = e3)) <=> (~(op(e0, e0) = e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1485])).
% 0.84/0.97 tff(1487,plain,
% 0.84/0.97 (~(op(e0, e0) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[468, 1486])).
% 0.84/0.97 tff(1488,plain,
% 0.84/0.97 (((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1489,plain,
% 0.84/0.97 ((((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1490,plain,
% 0.84/0.97 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1491,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1490])).
% 0.84/0.97 tff(1492,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.97 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.84/0.97 tff(1493,plain,
% 0.84/0.97 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)),
% 0.84/0.97 inference(and_elim,[status(thm)],[377])).
% 0.84/0.97 tff(1494,plain,
% 0.84/0.97 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.84/0.97 tff(1495,plain,
% 0.84/0.97 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1494, 1488])).
% 0.84/0.97 tff(1496,plain,
% 0.84/0.97 (op(e0, e1) = e3),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1495, 1487, 661, 1468])).
% 0.84/0.97 tff(1497,plain,
% 0.84/0.97 (e3 = op(e0, e1)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1496])).
% 0.84/0.97 tff(1498,plain,
% 0.84/0.97 (op(e3, op(e0, e3)) = op(op(e0, e1), e0)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1497, 771])).
% 0.84/0.97 tff(1499,plain,
% 0.84/0.97 (op(e0, e3) = op(e3, e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[467, 1341, 1498, 1462, 306])).
% 0.84/0.97 tff(1500,plain,
% 0.84/0.97 ($false),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1077, 1499])).
% 0.84/0.97 tff(1501,plain,((op(e2, e0) = e1) | (~(op(e3, e0) = op(e0, e3))) | (~(op(e3, e3) = e1)) | (~(op(e0, e3) = e0)) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e0, e3) = e3) | (~(op(e3, e2) = e3)) | (~(op(e1, e0) = e2)) | (op(e3, e3) = e3) | (op(e2, e2) = e1) | (op(e2, e0) = e2) | (op(e3, e0) = e1) | (op(e1, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.97 tff(1502,plain,
% 0.84/0.97 (op(e2, e0) = e1),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1501, 1336, 305, 771, 1332, 466, 1304, 1303, 1289, 1275, 661, 856, 920, 468, 1274, 982, 931, 929])).
% 0.84/0.97 tff(1503,plain,
% 0.84/0.97 (op(e2, e0) = op(e3, e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1502, 306])).
% 0.84/0.97 tff(1504,plain,
% 0.84/0.97 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1503])).
% 0.84/0.97 tff(1505,plain,
% 0.84/0.97 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[856])).
% 0.84/0.97 tff(1506,plain,
% 0.84/0.97 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1505, 159])).
% 0.84/0.97 tff(1507,plain,
% 0.84/0.97 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1506])).
% 0.84/0.97 tff(1508,plain,
% 0.84/0.97 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1507])).
% 0.84/0.97 tff(1509,plain,
% 0.84/0.97 (~(op(e3, e2) = e0)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[181, 1508])).
% 0.84/0.97 tff(1510,plain,
% 0.84/0.97 (op(e1, op(e1, e0)) = op(e3, e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[921, 1267, 306])).
% 0.84/0.97 tff(1511,plain,
% 0.84/0.97 ((op(e1, op(e1, e0)) = e0) <=> (op(e3, e3) = op(e0, e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1510, 772])).
% 0.84/0.97 tff(1512,plain,
% 0.84/0.97 ((op(e1, op(e1, e0)) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 0.84/0.97 inference(transitivity,[status(thm)],[1511, 659])).
% 0.84/0.97 tff(1513,plain,
% 0.84/0.97 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, op(e1, e0)) = e0)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1512])).
% 0.84/0.97 tff(1514,plain,
% 0.84/0.97 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e2) = e0)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1513, 924])).
% 0.84/0.97 tff(1515,plain,
% 0.84/0.97 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e2) = e0))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1514])).
% 0.84/0.97 tff(1516,plain,
% 0.84/0.97 (~(op(e1, e2) = e0)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1077, 1515])).
% 0.84/0.97 tff(1517,plain,
% 0.84/0.97 (op(e2, e2) = e0),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[973, 1516, 919, 1509])).
% 0.84/0.97 tff(1518,plain,
% 0.84/0.97 (op(e2, op(e2, e2)) = op(op(e1, e0), e0)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[975, 1517])).
% 0.84/0.97 tff(1519,plain,
% 0.84/0.97 (op(e2, op(e2, e2)) = op(e2, e0)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1518, 978, 980])).
% 0.84/0.97 tff(1520,plain,
% 0.84/0.97 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e0))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1519])).
% 0.84/0.97 tff(1521,plain,
% 0.84/0.97 (op(e2, op(e2, op(e2, e2))) = op(e2, e1)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1520, 1504, 1265, 1264])).
% 0.84/0.97 tff(1522,plain,
% 0.84/0.97 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (e3 = op(e2, e1))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1521])).
% 0.84/0.97 tff(1523,plain,
% 0.84/0.97 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e1) = e3)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1522, 1262])).
% 0.84/0.97 tff(1524,plain,
% 0.84/0.97 ((~(e3 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e1) = e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1523])).
% 0.84/0.97 tff(1525,plain,
% 0.84/0.97 (e0 = op(e2, e2)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1517, 995])).
% 0.84/0.97 tff(1526,plain,
% 0.84/0.97 ((e1 = op(e2, op(e2, e2))) <=> (e1 = op(e2, e0))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1519])).
% 0.84/0.97 tff(1527,plain,
% 0.84/0.97 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e1)),
% 0.84/0.97 inference(transitivity,[status(thm)],[1526, 16])).
% 0.84/0.97 tff(1528,plain,
% 0.84/0.97 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 0.84/0.97 inference(symmetry,[status(thm)],[1527])).
% 0.84/0.97 tff(1529,plain,
% 0.84/0.97 (e1 = op(e2, op(e2, e2))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1502, 1528])).
% 0.84/0.97 tff(1530,plain,
% 0.84/0.97 ((~(~((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2)))))) <=> ((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2))))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1531,plain,
% 0.84/0.97 (((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2)))))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1532,plain,
% 0.84/0.97 ((~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2))))))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1531])).
% 0.84/0.97 tff(1533,plain,
% 0.84/0.97 ((~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2))))),
% 0.84/0.97 inference(transitivity,[status(thm)],[1532, 1530])).
% 0.84/0.97 tff(1534,plain,
% 0.84/0.97 ((~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1535,plain,
% 0.84/0.97 ((~(((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2))) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1536,axiom,(~(((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2))) & (e3 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax20')).
% 0.84/0.97 tff(1537,plain,
% 0.84/0.97 (~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 0.84/0.97 tff(1538,plain,
% 0.84/0.97 (~((e1 = op(e2, op(e2, e2))) & (e0 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1537, 1534])).
% 0.84/0.97 tff(1539,plain,
% 0.84/0.97 ((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, e2)))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1538, 1533])).
% 0.84/0.97 tff(1540,plain,
% 0.84/0.97 (~(e3 = op(e2, op(e2, op(e2, e2))))),
% 0.84/0.97 inference(unit_resolution,[status(thm)],[1539, 1529, 1525])).
% 0.84/0.97 tff(1541,plain,
% 0.84/0.97 (~(op(e2, e1) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1540, 1524])).
% 0.84/0.97 tff(1542,plain,
% 0.84/0.97 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[856])).
% 0.84/0.97 tff(1543,plain,
% 0.84/0.97 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1542])).
% 0.84/0.97 tff(1544,plain,
% 0.84/0.97 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = op(e3, e2)))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1545,plain,
% 0.84/0.97 (~(op(e2, e2) = op(e3, e2))),
% 0.84/0.97 inference(and_elim,[status(thm)],[215])).
% 0.84/0.97 tff(1546,plain,
% 0.84/0.97 (~(op(e2, e2) = op(e3, e2))),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.84/0.97 tff(1547,plain,
% 0.84/0.97 (~(op(e2, e2) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[1546, 1543])).
% 0.84/0.97 tff(1548,plain,
% 0.84/0.97 ((op(e2, e0) = e3) <=> (op(e3, e3) = e3)),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1503])).
% 0.84/0.97 tff(1549,plain,
% 0.84/0.97 ((op(e3, e3) = e3) <=> (op(e2, e0) = e3)),
% 0.84/0.97 inference(symmetry,[status(thm)],[1548])).
% 0.84/0.97 tff(1550,plain,
% 0.84/0.97 ((~(op(e3, e3) = e3)) <=> (~(op(e2, e0) = e3))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1549])).
% 0.84/0.97 tff(1551,plain,
% 0.84/0.97 (~(op(e2, e0) = e3)),
% 0.84/0.97 inference(modus_ponens,[status(thm)],[468, 1550])).
% 0.84/0.97 tff(1552,plain,
% 0.84/0.97 (((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1553,plain,
% 0.84/0.97 ((((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))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1554,plain,
% 0.84/0.97 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3))),
% 0.84/0.97 inference(rewrite,[status(thm)],[])).
% 0.84/0.97 tff(1555,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.97 inference(monotonicity,[status(thm)],[1554])).
% 0.84/0.97 tff(1556,plain,
% 0.84/0.97 (((((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))),
% 0.84/0.98 inference(transitivity,[status(thm)],[1555, 1553])).
% 0.84/0.98 tff(1557,plain,
% 0.84/0.98 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)),
% 0.84/0.98 inference(and_elim,[status(thm)],[236])).
% 0.84/0.98 tff(1558,plain,
% 0.84/0.98 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.84/0.98 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 0.84/0.98 tff(1559,plain,
% 0.84/0.98 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.84/0.98 inference(modus_ponens,[status(thm)],[1558, 1552])).
% 0.84/0.98 tff(1560,plain,
% 0.84/0.98 (op(e2, e1) = e3),
% 0.84/0.98 inference(unit_resolution,[status(thm)],[1559, 1551, 124, 1547])).
% 0.84/0.98 tff(1561,plain,
% 0.84/0.98 ($false),
% 0.84/0.98 inference(unit_resolution,[status(thm)],[1560, 1541])).
% 0.84/0.98 tff(1562,plain,((op(e1, e1) = e1) | (~(op(e3, e3) = e1)) | (~(op(e0, e3) = e0)) | (~(op(e1, e0) = e2)) | (op(e2, e3) = e3) | (op(e3, e3) = e3) | (~(op(e3, e0) = op(e0, e3))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e0, e3) = e3) | (~(op(e3, e2) = e3)) | (op(e2, e0) = e2) | (op(e3, e0) = e1) | (op(e1, e0) = e1) | (op(e1, e1) = e3) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.98 tff(1563,plain,
% 0.84/0.98 (op(e1, e1) = e1),
% 0.84/0.98 inference(unit_resolution,[status(thm)],[1562, 1013, 862, 879, 1026, 850, 466, 1261, 1051, 661, 855, 903, 899, 870, 1017, 87])).
% 0.84/0.98 tff(1564,plain,
% 0.84/0.98 (op(e1, e1) = op(e3, e3)),
% 0.84/0.98 inference(transitivity,[status(thm)],[1563, 1014])).
% 0.84/0.98 tff(1565,plain,
% 0.84/0.98 ((op(e1, e1) = e0) <=> (op(e3, e3) = op(e0, e3))),
% 0.84/0.98 inference(monotonicity,[status(thm)],[1564, 863])).
% 0.84/0.98 tff(1566,plain,
% 0.84/0.98 ((op(e1, e1) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 0.84/0.98 inference(transitivity,[status(thm)],[1565, 659])).
% 0.84/0.98 tff(1567,plain,
% 0.84/0.98 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e1) = e0)),
% 0.84/0.98 inference(symmetry,[status(thm)],[1566])).
% 0.84/0.98 tff(1568,plain,
% 0.84/0.98 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e1) = e0))),
% 0.84/0.98 inference(monotonicity,[status(thm)],[1567])).
% 0.84/0.98 tff(1569,plain,
% 0.84/0.98 (~(op(e1, e1) = e0)),
% 0.84/0.98 inference(modus_ponens,[status(thm)],[1077, 1568])).
% 0.84/0.98 tff(1570,plain,
% 0.84/0.98 (op(e2, e1) = e0),
% 0.84/0.98 inference(unit_resolution,[status(thm)],[292, 1569, 890, 886])).
% 0.84/0.98 tff(1571,plain,
% 0.84/0.98 (op(op(e1, e0), e1) = op(e2, e1)),
% 0.84/0.98 inference(monotonicity,[status(thm)],[879])).
% 0.84/0.98 tff(1572,plain,
% 0.84/0.98 (e2 = op(e1, e0)),
% 0.84/0.98 inference(symmetry,[status(thm)],[879])).
% 0.84/0.98 tff(1573,plain,
% 0.84/0.98 (op(e2, op(e3, e3)) = op(op(e1, e0), e1)),
% 0.84/0.98 inference(monotonicity,[status(thm)],[1572, 1013])).
% 0.84/0.98 tff(1574,plain,
% 0.84/0.98 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e0))),
% 0.84/0.98 inference(monotonicity,[status(thm)],[1572])).
% 0.84/0.98 tff(1575,plain,
% 0.84/0.98 ((op(e1, e2) = e2) <=> (op(e1, e0) = op(e1, e2))),
% 0.84/0.98 inference(transitivity,[status(thm)],[1574, 1305])).
% 0.84/0.98 tff(1576,plain,
% 0.84/0.98 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.84/0.98 inference(symmetry,[status(thm)],[1575])).
% 0.84/0.98 tff(1577,plain,
% 0.84/0.98 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.84/0.98 inference(monotonicity,[status(thm)],[1576])).
% 0.88/0.98 tff(1578,plain,
% 0.88/0.98 (~(op(e1, e2) = e2)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1312, 1577])).
% 0.88/0.98 tff(1579,plain,
% 0.88/0.98 ((op(e3, e2) = e2) <=> (e3 = e2)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[855])).
% 0.88/0.98 tff(1580,plain,
% 0.88/0.98 ((op(e3, e2) = e2) <=> (e2 = e3)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1579, 1314])).
% 0.88/0.98 tff(1581,plain,
% 0.88/0.98 ((e2 = e3) <=> (op(e3, e2) = e2)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1580])).
% 0.88/0.98 tff(1582,plain,
% 0.88/0.98 ((~(e2 = e3)) <=> (~(op(e3, e2) = e2))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1581])).
% 0.88/0.98 tff(1583,plain,
% 0.88/0.98 (~(op(e3, e2) = e2)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1321, 1582])).
% 0.88/0.98 tff(1584,plain,
% 0.88/0.98 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1031])).
% 0.88/0.98 tff(1585,plain,
% 0.88/0.98 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1584])).
% 0.88/0.98 tff(1586,plain,
% 0.88/0.98 (~(op(e2, e2) = e2)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[515, 1585])).
% 0.88/0.98 tff(1587,plain,
% 0.88/0.98 (op(e0, e2) = e2),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1151, 1586, 1583, 1578])).
% 0.88/0.98 tff(1588,plain,
% 0.88/0.98 ((op(e0, e2) = e1) <=> (e2 = op(e3, e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1587, 1014])).
% 0.88/0.98 tff(1589,plain,
% 0.88/0.98 ((op(e0, e2) = e1) <=> (op(e3, e3) = e2)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1588, 565])).
% 0.88/0.98 tff(1590,plain,
% 0.88/0.98 ((op(e3, e3) = e2) <=> (op(e0, e2) = e1)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1589])).
% 0.88/0.98 tff(1591,plain,
% 0.88/0.98 ((~(op(e3, e3) = e2)) <=> (~(op(e0, e2) = e1))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1590])).
% 0.88/0.98 tff(1592,plain,
% 0.88/0.98 (~(op(e0, e2) = e1)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1048, 1591])).
% 0.88/0.98 tff(1593,plain,
% 0.88/0.98 (op(e1, op(e1, e0)) = op(e1, e2)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[879])).
% 0.88/0.98 tff(1594,plain,
% 0.88/0.98 (op(e1, e2) = op(e1, op(e1, e0))),
% 0.88/0.98 inference(symmetry,[status(thm)],[1593])).
% 0.88/0.98 tff(1595,plain,
% 0.88/0.98 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e0)) = e1)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1594])).
% 0.88/0.98 tff(1596,plain,
% 0.88/0.98 ((op(e1, op(e1, e0)) = e1) <=> (op(e1, e2) = e1)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1595])).
% 0.88/0.98 tff(1597,plain,
% 0.88/0.98 ((e1 = op(e1, op(e1, e0))) <=> (op(e1, op(e1, e0)) = e1)),
% 0.88/0.98 inference(commutativity,[status(thm)],[])).
% 0.88/0.98 tff(1598,plain,
% 0.88/0.98 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, op(e1, e0)))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1563, 1594])).
% 0.88/0.98 tff(1599,plain,
% 0.88/0.98 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, op(e1, e0)) = e1)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1598, 1597])).
% 0.88/0.98 tff(1600,plain,
% 0.88/0.98 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1599, 1596])).
% 0.88/0.98 tff(1601,plain,
% 0.88/0.98 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1600])).
% 0.88/0.98 tff(1602,plain,
% 0.88/0.98 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = op(e1, e2)))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1603,plain,
% 0.88/0.98 (~(op(e1, e1) = op(e1, e2))),
% 0.88/0.98 inference(and_elim,[status(thm)],[47])).
% 0.88/0.98 tff(1604,plain,
% 0.88/0.98 (~(op(e1, e1) = op(e1, e2))),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.88/0.98 tff(1605,plain,
% 0.88/0.98 (~(op(e1, e2) = e1)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1604, 1601])).
% 0.88/0.98 tff(1606,plain,
% 0.88/0.98 (((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))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1607,plain,
% 0.88/0.98 ((((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))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1608,plain,
% 0.88/0.98 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1609,plain,
% 0.88/0.98 (((((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))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1608])).
% 0.88/0.98 tff(1610,plain,
% 0.88/0.98 (((((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))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1609, 1607])).
% 0.88/0.98 tff(1611,plain,
% 0.88/0.98 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)),
% 0.88/0.98 inference(and_elim,[status(thm)],[239])).
% 0.88/0.98 tff(1612,plain,
% 0.88/0.98 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 0.88/0.98 tff(1613,plain,
% 0.88/0.98 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1612, 1606])).
% 0.88/0.98 tff(1614,plain,
% 0.88/0.98 (op(e2, e2) = e1),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1613, 1605, 1592, 895])).
% 0.88/0.98 tff(1615,plain,
% 0.88/0.98 (op(e2, e2) = op(e3, e3)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1614, 1014])).
% 0.88/0.98 tff(1616,plain,
% 0.88/0.98 (op(e2, op(e2, e2)) = op(e2, op(e3, e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1615])).
% 0.88/0.98 tff(1617,plain,
% 0.88/0.98 (op(e2, op(e2, e2)) = e0),
% 0.88/0.98 inference(transitivity,[status(thm)],[1616, 1573, 1571, 1570])).
% 0.88/0.98 tff(1618,plain,
% 0.88/0.98 (op(e2, op(e2, op(e2, e2))) = op(op(e1, e0), e0)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1572, 1617])).
% 0.88/0.98 tff(1619,plain,
% 0.88/0.98 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1618, 880, 865])).
% 0.88/0.98 tff(1620,plain,
% 0.88/0.98 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (e3 = op(e2, e0))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1619])).
% 0.88/0.98 tff(1621,plain,
% 0.88/0.98 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e3)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1620, 660])).
% 0.88/0.98 tff(1622,plain,
% 0.88/0.98 ((op(e2, e0) = e3) <=> (e3 = op(e2, op(e2, op(e2, e2))))),
% 0.88/0.98 inference(symmetry,[status(thm)],[1621])).
% 0.88/0.98 tff(1623,plain,
% 0.88/0.98 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[855])).
% 0.88/0.98 tff(1624,plain,
% 0.88/0.98 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1623])).
% 0.88/0.98 tff(1625,plain,
% 0.88/0.98 (~(op(e2, e2) = e3)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1546, 1624])).
% 0.88/0.98 tff(1626,plain,
% 0.88/0.98 (op(e2, e1) = op(e0, e3)),
% 0.88/0.98 inference(transitivity,[status(thm)],[1570, 863])).
% 0.88/0.98 tff(1627,plain,
% 0.88/0.98 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1626])).
% 0.88/0.98 tff(1628,plain,
% 0.88/0.98 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1627])).
% 0.88/0.98 tff(1629,plain,
% 0.88/0.98 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1628])).
% 0.88/0.98 tff(1630,plain,
% 0.88/0.98 (~(op(e2, e1) = e3)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[661, 1629])).
% 0.88/0.98 tff(1631,plain,
% 0.88/0.98 (op(e2, e0) = e3),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1559, 1630, 1026, 1625])).
% 0.88/0.98 tff(1632,plain,
% 0.88/0.98 (e3 = op(e2, op(e2, op(e2, e2)))),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1631, 1622])).
% 0.88/0.98 tff(1633,plain,
% 0.88/0.98 (e1 = op(e2, e2)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1614, 317])).
% 0.88/0.98 tff(1634,plain,
% 0.88/0.98 (op(e2, op(e3, e3)) = op(e2, op(e2, e2))),
% 0.88/0.98 inference(symmetry,[status(thm)],[1616])).
% 0.88/0.98 tff(1635,plain,
% 0.88/0.98 (op(op(e1, e0), e1) = op(e2, op(e3, e3))),
% 0.88/0.98 inference(symmetry,[status(thm)],[1573])).
% 0.88/0.98 tff(1636,plain,
% 0.88/0.98 (op(e2, e1) = op(op(e1, e0), e1)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1571])).
% 0.88/0.98 tff(1637,plain,
% 0.88/0.98 (e0 = op(e2, e1)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1570])).
% 0.88/0.98 tff(1638,plain,
% 0.88/0.98 (e0 = op(e2, op(e2, e2))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1637, 1636, 1635, 1634])).
% 0.88/0.98 tff(1639,plain,
% 0.88/0.98 ((~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2)))))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1640,plain,
% 0.88/0.98 (((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2)))))))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1641,plain,
% 0.88/0.98 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2))))))))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1640])).
% 0.88/0.98 tff(1642,plain,
% 0.88/0.98 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1641, 1639])).
% 0.88/0.98 tff(1643,plain,
% 0.88/0.98 ((~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1644,plain,
% 0.88/0.98 ((~(((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/0.98 inference(rewrite,[status(thm)],[])).
% 0.88/0.98 tff(1645,axiom,(~(((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2))) & (e3 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax18')).
% 0.88/0.98 tff(1646,plain,
% 0.88/0.98 (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.88/0.98 tff(1647,plain,
% 0.88/0.98 (~((e0 = op(e2, op(e2, e2))) & (e1 = op(e2, e2)) & (e3 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1646, 1643])).
% 0.88/0.98 tff(1648,plain,
% 0.88/0.98 ((~(e0 = op(e2, op(e2, e2)))) | (~(e1 = op(e2, e2))) | (~(e3 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1647, 1642])).
% 0.88/0.98 tff(1649,plain,
% 0.88/0.98 (~(e3 = op(e2, op(e2, op(e2, e2))))),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1648, 1638, 1633])).
% 0.88/0.98 tff(1650,plain,
% 0.88/0.98 ($false),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1649, 1632])).
% 0.88/0.98 tff(1651,plain,((op(e0, e3) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e3) = e1) | (op(e1, op(e0, e3)) = e1) | (op(e0, e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3) | (op(op(e1, e3), e1) = e3) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.98 tff(1652,plain,
% 0.88/0.98 (op(e0, e3) = e3),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1651, 87, 466, 652, 121, 651, 650, 655, 80])).
% 0.88/0.98 tff(1653,plain,
% 0.88/0.98 (e3 = op(e0, e3)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1652])).
% 0.88/0.98 tff(1654,plain,
% 0.88/0.98 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e0, e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.98 tff(1655,plain,
% 0.88/0.98 ((op(e3, e3) = e3) <=> (op(e0, e3) = op(e3, e3))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1654, 659])).
% 0.88/0.98 tff(1656,plain,
% 0.88/0.98 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1655])).
% 0.88/0.98 tff(1657,plain,
% 0.88/0.98 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1656])).
% 0.88/0.98 tff(1658,plain,
% 0.88/0.98 (~(op(e3, e3) = e3)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1077, 1657])).
% 0.88/0.98 tff(1659,plain,
% 0.88/0.98 ((op(e3, e3) = op(e1, e3)) <=> (op(e1, e3) = op(e3, e3))),
% 0.88/0.98 inference(commutativity,[status(thm)],[])).
% 0.88/0.98 tff(1660,plain,
% 0.88/0.98 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e0, e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.98 tff(1661,plain,
% 0.88/0.98 ((op(e1, e3) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1660, 654])).
% 0.88/0.98 tff(1662,plain,
% 0.88/0.98 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1661])).
% 0.88/0.98 tff(1663,plain,
% 0.88/0.98 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1662])).
% 0.88/0.98 tff(1664,plain,
% 0.88/0.98 (~(op(e1, e3) = e3)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[64, 1663])).
% 0.88/0.98 tff(1665,plain,
% 0.88/0.98 (op(e1, e3) = e2),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[104, 1664, 80, 87])).
% 0.88/0.98 tff(1666,plain,
% 0.88/0.98 (e2 = op(e1, e3)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1665])).
% 0.88/0.98 tff(1667,plain,
% 0.88/0.98 ((op(e3, e3) = e2) <=> (op(e3, e3) = op(e1, e3))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1666])).
% 0.88/0.98 tff(1668,plain,
% 0.88/0.98 ((op(e3, e3) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1667, 1659])).
% 0.88/0.98 tff(1669,plain,
% 0.88/0.98 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.88/0.98 inference(symmetry,[status(thm)],[1668])).
% 0.88/0.98 tff(1670,plain,
% 0.88/0.98 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1669])).
% 0.88/0.98 tff(1671,plain,
% 0.88/0.98 (~(op(e3, e3) = e2)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[571, 1670])).
% 0.88/0.98 tff(1672,plain,
% 0.88/0.98 (op(e3, e3) = e1),
% 0.88/0.98 inference(unit_resolution,[status(thm)],[1071, 1671, 1658, 656])).
% 0.88/0.98 tff(1673,plain,
% 0.88/0.98 (e1 = op(e3, e3)),
% 0.88/0.98 inference(modus_ponens,[status(thm)],[1672, 658])).
% 0.88/0.98 tff(1674,plain,
% 0.88/0.98 ((op(e1, e3) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 0.88/0.98 inference(commutativity,[status(thm)],[])).
% 0.88/0.98 tff(1675,plain,
% 0.88/0.98 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1672])).
% 0.88/0.98 tff(1676,plain,
% 0.88/0.98 ((e2 = op(e3, op(e3, e3))) <=> (op(e1, e3) = op(e3, e1))),
% 0.88/0.98 inference(monotonicity,[status(thm)],[1666, 1675])).
% 0.88/0.98 tff(1677,plain,
% 0.88/0.98 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = op(e1, e3))),
% 0.88/0.98 inference(transitivity,[status(thm)],[1676, 1674])).
% 0.88/0.99 tff(1678,plain,
% 0.88/0.99 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e3, op(e3, e3)))),
% 0.88/0.99 inference(symmetry,[status(thm)],[1677])).
% 0.88/0.99 tff(1679,plain,
% 0.88/0.99 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1666])).
% 0.88/0.99 tff(1680,plain,
% 0.88/0.99 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1679, 1678])).
% 0.88/0.99 tff(1681,plain,
% 0.88/0.99 ((e2 = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.88/0.99 inference(commutativity,[status(thm)],[])).
% 0.88/0.99 tff(1682,plain,
% 0.88/0.99 ((e2 = e3) <=> (e2 = op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1683,plain,
% 0.88/0.99 ((e2 = e3) <=> (op(e0, e3) = e2)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1682, 1681])).
% 0.88/0.99 tff(1684,plain,
% 0.88/0.99 ((e2 = e3) <=> (op(e3, e0) = e2)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1683, 668])).
% 0.88/0.99 tff(1685,plain,
% 0.88/0.99 ((~(e2 = e3)) <=> (~(op(e3, e0) = e2))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1684])).
% 0.88/0.99 tff(1686,plain,
% 0.88/0.99 (~(op(e3, e0) = e2)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1321, 1685])).
% 0.88/0.99 tff(1687,plain,
% 0.88/0.99 ((op(e2, e3) = op(e1, e3)) <=> (op(e1, e3) = op(e2, e3))),
% 0.88/0.99 inference(commutativity,[status(thm)],[])).
% 0.88/0.99 tff(1688,plain,
% 0.88/0.99 ((e0 = e3) <=> (e0 = op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1689,plain,
% 0.88/0.99 ((e0 = e3) <=> (op(e0, e3) = e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1688, 1079])).
% 0.88/0.99 tff(1690,plain,
% 0.88/0.99 ((~(e0 = e3)) <=> (~(op(e0, e3) = e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1689])).
% 0.88/0.99 tff(1691,plain,
% 0.88/0.99 (~(op(e0, e3) = e0)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[181, 1690])).
% 0.88/0.99 tff(1692,plain,
% 0.88/0.99 (op(e2, e3) = e0),
% 0.88/0.99 inference(unit_resolution,[status(thm)],[1098, 1691, 656, 80])).
% 0.88/0.99 tff(1693,plain,
% 0.88/0.99 (e0 = op(e2, e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1692])).
% 0.88/0.99 tff(1694,plain,
% 0.88/0.99 ((op(e3, e0) = e0) <=> (op(e0, e3) = e0)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[466])).
% 0.88/0.99 tff(1695,plain,
% 0.88/0.99 ((op(e0, e3) = e0) <=> (op(e3, e0) = e0)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1694])).
% 0.88/0.99 tff(1696,plain,
% 0.88/0.99 ((e0 = e3) <=> (op(e3, e0) = e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1689, 1695])).
% 0.88/0.99 tff(1697,plain,
% 0.88/0.99 ((~(e0 = e3)) <=> (~(op(e3, e0) = e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1696])).
% 0.88/0.99 tff(1698,plain,
% 0.88/0.99 (~(op(e3, e0) = e0)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[181, 1697])).
% 0.88/0.99 tff(1699,plain,
% 0.88/0.99 (e3 = op(e3, e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1653, 467])).
% 0.88/0.99 tff(1700,plain,
% 0.88/0.99 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1699])).
% 0.88/0.99 tff(1701,plain,
% 0.88/0.99 ((op(e3, e2) = e3) <=> (op(e3, e0) = op(e3, e2))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1700, 1123])).
% 0.88/0.99 tff(1702,plain,
% 0.88/0.99 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1701])).
% 0.88/0.99 tff(1703,plain,
% 0.88/0.99 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1702])).
% 0.88/0.99 tff(1704,plain,
% 0.88/0.99 (~(op(e3, e2) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1133, 1703])).
% 0.88/0.99 tff(1705,plain,
% 0.88/0.99 (op(e1, op(e1, e3)) = op(e1, e2)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1665])).
% 0.88/0.99 tff(1706,plain,
% 0.88/0.99 (op(e1, e3) = op(e1, op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1707,plain,
% 0.88/0.99 (op(e1, op(e0, e3)) = op(e1, e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1706])).
% 0.88/0.99 tff(1708,plain,
% 0.88/0.99 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1709,plain,
% 0.88/0.99 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1708])).
% 0.88/0.99 tff(1710,plain,
% 0.88/0.99 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1709])).
% 0.88/0.99 tff(1711,plain,
% 0.88/0.99 (~(op(e0, e1) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[818, 1710])).
% 0.88/0.99 tff(1712,plain,
% 0.88/0.99 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1699])).
% 0.88/0.99 tff(1713,plain,
% 0.88/0.99 ((op(e3, e1) = e3) <=> (op(e3, e0) = op(e3, e1))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1712, 881])).
% 0.88/0.99 tff(1714,plain,
% 0.88/0.99 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1713])).
% 0.88/0.99 tff(1715,plain,
% 0.88/0.99 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1714])).
% 0.88/0.99 tff(1716,plain,
% 0.88/0.99 (~(op(e3, e1) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[580, 1715])).
% 0.88/0.99 tff(1717,plain,
% 0.88/0.99 (op(op(e1, e3), e1) = op(e2, e1)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1665])).
% 0.88/0.99 tff(1718,plain,
% 0.88/0.99 (op(e2, e1) = op(op(e1, e3), e1)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1717])).
% 0.88/0.99 tff(1719,plain,
% 0.88/0.99 ((op(e2, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1718])).
% 0.88/0.99 tff(1720,plain,
% 0.88/0.99 ((op(op(e1, e3), e1) = e3) <=> (op(e2, e1) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1719])).
% 0.88/0.99 tff(1721,plain,
% 0.88/0.99 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e2, e1) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1720])).
% 0.88/0.99 tff(1722,plain,
% 0.88/0.99 (~(op(e2, e1) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[655, 1721])).
% 0.88/0.99 tff(1723,plain,
% 0.88/0.99 (((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))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1724,plain,
% 0.88/0.99 ((((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))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1725,plain,
% 0.88/0.99 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1726,plain,
% 0.88/0.99 (((((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))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1725])).
% 0.88/0.99 tff(1727,plain,
% 0.88/0.99 (((((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))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1726, 1724])).
% 0.88/0.99 tff(1728,plain,
% 0.88/0.99 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)),
% 0.88/0.99 inference(and_elim,[status(thm)],[243])).
% 0.88/0.99 tff(1729,plain,
% 0.88/0.99 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 0.88/0.99 tff(1730,plain,
% 0.88/0.99 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1729, 1723])).
% 0.88/0.99 tff(1731,plain,
% 0.88/0.99 (op(e1, e1) = e3),
% 0.88/0.99 inference(unit_resolution,[status(thm)],[1730, 1722, 1716, 1711])).
% 0.88/0.99 tff(1732,plain,
% 0.88/0.99 (op(e1, e1) = op(e0, e3)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1731, 1653])).
% 0.88/0.99 tff(1733,plain,
% 0.88/0.99 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1732])).
% 0.88/0.99 tff(1734,plain,
% 0.88/0.99 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1733, 1707])).
% 0.88/0.99 tff(1735,plain,
% 0.88/0.99 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1734])).
% 0.88/0.99 tff(1736,plain,
% 0.88/0.99 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1735, 1705])).
% 0.88/0.99 tff(1737,plain,
% 0.88/0.99 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1736])).
% 0.88/0.99 tff(1738,plain,
% 0.88/0.99 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1737, 67])).
% 0.88/0.99 tff(1739,plain,
% 0.88/0.99 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1738])).
% 0.88/0.99 tff(1740,plain,
% 0.88/0.99 ((op(e1, e1) = e3) <=> (e3 = op(e1, e1))),
% 0.88/0.99 inference(symmetry,[status(thm)],[1112])).
% 0.88/0.99 tff(1741,plain,
% 0.88/0.99 (e3 = op(e1, e1)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1731, 1740])).
% 0.88/0.99 tff(1742,plain,
% 0.88/0.99 (op(e1, op(e0, e3)) = op(e1, op(e1, e1))),
% 0.88/0.99 inference(symmetry,[status(thm)],[1733])).
% 0.88/0.99 tff(1743,plain,
% 0.88/0.99 (e2 = op(e1, op(e1, e1))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1666, 1706, 1742])).
% 0.88/0.99 tff(1744,plain,
% 0.88/0.99 ((~(~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1)))))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1745,plain,
% 0.88/0.99 (((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1)))))))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1746,plain,
% 0.88/0.99 ((~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1))))))))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1745])).
% 0.88/0.99 tff(1747,plain,
% 0.88/0.99 ((~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1746, 1744])).
% 0.88/0.99 tff(1748,plain,
% 0.88/0.99 ((~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1749,plain,
% 0.88/0.99 ((~(((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1))) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1750,axiom,(~(((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1))) & (e0 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax15')).
% 0.88/0.99 tff(1751,plain,
% 0.88/0.99 (~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 0.88/0.99 tff(1752,plain,
% 0.88/0.99 (~((e2 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1751, 1748])).
% 0.88/0.99 tff(1753,plain,
% 0.88/0.99 ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1752, 1747])).
% 0.88/0.99 tff(1754,plain,
% 0.88/0.99 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 0.88/0.99 inference(unit_resolution,[status(thm)],[1753, 1743, 1741])).
% 0.88/0.99 tff(1755,plain,
% 0.88/0.99 (~(op(e1, e2) = e0)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1754, 1739])).
% 0.88/0.99 tff(1756,plain,
% 0.88/0.99 (op(op(e3, e0), e3) = op(op(e0, e3), e3)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[466])).
% 0.88/0.99 tff(1757,plain,
% 0.88/0.99 ((op(op(e3, e0), e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1756])).
% 0.88/0.99 tff(1758,plain,
% 0.88/0.99 ((op(op(e0, e3), e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1757])).
% 0.88/0.99 tff(1759,plain,
% 0.88/0.99 (op(e3, e3) = op(op(e0, e3), e3)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1760,plain,
% 0.88/0.99 ((op(e3, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1759])).
% 0.88/0.99 tff(1761,plain,
% 0.88/0.99 ((op(e3, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1760, 1758])).
% 0.88/0.99 tff(1762,plain,
% 0.88/0.99 ((~(op(e3, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1761])).
% 0.88/0.99 tff(1763,plain,
% 0.88/0.99 (~(op(op(e3, e0), e3) = e0)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[656, 1762])).
% 0.88/0.99 tff(1764,plain,
% 0.88/0.99 (((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))) | (op(op(e3, e0), e3) = e0)),
% 0.88/0.99 inference(tautology,[status(thm)],[])).
% 0.88/0.99 tff(1765,plain,
% 0.88/0.99 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.88/0.99 inference(unit_resolution,[status(thm)],[1764, 1763])).
% 0.88/0.99 tff(1766,plain,
% 0.88/0.99 (e1 = op(e3, e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1672])).
% 0.88/0.99 tff(1767,plain,
% 0.88/0.99 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1699])).
% 0.88/0.99 tff(1768,plain,
% 0.88/0.99 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1767])).
% 0.88/0.99 tff(1769,plain,
% 0.88/0.99 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1768])).
% 0.88/0.99 tff(1770,plain,
% 0.88/0.99 (~(op(e2, e0) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[747, 1769])).
% 0.88/0.99 tff(1771,plain,
% 0.88/0.99 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1772,plain,
% 0.88/0.99 ((op(e2, e3) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1771, 925])).
% 0.88/0.99 tff(1773,plain,
% 0.88/0.99 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1772])).
% 0.88/0.99 tff(1774,plain,
% 0.88/0.99 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1773])).
% 0.88/0.99 tff(1775,plain,
% 0.88/0.99 (~(op(e2, e3) = e3)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[964, 1774])).
% 0.88/0.99 tff(1776,plain,
% 0.88/0.99 (op(e2, e2) = e3),
% 0.88/0.99 inference(unit_resolution,[status(thm)],[1559, 1722, 1775, 1770])).
% 0.88/0.99 tff(1777,plain,
% 0.88/0.99 (op(e2, e2) = op(e0, e3)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1776, 1653])).
% 0.88/0.99 tff(1778,plain,
% 0.88/0.99 ((op(e2, e2) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1777, 1766])).
% 0.88/0.99 tff(1779,plain,
% 0.88/0.99 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e2) = e1)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1778])).
% 0.88/0.99 tff(1780,plain,
% 0.88/0.99 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e1))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1779])).
% 0.88/0.99 tff(1781,plain,
% 0.88/0.99 (~(op(e2, e2) = e1)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1077, 1780])).
% 0.88/0.99 tff(1782,plain,
% 0.88/0.99 ((e0 = e1) <=> (op(e2, e3) = e1)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1693])).
% 0.88/0.99 tff(1783,plain,
% 0.88/0.99 ((~(e0 = e1)) <=> (~(op(e2, e3) = e1))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1782])).
% 0.88/0.99 tff(1784,plain,
% 0.88/0.99 (~(op(e2, e3) = e1)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[26, 1783])).
% 0.88/0.99 tff(1785,plain,
% 0.88/0.99 (op(e2, op(e2, e3)) = op(e2, e0)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1692])).
% 0.88/0.99 tff(1786,plain,
% 0.88/0.99 (op(e2, e3) = op(e2, op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1653])).
% 0.88/0.99 tff(1787,plain,
% 0.88/0.99 (op(e2, op(e0, e3)) = op(e2, e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1786])).
% 0.88/0.99 tff(1788,plain,
% 0.88/0.99 (op(op(e1, e3), e3) = op(e2, op(e0, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1665, 1653])).
% 0.88/0.99 tff(1789,plain,
% 0.88/0.99 (op(e2, op(e2, e2)) = op(op(e1, e3), e3)),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1666, 1776])).
% 0.88/0.99 tff(1790,plain,
% 0.88/0.99 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1789, 1788, 1787])).
% 0.88/0.99 tff(1791,plain,
% 0.88/0.99 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1790])).
% 0.88/0.99 tff(1792,plain,
% 0.88/0.99 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1791, 1785])).
% 0.88/0.99 tff(1793,plain,
% 0.88/0.99 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (e1 = op(e2, e0))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1792])).
% 0.88/0.99 tff(1794,plain,
% 0.88/0.99 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 0.88/0.99 inference(transitivity,[status(thm)],[1793, 16])).
% 0.88/0.99 tff(1795,plain,
% 0.88/0.99 ((~(e1 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e0) = e1))),
% 0.88/0.99 inference(monotonicity,[status(thm)],[1794])).
% 0.88/0.99 tff(1796,plain,
% 0.88/0.99 ((op(e2, e2) = e3) <=> (e3 = op(e2, e2))),
% 0.88/0.99 inference(symmetry,[status(thm)],[502])).
% 0.88/0.99 tff(1797,plain,
% 0.88/0.99 (e3 = op(e2, e2)),
% 0.88/0.99 inference(modus_ponens,[status(thm)],[1776, 1796])).
% 0.88/0.99 tff(1798,plain,
% 0.88/0.99 (op(op(e1, e3), e3) = op(e2, op(e2, e2))),
% 0.88/0.99 inference(symmetry,[status(thm)],[1789])).
% 0.88/0.99 tff(1799,plain,
% 0.88/0.99 (op(e2, op(e0, e3)) = op(op(e1, e3), e3)),
% 0.88/0.99 inference(symmetry,[status(thm)],[1788])).
% 0.88/0.99 tff(1800,plain,
% 0.88/0.99 (e0 = op(e2, op(e2, e2))),
% 0.88/0.99 inference(transitivity,[status(thm)],[1693, 1786, 1799, 1798])).
% 0.88/0.99 tff(1801,plain,
% 0.88/0.99 ((~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2)))))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/0.99 inference(rewrite,[status(thm)],[])).
% 0.88/0.99 tff(1802,plain,
% 0.88/0.99 (((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2)))))))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1803,plain,
% 0.88/1.00 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2))))))))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1802])).
% 0.88/1.00 tff(1804,plain,
% 0.88/1.00 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.88/1.00 tff(1805,plain,
% 0.88/1.00 ((~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1806,plain,
% 0.88/1.00 ((~(((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2))))))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1807,axiom,(~(((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e1 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax19')).
% 0.88/1.00 tff(1808,plain,
% 0.88/1.00 (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 0.88/1.00 tff(1809,plain,
% 0.88/1.00 (~((e0 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e1 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1808, 1805])).
% 0.88/1.00 tff(1810,plain,
% 0.88/1.00 ((~(e0 = op(e2, op(e2, e2)))) | (~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, op(e2, e2)))))),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1809, 1804])).
% 0.88/1.00 tff(1811,plain,
% 0.88/1.00 (~(e1 = op(e2, op(e2, op(e2, e2))))),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1810, 1800, 1797])).
% 0.88/1.00 tff(1812,plain,
% 0.88/1.00 (~(op(e2, e0) = e1)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1811, 1795])).
% 0.88/1.00 tff(1813,plain,
% 0.88/1.00 (op(e2, e1) = e1),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[345, 1812, 1784, 1781])).
% 0.88/1.00 tff(1814,plain,
% 0.88/1.00 (op(e2, op(e3, e3)) = op(op(e1, e3), e1)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1666, 1672])).
% 0.88/1.00 tff(1815,plain,
% 0.88/1.00 (op(e2, e1) = op(e3, e3)),
% 0.88/1.00 inference(transitivity,[status(thm)],[1813, 1766])).
% 0.88/1.00 tff(1816,plain,
% 0.88/1.00 (op(e2, op(e2, e1)) = op(e2, op(e3, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1815])).
% 0.88/1.00 tff(1817,plain,
% 0.88/1.00 (op(e2, op(e2, e1)) = e1),
% 0.88/1.00 inference(transitivity,[status(thm)],[1816, 1814, 1717, 1813])).
% 0.88/1.00 tff(1818,plain,
% 0.88/1.00 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1355, 1817])).
% 0.88/1.00 tff(1819,plain,
% 0.88/1.00 ((op(e1, e1) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1732, 1693])).
% 0.88/1.00 tff(1820,plain,
% 0.88/1.00 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e1) = e0)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1819])).
% 0.88/1.00 tff(1821,plain,
% 0.88/1.00 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e1) = e0))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1820])).
% 0.88/1.00 tff(1822,plain,
% 0.88/1.00 (~(op(e1, e1) = e0)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[964, 1821])).
% 0.88/1.00 tff(1823,plain,
% 0.88/1.00 (((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1824,plain,
% 0.88/1.00 ((((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1825,plain,
% 0.88/1.00 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1826,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1825])).
% 0.88/1.00 tff(1827,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1826, 1824])).
% 0.88/1.00 tff(1828,plain,
% 0.88/1.00 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)),
% 0.88/1.00 inference(and_elim,[status(thm)],[375])).
% 0.88/1.00 tff(1829,plain,
% 0.88/1.00 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 0.88/1.00 tff(1830,plain,
% 0.88/1.00 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1829, 1823])).
% 0.88/1.00 tff(1831,plain,
% 0.88/1.00 (op(e1, e0) = e0),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1830, 1755, 1822, 80])).
% 0.88/1.00 tff(1832,plain,
% 0.88/1.00 (op(e1, op(e2, e3)) = op(e1, e0)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1692])).
% 0.88/1.00 tff(1833,plain,
% 0.88/1.00 (op(e1, e0) = op(e2, e3)),
% 0.88/1.00 inference(transitivity,[status(thm)],[1831, 1693])).
% 0.88/1.00 tff(1834,plain,
% 0.88/1.00 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1833])).
% 0.88/1.00 tff(1835,plain,
% 0.88/1.00 (op(e1, op(e1, e0)) = e0),
% 0.88/1.00 inference(transitivity,[status(thm)],[1834, 1832, 1831])).
% 0.88/1.00 tff(1836,plain,
% 0.88/1.00 (((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))) | (~(op(e1, op(e1, e0)) = e0))),
% 0.88/1.00 inference(tautology,[status(thm)],[])).
% 0.88/1.00 tff(1837,plain,
% 0.88/1.00 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1836, 1835])).
% 0.88/1.00 tff(1838,plain,
% 0.88/1.00 (op(e1, e2) = op(e1, op(e1, e3))),
% 0.88/1.00 inference(symmetry,[status(thm)],[1705])).
% 0.88/1.00 tff(1839,plain,
% 0.88/1.00 ((op(e1, e2) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1838])).
% 0.88/1.00 tff(1840,plain,
% 0.88/1.00 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e2) = e3)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1839])).
% 0.88/1.00 tff(1841,plain,
% 0.88/1.00 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, op(e1, e3)) = e3)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1838, 1776])).
% 0.88/1.00 tff(1842,plain,
% 0.88/1.00 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 0.88/1.00 inference(transitivity,[status(thm)],[1841, 1840])).
% 0.88/1.00 tff(1843,plain,
% 0.88/1.00 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1842])).
% 0.88/1.00 tff(1844,plain,
% 0.88/1.00 (~(op(e1, e2) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1273, 1843])).
% 0.88/1.00 tff(1845,plain,
% 0.88/1.00 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1666])).
% 0.88/1.00 tff(1846,plain,
% 0.88/1.00 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1845])).
% 0.88/1.00 tff(1847,plain,
% 0.88/1.00 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1846])).
% 0.88/1.00 tff(1848,plain,
% 0.88/1.00 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e1, e3)))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1849,plain,
% 0.88/1.00 (~(op(e1, e2) = op(e1, e3))),
% 0.88/1.00 inference(and_elim,[status(thm)],[45])).
% 0.88/1.00 tff(1850,plain,
% 0.88/1.00 (~(op(e1, e2) = op(e1, e3))),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.88/1.00 tff(1851,plain,
% 0.88/1.00 (~(op(e1, e2) = e2)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1850, 1847])).
% 0.88/1.00 tff(1852,plain,
% 0.88/1.00 (((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1853,plain,
% 0.88/1.00 ((((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1854,plain,
% 0.88/1.00 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1855,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1854])).
% 0.88/1.00 tff(1856,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1855, 1853])).
% 0.88/1.00 tff(1857,plain,
% 0.88/1.00 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)),
% 0.88/1.00 inference(and_elim,[status(thm)],[626])).
% 0.88/1.00 tff(1858,plain,
% 0.88/1.00 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 0.88/1.00 tff(1859,plain,
% 0.88/1.00 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1858, 1852])).
% 0.88/1.00 tff(1860,plain,
% 0.88/1.00 (op(e1, e2) = e1),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1859, 1755, 1851, 1844])).
% 0.88/1.00 tff(1861,plain,
% 0.88/1.00 (op(op(e1, e2), e2) = op(e1, op(e1, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1860, 1666])).
% 0.88/1.00 tff(1862,plain,
% 0.88/1.00 (op(op(e1, e2), e2) = e1),
% 0.88/1.00 inference(transitivity,[status(thm)],[1861, 1705, 1860])).
% 0.88/1.00 tff(1863,plain,
% 0.88/1.00 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1335, 1862])).
% 0.88/1.00 tff(1864,plain,
% 0.88/1.00 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1693])).
% 0.88/1.00 tff(1865,plain,
% 0.88/1.00 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1864])).
% 0.88/1.00 tff(1866,plain,
% 0.88/1.00 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1865])).
% 0.88/1.00 tff(1867,plain,
% 0.88/1.00 (~(op(e2, e0) = e0)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[989, 1866])).
% 0.88/1.00 tff(1868,plain,
% 0.88/1.00 (op(e2, e0) = e2),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[765, 1812, 1770, 1867])).
% 0.88/1.00 tff(1869,assumption,(op(e0, e3) = e3), introduced(assumption)).
% 0.88/1.00 tff(1870,plain,
% 0.88/1.00 (e3 = op(e0, e3)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1869])).
% 0.88/1.00 tff(1871,plain,
% 0.88/1.00 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e0, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1870])).
% 0.88/1.00 tff(1872,plain,
% 0.88/1.00 ((op(e3, e3) = e3) <=> (op(e0, e3) = op(e3, e3))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1871, 659])).
% 0.88/1.00 tff(1873,plain,
% 0.88/1.00 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1872])).
% 0.88/1.00 tff(1874,plain,
% 0.88/1.00 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1873])).
% 0.88/1.00 tff(1875,plain,
% 0.88/1.00 (~(op(e3, e3) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1077, 1874])).
% 0.88/1.00 tff(1876,plain,
% 0.88/1.00 ((op(e3, e3) = e2) <=> (op(e3, e3) = op(e1, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[265])).
% 0.88/1.00 tff(1877,plain,
% 0.88/1.00 ((op(e3, e3) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1876, 1659])).
% 0.88/1.00 tff(1878,plain,
% 0.88/1.00 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1877])).
% 0.88/1.00 tff(1879,plain,
% 0.88/1.00 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1878])).
% 0.88/1.00 tff(1880,plain,
% 0.88/1.00 (~(op(e3, e3) = e2)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[571, 1879])).
% 0.88/1.00 tff(1881,plain,
% 0.88/1.00 (op(e3, e3) = e1),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1071, 1880, 1875, 656])).
% 0.88/1.00 tff(1882,plain,
% 0.88/1.00 (e1 = op(e3, e3)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1881])).
% 0.88/1.00 tff(1883,plain,
% 0.88/1.00 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1882])).
% 0.88/1.00 tff(1884,plain,
% 0.88/1.00 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 0.88/1.00 inference(symmetry,[status(thm)],[1883])).
% 0.88/1.00 tff(1885,plain,
% 0.88/1.00 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1884])).
% 0.88/1.00 tff(1886,plain,
% 0.88/1.00 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = op(e3, e3)))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1887,plain,
% 0.88/1.00 (~(op(e3, e2) = op(e3, e3))),
% 0.88/1.00 inference(and_elim,[status(thm)],[33])).
% 0.88/1.00 tff(1888,plain,
% 0.88/1.00 (~(op(e3, e2) = op(e3, e3))),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 0.88/1.00 tff(1889,plain,
% 0.88/1.00 (~(op(e3, e2) = e1)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1888, 1885])).
% 0.88/1.00 tff(1890,assumption,(~(op(e3, e2) = e3)), introduced(assumption)).
% 0.88/1.00 tff(1891,plain,
% 0.88/1.00 (((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1892,plain,
% 0.88/1.00 ((((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1893,plain,
% 0.88/1.00 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1894,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1893])).
% 0.88/1.00 tff(1895,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1894, 1892])).
% 0.88/1.00 tff(1896,plain,
% 0.88/1.00 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)),
% 0.88/1.00 inference(and_elim,[status(thm)],[94])).
% 0.88/1.00 tff(1897,plain,
% 0.88/1.00 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 0.88/1.00 tff(1898,plain,
% 0.88/1.00 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.88/1.00 inference(modus_ponens,[status(thm)],[1897, 1891])).
% 0.88/1.00 tff(1899,plain,
% 0.88/1.00 (op(e3, e2) = e2),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1898, 85, 1890, 1889])).
% 0.88/1.00 tff(1900,plain,
% 0.88/1.00 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[264])).
% 0.88/1.00 tff(1901,plain,
% 0.88/1.00 (op(e3, e2) = op(e1, e3)),
% 0.88/1.00 inference(transitivity,[status(thm)],[1899, 265])).
% 0.88/1.00 tff(1902,plain,
% 0.88/1.00 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1901])).
% 0.88/1.00 tff(1903,plain,
% 0.88/1.00 (op(e3, op(e3, e2)) = e2),
% 0.88/1.00 inference(transitivity,[status(thm)],[1902, 1900, 1899])).
% 0.88/1.00 tff(1904,plain,
% 0.88/1.00 (((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))) | (~(op(e3, op(e3, e2)) = e2))),
% 0.88/1.00 inference(tautology,[status(thm)],[])).
% 0.88/1.00 tff(1905,plain,
% 0.88/1.00 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.88/1.00 inference(unit_resolution,[status(thm)],[1904, 1903])).
% 0.88/1.00 tff(1906,plain,
% 0.88/1.00 (op(e0, op(e0, e3)) = op(e0, e3)),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1869])).
% 0.88/1.00 tff(1907,plain,
% 0.88/1.00 (op(op(e2, e3), e3) = op(e0, op(e0, e3))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[251, 1870])).
% 0.88/1.00 tff(1908,assumption,(~(op(e3, e0) = e0)), introduced(assumption)).
% 0.88/1.00 tff(1909,plain,
% 0.88/1.00 (((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1910,plain,
% 0.88/1.00 ((((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))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1911,plain,
% 0.88/1.00 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0))),
% 0.88/1.00 inference(rewrite,[status(thm)],[])).
% 0.88/1.00 tff(1912,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(monotonicity,[status(thm)],[1911])).
% 0.88/1.00 tff(1913,plain,
% 0.88/1.00 (((((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))),
% 0.88/1.00 inference(transitivity,[status(thm)],[1912, 1910])).
% 0.88/1.00 tff(1914,plain,
% 0.88/1.00 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)),
% 0.88/1.01 inference(and_elim,[status(thm)],[234])).
% 0.88/1.01 tff(1915,plain,
% 0.88/1.01 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 0.88/1.01 tff(1916,plain,
% 0.88/1.01 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1915, 1909])).
% 0.88/1.01 tff(1917,plain,
% 0.88/1.01 (op(e3, e1) = e0),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1916, 85, 1908, 656])).
% 0.88/1.01 tff(1918,plain,
% 0.88/1.01 (op(e3, e1) = op(e2, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1917, 252])).
% 0.88/1.01 tff(1919,plain,
% 0.88/1.01 (op(op(e3, e1), e3) = op(op(e2, e3), e3)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1918])).
% 0.88/1.01 tff(1920,plain,
% 0.88/1.01 (op(op(e3, e1), e3) = op(e0, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1919, 1907, 1906])).
% 0.88/1.01 tff(1921,plain,
% 0.88/1.01 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1920, 1882])).
% 0.88/1.01 tff(1922,plain,
% 0.88/1.01 ((op(e0, e3) = op(e3, e3)) <=> (op(op(e3, e1), e3) = e1)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1921])).
% 0.88/1.01 tff(1923,plain,
% 0.88/1.01 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(op(e3, e1), e3) = e1))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1922])).
% 0.88/1.01 tff(1924,plain,
% 0.88/1.01 (~(op(op(e3, e1), e3) = e1)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1077, 1923])).
% 0.88/1.01 tff(1925,plain,
% 0.88/1.01 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1050, 1924])).
% 0.88/1.01 tff(1926,assumption,((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))), introduced(assumption)).
% 0.88/1.01 tff(1927,plain,
% 0.88/1.01 (op(e0, op(e1, e3)) = op(e0, e2)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[264])).
% 0.88/1.01 tff(1928,plain,
% 0.88/1.01 (op(op(e2, e3), e2) = op(e0, op(e1, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[251, 265])).
% 0.88/1.01 tff(1929,plain,
% 0.88/1.01 (op(op(e2, e3), e2) = op(e0, e2)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1928, 1927])).
% 0.88/1.01 tff(1930,plain,
% 0.88/1.01 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1929, 1870])).
% 0.88/1.01 tff(1931,plain,
% 0.88/1.01 ((op(e0, e2) = op(e0, e3)) <=> (op(op(e2, e3), e2) = e3)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1930])).
% 0.88/1.01 tff(1932,plain,
% 0.88/1.01 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(op(e2, e3), e2) = e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1931])).
% 0.88/1.01 tff(1933,plain,
% 0.88/1.01 (~(op(op(e2, e3), e2) = e3)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[918, 1932])).
% 0.88/1.01 tff(1934,plain,
% 0.88/1.01 (((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))) | (op(op(e2, e3), e2) = e3)),
% 0.88/1.01 inference(tautology,[status(thm)],[])).
% 0.88/1.01 tff(1935,plain,
% 0.88/1.01 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1934, 1933])).
% 0.88/1.01 tff(1936,assumption,((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))), introduced(assumption)).
% 0.88/1.01 tff(1937,plain,
% 0.88/1.01 (op(e0, op(e0, e3)) = e3),
% 0.88/1.01 inference(transitivity,[status(thm)],[1906, 1869])).
% 0.88/1.01 tff(1938,plain,
% 0.88/1.01 (((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))) | (~(op(e0, op(e0, e3)) = e3))),
% 0.88/1.01 inference(tautology,[status(thm)],[])).
% 0.88/1.01 tff(1939,plain,
% 0.88/1.01 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1938, 1937])).
% 0.88/1.01 tff(1940,assumption,(op(e2, e0) = e2), introduced(assumption)).
% 0.88/1.01 tff(1941,plain,
% 0.88/1.01 (op(e2, e0) = op(e2, op(e2, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[252])).
% 0.88/1.01 tff(1942,plain,
% 0.88/1.01 (op(e2, op(e2, e3)) = op(e2, e0)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1941])).
% 0.88/1.01 tff(1943,plain,
% 0.88/1.01 (op(op(e2, e0), e0) = op(e2, op(e2, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1940, 252])).
% 0.88/1.01 tff(1944,plain,
% 0.88/1.01 (op(op(e2, e0), e0) = e2),
% 0.88/1.01 inference(transitivity,[status(thm)],[1943, 1942, 1940])).
% 0.88/1.01 tff(1945,plain,
% 0.88/1.01 (((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))) | (~(op(op(e2, e0), e0) = e2))),
% 0.88/1.01 inference(tautology,[status(thm)],[])).
% 0.88/1.01 tff(1946,plain,
% 0.88/1.01 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1945, 1944])).
% 0.88/1.01 tff(1947,assumption,(~(op(e1, e2) = e0)), introduced(assumption)).
% 0.88/1.01 tff(1948,plain,
% 0.88/1.01 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[252])).
% 0.88/1.01 tff(1949,plain,
% 0.88/1.01 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1948])).
% 0.88/1.01 tff(1950,plain,
% 0.88/1.01 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1949])).
% 0.88/1.01 tff(1951,plain,
% 0.88/1.01 (~(op(e2, e2) = e0)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[515, 1950])).
% 0.88/1.01 tff(1952,plain,
% 0.88/1.01 (op(e0, e2) = e0),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[973, 85, 1951, 1947])).
% 0.88/1.01 tff(1953,plain,
% 0.88/1.01 (op(e0, e2) = op(e2, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1952, 252])).
% 0.88/1.01 tff(1954,plain,
% 0.88/1.01 (op(op(e0, e2), e2) = op(op(e2, e3), e2)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1953])).
% 0.88/1.01 tff(1955,plain,
% 0.88/1.01 (op(op(e0, e2), e2) = e0),
% 0.88/1.01 inference(transitivity,[status(thm)],[1954, 1928, 1927, 1952])).
% 0.88/1.01 tff(1956,plain,
% 0.88/1.01 (((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))) | (~(op(op(e0, e2), e2) = e0))),
% 0.88/1.01 inference(tautology,[status(thm)],[])).
% 0.88/1.01 tff(1957,plain,
% 0.88/1.01 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1956, 1955])).
% 0.88/1.01 tff(1958,plain,
% 0.88/1.01 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1459, 1957, 1946, 1939, 1358, 1304, 1357, 1936, 1935, 1926, 1925, 1905])).
% 0.88/1.01 tff(1959,plain,
% 0.88/1.01 (op(op(e0, e1), e0) = e1),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1461, 1958])).
% 0.88/1.01 tff(1960,plain,
% 0.88/1.01 ((e2 = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.88/1.01 inference(commutativity,[status(thm)],[])).
% 0.88/1.01 tff(1961,plain,
% 0.88/1.01 ((op(e2, e0) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1940])).
% 0.88/1.01 tff(1962,plain,
% 0.88/1.01 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1961, 1960])).
% 0.88/1.01 tff(1963,plain,
% 0.88/1.01 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1962])).
% 0.88/1.01 tff(1964,plain,
% 0.88/1.01 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = op(e2, e1)))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(1965,plain,
% 0.88/1.01 (~(op(e2, e0) = op(e2, e1))),
% 0.88/1.01 inference(and_elim,[status(thm)],[44])).
% 0.88/1.01 tff(1966,plain,
% 0.88/1.01 (~(op(e2, e0) = op(e2, e1))),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 0.88/1.01 tff(1967,plain,
% 0.88/1.01 (~(op(e2, e1) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1966, 1963])).
% 0.88/1.01 tff(1968,plain,
% 0.88/1.01 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[265])).
% 0.88/1.01 tff(1969,plain,
% 0.88/1.01 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1968])).
% 0.88/1.01 tff(1970,plain,
% 0.88/1.01 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1969])).
% 0.88/1.01 tff(1971,plain,
% 0.88/1.01 (~(op(e1, e1) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[619, 1970])).
% 0.88/1.01 tff(1972,plain,
% 0.88/1.01 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[265])).
% 0.88/1.01 tff(1973,plain,
% 0.88/1.01 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1972])).
% 0.88/1.01 tff(1974,plain,
% 0.88/1.01 ((op(e3, op(e3, e3)) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.88/1.01 inference(commutativity,[status(thm)],[])).
% 0.88/1.01 tff(1975,plain,
% 0.88/1.01 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1881])).
% 0.88/1.01 tff(1976,plain,
% 0.88/1.01 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.88/1.01 inference(symmetry,[status(thm)],[1975])).
% 0.88/1.01 tff(1977,plain,
% 0.88/1.01 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, op(e3, e3)) = e2)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1976, 264])).
% 0.88/1.01 tff(1978,plain,
% 0.88/1.01 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e3, op(e3, e3)))),
% 0.88/1.01 inference(transitivity,[status(thm)],[1977, 1974])).
% 0.88/1.01 tff(1979,plain,
% 0.88/1.01 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = op(e1, e3))),
% 0.88/1.01 inference(symmetry,[status(thm)],[1978])).
% 0.88/1.01 tff(1980,plain,
% 0.88/1.01 (op(e3, op(e3, e3)) = op(e2, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1975, 1917, 252])).
% 0.88/1.01 tff(1981,plain,
% 0.88/1.01 ((e2 = op(e3, op(e3, e3))) <=> (op(e1, e3) = op(e2, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[265, 1980])).
% 0.88/1.01 tff(1982,plain,
% 0.88/1.01 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e3, op(e3, e3)))),
% 0.88/1.01 inference(symmetry,[status(thm)],[1981])).
% 0.88/1.01 tff(1983,plain,
% 0.88/1.01 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e1) = e2)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1982, 1979, 1973])).
% 0.88/1.01 tff(1984,plain,
% 0.88/1.01 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e2))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1983])).
% 0.88/1.01 tff(1985,plain,
% 0.88/1.01 (~(op(e3, e1) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[118, 1984])).
% 0.88/1.01 tff(1986,plain,
% 0.88/1.01 (((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))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(1987,plain,
% 0.88/1.01 ((((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))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(1988,plain,
% 0.88/1.01 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(1989,plain,
% 0.88/1.01 (((((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))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1988])).
% 0.88/1.01 tff(1990,plain,
% 0.88/1.01 (((((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))),
% 0.88/1.01 inference(transitivity,[status(thm)],[1989, 1987])).
% 0.88/1.01 tff(1991,plain,
% 0.88/1.01 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)),
% 0.88/1.01 inference(and_elim,[status(thm)],[285])).
% 0.88/1.01 tff(1992,plain,
% 0.88/1.01 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 0.88/1.01 tff(1993,plain,
% 0.88/1.01 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[1992, 1986])).
% 0.88/1.01 tff(1994,plain,
% 0.88/1.01 (op(e0, e1) = e2),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[1993, 1985, 1971, 1967])).
% 0.88/1.01 tff(1995,plain,
% 0.88/1.01 (e2 = op(e0, e1)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1994])).
% 0.88/1.01 tff(1996,plain,
% 0.88/1.01 (op(e2, op(e2, e3)) = op(op(e0, e1), e0)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1995, 251])).
% 0.88/1.01 tff(1997,plain,
% 0.88/1.01 (e2 = op(e2, e0)),
% 0.88/1.01 inference(symmetry,[status(thm)],[1940])).
% 0.88/1.01 tff(1998,plain,
% 0.88/1.01 (op(e1, e3) = op(e3, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[264, 1997, 1941, 1996, 1959, 1882])).
% 0.88/1.01 tff(1999,plain,
% 0.88/1.01 ($false),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[571, 1998])).
% 0.88/1.01 tff(2000,plain,((op(e3, e2) = e0) | (~(op(e1, e3) = e2)) | (~(op(e2, e0) = e2)) | (~(op(e2, e3) = e0)) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~(op(e0, e3) = e3)) | (op(e1, e2) = e0) | (op(e3, e2) = e3) | (op(e3, e0) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.01 tff(2001,plain,
% 0.88/1.01 (op(e3, e2) = e0),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[2000, 1665, 1868, 1692, 1863, 1261, 1837, 1818, 1765, 1652, 1755, 1704, 1698, 656])).
% 0.88/1.01 tff(2002,plain,
% 0.88/1.01 (op(e3, e2) = op(e2, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[2001, 1693])).
% 0.88/1.01 tff(2003,plain,
% 0.88/1.01 ((op(e3, e2) = e2) <=> (op(e2, e3) = op(e1, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[2002, 1666])).
% 0.88/1.01 tff(2004,plain,
% 0.88/1.01 ((op(e3, e2) = e2) <=> (op(e1, e3) = op(e2, e3))),
% 0.88/1.01 inference(transitivity,[status(thm)],[2003, 1687])).
% 0.88/1.01 tff(2005,plain,
% 0.88/1.01 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 0.88/1.01 inference(symmetry,[status(thm)],[2004])).
% 0.88/1.01 tff(2006,plain,
% 0.88/1.01 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e2) = e2))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[2005])).
% 0.88/1.01 tff(2007,plain,
% 0.88/1.01 (~(op(e3, e2) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[118, 2006])).
% 0.88/1.01 tff(2008,plain,
% 0.88/1.01 (((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))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(2009,plain,
% 0.88/1.01 ((((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))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(2010,plain,
% 0.88/1.01 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(2011,plain,
% 0.88/1.01 (((((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))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[2010])).
% 0.88/1.01 tff(2012,plain,
% 0.88/1.01 (((((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))),
% 0.88/1.01 inference(transitivity,[status(thm)],[2011, 2009])).
% 0.88/1.01 tff(2013,plain,
% 0.88/1.01 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)),
% 0.88/1.01 inference(and_elim,[status(thm)],[147])).
% 0.88/1.01 tff(2014,plain,
% 0.88/1.01 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.88/1.01 tff(2015,plain,
% 0.88/1.01 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[2014, 2008])).
% 0.88/1.01 tff(2016,plain,
% 0.88/1.01 (op(e3, e1) = e2),
% 0.88/1.01 inference(unit_resolution,[status(thm)],[2015, 2007, 1671, 1686])).
% 0.88/1.01 tff(2017,plain,
% 0.88/1.01 (e2 = op(e3, op(e3, e3))),
% 0.88/1.01 inference(modus_ponens,[status(thm)],[2016, 1680])).
% 0.88/1.01 tff(2018,plain,
% 0.88/1.01 (op(e3, op(e3, e3)) = op(e1, e3)),
% 0.88/1.01 inference(transitivity,[status(thm)],[1675, 2016, 1666])).
% 0.88/1.01 tff(2019,plain,
% 0.88/1.01 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e1, e3))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[2018])).
% 0.88/1.01 tff(2020,plain,
% 0.88/1.01 (op(e3, op(e1, e3)) = op(e3, op(e3, op(e3, e3)))),
% 0.88/1.01 inference(symmetry,[status(thm)],[2019])).
% 0.88/1.01 tff(2021,plain,
% 0.88/1.01 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.88/1.01 inference(monotonicity,[status(thm)],[1665])).
% 0.88/1.01 tff(2022,plain,
% 0.88/1.01 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.88/1.01 inference(symmetry,[status(thm)],[2021])).
% 0.88/1.01 tff(2023,plain,
% 0.88/1.01 (e0 = op(e3, e2)),
% 0.88/1.01 inference(symmetry,[status(thm)],[2001])).
% 0.88/1.01 tff(2024,plain,
% 0.88/1.01 (e0 = op(e3, op(e3, op(e3, e3)))),
% 0.88/1.01 inference(transitivity,[status(thm)],[2023, 2022, 2020])).
% 0.88/1.01 tff(2025,plain,
% 0.88/1.01 ((~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3))))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(2026,plain,
% 0.88/1.01 (((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3))))))),
% 0.88/1.01 inference(rewrite,[status(thm)],[])).
% 0.88/1.01 tff(2027,plain,
% 0.88/1.01 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3)))))))),
% 0.88/1.01 inference(monotonicity,[status(thm)],[2026])).
% 0.88/1.01 tff(2028,plain,
% 0.88/1.01 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.88/1.02 tff(2029,plain,
% 0.88/1.02 ((~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2030,plain,
% 0.88/1.02 ((~(((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2031,axiom,(~(((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e0 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax29')).
% 0.88/1.02 tff(2032,plain,
% 0.88/1.02 (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.88/1.02 tff(2033,plain,
% 0.88/1.02 (~((e2 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2032, 2029])).
% 0.88/1.02 tff(2034,plain,
% 0.88/1.02 ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, op(e3, e3))))) | (~(e2 = op(e3, op(e3, e3))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2033, 2028])).
% 0.88/1.02 tff(2035,plain,
% 0.88/1.02 ($false),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[2034, 2024, 2017, 1673])).
% 0.88/1.02 tff(2036,plain,((op(e1, e3) = e1) | (op(e3, e3) = e0) | (op(e1, e3) = e0) | (op(op(e1, e3), e1) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, op(e0, e3)) = e1) | (op(e0, e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.02 tff(2037,plain,
% 0.88/1.02 (op(e1, e3) = e1),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[2036, 80, 656, 655, 466, 652, 121, 651, 650])).
% 0.88/1.02 tff(2038,plain,
% 0.88/1.02 (op(op(e1, e3), e1) = op(e1, e1)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2037])).
% 0.88/1.02 tff(2039,plain,
% 0.88/1.02 ((op(op(e1, e3), e1) = e3) <=> (op(e1, e1) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2038])).
% 0.88/1.02 tff(2040,plain,
% 0.88/1.02 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e1, e1) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2039])).
% 0.88/1.02 tff(2041,plain,
% 0.88/1.02 (~(op(e1, e1) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[655, 2040])).
% 0.88/1.02 tff(2042,plain,
% 0.88/1.02 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[132])).
% 0.88/1.02 tff(2043,plain,
% 0.88/1.02 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2042])).
% 0.88/1.02 tff(2044,plain,
% 0.88/1.02 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2043])).
% 0.88/1.02 tff(2045,plain,
% 0.88/1.02 (~(op(e1, e3) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[303, 2044])).
% 0.88/1.02 tff(2046,plain,
% 0.88/1.02 (~(op(e3, e2) = e3)),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[860, 1124, 650])).
% 0.88/1.02 tff(2047,plain,
% 0.88/1.02 (op(e2, op(e0, e3)) = op(e2, e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1124])).
% 0.88/1.02 tff(2048,plain,
% 0.88/1.02 (op(e2, e2) = op(e2, op(e0, e3))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2047])).
% 0.88/1.02 tff(2049,plain,
% 0.88/1.02 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2048])).
% 0.88/1.02 tff(2050,plain,
% 0.88/1.02 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2049])).
% 0.88/1.02 tff(2051,plain,
% 0.88/1.02 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e2) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2050])).
% 0.88/1.02 tff(2052,plain,
% 0.88/1.02 (~(op(e2, e2) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[651, 2051])).
% 0.88/1.02 tff(2053,plain,
% 0.88/1.02 (op(e1, e2) = e2),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[1151, 1134, 2052, 1143])).
% 0.88/1.02 tff(2054,plain,
% 0.88/1.02 (op(e1, e2) = op(e0, e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2053, 1125])).
% 0.88/1.02 tff(2055,plain,
% 0.88/1.02 ((op(e1, e2) = e3) <=> (op(e0, e3) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2054])).
% 0.88/1.02 tff(2056,plain,
% 0.88/1.02 ((op(e0, e3) = e3) <=> (op(e1, e2) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2055])).
% 0.88/1.02 tff(2057,plain,
% 0.88/1.02 ((~(op(e0, e3) = e3)) <=> (~(op(e1, e2) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2056])).
% 0.88/1.02 tff(2058,plain,
% 0.88/1.02 (~(op(e1, e2) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[661, 2057])).
% 0.88/1.02 tff(2059,plain,
% 0.88/1.02 (op(e0, op(e0, e3)) = op(e0, e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1124])).
% 0.88/1.02 tff(2060,plain,
% 0.88/1.02 (op(e0, e2) = op(e0, op(e0, e3))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2059])).
% 0.88/1.02 tff(2061,plain,
% 0.88/1.02 ((op(e0, e2) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2060])).
% 0.88/1.02 tff(2062,plain,
% 0.88/1.02 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e2) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2061])).
% 0.88/1.02 tff(2063,plain,
% 0.88/1.02 ((e3 = op(e0, op(e0, e3))) <=> (op(e0, op(e0, e3)) = e3)),
% 0.88/1.02 inference(commutativity,[status(thm)],[])).
% 0.88/1.02 tff(2064,plain,
% 0.88/1.02 (op(e2, e3) = e0),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[1098, 1087, 656, 80])).
% 0.88/1.02 tff(2065,plain,
% 0.88/1.02 ((op(e2, e3) = e3) <=> (e0 = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2064])).
% 0.88/1.02 tff(2066,plain,
% 0.88/1.02 ((e0 = e3) <=> (op(e2, e3) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2065])).
% 0.88/1.02 tff(2067,plain,
% 0.88/1.02 ((~(e0 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2066])).
% 0.88/1.02 tff(2068,plain,
% 0.88/1.02 (~(op(e2, e3) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[181, 2067])).
% 0.88/1.02 tff(2069,plain,
% 0.88/1.02 (op(e3, e3) = e3),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[480, 2068, 661, 1080])).
% 0.88/1.02 tff(2070,plain,
% 0.88/1.02 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2069])).
% 0.88/1.02 tff(2071,plain,
% 0.88/1.02 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2070])).
% 0.88/1.02 tff(2072,plain,
% 0.88/1.02 (~(op(e3, e1) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[437, 2071])).
% 0.88/1.02 tff(2073,plain,
% 0.88/1.02 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2064])).
% 0.88/1.02 tff(2074,plain,
% 0.88/1.02 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2073])).
% 0.88/1.02 tff(2075,plain,
% 0.88/1.02 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2074])).
% 0.88/1.02 tff(2076,plain,
% 0.88/1.02 (~(op(e2, e3) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[14, 2075])).
% 0.88/1.02 tff(2077,plain,
% 0.88/1.02 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1126])).
% 0.88/1.02 tff(2078,plain,
% 0.88/1.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2077])).
% 0.88/1.02 tff(2079,plain,
% 0.88/1.02 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2078])).
% 0.88/1.02 tff(2080,plain,
% 0.88/1.02 (~(op(e2, e0) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[747, 2079])).
% 0.88/1.02 tff(2081,plain,
% 0.88/1.02 (((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2082,plain,
% 0.88/1.02 ((((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2083,plain,
% 0.88/1.02 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2084,plain,
% 0.88/1.02 (((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> (((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2083])).
% 0.88/1.02 tff(2085,plain,
% 0.88/1.02 (((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2084, 2082])).
% 0.88/1.02 tff(2086,plain,
% 0.88/1.02 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)),
% 0.88/1.02 inference(and_elim,[status(thm)],[238])).
% 0.88/1.02 tff(2087,plain,
% 0.88/1.02 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 0.88/1.02 tff(2088,plain,
% 0.88/1.02 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2087, 2081])).
% 0.88/1.02 tff(2089,plain,
% 0.88/1.02 (op(e2, e1) = e2),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[2088, 2080, 2076, 2052])).
% 0.88/1.02 tff(2090,plain,
% 0.88/1.02 (op(e2, e1) = op(e0, e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2089, 1125])).
% 0.88/1.02 tff(2091,plain,
% 0.88/1.02 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2090])).
% 0.88/1.02 tff(2092,plain,
% 0.88/1.02 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2091])).
% 0.88/1.02 tff(2093,plain,
% 0.88/1.02 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2092])).
% 0.88/1.02 tff(2094,plain,
% 0.88/1.02 (~(op(e2, e1) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[661, 2093])).
% 0.88/1.02 tff(2095,plain,
% 0.88/1.02 (op(e0, e1) = e3),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[1730, 2094, 1291, 2072])).
% 0.88/1.02 tff(2096,plain,
% 0.88/1.02 ((op(e0, e1) = op(e0, e2)) <=> (e3 = op(e0, op(e0, e3)))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2095, 2060])).
% 0.88/1.02 tff(2097,plain,
% 0.88/1.02 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2096, 2063])).
% 0.88/1.02 tff(2098,plain,
% 0.88/1.02 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2097, 2062])).
% 0.88/1.02 tff(2099,plain,
% 0.88/1.02 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2098])).
% 0.88/1.02 tff(2100,plain,
% 0.88/1.02 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = op(e0, e2)))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2101,plain,
% 0.88/1.02 (~(op(e0, e1) = op(e0, e2))),
% 0.88/1.02 inference(and_elim,[status(thm)],[53])).
% 0.88/1.02 tff(2102,plain,
% 0.88/1.02 (~(op(e0, e1) = op(e0, e2))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 0.88/1.02 tff(2103,plain,
% 0.88/1.02 (~(op(e0, e2) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2102, 2099])).
% 0.88/1.02 tff(2104,plain,
% 0.88/1.02 (((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))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2105,plain,
% 0.88/1.02 ((((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))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2106,plain,
% 0.88/1.02 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2107,plain,
% 0.88/1.02 (((((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))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2106])).
% 0.88/1.02 tff(2108,plain,
% 0.88/1.02 (((((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))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2107, 2105])).
% 0.88/1.02 tff(2109,plain,
% 0.88/1.02 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)),
% 0.88/1.02 inference(and_elim,[status(thm)],[235])).
% 0.88/1.02 tff(2110,plain,
% 0.88/1.02 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 0.88/1.02 tff(2111,plain,
% 0.88/1.02 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2110, 2104])).
% 0.88/1.02 tff(2112,plain,
% 0.88/1.02 (op(e2, e2) = e3),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[2111, 2103, 2058, 2046])).
% 0.88/1.02 tff(2113,plain,
% 0.88/1.02 (e3 = op(e2, e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2112, 1796])).
% 0.88/1.02 tff(2114,plain,
% 0.88/1.02 (op(e2, op(e2, e2)) = op(op(e0, e3), e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1125, 2112])).
% 0.88/1.02 tff(2115,plain,
% 0.88/1.02 (op(op(e0, e3), e3) = op(e2, op(e2, e2))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2114])).
% 0.88/1.02 tff(2116,plain,
% 0.88/1.02 (op(e2, e3) = op(op(e0, e3), e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1125])).
% 0.88/1.02 tff(2117,plain,
% 0.88/1.02 (e0 = op(e2, e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2064])).
% 0.88/1.02 tff(2118,plain,
% 0.88/1.02 (e0 = op(e2, op(e2, e2))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2117, 2116, 2115])).
% 0.88/1.02 tff(2119,plain,
% 0.88/1.02 (op(op(e0, e3), e3) = op(e2, e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2116])).
% 0.88/1.02 tff(2120,plain,
% 0.88/1.02 (op(e2, op(e2, e2)) = e0),
% 0.88/1.02 inference(transitivity,[status(thm)],[2114, 2119, 2064])).
% 0.88/1.02 tff(2121,plain,
% 0.88/1.02 (op(e2, op(e2, op(e2, e2))) = op(op(e0, e3), e0)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1125, 2120])).
% 0.88/1.02 tff(2122,plain,
% 0.88/1.02 (op(op(e0, e3), e0) = op(e2, op(e2, op(e2, e2)))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2121])).
% 0.88/1.02 tff(2123,plain,
% 0.88/1.02 (op(op(e0, e3), e0) = op(e2, e0)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1124])).
% 0.88/1.02 tff(2124,plain,
% 0.88/1.02 (op(e2, e0) = op(op(e0, e3), e0)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2123])).
% 0.88/1.02 tff(2125,plain,
% 0.88/1.02 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2064])).
% 0.88/1.02 tff(2126,plain,
% 0.88/1.02 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2125])).
% 0.88/1.02 tff(2127,plain,
% 0.88/1.02 (~(op(e2, e0) = e0)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[989, 2126])).
% 0.88/1.02 tff(2128,plain,
% 0.88/1.02 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2124])).
% 0.88/1.02 tff(2129,plain,
% 0.88/1.02 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2128])).
% 0.88/1.02 tff(2130,plain,
% 0.88/1.02 ((e3 = op(op(e0, e3), e0)) <=> (op(op(e0, e3), e0) = e3)),
% 0.88/1.02 inference(commutativity,[status(thm)],[])).
% 0.88/1.02 tff(2131,plain,
% 0.88/1.02 (op(e1, e0) = e3),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[247, 2058, 1080, 1291])).
% 0.88/1.02 tff(2132,plain,
% 0.88/1.02 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(op(e0, e3), e0))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2131, 2124])).
% 0.88/1.02 tff(2133,plain,
% 0.88/1.02 ((op(e1, e0) = op(e2, e0)) <=> (op(op(e0, e3), e0) = e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2132, 2130])).
% 0.88/1.02 tff(2134,plain,
% 0.88/1.02 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2133, 2129])).
% 0.88/1.02 tff(2135,plain,
% 0.88/1.02 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2134])).
% 0.88/1.02 tff(2136,plain,
% 0.88/1.02 (~(op(e2, e0) = e3)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[756, 2135])).
% 0.88/1.02 tff(2137,plain,
% 0.88/1.02 (op(e2, e0) = e1),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[765, 2136, 2080, 2127])).
% 0.88/1.02 tff(2138,plain,
% 0.88/1.02 (e1 = op(e2, e0)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2137])).
% 0.88/1.02 tff(2139,plain,
% 0.88/1.02 (e1 = op(e2, op(e2, op(e2, e2)))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2138, 2124, 2122])).
% 0.88/1.02 tff(2140,plain,
% 0.88/1.02 ($false),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[1810, 2139, 2118, 2113])).
% 0.88/1.02 tff(2141,plain,((op(e0, e3) = e0) | (op(e1, e3) = e3) | (op(e1, e1) = e3) | (op(e0, e3) = e3) | (op(e2, op(e0, e3)) = e2) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, op(e0, e3)) = e3) | (op(e0, e3) = e1) | (op(e3, e3) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.02 tff(2142,plain,
% 0.88/1.02 (op(e0, e3) = e0),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[2141, 661, 1291, 2045, 651, 466, 650, 121, 656, 80])).
% 0.88/1.02 tff(2143,plain,
% 0.88/1.02 (op(e2, op(e0, e3)) = op(e2, e0)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2142])).
% 0.88/1.02 tff(2144,plain,
% 0.88/1.02 (op(e2, e0) = op(e2, op(e0, e3))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2143])).
% 0.88/1.02 tff(2145,plain,
% 0.88/1.02 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2144])).
% 0.88/1.02 tff(2146,plain,
% 0.88/1.02 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2145])).
% 0.88/1.02 tff(2147,plain,
% 0.88/1.02 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e0) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2146])).
% 0.88/1.02 tff(2148,plain,
% 0.88/1.02 (~(op(e2, e0) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[651, 2147])).
% 0.88/1.02 tff(2149,plain,
% 0.88/1.02 (e0 = op(e0, e3)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2142])).
% 0.88/1.02 tff(2150,plain,
% 0.88/1.02 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2149])).
% 0.88/1.02 tff(2151,plain,
% 0.88/1.02 ((e0 = e2) <=> (op(e3, e0) = e2)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2150, 668])).
% 0.88/1.02 tff(2152,plain,
% 0.88/1.02 ((~(e0 = e2)) <=> (~(op(e3, e0) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2151])).
% 0.88/1.02 tff(2153,plain,
% 0.88/1.02 (~(op(e3, e0) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[14, 2152])).
% 0.88/1.02 tff(2154,plain,
% 0.88/1.02 ((e2 = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.88/1.02 inference(commutativity,[status(thm)],[])).
% 0.88/1.02 tff(2155,plain,
% 0.88/1.02 (e0 = op(e3, e0)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2149, 467])).
% 0.88/1.02 tff(2156,plain,
% 0.88/1.02 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2155])).
% 0.88/1.02 tff(2157,plain,
% 0.88/1.02 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2156])).
% 0.88/1.02 tff(2158,plain,
% 0.88/1.02 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2157])).
% 0.88/1.02 tff(2159,plain,
% 0.88/1.02 (~(op(e1, e0) = e0)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[410, 2158])).
% 0.88/1.02 tff(2160,plain,
% 0.88/1.02 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[132])).
% 0.88/1.02 tff(2161,plain,
% 0.88/1.02 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2160])).
% 0.88/1.02 tff(2162,plain,
% 0.88/1.02 (~(op(e1, e0) = e1)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[110, 2161])).
% 0.88/1.02 tff(2163,plain,
% 0.88/1.02 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[132])).
% 0.88/1.02 tff(2164,plain,
% 0.88/1.02 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2163])).
% 0.88/1.02 tff(2165,plain,
% 0.88/1.02 (~(op(e1, e1) = e1)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[619, 2164])).
% 0.88/1.02 tff(2166,plain,
% 0.88/1.02 ((e2 = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.88/1.02 inference(commutativity,[status(thm)],[])).
% 0.88/1.02 tff(2167,assumption,(~(op(e1, e0) = e0)), introduced(assumption)).
% 0.88/1.02 tff(2168,assumption,(~(op(e1, e0) = e3)), introduced(assumption)).
% 0.88/1.02 tff(2169,plain,
% 0.88/1.02 (op(e1, e0) = e2),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[728, 2168, 929, 2167])).
% 0.88/1.02 tff(2170,plain,
% 0.88/1.02 ((op(e1, e0) = op(e1, e1)) <=> (e2 = op(e1, e1))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2169])).
% 0.88/1.02 tff(2171,plain,
% 0.88/1.02 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2170, 2166])).
% 0.88/1.02 tff(2172,plain,
% 0.88/1.02 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2171])).
% 0.88/1.02 tff(2173,plain,
% 0.88/1.02 (~(op(e1, e1) = e2)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[737, 2172])).
% 0.88/1.02 tff(2174,plain,
% 0.88/1.02 (op(e1, e1) = e0),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[630, 2173, 1266, 1291])).
% 0.88/1.02 tff(2175,plain,
% 0.88/1.02 (e0 = op(e1, e1)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[2174, 123])).
% 0.88/1.02 tff(2176,plain,
% 0.88/1.02 (op(e1, e1) = op(e0, e3)),
% 0.88/1.02 inference(transitivity,[status(thm)],[2174, 772])).
% 0.88/1.02 tff(2177,plain,
% 0.88/1.02 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2176])).
% 0.88/1.02 tff(2178,plain,
% 0.88/1.02 (op(e1, op(e0, e3)) = op(e1, op(e1, e1))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2177])).
% 0.88/1.02 tff(2179,plain,
% 0.88/1.02 (op(e1, op(e0, e3)) = op(e1, e0)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[771])).
% 0.88/1.02 tff(2180,plain,
% 0.88/1.02 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2179])).
% 0.88/1.02 tff(2181,plain,
% 0.88/1.02 (e2 = op(e1, e0)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2169])).
% 0.88/1.02 tff(2182,plain,
% 0.88/1.02 (e2 = op(e1, op(e1, e1))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2181, 2180, 2178])).
% 0.88/1.02 tff(2183,plain,
% 0.88/1.02 (op(e1, op(e1, e1)) = e2),
% 0.88/1.02 inference(transitivity,[status(thm)],[2177, 2179, 2169])).
% 0.88/1.02 tff(2184,plain,
% 0.88/1.02 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 0.88/1.02 inference(monotonicity,[status(thm)],[2183])).
% 0.88/1.02 tff(2185,plain,
% 0.88/1.02 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 0.88/1.02 inference(symmetry,[status(thm)],[2184])).
% 0.88/1.02 tff(2186,plain,
% 0.88/1.02 (op(e1, e2) = e3),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[247, 2168, 1080, 1291])).
% 0.88/1.02 tff(2187,plain,
% 0.88/1.02 (e3 = op(e1, e2)),
% 0.88/1.02 inference(symmetry,[status(thm)],[2186])).
% 0.88/1.02 tff(2188,plain,
% 0.88/1.02 (e3 = op(e1, op(e1, op(e1, e1)))),
% 0.88/1.02 inference(transitivity,[status(thm)],[2187, 2185])).
% 0.88/1.02 tff(2189,plain,
% 0.88/1.02 ((~(~((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1)))))) <=> ((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1))))),
% 0.88/1.02 inference(rewrite,[status(thm)],[])).
% 0.88/1.02 tff(2190,plain,
% 0.88/1.02 (((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2191,plain,
% 0.88/1.03 ((~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2190])).
% 0.88/1.03 tff(2192,plain,
% 0.88/1.03 ((~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2191, 2189])).
% 0.88/1.03 tff(2193,plain,
% 0.88/1.03 ((~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2194,plain,
% 0.88/1.03 ((~(((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1))) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2195,axiom,(~(((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1))) & (e3 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax14')).
% 0.88/1.03 tff(2196,plain,
% 0.88/1.03 (~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.88/1.03 tff(2197,plain,
% 0.88/1.03 (~((e2 = op(e1, op(e1, e1))) & (e0 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2196, 2193])).
% 0.88/1.03 tff(2198,plain,
% 0.88/1.03 ((~(e3 = op(e1, op(e1, op(e1, e1))))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(e1, e1)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2197, 2192])).
% 0.88/1.03 tff(2199,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2198, 2188, 2182, 2175])).
% 0.88/1.03 tff(2200,plain,((op(e1, e0) = e3) | (~(op(e0, e3) = e0)) | (op(e1, e1) = e1) | (op(e1, e1) = e3) | (op(e1, e3) = e3) | (op(e1, e0) = e1) | (op(e1, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(2201,plain,
% 0.88/1.03 (op(e1, e0) = e3),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2200, 2142, 2165, 1291, 2045, 2162, 2159])).
% 0.88/1.03 tff(2202,plain,
% 0.88/1.03 (e3 = op(e1, e0)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2201])).
% 0.88/1.03 tff(2203,plain,
% 0.88/1.03 ((e2 = e3) <=> (e2 = op(e1, e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2202])).
% 0.88/1.03 tff(2204,plain,
% 0.88/1.03 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2203, 2154])).
% 0.88/1.03 tff(2205,plain,
% 0.88/1.03 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2204])).
% 0.88/1.03 tff(2206,plain,
% 0.88/1.03 (~(op(e1, e0) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1321, 2205])).
% 0.88/1.03 tff(2207,plain,
% 0.88/1.03 (op(e0, e0) = e2),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[589, 2206, 2153, 2148])).
% 0.88/1.03 tff(2208,plain,
% 0.88/1.03 (e2 = op(e0, e0)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2207, 78])).
% 0.88/1.03 tff(2209,plain,
% 0.88/1.03 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2207])).
% 0.88/1.03 tff(2210,plain,
% 0.88/1.03 ((e1 = op(e0, op(e0, e0))) <=> (e1 = op(e0, e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2209])).
% 0.88/1.03 tff(2211,plain,
% 0.88/1.03 ((e1 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e1)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2210, 697])).
% 0.88/1.03 tff(2212,plain,
% 0.88/1.03 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.88/1.03 inference(symmetry,[status(thm)],[2211])).
% 0.88/1.03 tff(2213,plain,
% 0.88/1.03 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2155])).
% 0.88/1.03 tff(2214,plain,
% 0.88/1.03 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2213])).
% 0.88/1.03 tff(2215,plain,
% 0.88/1.03 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2214])).
% 0.88/1.03 tff(2216,plain,
% 0.88/1.03 (~(op(e2, e0) = e0)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[747, 2215])).
% 0.88/1.03 tff(2217,plain,
% 0.88/1.03 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2202])).
% 0.88/1.03 tff(2218,plain,
% 0.88/1.03 ((op(e2, e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2217, 749])).
% 0.88/1.03 tff(2219,plain,
% 0.88/1.03 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2218])).
% 0.88/1.03 tff(2220,plain,
% 0.88/1.03 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2219])).
% 0.88/1.03 tff(2221,plain,
% 0.88/1.03 (~(op(e2, e0) = e3)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[756, 2220])).
% 0.88/1.03 tff(2222,plain,
% 0.88/1.03 (op(e2, e0) = e1),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[765, 2221, 2148, 2216])).
% 0.88/1.03 tff(2223,plain,
% 0.88/1.03 ((op(e2, e0) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2222])).
% 0.88/1.03 tff(2224,plain,
% 0.88/1.03 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2223, 316])).
% 0.88/1.03 tff(2225,plain,
% 0.88/1.03 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2224])).
% 0.88/1.03 tff(2226,plain,
% 0.88/1.03 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = op(e2, e2)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2227,plain,
% 0.88/1.03 (~(op(e2, e0) = op(e2, e2))),
% 0.88/1.03 inference(and_elim,[status(thm)],[43])).
% 0.88/1.03 tff(2228,plain,
% 0.88/1.03 (~(op(e2, e0) = op(e2, e2))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 0.88/1.03 tff(2229,plain,
% 0.88/1.03 (~(op(e2, e2) = e1)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2228, 2225])).
% 0.88/1.03 tff(2230,plain,
% 0.88/1.03 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 0.88/1.03 inference(monotonicity,[status(thm)],[132])).
% 0.88/1.03 tff(2231,plain,
% 0.88/1.03 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2230])).
% 0.88/1.03 tff(2232,plain,
% 0.88/1.03 (~(op(e1, e2) = e1)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1850, 2231])).
% 0.88/1.03 tff(2233,plain,
% 0.88/1.03 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2149])).
% 0.88/1.03 tff(2234,plain,
% 0.88/1.03 ((e2 = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(2235,plain,
% 0.88/1.03 ((op(e1, e3) = e2) <=> (e1 = e2)),
% 0.88/1.03 inference(monotonicity,[status(thm)],[132])).
% 0.88/1.03 tff(2236,plain,
% 0.88/1.03 ((e1 = e2) <=> (op(e1, e3) = e2)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2235])).
% 0.88/1.03 tff(2237,plain,
% 0.88/1.03 ((~(e1 = e2)) <=> (~(op(e1, e3) = e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2236])).
% 0.88/1.03 tff(2238,plain,
% 0.88/1.03 (~(op(e1, e3) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[708, 2237])).
% 0.88/1.03 tff(2239,plain,
% 0.88/1.03 ((e0 = op(e0, op(e0, e3))) <=> (op(e0, op(e0, e3)) = e0)),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(2240,plain,
% 0.88/1.03 (op(e0, e0) = op(e0, op(e0, e3))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2149])).
% 0.88/1.03 tff(2241,plain,
% 0.88/1.03 (e2 = op(e0, e0)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2207])).
% 0.88/1.03 tff(2242,plain,
% 0.88/1.03 (e2 = op(e0, op(e0, e3))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2241, 2240])).
% 0.88/1.03 tff(2243,plain,
% 0.88/1.03 (op(e1, e2) = e0),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1830, 84, 2167, 80])).
% 0.88/1.03 tff(2244,assumption,(op(e0, e0) = e2), introduced(assumption)).
% 0.88/1.03 tff(2245,plain,
% 0.88/1.03 (op(e1, op(e0, e0)) = op(e1, e2)),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2244])).
% 0.88/1.03 tff(2246,plain,
% 0.88/1.03 (e2 = op(e0, e0)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2244])).
% 0.88/1.03 tff(2247,plain,
% 0.88/1.03 (op(e1, e1) = e2),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[630, 84, 1266, 1291])).
% 0.88/1.03 tff(2248,plain,
% 0.88/1.03 (op(e1, e1) = op(e0, e0)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2247, 2246])).
% 0.88/1.03 tff(2249,plain,
% 0.88/1.03 (op(e1, op(e1, e1)) = op(e1, op(e0, e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2248])).
% 0.88/1.03 tff(2250,plain,
% 0.88/1.03 (op(e1, op(e1, e1)) = op(e0, e3)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2249, 2245, 2243, 772])).
% 0.88/1.03 tff(2251,plain,
% 0.88/1.03 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e0, e3))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2250])).
% 0.88/1.03 tff(2252,plain,
% 0.88/1.03 (op(e1, op(e0, e3)) = op(e1, op(e1, op(e1, e1)))),
% 0.88/1.03 inference(symmetry,[status(thm)],[2251])).
% 0.88/1.03 tff(2253,plain,
% 0.88/1.03 (e3 = op(e1, op(e1, op(e1, e1)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[259, 775, 2252])).
% 0.88/1.03 tff(2254,plain,
% 0.88/1.03 ((op(e1, e1) = e2) <=> (e2 = op(e1, e1))),
% 0.88/1.03 inference(symmetry,[status(thm)],[2166])).
% 0.88/1.03 tff(2255,plain,
% 0.88/1.03 (e2 = op(e1, e1)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2247, 2254])).
% 0.88/1.03 tff(2256,plain,
% 0.88/1.03 (op(e1, op(e0, e0)) = op(e1, op(e1, e1))),
% 0.88/1.03 inference(symmetry,[status(thm)],[2249])).
% 0.88/1.03 tff(2257,plain,
% 0.88/1.03 (op(e1, e2) = op(e1, op(e0, e0))),
% 0.88/1.03 inference(symmetry,[status(thm)],[2245])).
% 0.88/1.03 tff(2258,plain,
% 0.88/1.03 (e0 = op(e1, e2)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2243])).
% 0.88/1.03 tff(2259,plain,
% 0.88/1.03 (e0 = op(e1, op(e1, e1))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2258, 2257, 2256])).
% 0.88/1.03 tff(2260,plain,
% 0.88/1.03 ((~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1)))))))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2261,plain,
% 0.88/1.03 (((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1)))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2262,plain,
% 0.88/1.03 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1))))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2261])).
% 0.88/1.03 tff(2263,plain,
% 0.88/1.03 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2262, 2260])).
% 0.88/1.03 tff(2264,plain,
% 0.88/1.03 ((~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2265,plain,
% 0.88/1.03 ((~(((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2266,axiom,(~(((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e3 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax12')).
% 0.88/1.03 tff(2267,plain,
% 0.88/1.03 (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 0.88/1.03 tff(2268,plain,
% 0.88/1.03 (~((e0 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e3 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2267, 2264])).
% 0.88/1.03 tff(2269,plain,
% 0.88/1.03 ((~(e0 = op(e1, op(e1, e1)))) | (~(e2 = op(e1, e1))) | (~(e3 = op(e1, op(e1, op(e1, e1)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2268, 2263])).
% 0.88/1.03 tff(2270,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2269, 2259, 2255, 2253])).
% 0.88/1.03 tff(2271,plain,((op(e1, e1) = e0) | (~(op(e1, e0) = e3)) | (~(op(e0, e3) = e0)) | (~(op(e0, e0) = e2)) | (op(e1, e0) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(2272,plain,
% 0.88/1.03 (op(e1, e1) = e0),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2271, 2201, 2142, 2207, 2159, 80, 2165, 1291])).
% 0.88/1.03 tff(2273,plain,
% 0.88/1.03 ((op(e1, e1) = e2) <=> (e0 = op(e0, op(e0, e3)))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2272, 2242])).
% 0.88/1.03 tff(2274,plain,
% 0.88/1.03 ((op(e1, e1) = e2) <=> (op(e0, op(e0, e3)) = e0)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2273, 2239])).
% 0.88/1.03 tff(2275,plain,
% 0.88/1.03 ((op(e0, op(e0, e3)) = e0) <=> (op(e1, e1) = e2)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2274])).
% 0.88/1.03 tff(2276,plain,
% 0.88/1.03 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(e1, e1) = e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2275])).
% 0.88/1.03 tff(2277,plain,
% 0.88/1.03 (~(op(e1, e1) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[649, 2276])).
% 0.88/1.03 tff(2278,plain,
% 0.88/1.03 (((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))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2279,plain,
% 0.88/1.03 ((((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))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2280,plain,
% 0.88/1.03 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2281,plain,
% 0.88/1.03 (((((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))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2280])).
% 0.88/1.03 tff(2282,plain,
% 0.88/1.03 (((((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))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2281, 2279])).
% 0.88/1.03 tff(2283,plain,
% 0.88/1.03 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)),
% 0.88/1.03 inference(and_elim,[status(thm)],[286])).
% 0.88/1.03 tff(2284,plain,
% 0.88/1.03 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 0.88/1.03 tff(2285,plain,
% 0.88/1.03 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2284, 2278])).
% 0.88/1.03 tff(2286,plain,
% 0.88/1.03 (op(e1, e2) = e2),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2285, 2277, 2238, 2206])).
% 0.88/1.03 tff(2287,plain,
% 0.88/1.03 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2286])).
% 0.88/1.03 tff(2288,plain,
% 0.88/1.03 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2287, 2234])).
% 0.88/1.03 tff(2289,plain,
% 0.88/1.03 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2288])).
% 0.88/1.03 tff(2290,plain,
% 0.88/1.03 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e3, e2)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2291,plain,
% 0.88/1.03 (~(op(e1, e2) = op(e3, e2))),
% 0.88/1.03 inference(and_elim,[status(thm)],[216])).
% 0.88/1.03 tff(2292,plain,
% 0.88/1.03 (~(op(e1, e2) = op(e3, e2))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 0.88/1.03 tff(2293,plain,
% 0.88/1.03 (~(op(e3, e2) = e2)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2292, 2289])).
% 0.88/1.03 tff(2294,plain,
% 0.88/1.03 ((op(e3, e0) = op(e1, e0)) <=> (op(e1, e0) = op(e3, e0))),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(2295,plain,
% 0.88/1.03 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2149])).
% 0.88/1.03 tff(2296,plain,
% 0.88/1.03 ((op(e2, e3) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2295, 925])).
% 0.88/1.03 tff(2297,plain,
% 0.88/1.03 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.88/1.03 inference(symmetry,[status(thm)],[2296])).
% 0.88/1.03 tff(2298,plain,
% 0.88/1.03 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2297])).
% 0.88/1.03 tff(2299,plain,
% 0.88/1.03 (~(op(e2, e3) = e0)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[964, 2298])).
% 0.88/1.03 tff(2300,plain,
% 0.88/1.03 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2272])).
% 0.88/1.03 tff(2301,plain,
% 0.88/1.03 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.88/1.03 inference(transitivity,[status(thm)],[2300, 83])).
% 0.88/1.03 tff(2302,plain,
% 0.88/1.03 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2301])).
% 0.88/1.03 tff(2303,plain,
% 0.88/1.03 (~(op(e2, e1) = e0)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[225, 2302])).
% 0.88/1.03 tff(2304,plain,
% 0.88/1.03 (((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))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2305,plain,
% 0.88/1.03 ((((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))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2306,plain,
% 0.88/1.03 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2307,plain,
% 0.88/1.03 (((((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))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2306])).
% 0.88/1.04 tff(2308,plain,
% 0.88/1.04 (((((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))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2307, 2305])).
% 0.88/1.04 tff(2309,plain,
% 0.88/1.04 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)),
% 0.88/1.04 inference(and_elim,[status(thm)],[242])).
% 0.88/1.04 tff(2310,plain,
% 0.88/1.04 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 0.88/1.04 tff(2311,plain,
% 0.88/1.04 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2310, 2304])).
% 0.88/1.04 tff(2312,plain,
% 0.88/1.04 (op(e2, e2) = e0),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2311, 2303, 2216, 2299])).
% 0.88/1.04 tff(2313,plain,
% 0.88/1.04 (op(e2, e2) = op(e3, e0)),
% 0.88/1.04 inference(transitivity,[status(thm)],[2312, 2149, 467])).
% 0.88/1.04 tff(2314,plain,
% 0.88/1.04 ((op(e2, e2) = e3) <=> (op(e3, e0) = op(e1, e0))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2313, 2202])).
% 0.88/1.04 tff(2315,plain,
% 0.88/1.04 ((op(e2, e2) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2314, 2294])).
% 0.88/1.04 tff(2316,plain,
% 0.88/1.04 ((op(e1, e0) = op(e3, e0)) <=> (op(e2, e2) = e3)),
% 0.88/1.04 inference(symmetry,[status(thm)],[2315])).
% 0.88/1.04 tff(2317,plain,
% 0.88/1.04 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e2, e2) = e3))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2316])).
% 0.88/1.04 tff(2318,plain,
% 0.88/1.04 (~(op(e2, e2) = e3)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[410, 2317])).
% 0.88/1.04 tff(2319,plain,
% 0.88/1.04 (op(e2, e2) = op(e0, e3)),
% 0.88/1.04 inference(transitivity,[status(thm)],[2312, 2149])).
% 0.88/1.04 tff(2320,plain,
% 0.88/1.04 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2319])).
% 0.88/1.04 tff(2321,plain,
% 0.88/1.04 (op(e2, op(e2, e2)) = e1),
% 0.88/1.04 inference(transitivity,[status(thm)],[2320, 2143, 2222])).
% 0.88/1.04 tff(2322,plain,
% 0.88/1.04 (op(e2, op(e2, op(e2, e2))) = op(e2, e1)),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2321])).
% 0.88/1.04 tff(2323,plain,
% 0.88/1.04 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (e3 = op(e2, e1))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2322])).
% 0.88/1.04 tff(2324,plain,
% 0.88/1.04 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e1) = e3)),
% 0.88/1.04 inference(transitivity,[status(thm)],[2323, 1262])).
% 0.88/1.04 tff(2325,plain,
% 0.88/1.04 ((~(e3 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e1) = e3))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2324])).
% 0.88/1.04 tff(2326,plain,
% 0.88/1.04 (e0 = op(e2, e2)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2312, 995])).
% 0.88/1.04 tff(2327,plain,
% 0.88/1.04 (op(e2, op(e0, e3)) = op(e2, op(e2, e2))),
% 0.88/1.04 inference(symmetry,[status(thm)],[2320])).
% 0.88/1.04 tff(2328,plain,
% 0.88/1.04 (e1 = op(e2, e0)),
% 0.88/1.04 inference(symmetry,[status(thm)],[2222])).
% 0.88/1.04 tff(2329,plain,
% 0.88/1.04 (e1 = op(e2, op(e2, e2))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2328, 2144, 2327])).
% 0.88/1.04 tff(2330,plain,
% 0.88/1.04 (~(e3 = op(e2, op(e2, op(e2, e2))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1539, 2329, 2326])).
% 0.88/1.04 tff(2331,plain,
% 0.88/1.04 (~(op(e2, e1) = e3)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2330, 2325])).
% 0.88/1.04 tff(2332,plain,
% 0.88/1.04 (op(e2, e3) = e3),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1559, 2331, 2221, 2318])).
% 0.88/1.04 tff(2333,plain,
% 0.88/1.04 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2332])).
% 0.88/1.04 tff(2334,plain,
% 0.88/1.04 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.88/1.04 inference(transitivity,[status(thm)],[2333, 666])).
% 0.88/1.04 tff(2335,plain,
% 0.88/1.04 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2334])).
% 0.88/1.04 tff(2336,plain,
% 0.88/1.04 (~(op(e3, e3) = e3)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[368, 2335])).
% 0.88/1.04 tff(2337,plain,
% 0.88/1.04 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e1)),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2222])).
% 0.88/1.04 tff(2338,plain,
% 0.88/1.04 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e1))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2337])).
% 0.88/1.04 tff(2339,plain,
% 0.88/1.04 (~(op(e0, e0) = e1)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[359, 2338])).
% 0.88/1.04 tff(2340,plain,
% 0.94/1.04 (op(e2, op(e1, e0)) = op(e2, e3)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2201])).
% 0.94/1.04 tff(2341,plain,
% 0.94/1.04 (op(e2, e3) = op(e1, e0)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2332, 2202])).
% 0.94/1.04 tff(2342,plain,
% 0.94/1.04 (op(e2, op(e2, e3)) = op(e2, op(e1, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2341])).
% 0.94/1.04 tff(2343,plain,
% 0.94/1.04 (op(e2, op(e2, e3)) = e3),
% 0.94/1.04 inference(transitivity,[status(thm)],[2342, 2340, 2332])).
% 0.94/1.04 tff(2344,plain,
% 0.94/1.04 (((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))) | (~(op(e2, op(e2, e3)) = e3))),
% 0.94/1.04 inference(tautology,[status(thm)],[])).
% 0.94/1.04 tff(2345,plain,
% 0.94/1.04 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2344, 2343])).
% 0.94/1.04 tff(2346,plain,
% 0.94/1.04 (op(op(e2, e0), e2) = op(e1, e2)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2222])).
% 0.94/1.04 tff(2347,plain,
% 0.94/1.04 ((op(op(e2, e0), e2) = e0) <=> (op(e1, e2) = e0)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2346])).
% 0.94/1.04 tff(2348,plain,
% 0.94/1.04 ((op(e1, e2) = e0) <=> (op(op(e2, e0), e2) = e0)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2347])).
% 0.94/1.04 tff(2349,plain,
% 0.94/1.04 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2272])).
% 0.94/1.04 tff(2350,plain,
% 0.94/1.04 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2349, 67])).
% 0.94/1.04 tff(2351,plain,
% 0.94/1.04 ((op(e1, e1) = op(e1, e2)) <=> (op(op(e2, e0), e2) = e0)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2350, 2348])).
% 0.94/1.04 tff(2352,plain,
% 0.94/1.04 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(op(e2, e0), e2) = e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2351])).
% 0.94/1.04 tff(2353,plain,
% 0.94/1.04 (~(op(op(e2, e0), e2) = e0)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[1604, 2352])).
% 0.94/1.04 tff(2354,plain,
% 0.94/1.04 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[1379, 2353])).
% 0.94/1.04 tff(2355,plain,
% 0.94/1.04 ((e1 = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.94/1.04 inference(commutativity,[status(thm)],[])).
% 0.94/1.04 tff(2356,plain,
% 0.94/1.04 ((op(e2, e0) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2222])).
% 0.94/1.04 tff(2357,plain,
% 0.94/1.04 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2356, 2355])).
% 0.94/1.04 tff(2358,plain,
% 0.94/1.04 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2357])).
% 0.94/1.04 tff(2359,plain,
% 0.94/1.04 (~(op(e2, e1) = e1)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[1966, 2358])).
% 0.94/1.04 tff(2360,plain,
% 0.94/1.04 (((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))),
% 0.94/1.04 inference(rewrite,[status(thm)],[])).
% 0.94/1.04 tff(2361,plain,
% 0.94/1.04 ((((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))),
% 0.94/1.04 inference(rewrite,[status(thm)],[])).
% 0.94/1.04 tff(2362,plain,
% 0.94/1.04 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2))),
% 0.94/1.04 inference(rewrite,[status(thm)],[])).
% 0.94/1.04 tff(2363,plain,
% 0.94/1.04 (((((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))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2362])).
% 0.94/1.04 tff(2364,plain,
% 0.94/1.04 (((((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))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2363, 2361])).
% 0.94/1.04 tff(2365,plain,
% 0.94/1.04 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)),
% 0.94/1.04 inference(and_elim,[status(thm)],[99])).
% 0.94/1.04 tff(2366,plain,
% 0.94/1.04 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 0.94/1.04 tff(2367,plain,
% 0.94/1.04 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[2366, 2360])).
% 0.94/1.04 tff(2368,plain,
% 0.94/1.04 (op(e2, e1) = e2),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2367, 2331, 2359, 2303])).
% 0.94/1.04 tff(2369,plain,
% 0.94/1.04 (op(op(e2, e1), e1) = op(e2, e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2368])).
% 0.94/1.04 tff(2370,plain,
% 0.94/1.04 (op(op(e2, e1), e1) = e2),
% 0.94/1.04 inference(transitivity,[status(thm)],[2369, 2368])).
% 0.94/1.04 tff(2371,plain,
% 0.94/1.04 (((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))) | (~(op(op(e2, e1), e1) = e2))),
% 0.94/1.04 inference(tautology,[status(thm)],[])).
% 0.94/1.04 tff(2372,plain,
% 0.94/1.04 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2371, 2370])).
% 0.94/1.04 tff(2373,plain,
% 0.94/1.04 (op(e1, op(e0, e0)) = op(e1, e2)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2207])).
% 0.94/1.04 tff(2374,plain,
% 0.94/1.04 (op(e1, e2) = op(e0, e0)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2286, 2241])).
% 0.94/1.04 tff(2375,plain,
% 0.94/1.04 (op(e1, op(e1, e2)) = op(e1, op(e0, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2374])).
% 0.94/1.04 tff(2376,plain,
% 0.94/1.04 (op(e1, op(e1, e2)) = e2),
% 0.94/1.04 inference(transitivity,[status(thm)],[2375, 2373, 2286])).
% 0.94/1.04 tff(2377,plain,
% 0.94/1.04 (((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))) | (~(op(e1, op(e1, e2)) = e2))),
% 0.94/1.04 inference(tautology,[status(thm)],[])).
% 0.94/1.04 tff(2378,plain,
% 0.94/1.04 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2377, 2376])).
% 0.94/1.04 tff(2379,assumption,(~(op(e0, e0) = e1)), introduced(assumption)).
% 0.94/1.04 tff(2380,plain,
% 0.94/1.04 ((op(e0, op(e0, e0)) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.94/1.04 inference(commutativity,[status(thm)],[])).
% 0.94/1.04 tff(2381,plain,
% 0.94/1.04 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2244])).
% 0.94/1.04 tff(2382,plain,
% 0.94/1.04 (op(e0, e2) = op(e0, op(e0, e0))),
% 0.94/1.04 inference(symmetry,[status(thm)],[2381])).
% 0.94/1.04 tff(2383,plain,
% 0.94/1.04 ((op(e0, e2) = e1) <=> (op(e0, op(e0, e0)) = e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2382])).
% 0.94/1.04 tff(2384,plain,
% 0.94/1.04 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2383, 2380])).
% 0.94/1.04 tff(2385,plain,
% 0.94/1.04 ((e1 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e1)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2384])).
% 0.94/1.04 tff(2386,assumption,(~(op(e3, e2) = e2)), introduced(assumption)).
% 0.94/1.04 tff(2387,plain,
% 0.94/1.04 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[1366])).
% 0.94/1.04 tff(2388,plain,
% 0.94/1.04 ((op(e3, e2) = e0) <=> (op(e3, e0) = op(e3, e2))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2387, 1123])).
% 0.94/1.04 tff(2389,plain,
% 0.94/1.04 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2388])).
% 0.94/1.04 tff(2390,plain,
% 0.94/1.04 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2389])).
% 0.94/1.04 tff(2391,plain,
% 0.94/1.04 (~(op(e3, e2) = e0)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[1133, 2390])).
% 0.94/1.04 tff(2392,plain,
% 0.94/1.04 (op(e3, e2) = e1),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[1898, 1890, 2391, 2386])).
% 0.94/1.04 tff(2393,plain,
% 0.94/1.04 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, op(e0, e0)) = e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2382, 2392])).
% 0.94/1.04 tff(2394,plain,
% 0.94/1.04 ((op(e0, e2) = op(e3, e2)) <=> (e1 = op(e0, op(e0, e0)))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2393, 2380])).
% 0.94/1.04 tff(2395,plain,
% 0.94/1.04 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e1)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2394, 2385])).
% 0.94/1.04 tff(2396,plain,
% 0.94/1.04 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e1))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2395])).
% 0.94/1.04 tff(2397,plain,
% 0.94/1.04 (~(op(e0, e2) = e1)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[1467, 2396])).
% 0.94/1.04 tff(2398,plain,
% 0.94/1.04 (op(e0, e1) = e1),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[384, 2397, 121, 2379])).
% 0.94/1.04 tff(2399,plain,
% 0.94/1.04 (op(e0, op(e0, e1)) = op(e0, e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2398])).
% 0.94/1.04 tff(2400,plain,
% 0.94/1.04 (op(e0, op(e0, e1)) = e1),
% 0.94/1.04 inference(transitivity,[status(thm)],[2399, 2398])).
% 0.94/1.04 tff(2401,plain,
% 0.94/1.04 (op(op(e3, e2), e3) = op(e1, op(e1, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2392, 259])).
% 0.94/1.04 tff(2402,plain,
% 0.94/1.04 (op(op(e3, e2), e3) = e1),
% 0.94/1.04 inference(transitivity,[status(thm)],[2401, 781, 132])).
% 0.94/1.04 tff(2403,plain,
% 0.94/1.04 ((op(op(e3, e2), e3) = e2) <=> (e1 = op(e0, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2402, 2246])).
% 0.94/1.04 tff(2404,plain,
% 0.94/1.04 ((op(op(e3, e2), e3) = e2) <=> (op(e0, e0) = e1)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2403, 73])).
% 0.94/1.04 tff(2405,plain,
% 0.94/1.04 ((op(e0, e0) = e1) <=> (op(op(e3, e2), e3) = e2)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2404])).
% 0.94/1.04 tff(2406,plain,
% 0.94/1.04 ((~(op(e0, e0) = e1)) <=> (~(op(op(e3, e2), e3) = e2))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2405])).
% 0.94/1.04 tff(2407,plain,
% 0.94/1.04 (~(op(op(e3, e2), e3) = e2)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[2379, 2406])).
% 0.94/1.04 tff(2408,plain,
% 0.94/1.04 (((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))) | (op(op(e3, e2), e3) = e2)),
% 0.94/1.04 inference(tautology,[status(thm)],[])).
% 0.94/1.04 tff(2409,plain,
% 0.94/1.04 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2408, 2407])).
% 0.94/1.04 tff(2410,assumption,(~(op(e3, e0) = e3)), introduced(assumption)).
% 0.94/1.04 tff(2411,plain,
% 0.94/1.04 (op(e3, e1) = e3),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[422, 1890, 2410, 468])).
% 0.94/1.04 tff(2412,plain,
% 0.94/1.04 (op(op(e1, e0), e1) = op(e3, e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[258])).
% 0.94/1.04 tff(2413,plain,
% 0.94/1.04 (op(e3, e1) = op(e1, e0)),
% 0.94/1.04 inference(transitivity,[status(thm)],[2411, 259])).
% 0.94/1.04 tff(2414,plain,
% 0.94/1.04 (op(op(e3, e1), e1) = op(op(e1, e0), e1)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2413])).
% 0.94/1.04 tff(2415,plain,
% 0.94/1.04 (op(op(e3, e1), e1) = e3),
% 0.94/1.04 inference(transitivity,[status(thm)],[2414, 2412, 2411])).
% 0.94/1.04 tff(2416,plain,
% 0.94/1.04 (((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))) | (~(op(op(e3, e1), e1) = e3))),
% 0.94/1.04 inference(tautology,[status(thm)],[])).
% 0.94/1.04 tff(2417,plain,
% 0.94/1.04 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[2416, 2415])).
% 0.94/1.04 tff(2418,plain,
% 0.94/1.04 (op(e3, op(e0, e3)) = op(e3, e0)),
% 0.94/1.04 inference(monotonicity,[status(thm)],[771])).
% 0.94/1.04 tff(2419,plain,
% 0.94/1.04 (op(e3, op(e3, e0)) = e0),
% 0.94/1.04 inference(transitivity,[status(thm)],[1343, 2418, 466, 771])).
% 0.94/1.04 tff(2420,plain,
% 0.94/1.04 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[1345, 2419])).
% 0.94/1.04 tff(2421,assumption,((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))), introduced(assumption)).
% 0.94/1.04 tff(2422,plain,
% 0.94/1.04 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e1) = op(e3, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2412, 1366])).
% 0.94/1.04 tff(2423,plain,
% 0.94/1.04 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2422, 881])).
% 0.94/1.04 tff(2424,plain,
% 0.94/1.04 ((op(e3, e0) = op(e3, e1)) <=> (op(op(e1, e0), e1) = e0)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2423])).
% 0.94/1.04 tff(2425,plain,
% 0.94/1.04 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(op(e1, e0), e1) = e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[2424])).
% 0.94/1.04 tff(2426,plain,
% 0.94/1.04 (~(op(op(e1, e0), e1) = e0)),
% 0.94/1.04 inference(modus_ponens,[status(thm)],[580, 2425])).
% 0.94/1.04 tff(2427,plain,
% 0.94/1.04 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.94/1.04 inference(unit_resolution,[status(thm)],[1302, 2426])).
% 0.94/1.04 tff(2428,plain,
% 0.94/1.04 (op(e0, e0) = op(e0, op(e0, e3))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[772])).
% 0.94/1.04 tff(2429,plain,
% 0.94/1.04 (e2 = op(e0, op(e0, e3))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2246, 2428])).
% 0.94/1.04 tff(2430,plain,
% 0.94/1.04 (op(op(e1, e0), e0) = op(e3, op(e0, e3))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[258, 772])).
% 0.94/1.04 tff(2431,assumption,(~(op(e2, e2) = e3)), introduced(assumption)).
% 0.94/1.04 tff(2432,plain,
% 0.94/1.04 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e1, e0))),
% 0.94/1.04 inference(monotonicity,[status(thm)],[259])).
% 0.94/1.04 tff(2433,plain,
% 0.94/1.04 ((op(e1, e2) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 0.94/1.04 inference(transitivity,[status(thm)],[2432, 1305])).
% 0.94/1.04 tff(2434,plain,
% 0.94/1.04 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.94/1.04 inference(symmetry,[status(thm)],[2433])).
% 0.94/1.05 tff(2435,plain,
% 0.94/1.05 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2434])).
% 0.94/1.05 tff(2436,plain,
% 0.94/1.05 (~(op(e1, e2) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1312, 2435])).
% 0.94/1.05 tff(2437,plain,
% 0.94/1.05 (op(e0, e2) = e3),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2111, 1890, 2436, 2431])).
% 0.94/1.05 tff(2438,plain,
% 0.94/1.05 (op(e0, e2) = op(e1, e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2437, 259])).
% 0.94/1.05 tff(2439,plain,
% 0.94/1.05 (op(op(e0, e2), e0) = op(op(e1, e0), e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2438])).
% 0.94/1.05 tff(2440,plain,
% 0.94/1.05 (op(op(e0, e2), e0) = e0),
% 0.94/1.05 inference(transitivity,[status(thm)],[2439, 2430, 2418, 466, 771])).
% 0.94/1.05 tff(2441,plain,
% 0.94/1.05 ((op(op(e0, e2), e0) = e2) <=> (e0 = op(e0, op(e0, e3)))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2440, 2429])).
% 0.94/1.05 tff(2442,plain,
% 0.94/1.05 ((op(op(e0, e2), e0) = e2) <=> (op(e0, op(e0, e3)) = e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2441, 2239])).
% 0.94/1.05 tff(2443,plain,
% 0.94/1.05 ((op(e0, op(e0, e3)) = e0) <=> (op(op(e0, e2), e0) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2442])).
% 0.94/1.05 tff(2444,plain,
% 0.94/1.05 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(op(e0, e2), e0) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2443])).
% 0.94/1.05 tff(2445,plain,
% 0.94/1.05 (~(op(op(e0, e2), e0) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[649, 2444])).
% 0.94/1.05 tff(2446,plain,
% 0.94/1.05 (((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))) | (op(op(e0, e2), e0) = e2)),
% 0.94/1.05 inference(tautology,[status(thm)],[])).
% 0.94/1.05 tff(2447,plain,
% 0.94/1.05 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2446, 2445])).
% 0.94/1.05 tff(2448,plain,
% 0.94/1.05 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1459, 2447, 1358, 1362, 1936, 1304, 2427, 2421, 1347, 2420, 2417, 2409])).
% 0.94/1.05 tff(2449,plain,
% 0.94/1.05 (((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))) | (~(op(e0, op(e0, e1)) = e1))),
% 0.94/1.05 inference(tautology,[status(thm)],[])).
% 0.94/1.05 tff(2450,plain,
% 0.94/1.05 (~(op(e0, op(e0, e1)) = e1)),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2449, 2448])).
% 0.94/1.05 tff(2451,plain,
% 0.94/1.05 ($false),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2450, 2400])).
% 0.94/1.05 tff(2452,plain,((op(e3, e2) = e3) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e0, e3) = e1) | (op(e0, e0) = e1) | (op(e0, op(e0, e3)) = e0) | (~(op(e0, e0) = e2)) | (~(op(e0, e3) = e0)) | (~(op(e3, e0) = op(e0, e3))) | (~(op(e1, e0) = e3)) | (~(op(e1, e3) = e1)) | (op(e2, e2) = e3) | (op(e3, e0) = e3) | (op(e3, e3) = e3) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.05 tff(2453,plain,
% 0.94/1.05 (op(e3, e2) = e3),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2452, 2378, 2372, 1261, 2354, 2345, 121, 2339, 649, 2207, 2142, 466, 2201, 132, 2318, 665, 2336, 2293])).
% 0.94/1.05 tff(2454,plain,
% 0.94/1.05 (op(e3, e2) = op(e1, op(e0, e3))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2453, 2202, 2233])).
% 0.94/1.05 tff(2455,plain,
% 0.94/1.05 ((op(e3, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2454])).
% 0.94/1.05 tff(2456,plain,
% 0.94/1.05 ((op(e1, op(e0, e3)) = e1) <=> (op(e3, e2) = e1)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2455])).
% 0.94/1.05 tff(2457,plain,
% 0.94/1.05 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e3, e2) = e1))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2456])).
% 0.94/1.05 tff(2458,plain,
% 0.94/1.05 (~(op(e3, e2) = e1)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[652, 2457])).
% 0.94/1.05 tff(2459,plain,
% 0.94/1.05 (op(e0, e2) = e1),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1613, 2458, 2232, 2229])).
% 0.94/1.05 tff(2460,plain,
% 0.94/1.05 (e1 = op(e0, op(e0, e0))),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[2459, 2212])).
% 0.94/1.05 tff(2461,plain,
% 0.94/1.05 (op(e0, op(e0, e0)) = e1),
% 0.94/1.05 inference(transitivity,[status(thm)],[2209, 2459])).
% 0.94/1.05 tff(2462,plain,
% 0.94/1.05 (op(e0, op(e0, op(e0, e0))) = op(e0, e1)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2461])).
% 0.94/1.05 tff(2463,plain,
% 0.94/1.05 (op(e0, e1) = op(e0, op(e0, op(e0, e0)))),
% 0.94/1.05 inference(symmetry,[status(thm)],[2462])).
% 0.94/1.05 tff(2464,plain,
% 0.94/1.05 (op(e0, op(e0, e3)) = op(e0, e0)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2240])).
% 0.94/1.05 tff(2465,plain,
% 0.94/1.05 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e0) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2464])).
% 0.94/1.05 tff(2466,plain,
% 0.94/1.05 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, op(e0, e3)) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2240, 2201])).
% 0.94/1.05 tff(2467,plain,
% 0.94/1.05 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2466, 2465])).
% 0.94/1.05 tff(2468,plain,
% 0.94/1.05 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2467])).
% 0.94/1.05 tff(2469,plain,
% 0.94/1.05 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = op(e1, e0)))),
% 0.94/1.05 inference(rewrite,[status(thm)],[])).
% 0.94/1.05 tff(2470,plain,
% 0.94/1.05 (~(op(e0, e0) = op(e1, e0))),
% 0.94/1.05 inference(and_elim,[status(thm)],[357])).
% 0.94/1.05 tff(2471,plain,
% 0.94/1.05 (~(op(e0, e0) = op(e1, e0))),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 0.94/1.05 tff(2472,plain,
% 0.94/1.05 (~(op(e0, e0) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[2471, 2468])).
% 0.94/1.05 tff(2473,plain,
% 0.94/1.05 ((op(e0, op(e0, e0)) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 0.94/1.05 inference(commutativity,[status(thm)],[])).
% 0.94/1.05 tff(2474,plain,
% 0.94/1.05 (op(e0, e2) = op(e0, op(e0, e0))),
% 0.94/1.05 inference(symmetry,[status(thm)],[2209])).
% 0.94/1.05 tff(2475,plain,
% 0.94/1.05 ((op(e0, e2) = e3) <=> (op(e0, op(e0, e0)) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2474])).
% 0.94/1.05 tff(2476,plain,
% 0.94/1.05 ((op(e0, e2) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2475, 2473])).
% 0.94/1.05 tff(2477,plain,
% 0.94/1.05 ((e3 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e3)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2476])).
% 0.94/1.05 tff(2478,plain,
% 0.94/1.05 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, op(e0, e0)) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2474, 2453])).
% 0.94/1.05 tff(2479,plain,
% 0.94/1.05 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e0, op(e0, e0)))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2478, 2473])).
% 0.94/1.05 tff(2480,plain,
% 0.94/1.05 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2479, 2477])).
% 0.94/1.05 tff(2481,plain,
% 0.94/1.05 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2480])).
% 0.94/1.05 tff(2482,plain,
% 0.94/1.05 (~(op(e0, e2) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1467, 2481])).
% 0.94/1.05 tff(2483,plain,
% 0.94/1.05 (op(e0, e1) = e3),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1495, 2482, 661, 2472])).
% 0.94/1.05 tff(2484,plain,
% 0.94/1.05 (e3 = op(e0, e1)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2483])).
% 0.94/1.05 tff(2485,plain,
% 0.94/1.05 (e3 = op(e0, op(e0, op(e0, e0)))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2484, 2463])).
% 0.94/1.05 tff(2486,plain,
% 0.94/1.05 ($false),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[842, 2485, 2460, 2208])).
% 0.94/1.05 tff(2487,plain,((op(e0, e3) = e3) | (op(e1, op(e0, e3)) = e1) | (op(e0, e3) = e1) | (op(e0, op(e0, e3)) = e0) | (~(op(e3, e0) = op(e0, e3))) | (~(op(e1, e3) = e1)) | (op(e1, e3) = e0) | (op(e1, e1) = e3) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.05 tff(2488,plain,
% 0.94/1.05 (op(e0, e3) = e3),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2487, 2037, 121, 649, 466, 652, 80, 2041, 651, 650, 656])).
% 0.94/1.05 tff(2489,plain,
% 0.94/1.05 (op(e1, op(e0, e3)) = op(e1, e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2488])).
% 0.94/1.05 tff(2490,plain,
% 0.94/1.05 (op(e1, op(e0, e3)) = e1),
% 0.94/1.05 inference(transitivity,[status(thm)],[2489, 2037])).
% 0.94/1.05 tff(2491,plain,
% 0.94/1.05 ($false),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[652, 2490])).
% 0.94/1.05 tff(2492,plain,((op(e1, e3) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e0, e3) = e1) | (op(e0, op(e0, e3)) = e0) | (~(op(e3, e0) = op(e0, e3))) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3) | (op(e3, e3) = e0) | (op(op(e1, e3), e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.05 tff(2493,plain,
% 0.94/1.05 (op(e1, e3) = e0),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2492, 656, 121, 649, 466, 651, 650, 652, 655])).
% 0.94/1.05 tff(2494,plain,
% 0.94/1.05 (op(op(e1, e3), e1) = op(e0, e1)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2493])).
% 0.94/1.05 tff(2495,plain,
% 0.94/1.05 ((op(op(e1, e3), e1) = e3) <=> (op(e0, e1) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2494])).
% 0.94/1.05 tff(2496,plain,
% 0.94/1.05 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e0, e1) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2495])).
% 0.94/1.05 tff(2497,plain,
% 0.94/1.05 (~(op(e0, e1) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[655, 2496])).
% 0.94/1.05 tff(2498,plain,
% 0.94/1.05 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[1219])).
% 0.94/1.05 tff(2499,plain,
% 0.94/1.05 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2498])).
% 0.94/1.05 tff(2500,plain,
% 0.94/1.05 (~(op(e0, e3) = e0)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[64, 2499])).
% 0.94/1.05 tff(2501,plain,
% 0.94/1.05 (op(e0, e3) = e2),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[687, 661, 121, 2500])).
% 0.94/1.05 tff(2502,plain,
% 0.94/1.05 (e2 = op(e0, e3)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2501])).
% 0.94/1.05 tff(2503,plain,
% 0.94/1.05 (op(e0, e2) = op(e0, op(e0, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2502])).
% 0.94/1.05 tff(2504,plain,
% 0.94/1.05 (op(e0, op(e0, e3)) = op(e0, e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2503])).
% 0.94/1.05 tff(2505,plain,
% 0.94/1.05 (op(e2, op(e0, e3)) = op(e2, e2)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2501])).
% 0.94/1.05 tff(2506,plain,
% 0.94/1.05 (op(e2, e2) = op(e2, op(e0, e3))),
% 0.94/1.05 inference(symmetry,[status(thm)],[2505])).
% 0.94/1.05 tff(2507,plain,
% 0.94/1.05 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2506])).
% 0.94/1.05 tff(2508,plain,
% 0.94/1.05 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2507])).
% 0.94/1.05 tff(2509,plain,
% 0.94/1.05 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e2) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2508])).
% 0.94/1.05 tff(2510,plain,
% 0.94/1.05 (~(op(e2, e2) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[651, 2509])).
% 0.94/1.05 tff(2511,plain,
% 0.94/1.05 (e2 = op(e3, e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2502, 467])).
% 0.94/1.05 tff(2512,plain,
% 0.94/1.05 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2511])).
% 0.94/1.05 tff(2513,plain,
% 0.94/1.05 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2512])).
% 0.94/1.05 tff(2514,plain,
% 0.94/1.05 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2513])).
% 0.94/1.05 tff(2515,plain,
% 0.94/1.05 (~(op(e2, e0) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[747, 2514])).
% 0.94/1.05 tff(2516,plain,
% 0.94/1.05 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2502])).
% 0.94/1.05 tff(2517,plain,
% 0.94/1.05 ((op(e2, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2516, 925])).
% 0.94/1.05 tff(2518,plain,
% 0.94/1.05 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2517])).
% 0.94/1.05 tff(2519,plain,
% 0.94/1.05 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2518])).
% 0.94/1.05 tff(2520,plain,
% 0.94/1.05 (~(op(e2, e3) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[964, 2519])).
% 0.94/1.05 tff(2521,plain,
% 0.94/1.05 (op(e2, e1) = e2),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2088, 2520, 2515, 2510])).
% 0.94/1.05 tff(2522,plain,
% 0.94/1.05 (op(e2, e1) = op(e0, e3)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2521, 2502])).
% 0.94/1.05 tff(2523,plain,
% 0.94/1.05 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2522])).
% 0.94/1.05 tff(2524,plain,
% 0.94/1.05 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2523])).
% 0.94/1.05 tff(2525,plain,
% 0.94/1.05 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2524])).
% 0.94/1.05 tff(2526,plain,
% 0.94/1.05 (~(op(e2, e1) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[661, 2525])).
% 0.94/1.05 tff(2527,assumption,(~(op(e0, e1) = e3)), introduced(assumption)).
% 0.94/1.05 tff(2528,plain,
% 0.94/1.05 (~(op(e3, e2) = e3)),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[860, 2501, 650])).
% 0.94/1.05 tff(2529,plain,
% 0.94/1.05 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2511])).
% 0.94/1.05 tff(2530,plain,
% 0.94/1.05 ((op(e3, e2) = e2) <=> (op(e3, e0) = op(e3, e2))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2529, 1123])).
% 0.94/1.05 tff(2531,plain,
% 0.94/1.05 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2530])).
% 0.94/1.05 tff(2532,plain,
% 0.94/1.05 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2531])).
% 0.94/1.05 tff(2533,plain,
% 0.94/1.05 (~(op(e3, e2) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1133, 2532])).
% 0.94/1.05 tff(2534,plain,
% 0.94/1.05 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2502])).
% 0.94/1.05 tff(2535,plain,
% 0.94/1.05 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2534])).
% 0.94/1.05 tff(2536,plain,
% 0.94/1.05 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2535])).
% 0.94/1.05 tff(2537,plain,
% 0.94/1.05 (~(op(e0, e2) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[918, 2536])).
% 0.94/1.05 tff(2538,plain,
% 0.94/1.05 (op(e1, e2) = e2),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1151, 2510, 2537, 2533])).
% 0.94/1.05 tff(2539,plain,
% 0.94/1.05 (op(e1, e2) = op(e0, e3)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2538, 2502])).
% 0.94/1.05 tff(2540,plain,
% 0.94/1.05 ((op(e1, e2) = e3) <=> (op(e0, e3) = e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2539])).
% 0.94/1.05 tff(2541,plain,
% 0.94/1.05 ((op(e0, e3) = e3) <=> (op(e1, e2) = e3)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2540])).
% 0.94/1.05 tff(2542,plain,
% 0.94/1.05 ((~(op(e0, e3) = e3)) <=> (~(op(e1, e2) = e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2541])).
% 0.94/1.05 tff(2543,plain,
% 0.94/1.05 (~(op(e1, e2) = e3)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[661, 2542])).
% 0.94/1.05 tff(2544,plain,
% 0.94/1.05 ((op(e2, e1) = e0) <=> (op(e0, e3) = e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2522])).
% 0.94/1.05 tff(2545,plain,
% 0.94/1.05 ((op(e0, e3) = e0) <=> (op(e2, e1) = e0)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2544])).
% 0.94/1.05 tff(2546,plain,
% 0.94/1.05 ((~(op(e0, e3) = e0)) <=> (~(op(e2, e1) = e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2545])).
% 0.94/1.05 tff(2547,plain,
% 0.94/1.05 (~(op(e2, e1) = e0)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[2500, 2546])).
% 0.94/1.05 tff(2548,plain,
% 0.94/1.05 (op(op(e2, e1), e1) = op(e2, e1)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2521])).
% 0.94/1.05 tff(2549,plain,
% 0.94/1.05 (op(op(e2, e1), e1) = e2),
% 0.94/1.05 inference(transitivity,[status(thm)],[2548, 2521])).
% 0.94/1.05 tff(2550,plain,
% 0.94/1.05 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2371, 2549])).
% 0.94/1.05 tff(2551,plain,
% 0.94/1.05 (op(e1, op(e0, e3)) = op(e1, e2)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2501])).
% 0.94/1.05 tff(2552,plain,
% 0.94/1.05 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2539])).
% 0.94/1.05 tff(2553,plain,
% 0.94/1.05 (op(e1, op(e1, e2)) = e2),
% 0.94/1.05 inference(transitivity,[status(thm)],[2552, 2551, 2538])).
% 0.94/1.05 tff(2554,plain,
% 0.94/1.05 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2377, 2553])).
% 0.94/1.05 tff(2555,plain,
% 0.94/1.05 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[1219])).
% 0.94/1.05 tff(2556,plain,
% 0.94/1.05 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2555, 86])).
% 0.94/1.05 tff(2557,plain,
% 0.94/1.05 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2556])).
% 0.94/1.05 tff(2558,plain,
% 0.94/1.05 (~(op(e2, e3) = e0)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[118, 2557])).
% 0.94/1.05 tff(2559,assumption,(~(op(e2, e1) = e0)), introduced(assumption)).
% 0.94/1.05 tff(2560,plain,
% 0.94/1.05 (e2 = op(e0, e3)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2])).
% 0.94/1.05 tff(2561,plain,
% 0.94/1.05 (e2 = op(e3, e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2560, 467])).
% 0.94/1.05 tff(2562,plain,
% 0.94/1.05 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2561])).
% 0.94/1.05 tff(2563,plain,
% 0.94/1.05 ((op(e3, e2) = e2) <=> (op(e3, e0) = op(e3, e2))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2562, 1123])).
% 0.94/1.05 tff(2564,plain,
% 0.94/1.05 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2563])).
% 0.94/1.05 tff(2565,plain,
% 0.94/1.05 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2564])).
% 0.94/1.05 tff(2566,plain,
% 0.94/1.05 (~(op(e3, e2) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1133, 2565])).
% 0.94/1.05 tff(2567,plain,
% 0.94/1.05 ((op(e3, e3) = e2) <=> (op(e3, e3) = op(e0, e3))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2560])).
% 0.94/1.05 tff(2568,plain,
% 0.94/1.05 ((op(e3, e3) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 0.94/1.05 inference(transitivity,[status(thm)],[2567, 659])).
% 0.94/1.05 tff(2569,plain,
% 0.94/1.05 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2568])).
% 0.94/1.05 tff(2570,plain,
% 0.94/1.05 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2569])).
% 0.94/1.05 tff(2571,plain,
% 0.94/1.05 (~(op(e3, e3) = e2)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1077, 2570])).
% 0.94/1.05 tff(2572,plain,
% 0.94/1.05 (op(e3, e3) = e1),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1071, 468, 2571, 656])).
% 0.94/1.05 tff(2573,plain,
% 0.94/1.05 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2572])).
% 0.94/1.05 tff(2574,plain,
% 0.94/1.05 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2573])).
% 0.94/1.05 tff(2575,plain,
% 0.94/1.05 (~(op(e3, e2) = e1)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1888, 2574])).
% 0.94/1.05 tff(2576,plain,
% 0.94/1.05 (op(e3, e2) = e0),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1898, 2575, 1890, 2566])).
% 0.94/1.05 tff(2577,plain,
% 0.94/1.05 (e0 = op(e3, e2)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2576])).
% 0.94/1.05 tff(2578,plain,
% 0.94/1.05 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e3, e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2577])).
% 0.94/1.05 tff(2579,plain,
% 0.94/1.05 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e0)),
% 0.94/1.05 inference(symmetry,[status(thm)],[2578])).
% 0.94/1.05 tff(2580,plain,
% 0.94/1.05 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2579])).
% 0.94/1.05 tff(2581,plain,
% 0.94/1.05 (~(op(e2, e2) = e0)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[1546, 2580])).
% 0.94/1.05 tff(2582,plain,
% 0.94/1.05 (op(e2, e0) = e0),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2311, 2581, 2559, 2558])).
% 0.94/1.05 tff(2583,plain,
% 0.94/1.05 (op(op(e0, e3), e0) = op(e2, e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2])).
% 0.94/1.05 tff(2584,plain,
% 0.94/1.05 (op(e2, op(e3, e2)) = op(op(e0, e3), e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2560, 2576])).
% 0.94/1.05 tff(2585,plain,
% 0.94/1.05 (op(e2, e0) = op(e3, e2)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2582, 2577])).
% 0.94/1.05 tff(2586,plain,
% 0.94/1.05 (op(e2, op(e2, e0)) = op(e2, op(e3, e2))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2585])).
% 0.94/1.05 tff(2587,plain,
% 0.94/1.05 (op(e2, op(e2, e0)) = e0),
% 0.94/1.05 inference(transitivity,[status(thm)],[2586, 2584, 2583, 2582])).
% 0.94/1.05 tff(2588,plain,
% 0.94/1.05 (op(e3, op(e3, e2)) = op(e3, e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2576])).
% 0.94/1.05 tff(2589,plain,
% 0.94/1.05 (op(e3, op(e3, e2)) = e2),
% 0.94/1.05 inference(transitivity,[status(thm)],[2588, 466, 2])).
% 0.94/1.05 tff(2590,plain,
% 0.94/1.05 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[1904, 2589])).
% 0.94/1.05 tff(2591,plain,
% 0.94/1.05 (op(e3, e1) = e3),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[422, 468, 1890, 665])).
% 0.94/1.05 tff(2592,plain,
% 0.94/1.05 (op(e3, op(e3, e1)) = op(e3, e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2591])).
% 0.94/1.05 tff(2593,plain,
% 0.94/1.05 (op(e3, op(e3, e1)) = e1),
% 0.94/1.05 inference(transitivity,[status(thm)],[2592, 2572])).
% 0.94/1.05 tff(2594,plain,
% 0.94/1.05 (((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))) | (~(op(e3, op(e3, e1)) = e1))),
% 0.94/1.05 inference(tautology,[status(thm)],[])).
% 0.94/1.05 tff(2595,plain,
% 0.94/1.05 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.94/1.05 inference(unit_resolution,[status(thm)],[2594, 2593])).
% 0.94/1.05 tff(2596,plain,
% 0.94/1.05 (op(e2, e3) = op(op(e0, e3), e3)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2560])).
% 0.94/1.05 tff(2597,plain,
% 0.94/1.05 ((op(e2, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2596])).
% 0.94/1.05 tff(2598,plain,
% 0.94/1.05 ((op(e2, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 0.94/1.05 inference(transitivity,[status(thm)],[2597, 1758])).
% 0.94/1.05 tff(2599,plain,
% 0.94/1.05 ((~(op(e2, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 0.94/1.05 inference(monotonicity,[status(thm)],[2598])).
% 0.94/1.05 tff(2600,plain,
% 0.94/1.05 (~(op(op(e3, e0), e3) = e0)),
% 0.94/1.05 inference(modus_ponens,[status(thm)],[2558, 2599])).
% 0.94/1.06 tff(2601,plain,
% 0.94/1.06 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1764, 2600])).
% 0.94/1.06 tff(2602,plain,
% 0.94/1.06 ((op(e1, e3) = e3) <=> (e0 = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[1219])).
% 0.94/1.06 tff(2603,plain,
% 0.94/1.06 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2602])).
% 0.94/1.06 tff(2604,plain,
% 0.94/1.06 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2603])).
% 0.94/1.06 tff(2605,plain,
% 0.94/1.06 (~(op(e1, e3) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[181, 2604])).
% 0.94/1.06 tff(2606,plain,
% 0.94/1.06 (op(e2, e3) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[480, 468, 661, 2605])).
% 0.94/1.06 tff(2607,plain,
% 0.94/1.06 (op(op(e0, e3), e3) = op(e2, e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2596])).
% 0.94/1.06 tff(2608,plain,
% 0.94/1.06 (op(e2, op(e2, e3)) = op(op(e0, e3), e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2560, 2606])).
% 0.94/1.06 tff(2609,plain,
% 0.94/1.06 (op(e2, op(e2, e3)) = e3),
% 0.94/1.06 inference(transitivity,[status(thm)],[2608, 2607, 2606])).
% 0.94/1.06 tff(2610,plain,
% 0.94/1.06 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2344, 2609])).
% 0.94/1.06 tff(2611,plain,
% 0.94/1.06 (op(e0, op(e2, e3)) = op(e0, e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2606])).
% 0.94/1.06 tff(2612,plain,
% 0.94/1.06 (e3 = op(e2, e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2606])).
% 0.94/1.06 tff(2613,plain,
% 0.94/1.06 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2612])).
% 0.94/1.06 tff(2614,plain,
% 0.94/1.06 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2613])).
% 0.94/1.06 tff(2615,plain,
% 0.94/1.06 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2614])).
% 0.94/1.06 tff(2616,plain,
% 0.94/1.06 (~(op(e2, e2) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[515, 2615])).
% 0.94/1.06 tff(2617,plain,
% 0.94/1.06 (op(e0, e2) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2111, 2616, 1890, 75])).
% 0.94/1.06 tff(2618,plain,
% 0.94/1.06 (op(e0, e2) = op(e2, e3)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2617, 2612])).
% 0.94/1.06 tff(2619,plain,
% 0.94/1.06 (op(e0, op(e0, e2)) = op(e0, op(e2, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2618])).
% 0.94/1.06 tff(2620,plain,
% 0.94/1.06 (op(e0, op(e0, e2)) = e2),
% 0.94/1.06 inference(transitivity,[status(thm)],[2619, 2611, 2])).
% 0.94/1.06 tff(2621,plain,
% 0.94/1.06 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1331, 2620])).
% 0.94/1.06 tff(2622,plain,
% 0.94/1.06 (op(e1, op(e2, e3)) = op(e1, e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2606])).
% 0.94/1.06 tff(2623,plain,
% 0.94/1.06 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2591])).
% 0.94/1.06 tff(2624,plain,
% 0.94/1.06 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2623])).
% 0.94/1.06 tff(2625,plain,
% 0.94/1.06 (~(op(e1, e1) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[945, 2624])).
% 0.94/1.06 tff(2626,plain,
% 0.94/1.06 (op(e1, e0) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[247, 2625, 2605, 75])).
% 0.94/1.06 tff(2627,plain,
% 0.94/1.06 (op(e1, e0) = op(e2, e3)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2626, 2612])).
% 0.94/1.06 tff(2628,plain,
% 0.94/1.06 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2627])).
% 0.94/1.06 tff(2629,plain,
% 0.94/1.06 (op(e1, op(e1, e0)) = e0),
% 0.94/1.06 inference(transitivity,[status(thm)],[2628, 2622, 1219])).
% 0.94/1.06 tff(2630,plain,
% 0.94/1.06 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1836, 2629])).
% 0.94/1.06 tff(2631,plain,
% 0.94/1.06 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = op(e2, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2583, 2612])).
% 0.94/1.06 tff(2632,plain,
% 0.94/1.06 ((op(e2, e0) = op(e2, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2631])).
% 0.94/1.06 tff(2633,plain,
% 0.94/1.06 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2632])).
% 0.94/1.06 tff(2634,plain,
% 0.94/1.06 (~(op(op(e0, e3), e0) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[989, 2633])).
% 0.94/1.06 tff(2635,plain,
% 0.94/1.06 (((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))) | (op(op(e0, e3), e0) = e3)),
% 0.94/1.06 inference(tautology,[status(thm)],[])).
% 0.94/1.06 tff(2636,plain,
% 0.94/1.06 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2635, 2634])).
% 0.94/1.06 tff(2637,plain,
% 0.94/1.06 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[1219])).
% 0.94/1.06 tff(2638,plain,
% 0.94/1.06 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2637])).
% 0.94/1.06 tff(2639,plain,
% 0.94/1.06 (~(op(e1, e1) = e0)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[619, 2638])).
% 0.94/1.06 tff(2640,plain,
% 0.94/1.06 (op(e3, e1) = op(op(e0, e3), e3)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2591, 2612, 2596])).
% 0.94/1.06 tff(2641,plain,
% 0.94/1.06 ((op(e3, e1) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2640])).
% 0.94/1.06 tff(2642,plain,
% 0.94/1.06 ((op(op(e0, e3), e3) = e0) <=> (op(e3, e1) = e0)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2641])).
% 0.94/1.06 tff(2643,plain,
% 0.94/1.06 ((~(op(op(e0, e3), e3) = e0)) <=> (~(op(e3, e1) = e0))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2642])).
% 0.94/1.06 tff(2644,plain,
% 0.94/1.06 ((~(op(e2, e3) = e0)) <=> (~(op(op(e0, e3), e3) = e0))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2597])).
% 0.94/1.06 tff(2645,plain,
% 0.94/1.06 (~(op(op(e0, e3), e3) = e0)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[2558, 2644])).
% 0.94/1.06 tff(2646,plain,
% 0.94/1.06 (~(op(e3, e1) = e0)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[2645, 2643])).
% 0.94/1.06 tff(2647,plain,
% 0.94/1.06 (op(e0, e1) = e0),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[292, 2646, 2639, 2559])).
% 0.94/1.06 tff(2648,plain,
% 0.94/1.06 (op(op(e0, e1), e1) = op(e0, e1)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2647])).
% 0.94/1.06 tff(2649,plain,
% 0.94/1.06 (op(op(e0, e1), e1) = e0),
% 0.94/1.06 inference(transitivity,[status(thm)],[2648, 2647])).
% 0.94/1.06 tff(2650,plain,
% 0.94/1.06 (((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))) | (~(op(op(e0, e1), e1) = e0))),
% 0.94/1.06 inference(tautology,[status(thm)],[])).
% 0.94/1.06 tff(2651,plain,
% 0.94/1.06 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2650, 2649])).
% 0.94/1.06 tff(2652,plain,
% 0.94/1.06 (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1459, 2651, 1358, 2636, 1936, 1304, 2630, 2621, 2610, 2601, 2595, 2590])).
% 0.94/1.06 tff(2653,plain,
% 0.94/1.06 (((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))) | (~(op(e2, op(e2, e0)) = e0))),
% 0.94/1.06 inference(tautology,[status(thm)],[])).
% 0.94/1.06 tff(2654,plain,
% 0.94/1.06 (~(op(e2, op(e2, e0)) = e0)),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2653, 2652])).
% 0.94/1.06 tff(2655,plain,
% 0.94/1.06 ($false),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2654, 2587])).
% 0.94/1.06 tff(2656,plain,((op(e3, e3) = e3) | (~(op(e0, e3) = e2)) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e1) = e0) | (~(op(e1, e3) = e0)) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e2) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e0) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.06 tff(2657,plain,
% 0.94/1.06 (op(e3, e3) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2656, 2501, 2554, 2550, 1304, 2547, 1219, 466, 2543, 2528, 656, 661])).
% 0.94/1.06 tff(2658,plain,
% 0.94/1.06 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2657])).
% 0.94/1.06 tff(2659,plain,
% 0.94/1.06 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2658])).
% 0.94/1.06 tff(2660,plain,
% 0.94/1.06 (~(op(e3, e1) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[437, 2659])).
% 0.94/1.06 tff(2661,plain,
% 0.94/1.06 (op(e1, e1) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1730, 2660, 2527, 2526])).
% 0.94/1.06 tff(2662,plain,
% 0.94/1.06 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2661])).
% 0.94/1.06 tff(2663,plain,
% 0.94/1.06 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2662])).
% 0.94/1.06 tff(2664,plain,
% 0.94/1.06 (~(op(e1, e0) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[737, 2663])).
% 0.94/1.06 tff(2665,plain,
% 0.94/1.06 (op(op(e0, e3), e0) = op(e2, e0)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2501])).
% 0.94/1.06 tff(2666,plain,
% 0.94/1.06 (op(e2, e0) = op(op(e0, e3), e0)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2665])).
% 0.94/1.06 tff(2667,plain,
% 0.94/1.06 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2666])).
% 0.94/1.06 tff(2668,plain,
% 0.94/1.06 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2667])).
% 0.94/1.06 tff(2669,plain,
% 0.94/1.06 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[1219])).
% 0.94/1.06 tff(2670,plain,
% 0.94/1.06 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2669])).
% 0.94/1.06 tff(2671,plain,
% 0.94/1.06 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2670])).
% 0.94/1.06 tff(2672,plain,
% 0.94/1.06 (~(op(e1, e3) = e1)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[26, 2671])).
% 0.94/1.06 tff(2673,plain,
% 0.94/1.06 (e3 = op(e3, e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2657])).
% 0.94/1.06 tff(2674,plain,
% 0.94/1.06 ((e1 = e3) <=> (e1 = op(e3, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2673])).
% 0.94/1.06 tff(2675,plain,
% 0.94/1.06 ((e1 = e3) <=> (op(e3, e3) = e1)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2674, 657])).
% 0.94/1.06 tff(2676,plain,
% 0.94/1.06 ((~(e1 = e3)) <=> (~(op(e3, e3) = e1))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2675])).
% 0.94/1.06 tff(2677,plain,
% 0.94/1.06 (~(op(e3, e3) = e1)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[303, 2676])).
% 0.94/1.06 tff(2678,plain,
% 0.94/1.06 (op(e2, e3) = e1),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[151, 2677, 121, 2672])).
% 0.94/1.06 tff(2679,plain,
% 0.94/1.06 (op(e2, e2) = e0),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2311, 983, 2559, 1063])).
% 0.94/1.06 tff(2680,plain,
% 0.94/1.06 (e0 = op(e2, e2)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[2679, 995])).
% 0.94/1.06 tff(2681,plain,
% 0.94/1.06 (op(e2, op(e2, e2)) = op(op(e0, e3), e0)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2560, 2679])).
% 0.94/1.06 tff(2682,plain,
% 0.94/1.06 (op(op(e0, e3), e0) = op(e2, op(e2, e2))),
% 0.94/1.06 inference(symmetry,[status(thm)],[2681])).
% 0.94/1.06 tff(2683,plain,
% 0.94/1.06 (op(e2, e0) = op(op(e0, e3), e0)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2583])).
% 0.94/1.06 tff(2684,assumption,(op(e2, e3) = e1), introduced(assumption)).
% 0.94/1.06 tff(2685,plain,
% 0.94/1.06 (e1 = op(e2, e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2684])).
% 0.94/1.06 tff(2686,plain,
% 0.94/1.06 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e2, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2685])).
% 0.94/1.06 tff(2687,plain,
% 0.94/1.06 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2686])).
% 0.94/1.06 tff(2688,plain,
% 0.94/1.06 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2687])).
% 0.94/1.06 tff(2689,plain,
% 0.94/1.06 (~(op(e2, e0) = e1)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[989, 2688])).
% 0.94/1.06 tff(2690,plain,
% 0.94/1.06 (op(e2, e0) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[765, 983, 982, 2689])).
% 0.94/1.06 tff(2691,plain,
% 0.94/1.06 (e3 = op(e2, e0)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2690])).
% 0.94/1.06 tff(2692,plain,
% 0.94/1.06 (e3 = op(e2, op(e2, e2))),
% 0.94/1.06 inference(transitivity,[status(thm)],[2691, 2683, 2682])).
% 0.94/1.06 tff(2693,plain,
% 0.94/1.06 (op(e2, op(e2, e2)) = e3),
% 0.94/1.06 inference(transitivity,[status(thm)],[2681, 2583, 2690])).
% 0.94/1.06 tff(2694,plain,
% 0.94/1.06 (op(e2, op(e2, op(e2, e2))) = op(op(e0, e3), e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2560, 2693])).
% 0.94/1.06 tff(2695,plain,
% 0.94/1.06 (op(op(e0, e3), e3) = op(e2, op(e2, op(e2, e2)))),
% 0.94/1.06 inference(symmetry,[status(thm)],[2694])).
% 0.94/1.06 tff(2696,plain,
% 0.94/1.06 (e1 = op(e2, op(e2, op(e2, e2)))),
% 0.94/1.06 inference(transitivity,[status(thm)],[2685, 2596, 2695])).
% 0.94/1.06 tff(2697,plain,
% 0.94/1.06 ($false),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1010, 2696, 2692, 2680])).
% 0.94/1.06 tff(2698,plain,((op(e2, e0) = e0) | (~(op(e2, e3) = e1)) | (~(op(e0, e3) = e2)) | (op(e2, e0) = e2) | (op(e2, e1) = e0) | (op(e2, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.06 tff(2699,plain,
% 0.94/1.06 (op(e2, e0) = e0),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2698, 2678, 2501, 2515, 2547, 2558])).
% 0.94/1.06 tff(2700,plain,
% 0.94/1.06 (op(op(e0, e3), e0) = e0),
% 0.94/1.06 inference(transitivity,[status(thm)],[2665, 2699])).
% 0.94/1.06 tff(2701,plain,
% 0.94/1.06 ((op(op(e0, e3), e0) = e3) <=> (e0 = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2700])).
% 0.94/1.06 tff(2702,plain,
% 0.94/1.06 ((e0 = e3) <=> (op(op(e0, e3), e0) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2701])).
% 0.94/1.06 tff(2703,plain,
% 0.94/1.06 ((e0 = e3) <=> (op(e2, e0) = e3)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2702, 2668])).
% 0.94/1.06 tff(2704,plain,
% 0.94/1.06 ((~(e0 = e3)) <=> (~(op(e2, e0) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2703])).
% 0.94/1.06 tff(2705,plain,
% 0.94/1.06 (~(op(e2, e0) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[181, 2704])).
% 0.94/1.06 tff(2706,plain,
% 0.94/1.06 (((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))),
% 0.94/1.06 inference(rewrite,[status(thm)],[])).
% 0.94/1.06 tff(2707,plain,
% 0.94/1.06 ((((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))),
% 0.94/1.06 inference(rewrite,[status(thm)],[])).
% 0.94/1.06 tff(2708,plain,
% 0.94/1.06 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3))),
% 0.94/1.06 inference(rewrite,[status(thm)],[])).
% 0.94/1.06 tff(2709,plain,
% 0.94/1.06 (((((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))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2708])).
% 0.94/1.06 tff(2710,plain,
% 0.94/1.06 (((((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))),
% 0.94/1.06 inference(transitivity,[status(thm)],[2709, 2707])).
% 0.94/1.06 tff(2711,plain,
% 0.94/1.06 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)),
% 0.94/1.06 inference(and_elim,[status(thm)],[376])).
% 0.94/1.06 tff(2712,plain,
% 0.94/1.06 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 0.94/1.06 tff(2713,plain,
% 0.94/1.06 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[2712, 2706])).
% 0.94/1.06 tff(2714,plain,
% 0.94/1.06 (op(e0, e0) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[2713, 2705, 665, 2664])).
% 0.94/1.06 tff(2715,plain,
% 0.94/1.06 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2714])).
% 0.94/1.06 tff(2716,plain,
% 0.94/1.06 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2715])).
% 0.94/1.06 tff(2717,plain,
% 0.94/1.06 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2716, 2504])).
% 0.94/1.06 tff(2718,plain,
% 0.94/1.06 ((e1 = op(e0, op(e0, op(e0, e0)))) <=> (e1 = op(e0, e2))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2717])).
% 0.94/1.06 tff(2719,plain,
% 0.94/1.06 ((e1 = op(e0, op(e0, op(e0, e0)))) <=> (op(e0, e2) = e1)),
% 0.94/1.06 inference(transitivity,[status(thm)],[2718, 697])).
% 0.94/1.06 tff(2720,plain,
% 0.94/1.06 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, op(e0, e0))))),
% 0.94/1.06 inference(symmetry,[status(thm)],[2719])).
% 0.94/1.06 tff(2721,plain,
% 0.94/1.06 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2503])).
% 0.94/1.06 tff(2722,plain,
% 0.94/1.06 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2721])).
% 0.94/1.06 tff(2723,plain,
% 0.94/1.06 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(e0, e2) = e0))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2722])).
% 0.94/1.06 tff(2724,plain,
% 0.94/1.06 (~(op(e0, e2) = e0)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[649, 2723])).
% 0.94/1.06 tff(2725,plain,
% 0.94/1.06 ((op(e0, e2) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2503])).
% 0.94/1.06 tff(2726,plain,
% 0.94/1.06 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e2) = e3)),
% 0.94/1.06 inference(symmetry,[status(thm)],[2725])).
% 0.94/1.06 tff(2727,plain,
% 0.94/1.06 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2657])).
% 0.94/1.06 tff(2728,plain,
% 0.94/1.06 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.94/1.06 inference(monotonicity,[status(thm)],[2727])).
% 0.94/1.06 tff(2729,plain,
% 0.94/1.06 (~(op(e2, e3) = e3)),
% 0.94/1.06 inference(modus_ponens,[status(thm)],[368, 2728])).
% 0.94/1.06 tff(2730,plain,
% 0.94/1.06 (op(e2, e2) = e3),
% 0.94/1.06 inference(unit_resolution,[status(thm)],[1559, 2705, 2526, 2729])).
% 0.94/1.07 tff(2731,plain,
% 0.94/1.07 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, op(e0, e3)) = e3)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2503, 2730])).
% 0.94/1.07 tff(2732,plain,
% 0.94/1.07 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2731, 2726])).
% 0.94/1.07 tff(2733,plain,
% 0.94/1.07 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2732])).
% 0.94/1.07 tff(2734,plain,
% 0.94/1.07 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = op(e2, e2)))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2735,plain,
% 0.94/1.07 (~(op(e0, e2) = op(e2, e2))),
% 0.94/1.07 inference(and_elim,[status(thm)],[219])).
% 0.94/1.07 tff(2736,plain,
% 0.94/1.07 (~(op(e0, e2) = op(e2, e2))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 0.94/1.07 tff(2737,plain,
% 0.94/1.07 (~(op(e0, e2) = e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2736, 2733])).
% 0.94/1.07 tff(2738,plain,
% 0.94/1.07 (((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))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2739,plain,
% 0.94/1.07 ((((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))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2740,plain,
% 0.94/1.07 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2741,plain,
% 0.94/1.07 (((((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))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2740])).
% 0.94/1.07 tff(2742,plain,
% 0.94/1.07 (((((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))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2741, 2739])).
% 0.94/1.07 tff(2743,plain,
% 0.94/1.07 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)),
% 0.94/1.07 inference(and_elim,[status(thm)],[825])).
% 0.94/1.07 tff(2744,plain,
% 0.94/1.07 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 0.94/1.07 tff(2745,plain,
% 0.94/1.07 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2744, 2738])).
% 0.94/1.07 tff(2746,plain,
% 0.94/1.07 (op(e0, e2) = e1),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[2745, 2737, 2537, 2724])).
% 0.94/1.07 tff(2747,plain,
% 0.94/1.07 (e1 = op(e0, op(e0, op(e0, e0)))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2746, 2720])).
% 0.94/1.07 tff(2748,plain,
% 0.94/1.07 (e3 = op(e0, e0)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2714, 71])).
% 0.94/1.07 tff(2749,plain,
% 0.94/1.07 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.94/1.07 inference(symmetry,[status(thm)],[2715])).
% 0.94/1.07 tff(2750,plain,
% 0.94/1.07 (e2 = op(e0, op(e0, e0))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2502, 2749])).
% 0.94/1.07 tff(2751,plain,
% 0.94/1.07 ((~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0)))))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0))))))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2752,plain,
% 0.94/1.07 (((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0)))))))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2753,plain,
% 0.94/1.07 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0))))))))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2752])).
% 0.94/1.07 tff(2754,plain,
% 0.94/1.07 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0))))))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2753, 2751])).
% 0.94/1.07 tff(2755,plain,
% 0.94/1.07 ((~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2756,plain,
% 0.94/1.07 ((~(((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2757,axiom,(~(((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e1 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax9')).
% 0.94/1.07 tff(2758,plain,
% 0.94/1.07 (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 0.94/1.07 tff(2759,plain,
% 0.94/1.07 (~((e2 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2758, 2755])).
% 0.94/1.07 tff(2760,plain,
% 0.94/1.07 ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, op(e0, op(e0, e0)))))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2759, 2754])).
% 0.94/1.07 tff(2761,plain,
% 0.94/1.07 (~(e1 = op(e0, op(e0, op(e0, e0))))),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[2760, 2750, 2748])).
% 0.94/1.07 tff(2762,plain,
% 0.94/1.07 ($false),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[2761, 2747])).
% 0.94/1.07 tff(2763,plain,((op(e0, e3) = e3) | (op(e0, e1) = e3) | (op(e0, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e1, e3) = e0)) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, e3) = e0) | (op(e2, op(e0, e3)) = e2) | (op(e0, op(e0, e3)) = e0) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.94/1.07 tff(2764,plain,
% 0.94/1.07 (op(e0, e3) = e3),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[2763, 2497, 121, 1261, 2493, 466, 656, 651, 649, 650])).
% 0.94/1.07 tff(2765,plain,
% 0.94/1.07 (e3 = op(e0, e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2764])).
% 0.94/1.07 tff(2766,plain,
% 0.94/1.07 (op(e2, e3) = op(e2, op(e0, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2765])).
% 0.94/1.07 tff(2767,plain,
% 0.94/1.07 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2766])).
% 0.94/1.07 tff(2768,plain,
% 0.94/1.07 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2767])).
% 0.94/1.07 tff(2769,plain,
% 0.94/1.07 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e3) = e2))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2768])).
% 0.94/1.07 tff(2770,plain,
% 0.94/1.07 (~(op(e2, e3) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[651, 2769])).
% 0.94/1.07 tff(2771,plain,
% 0.94/1.07 ((op(e1, e3) = e2) <=> (e0 = e2)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2493])).
% 0.94/1.07 tff(2772,plain,
% 0.94/1.07 ((e0 = e2) <=> (op(e1, e3) = e2)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2771])).
% 0.94/1.07 tff(2773,plain,
% 0.94/1.07 ((~(e0 = e2)) <=> (~(op(e1, e3) = e2))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2772])).
% 0.94/1.07 tff(2774,plain,
% 0.94/1.07 (~(op(e1, e3) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[14, 2773])).
% 0.94/1.07 tff(2775,plain,
% 0.94/1.07 ((e2 = e3) <=> (e2 = op(e0, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2765])).
% 0.94/1.07 tff(2776,plain,
% 0.94/1.07 ((e2 = e3) <=> (op(e0, e3) = e2)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2775, 1681])).
% 0.94/1.07 tff(2777,plain,
% 0.94/1.07 ((~(e2 = e3)) <=> (~(op(e0, e3) = e2))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2776])).
% 0.94/1.07 tff(2778,plain,
% 0.94/1.07 (~(op(e0, e3) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[1321, 2777])).
% 0.94/1.07 tff(2779,plain,
% 0.94/1.07 (((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))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2780,plain,
% 0.94/1.07 ((((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))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2781,plain,
% 0.94/1.07 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2))),
% 0.94/1.07 inference(rewrite,[status(thm)],[])).
% 0.94/1.07 tff(2782,plain,
% 0.94/1.07 (((((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))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2781])).
% 0.94/1.07 tff(2783,plain,
% 0.94/1.07 (((((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))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2782, 2780])).
% 0.94/1.07 tff(2784,plain,
% 0.94/1.07 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)),
% 0.94/1.07 inference(and_elim,[status(thm)],[146])).
% 0.94/1.07 tff(2785,plain,
% 0.94/1.07 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2784, 2783])).
% 0.94/1.07 tff(2786,plain,
% 0.94/1.07 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2785, 2779])).
% 0.94/1.07 tff(2787,plain,
% 0.94/1.07 (op(e3, e3) = e2),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[2786, 2778, 2774, 2770])).
% 0.94/1.07 tff(2788,plain,
% 0.94/1.07 (e2 = op(e3, e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2787])).
% 0.94/1.07 tff(2789,plain,
% 0.94/1.07 (op(e0, op(e0, e3)) = op(e0, e3)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2764])).
% 0.94/1.07 tff(2790,plain,
% 0.94/1.07 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2493])).
% 0.94/1.07 tff(2791,plain,
% 0.94/1.07 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e0) = e0)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2790, 1695])).
% 0.94/1.07 tff(2792,plain,
% 0.94/1.07 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e0) = e0))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2791])).
% 0.94/1.07 tff(2793,plain,
% 0.94/1.07 (~(op(e3, e0) = e0)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[64, 2792])).
% 0.94/1.07 tff(2794,plain,
% 0.94/1.07 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2493])).
% 0.94/1.07 tff(2795,plain,
% 0.94/1.07 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2794, 86])).
% 0.94/1.07 tff(2796,plain,
% 0.94/1.07 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2795])).
% 0.94/1.07 tff(2797,plain,
% 0.94/1.07 (~(op(e2, e3) = e0)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[118, 2796])).
% 0.94/1.07 tff(2798,plain,
% 0.94/1.07 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e0, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2765])).
% 0.94/1.07 tff(2799,plain,
% 0.94/1.07 ((op(e2, e3) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2798, 925])).
% 0.94/1.07 tff(2800,plain,
% 0.94/1.07 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2799])).
% 0.94/1.07 tff(2801,plain,
% 0.94/1.07 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2800])).
% 0.94/1.07 tff(2802,plain,
% 0.94/1.07 (~(op(e2, e3) = e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[964, 2801])).
% 0.94/1.07 tff(2803,plain,
% 0.94/1.07 (op(e2, e3) = e1),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[206, 2802, 2770, 2797])).
% 0.94/1.07 tff(2804,plain,
% 0.94/1.07 (e1 = op(e2, e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2803])).
% 0.94/1.07 tff(2805,plain,
% 0.94/1.07 (e3 = op(e3, e0)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2765, 467])).
% 0.94/1.07 tff(2806,plain,
% 0.94/1.07 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e0))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2805])).
% 0.94/1.07 tff(2807,plain,
% 0.94/1.07 ((op(e3, e1) = e3) <=> (op(e3, e0) = op(e3, e1))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2806, 881])).
% 0.94/1.07 tff(2808,plain,
% 0.94/1.07 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2807])).
% 0.94/1.07 tff(2809,plain,
% 0.94/1.07 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2808])).
% 0.94/1.07 tff(2810,plain,
% 0.94/1.07 (~(op(e3, e1) = e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[580, 2809])).
% 0.94/1.07 tff(2811,plain,
% 0.94/1.07 ((op(e3, e3) = e2) <=> (e2 = op(e3, e3))),
% 0.94/1.07 inference(symmetry,[status(thm)],[565])).
% 0.94/1.07 tff(2812,assumption,(op(e3, e3) = e2), introduced(assumption)).
% 0.94/1.07 tff(2813,plain,
% 0.94/1.07 (e2 = op(e3, e3)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 0.94/1.07 tff(2814,plain,
% 0.94/1.07 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2812])).
% 0.94/1.07 tff(2815,plain,
% 0.94/1.07 ((e1 = op(e3, op(e3, e3))) <=> (op(e2, e3) = op(e3, e2))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2685, 2814])).
% 0.94/1.07 tff(2816,plain,
% 0.94/1.07 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e2) = op(e2, e3))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2815, 394])).
% 0.94/1.07 tff(2817,plain,
% 0.94/1.07 ((op(e3, e2) = op(e2, e3)) <=> (e1 = op(e3, op(e3, e3)))),
% 0.94/1.07 inference(symmetry,[status(thm)],[2816])).
% 0.94/1.07 tff(2818,plain,
% 0.94/1.07 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2685])).
% 0.94/1.07 tff(2819,plain,
% 0.94/1.07 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2818, 2817])).
% 0.94/1.07 tff(2820,plain,
% 0.94/1.07 ((op(e3, e3) = op(e2, e3)) <=> (op(e2, e3) = op(e3, e3))),
% 0.94/1.07 inference(commutativity,[status(thm)],[])).
% 0.94/1.07 tff(2821,plain,
% 0.94/1.07 ((op(e3, e3) = e1) <=> (op(e3, e3) = op(e2, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2685])).
% 0.94/1.07 tff(2822,plain,
% 0.94/1.07 ((op(e3, e3) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2821, 2820])).
% 0.94/1.07 tff(2823,plain,
% 0.94/1.07 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2822])).
% 0.94/1.07 tff(2824,plain,
% 0.94/1.07 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2823])).
% 0.94/1.07 tff(2825,plain,
% 0.94/1.07 (~(op(e3, e3) = e1)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[368, 2824])).
% 0.94/1.07 tff(2826,assumption,(~(op(e3, e1) = e1)), introduced(assumption)).
% 0.94/1.07 tff(2827,plain,
% 0.94/1.07 (op(e3, e2) = e1),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[939, 2826, 931, 2825])).
% 0.94/1.07 tff(2828,plain,
% 0.94/1.07 (e1 = op(e3, op(e3, e3))),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[2827, 2819])).
% 0.94/1.07 tff(2829,plain,
% 0.94/1.07 (op(e3, op(e3, e3)) = op(e2, e3)),
% 0.94/1.07 inference(transitivity,[status(thm)],[2814, 2827, 2685])).
% 0.94/1.07 tff(2830,plain,
% 0.94/1.07 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e2, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2829])).
% 0.94/1.07 tff(2831,plain,
% 0.94/1.07 (op(e3, op(e2, e3)) = op(e3, op(e3, op(e3, e3)))),
% 0.94/1.07 inference(symmetry,[status(thm)],[2830])).
% 0.94/1.07 tff(2832,plain,
% 0.94/1.07 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2684])).
% 0.94/1.07 tff(2833,plain,
% 0.94/1.07 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.94/1.07 inference(symmetry,[status(thm)],[2832])).
% 0.94/1.07 tff(2834,plain,
% 0.94/1.07 (e2 = op(e3, e3)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2812])).
% 0.94/1.07 tff(2835,plain,
% 0.94/1.07 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e3, e3))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2834])).
% 0.94/1.07 tff(2836,plain,
% 0.94/1.07 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2835])).
% 0.94/1.07 tff(2837,plain,
% 0.94/1.07 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.94/1.07 inference(monotonicity,[status(thm)],[2836])).
% 0.94/1.07 tff(2838,plain,
% 0.94/1.07 (~(op(e3, e1) = e2)),
% 0.94/1.07 inference(modus_ponens,[status(thm)],[437, 2837])).
% 0.94/1.07 tff(2839,assumption,(~(op(e3, e1) = e3)), introduced(assumption)).
% 0.94/1.07 tff(2840,plain,
% 0.94/1.07 (op(e3, e1) = e0),
% 0.94/1.07 inference(unit_resolution,[status(thm)],[446, 2826, 2839, 2838])).
% 0.94/1.07 tff(2841,plain,
% 0.94/1.07 (e0 = op(e3, e1)),
% 0.94/1.07 inference(symmetry,[status(thm)],[2840])).
% 0.94/1.07 tff(2842,plain,
% 0.94/1.07 (e0 = op(e3, op(e3, op(e3, e3)))),
% 0.94/1.07 inference(transitivity,[status(thm)],[2841, 2833, 2831])).
% 0.94/1.07 tff(2843,plain,
% 0.94/1.07 ((~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3)))))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(2844,plain,
% 0.98/1.07 (((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3)))))))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(2845,plain,
% 0.98/1.07 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3))))))))),
% 0.98/1.07 inference(monotonicity,[status(thm)],[2844])).
% 0.98/1.07 tff(2846,plain,
% 0.98/1.07 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.07 inference(transitivity,[status(thm)],[2845, 2843])).
% 0.98/1.07 tff(2847,plain,
% 0.98/1.07 ((~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2848,plain,
% 0.98/1.08 ((~(((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2849,axiom,(~(((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e0 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax27')).
% 0.98/1.08 tff(2850,plain,
% 0.98/1.08 (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 0.98/1.08 tff(2851,plain,
% 0.98/1.08 (~((e1 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e0 = op(e3, op(e3, op(e3, e3)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2850, 2847])).
% 0.98/1.08 tff(2852,plain,
% 0.98/1.08 ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, op(e3, op(e3, e3)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2851, 2846])).
% 0.98/1.08 tff(2853,plain,
% 0.98/1.08 ($false),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2852, 2842, 2828, 2813])).
% 0.98/1.08 tff(2854,plain,((op(e3, e1) = e1) | (~(op(e2, e3) = e1)) | (~(op(e3, e3) = e2)) | (op(e3, e0) = e1) | (op(e3, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.08 tff(2855,plain,
% 0.98/1.08 (op(e3, e1) = e1),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2854, 2803, 2787, 899, 2810])).
% 0.98/1.08 tff(2856,plain,
% 0.98/1.08 (op(e3, e1) = op(e2, e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2855, 2804])).
% 0.98/1.08 tff(2857,plain,
% 0.98/1.08 ((op(e3, e1) = e0) <=> (op(e2, e3) = e0)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2856])).
% 0.98/1.08 tff(2858,plain,
% 0.98/1.08 ((op(e2, e3) = e0) <=> (op(e3, e1) = e0)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2857])).
% 0.98/1.08 tff(2859,plain,
% 0.98/1.08 ((~(op(e2, e3) = e0)) <=> (~(op(e3, e1) = e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2858])).
% 0.98/1.08 tff(2860,plain,
% 0.98/1.08 (~(op(e3, e1) = e0)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2797, 2859])).
% 0.98/1.08 tff(2861,plain,
% 0.98/1.08 (op(e3, e2) = e0),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[1916, 2860, 2793, 656])).
% 0.98/1.08 tff(2862,plain,
% 0.98/1.08 (op(op(e3, e2), e3) = op(e0, op(e0, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2861, 2765])).
% 0.98/1.08 tff(2863,plain,
% 0.98/1.08 (op(op(e3, e2), e3) = op(e0, e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2862, 2789])).
% 0.98/1.08 tff(2864,plain,
% 0.98/1.08 ((op(op(e3, e2), e3) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2863, 2788])).
% 0.98/1.08 tff(2865,plain,
% 0.98/1.08 ((op(e0, e3) = op(e3, e3)) <=> (op(op(e3, e2), e3) = e2)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2864])).
% 0.98/1.08 tff(2866,plain,
% 0.98/1.08 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(op(e3, e2), e3) = e2))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2865])).
% 0.98/1.08 tff(2867,plain,
% 0.98/1.08 (~(op(op(e3, e2), e3) = e2)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[1077, 2866])).
% 0.98/1.08 tff(2868,plain,
% 0.98/1.08 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2408, 2867])).
% 0.98/1.08 tff(2869,plain,
% 0.98/1.08 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2493])).
% 0.98/1.08 tff(2870,plain,
% 0.98/1.08 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2869])).
% 0.98/1.08 tff(2871,plain,
% 0.98/1.08 (~(op(e1, e1) = e0)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[619, 2870])).
% 0.98/1.08 tff(2872,plain,
% 0.98/1.08 (op(e2, op(e2, e3)) = op(e2, e1)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2803])).
% 0.98/1.08 tff(2873,plain,
% 0.98/1.08 (op(e2, op(e0, e3)) = op(e2, e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2766])).
% 0.98/1.08 tff(2874,plain,
% 0.98/1.08 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2805])).
% 0.98/1.08 tff(2875,plain,
% 0.98/1.08 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2874])).
% 0.98/1.08 tff(2876,plain,
% 0.98/1.08 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2875])).
% 0.98/1.08 tff(2877,plain,
% 0.98/1.08 (~(op(e2, e0) = e3)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[747, 2876])).
% 0.98/1.08 tff(2878,plain,
% 0.98/1.08 (op(e2, e1) = op(e2, op(e2, e3))),
% 0.98/1.08 inference(symmetry,[status(thm)],[2872])).
% 0.98/1.08 tff(2879,plain,
% 0.98/1.08 ((op(e2, e1) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2878])).
% 0.98/1.08 tff(2880,plain,
% 0.98/1.08 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e1) = e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2879])).
% 0.98/1.08 tff(2881,plain,
% 0.98/1.08 ((e3 = op(e2, op(e2, e3))) <=> (op(e2, op(e2, e3)) = e3)),
% 0.98/1.08 inference(commutativity,[status(thm)],[])).
% 0.98/1.08 tff(2882,plain,
% 0.98/1.08 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2805])).
% 0.98/1.08 tff(2883,plain,
% 0.98/1.08 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2882])).
% 0.98/1.08 tff(2884,plain,
% 0.98/1.08 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2883])).
% 0.98/1.08 tff(2885,plain,
% 0.98/1.08 (~(op(e1, e0) = e3)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[410, 2884])).
% 0.98/1.08 tff(2886,plain,
% 0.98/1.08 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2855])).
% 0.98/1.08 tff(2887,plain,
% 0.98/1.08 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2886])).
% 0.98/1.08 tff(2888,plain,
% 0.98/1.08 (~(op(e1, e1) = e1)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[945, 2887])).
% 0.98/1.08 tff(2889,plain,
% 0.98/1.08 (op(e1, e2) = e3),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[247, 1291, 2605, 2168])).
% 0.98/1.08 tff(2890,plain,
% 0.98/1.08 (op(e1, e1) = e2),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[630, 1291, 2639, 1266])).
% 0.98/1.08 tff(2891,assumption,(op(e1, e1) = e2), introduced(assumption)).
% 0.98/1.08 tff(2892,plain,
% 0.98/1.08 (op(e1, e1) = op(e3, e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2891, 2834])).
% 0.98/1.08 tff(2893,plain,
% 0.98/1.08 (op(e1, op(e1, e1)) = op(e1, op(e3, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2892])).
% 0.98/1.08 tff(2894,plain,
% 0.98/1.08 (op(e1, op(e3, e3)) = op(e1, op(e1, e1))),
% 0.98/1.08 inference(symmetry,[status(thm)],[2893])).
% 0.98/1.08 tff(2895,plain,
% 0.98/1.08 (op(e1, op(e3, e3)) = op(op(e2, e3), e2)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2685, 2812])).
% 0.98/1.08 tff(2896,plain,
% 0.98/1.08 (op(op(e2, e3), e2) = op(e1, op(e3, e3))),
% 0.98/1.08 inference(symmetry,[status(thm)],[2895])).
% 0.98/1.08 tff(2897,plain,
% 0.98/1.08 (op(op(e2, e3), e2) = op(e1, e2)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2684])).
% 0.98/1.08 tff(2898,plain,
% 0.98/1.08 (op(e1, e2) = op(op(e2, e3), e2)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2897])).
% 0.98/1.08 tff(2899,assumption,(op(e1, e2) = e3), introduced(assumption)).
% 0.98/1.08 tff(2900,plain,
% 0.98/1.08 (e3 = op(e1, e2)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2899])).
% 0.98/1.08 tff(2901,plain,
% 0.98/1.08 (e3 = op(e1, op(e1, e1))),
% 0.98/1.08 inference(transitivity,[status(thm)],[2900, 2898, 2896, 2894])).
% 0.98/1.08 tff(2902,plain,
% 0.98/1.08 (e2 = op(e1, e1)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2891, 2254])).
% 0.98/1.08 tff(2903,plain,
% 0.98/1.08 (op(e1, op(e1, e1)) = e3),
% 0.98/1.08 inference(transitivity,[status(thm)],[2893, 2895, 2897, 2899])).
% 0.98/1.08 tff(2904,plain,
% 0.98/1.08 (op(e1, op(e1, op(e1, e1))) = op(op(e2, e3), e3)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2685, 2903])).
% 0.98/1.08 tff(2905,plain,
% 0.98/1.08 (op(op(e2, e3), e3) = op(e1, op(e1, op(e1, e1)))),
% 0.98/1.08 inference(symmetry,[status(thm)],[2904])).
% 0.98/1.08 tff(2906,plain,
% 0.98/1.08 (op(op(e2, e3), e3) = op(e1, op(e0, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2684, 1870])).
% 0.98/1.08 tff(2907,plain,
% 0.98/1.08 (op(e1, op(e0, e3)) = op(op(e2, e3), e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2906])).
% 0.98/1.08 tff(2908,plain,
% 0.98/1.08 (op(e1, e3) = op(e1, op(e0, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[1870])).
% 0.98/1.08 tff(2909,plain,
% 0.98/1.08 (e0 = op(e1, e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[1219])).
% 0.98/1.08 tff(2910,plain,
% 0.98/1.08 (e0 = op(e1, op(e1, op(e1, e1)))),
% 0.98/1.08 inference(transitivity,[status(thm)],[2909, 2908, 2907, 2905])).
% 0.98/1.08 tff(2911,plain,
% 0.98/1.08 ((~(~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1))))))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2912,plain,
% 0.98/1.08 (((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2913,plain,
% 0.98/1.08 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1)))))))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2912])).
% 0.98/1.08 tff(2914,plain,
% 0.98/1.08 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1)))))),
% 0.98/1.08 inference(transitivity,[status(thm)],[2913, 2911])).
% 0.98/1.08 tff(2915,plain,
% 0.98/1.08 ((~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2916,plain,
% 0.98/1.08 ((~(((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2917,axiom,(~(((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1))) & (e0 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax17')).
% 0.98/1.08 tff(2918,plain,
% 0.98/1.08 (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 0.98/1.08 tff(2919,plain,
% 0.98/1.08 (~((e3 = op(e1, op(e1, e1))) & (e2 = op(e1, e1)) & (e0 = op(e1, op(e1, op(e1, e1)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2918, 2915])).
% 0.98/1.08 tff(2920,plain,
% 0.98/1.08 ((~(e2 = op(e1, e1))) | (~(e0 = op(e1, op(e1, op(e1, e1))))) | (~(e3 = op(e1, op(e1, e1))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2919, 2914])).
% 0.98/1.08 tff(2921,plain,
% 0.98/1.08 ($false),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2920, 2910, 2902, 2901])).
% 0.98/1.08 tff(2922,plain,((~(op(e1, e1) = e2)) | (~(op(e1, e3) = e0)) | (~(op(e1, e2) = e3)) | (~(op(e3, e3) = e2)) | (~(op(e2, e3) = e1)) | (~(op(e0, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.08 tff(2923,plain,
% 0.98/1.08 ($false),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2922, 2890, 2889, 1219, 2812, 2684, 1869])).
% 0.98/1.08 tff(2924,plain,((op(e1, e1) = e3) | (~(op(e1, e3) = e0)) | (~(op(e3, e3) = e2)) | (~(op(e2, e3) = e1)) | (~(op(e0, e3) = e3)) | (op(e1, e1) = e1) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.08 tff(2925,plain,
% 0.98/1.08 (op(e1, e1) = e3),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2924, 2493, 2787, 2803, 2764, 2888, 2885])).
% 0.98/1.08 tff(2926,plain,
% 0.98/1.08 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, op(e2, e3)))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2925, 2878])).
% 0.98/1.08 tff(2927,plain,
% 0.98/1.08 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, op(e2, e3)) = e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2926, 2881])).
% 0.98/1.08 tff(2928,plain,
% 0.98/1.08 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2927, 2880])).
% 0.98/1.08 tff(2929,plain,
% 0.98/1.08 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2928])).
% 0.98/1.08 tff(2930,plain,
% 0.98/1.08 (~(op(e2, e1) = e3)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[225, 2929])).
% 0.98/1.08 tff(2931,plain,
% 0.98/1.08 (op(e2, e2) = e3),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[1559, 2930, 2877, 2802])).
% 0.98/1.08 tff(2932,plain,
% 0.98/1.08 (op(e2, e2) = op(e0, e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2931, 2765])).
% 0.98/1.08 tff(2933,plain,
% 0.98/1.08 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2932])).
% 0.98/1.08 tff(2934,plain,
% 0.98/1.08 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2933, 2873])).
% 0.98/1.08 tff(2935,plain,
% 0.98/1.08 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2934])).
% 0.98/1.08 tff(2936,plain,
% 0.98/1.08 (op(e2, op(e2, op(e2, e2))) = op(e2, e1)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2935, 2872])).
% 0.98/1.08 tff(2937,plain,
% 0.98/1.08 ((e0 = op(e2, op(e2, op(e2, e2)))) <=> (e0 = op(e2, e1))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2936])).
% 0.98/1.08 tff(2938,plain,
% 0.98/1.08 ((e0 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e1) = e0)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2937, 83])).
% 0.98/1.08 tff(2939,plain,
% 0.98/1.08 ((~(e0 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e1) = e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2938])).
% 0.98/1.08 tff(2940,plain,
% 0.98/1.08 (e3 = op(e2, e2)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2931, 1796])).
% 0.98/1.08 tff(2941,plain,
% 0.98/1.08 (op(e2, op(e0, e3)) = op(e2, op(e2, e2))),
% 0.98/1.08 inference(symmetry,[status(thm)],[2933])).
% 0.98/1.08 tff(2942,plain,
% 0.98/1.08 (e1 = op(e2, op(e2, e2))),
% 0.98/1.08 inference(transitivity,[status(thm)],[2804, 2766, 2941])).
% 0.98/1.08 tff(2943,plain,
% 0.98/1.08 ((~(~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2)))))))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2944,plain,
% 0.98/1.08 (((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))) <=> (~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2)))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2945,plain,
% 0.98/1.08 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~(~((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2))))))))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2944])).
% 0.98/1.08 tff(2946,plain,
% 0.98/1.08 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.98/1.08 inference(transitivity,[status(thm)],[2945, 2943])).
% 0.98/1.08 tff(2947,plain,
% 0.98/1.08 ((~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2948,plain,
% 0.98/1.08 ((~(((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(e2, op(e2, op(e2, e2)))))) <=> (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2))))))),
% 0.98/1.08 inference(rewrite,[status(thm)],[])).
% 0.98/1.08 tff(2949,axiom,(~(((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2))) & (e0 = op(e2, op(e2, op(e2, e2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax21')).
% 0.98/1.08 tff(2950,plain,
% 0.98/1.08 (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2949, 2948])).
% 0.98/1.08 tff(2951,plain,
% 0.98/1.08 (~((e1 = op(e2, op(e2, e2))) & (e3 = op(e2, e2)) & (e0 = op(e2, op(e2, op(e2, e2)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2950, 2947])).
% 0.98/1.08 tff(2952,plain,
% 0.98/1.08 ((~(e3 = op(e2, e2))) | (~(e1 = op(e2, op(e2, e2)))) | (~(e0 = op(e2, op(e2, op(e2, e2)))))),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2951, 2946])).
% 0.98/1.08 tff(2953,plain,
% 0.98/1.08 (~(e0 = op(e2, op(e2, op(e2, e2))))),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2952, 2942, 2940])).
% 0.98/1.08 tff(2954,plain,
% 0.98/1.08 (~(op(e2, e1) = e0)),
% 0.98/1.08 inference(modus_ponens,[status(thm)],[2953, 2939])).
% 0.98/1.08 tff(2955,plain,
% 0.98/1.08 (op(e0, e1) = e0),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[292, 2954, 2871, 2860])).
% 0.98/1.08 tff(2956,plain,
% 0.98/1.08 (op(e0, op(e2, e3)) = op(e0, e1)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2803])).
% 0.98/1.08 tff(2957,plain,
% 0.98/1.08 (op(op(e0, e1), e1) = op(e0, op(e2, e3))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2955, 2804])).
% 0.98/1.08 tff(2958,plain,
% 0.98/1.08 (op(op(e0, e1), e1) = e0),
% 0.98/1.08 inference(transitivity,[status(thm)],[2957, 2956, 2955])).
% 0.98/1.08 tff(2959,plain,
% 0.98/1.08 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 0.98/1.08 inference(unit_resolution,[status(thm)],[2650, 2958])).
% 0.98/1.08 tff(2960,plain,
% 0.98/1.08 (op(e3, e3) = op(op(e0, e3), e3)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2765])).
% 0.98/1.08 tff(2961,plain,
% 0.98/1.08 (op(op(e0, e3), e3) = op(e3, e3)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2960])).
% 0.98/1.08 tff(2962,plain,
% 0.98/1.08 ((op(op(e0, e3), e3) = e0) <=> (op(e3, e3) = e0)),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2961])).
% 0.98/1.08 tff(2963,plain,
% 0.98/1.08 ((op(e3, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 0.98/1.08 inference(symmetry,[status(thm)],[2962])).
% 0.98/1.08 tff(2964,plain,
% 0.98/1.08 ((op(e3, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 0.98/1.08 inference(transitivity,[status(thm)],[2963, 1758])).
% 0.98/1.08 tff(2965,plain,
% 0.98/1.08 ((~(op(e3, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 0.98/1.08 inference(monotonicity,[status(thm)],[2964])).
% 0.98/1.09 tff(2966,plain,
% 0.98/1.09 (~(op(op(e3, e0), e3) = e0)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[656, 2965])).
% 0.98/1.09 tff(2967,plain,
% 0.98/1.09 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[1764, 2966])).
% 0.98/1.09 tff(2968,plain,
% 0.98/1.09 ((e3 = op(op(e2, e3), e2)) <=> (op(op(e2, e3), e2) = e3)),
% 0.98/1.09 inference(commutativity,[status(thm)],[])).
% 0.98/1.09 tff(2969,plain,
% 0.98/1.09 (op(op(e2, e3), e2) = op(e1, e2)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2803])).
% 0.98/1.09 tff(2970,plain,
% 0.98/1.09 (op(e1, e2) = op(op(e2, e3), e2)),
% 0.98/1.09 inference(symmetry,[status(thm)],[2969])).
% 0.98/1.09 tff(2971,plain,
% 0.98/1.09 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(op(e2, e3), e2))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2925, 2970])).
% 0.98/1.09 tff(2972,plain,
% 0.98/1.09 ((op(e1, e1) = op(e1, e2)) <=> (op(op(e2, e3), e2) = e3)),
% 0.98/1.09 inference(transitivity,[status(thm)],[2971, 2968])).
% 0.98/1.09 tff(2973,plain,
% 0.98/1.09 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(op(e2, e3), e2) = e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2972])).
% 0.98/1.09 tff(2974,plain,
% 0.98/1.09 (~(op(op(e2, e3), e2) = e3)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[1604, 2973])).
% 0.98/1.09 tff(2975,plain,
% 0.98/1.09 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[1934, 2974])).
% 0.98/1.09 tff(2976,plain,
% 0.98/1.09 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2861])).
% 0.98/1.09 tff(2977,plain,
% 0.98/1.09 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e0))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2976])).
% 0.98/1.09 tff(2978,plain,
% 0.98/1.09 (~(op(e2, e2) = e0)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[1546, 2977])).
% 0.98/1.09 tff(2979,plain,
% 0.98/1.09 (op(e2, e0) = e0),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2311, 2954, 2978, 2797])).
% 0.98/1.09 tff(2980,plain,
% 0.98/1.09 (op(e2, op(e2, e0)) = op(e2, e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2979])).
% 0.98/1.09 tff(2981,plain,
% 0.98/1.09 (op(e2, op(e2, e0)) = e0),
% 0.98/1.09 inference(transitivity,[status(thm)],[2980, 2979])).
% 0.98/1.09 tff(2982,plain,
% 0.98/1.09 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2653, 2981])).
% 0.98/1.09 tff(2983,plain,
% 0.98/1.09 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2493])).
% 0.98/1.09 tff(2984,plain,
% 0.98/1.09 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e0))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2983])).
% 0.98/1.09 tff(2985,plain,
% 0.98/1.09 (~(op(e1, e0) = e0)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[110, 2984])).
% 0.98/1.09 tff(2986,plain,
% 0.98/1.09 (op(e1, e3) = op(e1, op(e0, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2765])).
% 0.98/1.09 tff(2987,plain,
% 0.98/1.09 (op(e1, op(e0, e3)) = op(e1, e3)),
% 0.98/1.09 inference(symmetry,[status(thm)],[2986])).
% 0.98/1.09 tff(2988,plain,
% 0.98/1.09 (op(op(e2, e3), e3) = op(e1, op(e0, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2803, 2765])).
% 0.98/1.09 tff(2989,plain,
% 0.98/1.09 (op(e1, op(e1, e1)) = op(op(e2, e3), e3)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2804, 2925])).
% 0.98/1.09 tff(2990,plain,
% 0.98/1.09 (op(e1, op(e1, e1)) = e0),
% 0.98/1.09 inference(transitivity,[status(thm)],[2989, 2988, 2987, 2493])).
% 0.98/1.09 tff(2991,plain,
% 0.98/1.09 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2990])).
% 0.98/1.09 tff(2992,plain,
% 0.98/1.09 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2991])).
% 0.98/1.09 tff(2993,plain,
% 0.98/1.09 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 0.98/1.09 inference(transitivity,[status(thm)],[2992, 2154])).
% 0.98/1.09 tff(2994,plain,
% 0.98/1.09 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2993])).
% 0.98/1.09 tff(2995,plain,
% 0.98/1.09 (e3 = op(e1, e1)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[2925, 1740])).
% 0.98/1.09 tff(2996,plain,
% 0.98/1.09 (op(op(e2, e3), e3) = op(e1, op(e1, e1))),
% 0.98/1.09 inference(symmetry,[status(thm)],[2989])).
% 0.98/1.09 tff(2997,plain,
% 0.98/1.09 (op(e1, op(e0, e3)) = op(op(e2, e3), e3)),
% 0.98/1.09 inference(symmetry,[status(thm)],[2988])).
% 0.98/1.09 tff(2998,plain,
% 0.98/1.09 (e0 = op(e1, e3)),
% 0.98/1.09 inference(symmetry,[status(thm)],[2493])).
% 0.98/1.09 tff(2999,plain,
% 0.98/1.09 (e0 = op(e1, op(e1, e1))),
% 0.98/1.09 inference(transitivity,[status(thm)],[2998, 2986, 2997, 2996])).
% 0.98/1.09 tff(3000,plain,
% 0.98/1.09 ((~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1)))))))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3001,plain,
% 0.98/1.09 (((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))) <=> (~((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1)))))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3002,plain,
% 0.98/1.09 ((~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~(~((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1))))))))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3001])).
% 0.98/1.09 tff(3003,plain,
% 0.98/1.09 ((~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> ((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.09 inference(transitivity,[status(thm)],[3002, 3000])).
% 0.98/1.09 tff(3004,plain,
% 0.98/1.09 ((~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3005,plain,
% 0.98/1.09 ((~(((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1))) & (e2 = op(e1, op(e1, op(e1, e1)))))) <=> (~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1))))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3006,axiom,(~(((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1))) & (e2 = op(e1, op(e1, op(e1, e1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax13')).
% 0.98/1.09 tff(3007,plain,
% 0.98/1.09 (~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 0.98/1.09 tff(3008,plain,
% 0.98/1.09 (~((e0 = op(e1, op(e1, e1))) & (e3 = op(e1, e1)) & (e2 = op(e1, op(e1, op(e1, e1)))))),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3007, 3004])).
% 0.98/1.09 tff(3009,plain,
% 0.98/1.09 ((~(e0 = op(e1, op(e1, e1)))) | (~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, op(e1, e1)))))),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3008, 3003])).
% 0.98/1.09 tff(3010,plain,
% 0.98/1.09 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[3009, 2999, 2995])).
% 0.98/1.09 tff(3011,plain,
% 0.98/1.09 (~(op(e1, e0) = e2)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3010, 2994])).
% 0.98/1.09 tff(3012,plain,
% 0.98/1.09 (op(e1, e0) = e1),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[728, 3011, 2885, 2985])).
% 0.98/1.09 tff(3013,plain,
% 0.98/1.09 (op(op(e1, e0), e0) = op(e1, e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3012])).
% 0.98/1.09 tff(3014,plain,
% 0.98/1.09 (op(op(e1, e0), e0) = e1),
% 0.98/1.09 inference(transitivity,[status(thm)],[3013, 3012])).
% 0.98/1.09 tff(3015,plain,
% 0.98/1.09 (((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))) | (~(op(op(e1, e0), e0) = e1))),
% 0.98/1.09 inference(tautology,[status(thm)],[])).
% 0.98/1.09 tff(3016,plain,
% 0.98/1.09 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[3015, 3014])).
% 0.98/1.09 tff(3017,plain,
% 0.98/1.09 (op(e1, e1) = op(e0, e3)),
% 0.98/1.09 inference(transitivity,[status(thm)],[2925, 2765])).
% 0.98/1.09 tff(3018,plain,
% 0.98/1.09 ((op(e1, e1) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3017, 2788])).
% 0.98/1.09 tff(3019,plain,
% 0.98/1.09 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e1) = e2)),
% 0.98/1.09 inference(symmetry,[status(thm)],[3018])).
% 0.98/1.09 tff(3020,plain,
% 0.98/1.09 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e1) = e2))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3019])).
% 0.98/1.09 tff(3021,plain,
% 0.98/1.09 (~(op(e1, e1) = e2)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[1077, 3020])).
% 0.98/1.09 tff(3022,plain,
% 0.98/1.09 (op(e1, e2) = e2),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2285, 3011, 2774, 3021])).
% 0.98/1.09 tff(3023,plain,
% 0.98/1.09 (op(e1, op(e3, e3)) = op(op(e2, e3), e2)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2804, 2787])).
% 0.98/1.09 tff(3024,plain,
% 0.98/1.09 (op(e1, e2) = op(e3, e3)),
% 0.98/1.09 inference(transitivity,[status(thm)],[3022, 2788])).
% 0.98/1.09 tff(3025,plain,
% 0.98/1.09 (op(e1, op(e1, e2)) = op(e1, op(e3, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3024])).
% 0.98/1.09 tff(3026,plain,
% 0.98/1.09 (op(e1, op(e1, e2)) = e2),
% 0.98/1.09 inference(transitivity,[status(thm)],[3025, 3023, 2969, 3022])).
% 0.98/1.09 tff(3027,plain,
% 0.98/1.09 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2377, 3026])).
% 0.98/1.09 tff(3028,plain,
% 0.98/1.09 (op(e0, op(e0, e3)) = e3),
% 0.98/1.09 inference(transitivity,[status(thm)],[2789, 2764])).
% 0.98/1.09 tff(3029,plain,
% 0.98/1.09 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[1938, 3028])).
% 0.98/1.09 tff(3030,plain,
% 0.98/1.09 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2803])).
% 0.98/1.09 tff(3031,plain,
% 0.98/1.09 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2856])).
% 0.98/1.09 tff(3032,plain,
% 0.98/1.09 (op(e3, op(e3, e1)) = e1),
% 0.98/1.09 inference(transitivity,[status(thm)],[3031, 3030, 2855])).
% 0.98/1.09 tff(3033,plain,
% 0.98/1.09 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2594, 3032])).
% 0.98/1.09 tff(3034,plain,
% 0.98/1.09 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2804])).
% 0.98/1.09 tff(3035,plain,
% 0.98/1.09 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 0.98/1.09 inference(symmetry,[status(thm)],[3034])).
% 0.98/1.09 tff(3036,plain,
% 0.98/1.09 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3035])).
% 0.98/1.09 tff(3037,plain,
% 0.98/1.09 (~(op(e2, e1) = e1)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[197, 3036])).
% 0.98/1.09 tff(3038,plain,
% 0.98/1.09 (op(e2, e1) = e2),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2367, 2954, 3037, 2930])).
% 0.98/1.09 tff(3039,plain,
% 0.98/1.09 (op(op(e2, e1), e1) = op(e2, op(e2, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3038, 2804])).
% 0.98/1.09 tff(3040,plain,
% 0.98/1.09 (op(op(e2, e1), e1) = e2),
% 0.98/1.09 inference(transitivity,[status(thm)],[3039, 2872, 3038])).
% 0.98/1.09 tff(3041,plain,
% 0.98/1.09 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2371, 3040])).
% 0.98/1.09 tff(3042,plain,
% 0.98/1.09 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2855])).
% 0.98/1.09 tff(3043,plain,
% 0.98/1.09 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3042])).
% 0.98/1.09 tff(3044,plain,
% 0.98/1.09 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = op(e3, e1)))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3045,plain,
% 0.98/1.09 (~(op(e0, e1) = op(e3, e1))),
% 0.98/1.09 inference(and_elim,[status(thm)],[350])).
% 0.98/1.09 tff(3046,plain,
% 0.98/1.09 (~(op(e0, e1) = op(e3, e1))),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3045, 3044])).
% 0.98/1.09 tff(3047,plain,
% 0.98/1.09 (~(op(e0, e1) = e1)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3046, 3043])).
% 0.98/1.09 tff(3048,plain,
% 0.98/1.09 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e1)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3012])).
% 0.98/1.09 tff(3049,plain,
% 0.98/1.09 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e1))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3048])).
% 0.98/1.09 tff(3050,plain,
% 0.98/1.09 (~(op(e0, e0) = e1)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[2471, 3049])).
% 0.98/1.09 tff(3051,plain,
% 0.98/1.09 (op(e0, e2) = e1),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[384, 3050, 121, 3047])).
% 0.98/1.09 tff(3052,plain,
% 0.98/1.09 (op(op(e0, e2), e0) = op(e1, e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3051])).
% 0.98/1.09 tff(3053,plain,
% 0.98/1.09 (op(op(e0, e2), e0) = op(e2, e3)),
% 0.98/1.09 inference(transitivity,[status(thm)],[3052, 3012, 2804])).
% 0.98/1.09 tff(3054,plain,
% 0.98/1.09 ((op(op(e0, e2), e0) = e2) <=> (op(e2, e3) = op(e3, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3053, 2788])).
% 0.98/1.09 tff(3055,plain,
% 0.98/1.09 ((op(e2, e3) = op(e3, e3)) <=> (op(op(e0, e2), e0) = e2)),
% 0.98/1.09 inference(symmetry,[status(thm)],[3054])).
% 0.98/1.09 tff(3056,plain,
% 0.98/1.09 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(op(e0, e2), e0) = e2))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3055])).
% 0.98/1.09 tff(3057,plain,
% 0.98/1.09 (~(op(op(e0, e2), e0) = e2)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[368, 3056])).
% 0.98/1.09 tff(3058,plain,
% 0.98/1.09 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[2446, 3057])).
% 0.98/1.09 tff(3059,plain,
% 0.98/1.09 ($false),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[1459, 3058, 3041, 3033, 3029, 3027, 1261, 3016, 2982, 2975, 2967, 2959, 2868])).
% 0.98/1.09 tff(3060,plain,((op(e3, e3) = e0) | (op(e0, e3) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e2, op(e0, e3)) = e2) | (op(e0, op(e0, e3)) = e0) | (op(e3, op(e0, e3)) = e3) | (op(op(e1, e3), e1) = e3) | (op(e1, op(e0, e3)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.09 tff(3061,plain,
% 0.98/1.09 (op(e3, e3) = e0),
% 0.98/1.09 inference(unit_resolution,[status(thm)],[3060, 655, 466, 651, 649, 650, 121, 652])).
% 0.98/1.09 tff(3062,plain,
% 0.98/1.09 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3061])).
% 0.98/1.09 tff(3063,plain,
% 0.98/1.09 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3062])).
% 0.98/1.09 tff(3064,plain,
% 0.98/1.09 (~(op(e0, e3) = e0)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[1077, 3063])).
% 0.98/1.09 tff(3065,plain,
% 0.98/1.09 ((op(e3, op(e3, op(e3, e3))) = e1) <=> (e1 = op(e3, op(e3, op(e3, e3))))),
% 0.98/1.09 inference(commutativity,[status(thm)],[])).
% 0.98/1.09 tff(3066,assumption,(op(e3, e3) = e0), introduced(assumption)).
% 0.98/1.09 tff(3067,plain,
% 0.98/1.09 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3066])).
% 0.98/1.09 tff(3068,plain,
% 0.98/1.09 (op(e3, op(e3, e3)) = op(e0, e3)),
% 0.98/1.09 inference(transitivity,[status(thm)],[3067, 466])).
% 0.98/1.09 tff(3069,plain,
% 0.98/1.09 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e0, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3068])).
% 0.98/1.09 tff(3070,plain,
% 0.98/1.09 (op(e3, op(e0, e3)) = op(e3, op(e3, op(e3, e3)))),
% 0.98/1.09 inference(symmetry,[status(thm)],[3069])).
% 0.98/1.09 tff(3071,plain,
% 0.98/1.09 (op(e3, e2) = op(e3, op(e0, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[2560])).
% 0.98/1.09 tff(3072,plain,
% 0.98/1.09 (op(e3, e2) = op(e3, op(e3, op(e3, e3)))),
% 0.98/1.09 inference(transitivity,[status(thm)],[3071, 3070])).
% 0.98/1.09 tff(3073,plain,
% 0.98/1.09 ((op(e3, e2) = e1) <=> (op(e3, op(e3, op(e3, e3))) = e1)),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3072])).
% 0.98/1.09 tff(3074,plain,
% 0.98/1.09 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(e3, op(e3, e3))))),
% 0.98/1.09 inference(transitivity,[status(thm)],[3073, 3065])).
% 0.98/1.09 tff(3075,plain,
% 0.98/1.09 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 0.98/1.09 inference(symmetry,[status(thm)],[3074])).
% 0.98/1.09 tff(3076,plain,
% 0.98/1.09 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3075])).
% 0.98/1.09 tff(3077,plain,
% 0.98/1.09 ((e0 = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.98/1.09 inference(commutativity,[status(thm)],[])).
% 0.98/1.09 tff(3078,plain,
% 0.98/1.09 ((op(e3, e3) = e0) <=> (e0 = op(e3, e3))),
% 0.98/1.09 inference(symmetry,[status(thm)],[3077])).
% 0.98/1.09 tff(3079,plain,
% 0.98/1.09 (e0 = op(e3, e3)),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[3066, 3078])).
% 0.98/1.09 tff(3080,plain,
% 0.98/1.09 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e0, e3))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3068])).
% 0.98/1.09 tff(3081,plain,
% 0.98/1.09 ((e2 = op(e3, op(e3, e3))) <=> (op(e0, e3) = e2)),
% 0.98/1.09 inference(transitivity,[status(thm)],[3080, 1681])).
% 0.98/1.09 tff(3082,plain,
% 0.98/1.09 ((op(e0, e3) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.98/1.09 inference(symmetry,[status(thm)],[3081])).
% 0.98/1.09 tff(3083,plain,
% 0.98/1.09 (e2 = op(e3, op(e3, e3))),
% 0.98/1.09 inference(modus_ponens,[status(thm)],[2, 3082])).
% 0.98/1.09 tff(3084,plain,
% 0.98/1.09 ((~(~((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))))) <=> ((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3085,plain,
% 0.98/1.09 (((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))))),
% 0.98/1.09 inference(rewrite,[status(thm)],[])).
% 0.98/1.09 tff(3086,plain,
% 0.98/1.09 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))))),
% 0.98/1.09 inference(monotonicity,[status(thm)],[3085])).
% 0.98/1.09 tff(3087,plain,
% 0.98/1.09 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))))),
% 0.98/1.09 inference(transitivity,[status(thm)],[3086, 3084])).
% 0.98/1.10 tff(3088,plain,
% 0.98/1.10 ((~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.10 inference(rewrite,[status(thm)],[])).
% 0.98/1.10 tff(3089,plain,
% 0.98/1.10 ((~(((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))))),
% 0.98/1.10 inference(rewrite,[status(thm)],[])).
% 0.98/1.10 tff(3090,axiom,(~(((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e1 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax28')).
% 0.98/1.10 tff(3091,plain,
% 0.98/1.10 (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3090, 3089])).
% 0.98/1.10 tff(3092,plain,
% 0.98/1.10 (~((e2 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3091, 3088])).
% 0.98/1.10 tff(3093,plain,
% 0.98/1.10 ((~(e1 = op(e3, op(e3, op(e3, e3))))) | (~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3))))),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3092, 3087])).
% 0.98/1.10 tff(3094,plain,
% 0.98/1.10 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3093, 3083, 3079])).
% 0.98/1.10 tff(3095,plain,
% 0.98/1.10 (~(op(e3, e2) = e1)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3094, 3076])).
% 0.98/1.10 tff(3096,plain,
% 0.98/1.10 (~(op(e3, e2) = e3)),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[860, 2, 650])).
% 0.98/1.10 tff(3097,plain,
% 0.98/1.10 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3066])).
% 0.98/1.10 tff(3098,plain,
% 0.98/1.10 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3097])).
% 0.98/1.10 tff(3099,plain,
% 0.98/1.10 (~(op(e3, e2) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[1888, 3098])).
% 0.98/1.10 tff(3100,plain,
% 0.98/1.10 (op(e3, e2) = e1),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1898, 2566, 3099, 3096])).
% 0.98/1.10 tff(3101,plain,
% 0.98/1.10 ($false),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3100, 3095])).
% 0.98/1.10 tff(3102,plain,((~(op(e0, e3) = e2)) | (~(op(e3, e0) = op(e0, e3))) | (~(op(e3, e3) = e0)) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.10 tff(3103,plain,
% 0.98/1.10 (~(op(e0, e3) = e2)),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3102, 3061, 466, 650])).
% 0.98/1.10 tff(3104,plain,
% 0.98/1.10 (op(e0, e3) = e3),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[687, 3103, 121, 3064])).
% 0.98/1.10 tff(3105,plain,
% 0.98/1.10 (e3 = op(e0, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3104])).
% 0.98/1.10 tff(3106,plain,
% 0.98/1.10 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3105])).
% 0.98/1.10 tff(3107,plain,
% 0.98/1.10 ((op(e1, e3) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 0.98/1.10 inference(transitivity,[status(thm)],[3106, 654])).
% 0.98/1.10 tff(3108,plain,
% 0.98/1.10 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3107])).
% 0.98/1.10 tff(3109,plain,
% 0.98/1.10 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3108])).
% 0.98/1.10 tff(3110,plain,
% 0.98/1.10 (~(op(e1, e3) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[64, 3109])).
% 0.98/1.10 tff(3111,plain,
% 0.98/1.10 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3061])).
% 0.98/1.10 tff(3112,plain,
% 0.98/1.10 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3111])).
% 0.98/1.10 tff(3113,plain,
% 0.98/1.10 (~(op(e1, e3) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[571, 3112])).
% 0.98/1.10 tff(3114,plain,
% 0.98/1.10 (op(e1, e3) = op(e1, op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3105])).
% 0.98/1.10 tff(3115,plain,
% 0.98/1.10 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3114])).
% 0.98/1.10 tff(3116,plain,
% 0.98/1.10 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e1)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3115])).
% 0.98/1.10 tff(3117,plain,
% 0.98/1.10 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e3) = e1))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3116])).
% 0.98/1.10 tff(3118,plain,
% 0.98/1.10 (~(op(e1, e3) = e1)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[652, 3117])).
% 0.98/1.10 tff(3119,plain,
% 0.98/1.10 (op(e1, e3) = e2),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[104, 3118, 3113, 3110])).
% 0.98/1.10 tff(3120,plain,
% 0.98/1.10 (op(e0, op(e1, e3)) = op(e0, e2)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3119])).
% 0.98/1.10 tff(3121,plain,
% 0.98/1.10 (op(e0, e2) = op(e0, op(e1, e3))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3120])).
% 0.98/1.10 tff(3122,plain,
% 0.98/1.10 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3061])).
% 0.98/1.10 tff(3123,plain,
% 0.98/1.10 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3122])).
% 0.98/1.10 tff(3124,plain,
% 0.98/1.10 (~(op(e3, e1) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[437, 3123])).
% 0.98/1.10 tff(3125,plain,
% 0.98/1.10 (e3 = op(e3, e0)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3105, 467])).
% 0.98/1.10 tff(3126,plain,
% 0.98/1.10 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3125])).
% 0.98/1.10 tff(3127,plain,
% 0.98/1.10 ((op(e3, e1) = e3) <=> (op(e3, e0) = op(e3, e1))),
% 0.98/1.10 inference(transitivity,[status(thm)],[3126, 881])).
% 0.98/1.10 tff(3128,plain,
% 0.98/1.10 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3127])).
% 0.98/1.10 tff(3129,plain,
% 0.98/1.10 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3128])).
% 0.98/1.10 tff(3130,plain,
% 0.98/1.10 (~(op(e3, e1) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[580, 3129])).
% 0.98/1.10 tff(3131,plain,
% 0.98/1.10 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3105])).
% 0.98/1.10 tff(3132,plain,
% 0.98/1.10 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3131])).
% 0.98/1.10 tff(3133,plain,
% 0.98/1.10 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3132])).
% 0.98/1.10 tff(3134,plain,
% 0.98/1.10 (~(op(e0, e1) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[818, 3133])).
% 0.98/1.10 tff(3135,plain,
% 0.98/1.10 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3061])).
% 0.98/1.10 tff(3136,plain,
% 0.98/1.10 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3135])).
% 0.98/1.10 tff(3137,plain,
% 0.98/1.10 (~(op(e2, e3) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[368, 3136])).
% 0.98/1.10 tff(3138,plain,
% 0.98/1.10 (op(e2, e3) = op(e2, op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3105])).
% 0.98/1.10 tff(3139,plain,
% 0.98/1.10 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3138])).
% 0.98/1.10 tff(3140,plain,
% 0.98/1.10 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3139])).
% 0.98/1.10 tff(3141,plain,
% 0.98/1.10 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e3) = e2))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3140])).
% 0.98/1.10 tff(3142,plain,
% 0.98/1.10 (~(op(e2, e3) = e2)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[651, 3141])).
% 0.98/1.10 tff(3143,plain,
% 0.98/1.10 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3105])).
% 0.98/1.10 tff(3144,plain,
% 0.98/1.10 ((op(e2, e3) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 0.98/1.10 inference(transitivity,[status(thm)],[3143, 925])).
% 0.98/1.10 tff(3145,plain,
% 0.98/1.10 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3144])).
% 0.98/1.10 tff(3146,plain,
% 0.98/1.10 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3145])).
% 0.98/1.10 tff(3147,plain,
% 0.98/1.10 (~(op(e2, e3) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[964, 3146])).
% 0.98/1.10 tff(3148,plain,
% 0.98/1.10 (op(e2, e3) = e1),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[206, 3147, 3142, 3137])).
% 0.98/1.10 tff(3149,plain,
% 0.98/1.10 (op(e2, op(e2, e3)) = op(e2, e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3148])).
% 0.98/1.10 tff(3150,plain,
% 0.98/1.10 (op(e2, e1) = op(e2, op(e2, e3))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3149])).
% 0.98/1.10 tff(3151,plain,
% 0.98/1.10 ((op(e2, e1) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3150])).
% 0.98/1.10 tff(3152,plain,
% 0.98/1.10 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e1) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3151])).
% 0.98/1.10 tff(3153,plain,
% 0.98/1.10 (e1 = op(e2, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3148])).
% 0.98/1.10 tff(3154,plain,
% 0.98/1.10 (op(op(e1, e3), e1) = op(e2, op(e2, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3119, 3153])).
% 0.98/1.10 tff(3155,plain,
% 0.98/1.10 ((op(op(e1, e3), e1) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3154])).
% 0.98/1.10 tff(3156,plain,
% 0.98/1.10 ((op(op(e1, e3), e1) = e3) <=> (op(e2, e1) = e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3155, 3152])).
% 0.98/1.10 tff(3157,plain,
% 0.98/1.10 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e2, e1) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3156])).
% 0.98/1.10 tff(3158,plain,
% 0.98/1.10 (~(op(e2, e1) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[655, 3157])).
% 0.98/1.10 tff(3159,plain,
% 0.98/1.10 (op(e1, e1) = e3),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1730, 3158, 3134, 3130])).
% 0.98/1.10 tff(3160,plain,
% 0.98/1.10 (op(e1, e1) = op(e0, e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3159, 3105])).
% 0.98/1.10 tff(3161,plain,
% 0.98/1.10 ((op(e1, e1) = e0) <=> (op(e0, e3) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3160])).
% 0.98/1.10 tff(3162,plain,
% 0.98/1.10 ((op(e0, e3) = e0) <=> (op(e1, e1) = e0)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3161])).
% 0.98/1.10 tff(3163,plain,
% 0.98/1.10 ((~(op(e0, e3) = e0)) <=> (~(op(e1, e1) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3162])).
% 0.98/1.10 tff(3164,plain,
% 0.98/1.10 (~(op(e1, e1) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3064, 3163])).
% 0.98/1.10 tff(3165,plain,
% 0.98/1.10 (op(e2, op(e0, e3)) = op(e2, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3138])).
% 0.98/1.10 tff(3166,plain,
% 0.98/1.10 (op(op(e1, e3), e3) = op(e2, op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3119, 3105])).
% 0.98/1.10 tff(3167,plain,
% 0.98/1.10 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3125])).
% 0.98/1.10 tff(3168,plain,
% 0.98/1.10 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3167])).
% 0.98/1.10 tff(3169,plain,
% 0.98/1.10 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3168])).
% 0.98/1.10 tff(3170,plain,
% 0.98/1.10 (~(op(e2, e0) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[747, 3169])).
% 0.98/1.10 tff(3171,plain,
% 0.98/1.10 (op(e2, e2) = e3),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1559, 3158, 3170, 3147])).
% 0.98/1.10 tff(3172,plain,
% 0.98/1.10 (e2 = op(e1, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3119])).
% 0.98/1.10 tff(3173,plain,
% 0.98/1.10 (op(e2, op(e2, e2)) = op(op(e1, e3), e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3172, 3171])).
% 0.98/1.10 tff(3174,plain,
% 0.98/1.10 (op(e2, op(e2, e2)) = e1),
% 0.98/1.10 inference(transitivity,[status(thm)],[3173, 3166, 3165, 3148])).
% 0.98/1.10 tff(3175,plain,
% 0.98/1.10 (op(e2, op(e2, op(e2, e2))) = op(op(e1, e3), e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3172, 3174])).
% 0.98/1.10 tff(3176,plain,
% 0.98/1.10 (op(e2, op(e2, op(e2, e2))) = op(e2, e1)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3175, 3154, 3149])).
% 0.98/1.10 tff(3177,plain,
% 0.98/1.10 ((e0 = op(e2, op(e2, op(e2, e2)))) <=> (e0 = op(e2, e1))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3176])).
% 0.98/1.10 tff(3178,plain,
% 0.98/1.10 ((e0 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e1) = e0)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3177, 83])).
% 0.98/1.10 tff(3179,plain,
% 0.98/1.10 ((~(e0 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e1) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3178])).
% 0.98/1.10 tff(3180,plain,
% 0.98/1.10 (e3 = op(e2, e2)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3171, 1796])).
% 0.98/1.10 tff(3181,plain,
% 0.98/1.10 (op(op(e1, e3), e3) = op(e2, op(e2, e2))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3173])).
% 0.98/1.10 tff(3182,plain,
% 0.98/1.10 (op(e2, op(e0, e3)) = op(op(e1, e3), e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3166])).
% 0.98/1.10 tff(3183,plain,
% 0.98/1.10 (e1 = op(e2, op(e2, e2))),
% 0.98/1.10 inference(transitivity,[status(thm)],[3153, 3138, 3182, 3181])).
% 0.98/1.10 tff(3184,plain,
% 0.98/1.10 (~(e0 = op(e2, op(e2, op(e2, e2))))),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[2952, 3183, 3180])).
% 0.98/1.10 tff(3185,plain,
% 0.98/1.10 (~(op(e2, e1) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3184, 3179])).
% 0.98/1.10 tff(3186,plain,
% 0.98/1.10 (op(e0, e1) = e0),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[292, 3185, 3164, 3124])).
% 0.98/1.10 tff(3187,plain,
% 0.98/1.10 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, op(e1, e3)))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3186, 3121])).
% 0.98/1.10 tff(3188,plain,
% 0.98/1.10 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e1, e3)) = e0)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3187, 653])).
% 0.98/1.10 tff(3189,plain,
% 0.98/1.10 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = op(e0, e2))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3188])).
% 0.98/1.10 tff(3190,plain,
% 0.98/1.10 ((op(e0, e2) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3121])).
% 0.98/1.10 tff(3191,plain,
% 0.98/1.10 (op(e2, e2) = op(e0, e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3171, 3105])).
% 0.98/1.10 tff(3192,plain,
% 0.98/1.10 ((op(e2, e2) = e0) <=> (op(e0, e3) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3191])).
% 0.98/1.10 tff(3193,plain,
% 0.98/1.10 ((op(e0, e3) = e0) <=> (op(e2, e2) = e0)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3192])).
% 0.98/1.10 tff(3194,plain,
% 0.98/1.10 ((~(op(e0, e3) = e0)) <=> (~(op(e2, e2) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3193])).
% 0.98/1.10 tff(3195,plain,
% 0.98/1.10 (~(op(e2, e2) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3064, 3194])).
% 0.98/1.10 tff(3196,plain,
% 0.98/1.10 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3061])).
% 0.98/1.10 tff(3197,plain,
% 0.98/1.10 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3196])).
% 0.98/1.10 tff(3198,plain,
% 0.98/1.10 (~(op(e3, e2) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[1888, 3197])).
% 0.98/1.10 tff(3199,plain,
% 0.98/1.10 (op(op(e2, e3), e2) = op(e1, e2)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3148])).
% 0.98/1.10 tff(3200,plain,
% 0.98/1.10 (op(e1, op(e1, e3)) = op(op(e2, e3), e2)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3153, 3119])).
% 0.98/1.10 tff(3201,plain,
% 0.98/1.10 (op(e1, op(e0, e3)) = op(e1, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3114])).
% 0.98/1.10 tff(3202,plain,
% 0.98/1.10 (op(op(e2, e3), e3) = op(e1, op(e0, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3148, 3105])).
% 0.98/1.10 tff(3203,plain,
% 0.98/1.10 (op(e1, op(e1, e1)) = op(op(e2, e3), e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3153, 3159])).
% 0.98/1.10 tff(3204,plain,
% 0.98/1.10 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3203, 3202, 3201])).
% 0.98/1.10 tff(3205,plain,
% 0.98/1.10 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3204])).
% 0.98/1.10 tff(3206,plain,
% 0.98/1.10 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3205, 3200, 3199])).
% 0.98/1.10 tff(3207,plain,
% 0.98/1.10 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3206])).
% 0.98/1.10 tff(3208,plain,
% 0.98/1.10 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3207, 67])).
% 0.98/1.10 tff(3209,plain,
% 0.98/1.10 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3208])).
% 0.98/1.10 tff(3210,plain,
% 0.98/1.10 (e3 = op(e1, e1)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3159, 1740])).
% 0.98/1.10 tff(3211,plain,
% 0.98/1.10 (op(op(e2, e3), e3) = op(e1, op(e1, e1))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3203])).
% 0.98/1.10 tff(3212,plain,
% 0.98/1.10 (op(e1, op(e0, e3)) = op(op(e2, e3), e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3202])).
% 0.98/1.10 tff(3213,plain,
% 0.98/1.10 (e2 = op(e1, op(e1, e1))),
% 0.98/1.10 inference(transitivity,[status(thm)],[3172, 3114, 3212, 3211])).
% 0.98/1.10 tff(3214,plain,
% 0.98/1.10 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1753, 3213, 3210])).
% 0.98/1.10 tff(3215,plain,
% 0.98/1.10 (~(op(e1, e2) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3214, 3209])).
% 0.98/1.10 tff(3216,plain,
% 0.98/1.10 (op(e0, e2) = e0),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[973, 3215, 3198, 3195])).
% 0.98/1.10 tff(3217,plain,
% 0.98/1.10 (op(e0, op(e1, e3)) = e0),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3216, 3190])).
% 0.98/1.10 tff(3218,plain,
% 0.98/1.10 (op(e0, e1) = op(e0, e2)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3217, 3189])).
% 0.98/1.10 tff(3219,plain,
% 0.98/1.10 ($false),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[2102, 3218])).
% 0.98/1.10 tff(3220,plain,((op(op(e1, e3), e1) = e3) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e0, e3)) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e1) | (op(e3, op(e0, e3)) = e3) | (op(e0, op(e0, e3)) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.10 tff(3221,plain,
% 0.98/1.10 (op(op(e1, e3), e1) = e3),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3220, 121, 652, 466, 651, 650, 649])).
% 0.98/1.10 tff(3222,plain,
% 0.98/1.10 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3066])).
% 0.98/1.10 tff(3223,plain,
% 0.98/1.10 ((op(e0, e3) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 0.98/1.10 inference(symmetry,[status(thm)],[3222])).
% 0.98/1.10 tff(3224,plain,
% 0.98/1.10 (~(op(e0, e3) = e2)),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3102, 3066, 466, 650])).
% 0.98/1.10 tff(3225,plain,
% 0.98/1.10 (op(e0, e3) = e0),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[687, 3224, 121, 661])).
% 0.98/1.10 tff(3226,plain,
% 0.98/1.10 (op(e0, e3) = op(e3, e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3225, 3223])).
% 0.98/1.10 tff(3227,plain,
% 0.98/1.10 ($false),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1077, 3226])).
% 0.98/1.10 tff(3228,plain,((~(op(e3, e3) = e0)) | (op(e0, e3) = e1) | (op(e0, e3) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.10 tff(3229,plain,
% 0.98/1.10 (~(op(e3, e3) = e0)),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[3228, 661, 121, 466, 650])).
% 0.98/1.10 tff(3230,plain,
% 0.98/1.10 ((e3 = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 0.98/1.10 inference(commutativity,[status(thm)],[])).
% 0.98/1.10 tff(3231,plain,
% 0.98/1.10 (~(op(e1, e3) = e1)),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[2487, 1291, 121, 649, 466, 652, 80, 661, 651, 650, 656])).
% 0.98/1.10 tff(3232,plain,
% 0.98/1.10 (op(e1, e3) = e3),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[104, 3231, 845, 80])).
% 0.98/1.10 tff(3233,plain,
% 0.98/1.10 (e3 = op(e1, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3232])).
% 0.98/1.10 tff(3234,plain,
% 0.98/1.10 (op(e3, e1) = op(op(e1, e3), e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3233])).
% 0.98/1.10 tff(3235,plain,
% 0.98/1.10 (op(e3, e1) = e3),
% 0.98/1.10 inference(transitivity,[status(thm)],[3234, 3221])).
% 0.98/1.10 tff(3236,plain,
% 0.98/1.10 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.10 tff(3237,plain,
% 0.98/1.10 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3236])).
% 0.98/1.10 tff(3238,plain,
% 0.98/1.10 (~(op(e2, e1) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[402, 3237])).
% 0.98/1.10 tff(3239,plain,
% 0.98/1.10 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.10 tff(3240,plain,
% 0.98/1.10 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3239])).
% 0.98/1.10 tff(3241,plain,
% 0.98/1.10 (~(op(e0, e1) = e3)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[3046, 3240])).
% 0.98/1.10 tff(3242,plain,
% 0.98/1.10 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.10 tff(3243,plain,
% 0.98/1.10 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3242, 159])).
% 0.98/1.10 tff(3244,plain,
% 0.98/1.10 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3243])).
% 0.98/1.10 tff(3245,plain,
% 0.98/1.10 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3244])).
% 0.98/1.10 tff(3246,plain,
% 0.98/1.10 (~(op(e3, e1) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[181, 3245])).
% 0.98/1.10 tff(3247,plain,
% 0.98/1.10 ((op(e3, e1) = e1) <=> (e3 = e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.10 tff(3248,plain,
% 0.98/1.10 ((op(e3, e1) = e1) <=> (e1 = e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3247, 128])).
% 0.98/1.10 tff(3249,plain,
% 0.98/1.10 ((e1 = e3) <=> (op(e3, e1) = e1)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3248])).
% 0.98/1.10 tff(3250,plain,
% 0.98/1.10 ((~(e1 = e3)) <=> (~(op(e3, e1) = e1))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3249])).
% 0.98/1.10 tff(3251,plain,
% 0.98/1.10 (~(op(e3, e1) = e1)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[303, 3250])).
% 0.98/1.10 tff(3252,plain,
% 0.98/1.10 (op(op(e3, e1), e1) = op(e3, e1)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.10 tff(3253,plain,
% 0.98/1.10 (op(op(e3, e1), e1) = e3),
% 0.98/1.10 inference(transitivity,[status(thm)],[3252, 3234, 3221])).
% 0.98/1.10 tff(3254,plain,
% 0.98/1.10 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[2416, 3253])).
% 0.98/1.10 tff(3255,plain,
% 0.98/1.10 (op(e2, e3) = e0),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1098, 1087, 80, 656])).
% 0.98/1.10 tff(3256,plain,
% 0.98/1.10 (op(e3, op(e2, e3)) = op(e3, e0)),
% 0.98/1.10 inference(monotonicity,[status(thm)],[3255])).
% 0.98/1.10 tff(3257,plain,
% 0.98/1.10 (e0 = op(e2, e3)),
% 0.98/1.10 inference(symmetry,[status(thm)],[3255])).
% 0.98/1.10 tff(3258,plain,
% 0.98/1.10 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e0) = e0))),
% 0.98/1.10 inference(monotonicity,[status(thm)],[1695])).
% 0.98/1.10 tff(3259,plain,
% 0.98/1.10 (~(op(e3, e0) = e0)),
% 0.98/1.10 inference(modus_ponens,[status(thm)],[1087, 3258])).
% 0.98/1.10 tff(3260,plain,
% 0.98/1.10 (op(e3, e2) = e0),
% 0.98/1.10 inference(unit_resolution,[status(thm)],[1916, 3259, 656, 183])).
% 0.98/1.10 tff(3261,plain,
% 0.98/1.10 (op(e3, e2) = op(e2, e3)),
% 0.98/1.10 inference(transitivity,[status(thm)],[3260, 3257])).
% 0.98/1.11 tff(3262,plain,
% 0.98/1.11 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3261])).
% 0.98/1.11 tff(3263,plain,
% 0.98/1.11 (op(e3, op(e3, e2)) = e2),
% 0.98/1.11 inference(transitivity,[status(thm)],[3262, 3256, 466, 1124])).
% 0.98/1.11 tff(3264,plain,
% 0.98/1.11 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1904, 3263])).
% 0.98/1.11 tff(3265,plain,
% 0.98/1.11 (op(op(e2, e3), e3) = op(e0, e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3255])).
% 0.98/1.11 tff(3266,plain,
% 0.98/1.11 (op(e1, e3) = e3),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[104, 87, 845, 80])).
% 0.98/1.11 tff(3267,plain,
% 0.98/1.11 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3266])).
% 0.98/1.11 tff(3268,plain,
% 0.98/1.11 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3267, 112])).
% 0.98/1.11 tff(3269,plain,
% 0.98/1.11 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3268])).
% 0.98/1.11 tff(3270,plain,
% 0.98/1.11 (~(op(e2, e3) = e3)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[118, 3269])).
% 0.98/1.11 tff(3271,assumption,(~(op(e2, e1) = e3)), introduced(assumption)).
% 0.98/1.11 tff(3272,assumption,(~(op(e2, e0) = e3)), introduced(assumption)).
% 0.98/1.11 tff(3273,plain,
% 0.98/1.11 (op(e2, e2) = e3),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1559, 3272, 3271, 124])).
% 0.98/1.11 tff(3274,plain,
% 0.98/1.11 (e3 = op(e2, e2)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[3273, 1796])).
% 0.98/1.11 tff(3275,plain,
% 0.98/1.11 (op(e2, op(e2, e2)) = op(op(e0, e3), e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[2560, 3273])).
% 0.98/1.11 tff(3276,plain,
% 0.98/1.11 (op(op(e0, e3), e3) = op(e2, op(e2, e2))),
% 0.98/1.11 inference(symmetry,[status(thm)],[3275])).
% 0.98/1.11 tff(3277,plain,
% 0.98/1.11 (op(op(e0, e3), e3) = op(e2, e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[2])).
% 0.98/1.11 tff(3278,plain,
% 0.98/1.11 (op(e2, e3) = op(op(e0, e3), e3)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3277])).
% 0.98/1.11 tff(3279,plain,
% 0.98/1.11 (e0 = op(e2, op(e2, e2))),
% 0.98/1.11 inference(transitivity,[status(thm)],[252, 3278, 3276])).
% 0.98/1.11 tff(3280,plain,
% 0.98/1.11 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3275, 3277])).
% 0.98/1.11 tff(3281,plain,
% 0.98/1.11 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3280])).
% 0.98/1.11 tff(3282,plain,
% 0.98/1.11 (op(e2, op(e2, e3)) = op(e2, op(e2, op(e2, e2)))),
% 0.98/1.11 inference(symmetry,[status(thm)],[3281])).
% 0.98/1.11 tff(3283,plain,
% 0.98/1.11 (op(e2, op(e2, e3)) = op(op(e0, e3), e0)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[2560, 251])).
% 0.98/1.11 tff(3284,plain,
% 0.98/1.11 (op(op(e0, e3), e0) = op(e2, op(e2, e3))),
% 0.98/1.11 inference(symmetry,[status(thm)],[3283])).
% 0.98/1.11 tff(3285,plain,
% 0.98/1.11 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[252])).
% 0.98/1.11 tff(3286,plain,
% 0.98/1.11 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3285])).
% 0.98/1.11 tff(3287,plain,
% 0.98/1.11 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3286])).
% 0.98/1.11 tff(3288,plain,
% 0.98/1.11 (~(op(e2, e0) = e0)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[989, 3287])).
% 0.98/1.11 tff(3289,plain,
% 0.98/1.11 (op(e2, e0) = e1),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[765, 3272, 982, 3288])).
% 0.98/1.11 tff(3290,plain,
% 0.98/1.11 (e1 = op(e2, e0)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3289])).
% 0.98/1.11 tff(3291,plain,
% 0.98/1.11 (e1 = op(e2, op(e2, op(e2, e2)))),
% 0.98/1.11 inference(transitivity,[status(thm)],[3290, 2683, 3284, 3282])).
% 0.98/1.11 tff(3292,plain,
% 0.98/1.11 ($false),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1810, 3291, 3279, 3274])).
% 0.98/1.11 tff(3293,plain,((op(e2, e0) = e3) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e2)) | (op(e2, e0) = e2) | (op(e2, e1) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.11 tff(3294,plain,
% 0.98/1.11 (op(e2, e0) = e3),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[3293, 3255, 1124, 2080, 3271, 3270])).
% 0.98/1.11 tff(3295,plain,
% 0.98/1.11 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3294])).
% 0.98/1.11 tff(3296,plain,
% 0.98/1.11 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3295])).
% 0.98/1.11 tff(3297,plain,
% 0.98/1.11 (~(op(e0, e0) = e3)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[359, 3296])).
% 0.98/1.11 tff(3298,plain,
% 0.98/1.11 (op(e0, e2) = e3),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1495, 3297, 661, 2527])).
% 0.98/1.11 tff(3299,plain,
% 0.98/1.11 (op(e0, op(e0, e2)) = op(op(e2, e3), e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3257, 3298])).
% 0.98/1.11 tff(3300,plain,
% 0.98/1.11 (op(e0, op(e0, e2)) = e2),
% 0.98/1.11 inference(transitivity,[status(thm)],[3299, 3265, 1124])).
% 0.98/1.11 tff(3301,plain,
% 0.98/1.11 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1331, 3300])).
% 0.98/1.11 tff(3302,plain,
% 0.98/1.11 (op(e3, op(e0, e3)) = op(e3, e2)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1124])).
% 0.98/1.11 tff(3303,plain,
% 0.98/1.11 (op(e3, op(e3, e0)) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[1343, 3302, 3260])).
% 0.98/1.11 tff(3304,plain,
% 0.98/1.11 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1345, 3303])).
% 0.98/1.11 tff(3305,plain,
% 0.98/1.11 (op(op(e2, e3), e3) = e2),
% 0.98/1.11 inference(transitivity,[status(thm)],[3265, 1124])).
% 0.98/1.11 tff(3306,plain,
% 0.98/1.11 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1288, 3305])).
% 0.98/1.11 tff(3307,plain,
% 0.98/1.11 (op(op(e0, e3), e3) = op(e2, e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1124])).
% 0.98/1.11 tff(3308,plain,
% 0.98/1.11 (op(e2, op(e2, e0)) = op(op(e0, e3), e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1125, 3294])).
% 0.98/1.11 tff(3309,plain,
% 0.98/1.11 (op(e2, op(e2, e0)) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[3308, 3307, 3255])).
% 0.98/1.11 tff(3310,plain,
% 0.98/1.11 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2653, 3309])).
% 0.98/1.11 tff(3311,plain,
% 0.98/1.11 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1125])).
% 0.98/1.11 tff(3312,plain,
% 0.98/1.11 ((op(e2, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 0.98/1.11 inference(transitivity,[status(thm)],[3311, 925])).
% 0.98/1.11 tff(3313,plain,
% 0.98/1.11 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3312])).
% 0.98/1.11 tff(3314,plain,
% 0.98/1.11 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3313])).
% 0.98/1.11 tff(3315,plain,
% 0.98/1.11 (~(op(e2, e3) = e2)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[964, 3314])).
% 0.98/1.11 tff(3316,plain,
% 0.98/1.11 (op(e2, e1) = e2),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2088, 2080, 3315, 2052])).
% 0.98/1.11 tff(3317,plain,
% 0.98/1.11 (op(op(e2, e1), e1) = op(e2, e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3316])).
% 0.98/1.11 tff(3318,plain,
% 0.98/1.11 (op(op(e2, e1), e1) = e2),
% 0.98/1.11 inference(transitivity,[status(thm)],[3317, 3316])).
% 0.98/1.11 tff(3319,plain,
% 0.98/1.11 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2371, 3318])).
% 0.98/1.11 tff(3320,plain,
% 0.98/1.11 (op(e1, e2) = e2),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1151, 1134, 1143, 2052])).
% 0.98/1.11 tff(3321,plain,
% 0.98/1.11 (op(e1, op(e0, e3)) = op(e1, e2)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1124])).
% 0.98/1.11 tff(3322,plain,
% 0.98/1.11 (op(e1, e2) = op(e0, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3320, 1125])).
% 0.98/1.11 tff(3323,plain,
% 0.98/1.11 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3322])).
% 0.98/1.11 tff(3324,plain,
% 0.98/1.11 (op(e1, op(e1, e2)) = e2),
% 0.98/1.11 inference(transitivity,[status(thm)],[3323, 3321, 3320])).
% 0.98/1.11 tff(3325,plain,
% 0.98/1.11 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2377, 3324])).
% 0.98/1.11 tff(3326,plain,
% 0.98/1.11 (op(op(e0, e3), e3) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[3307, 3255])).
% 0.98/1.11 tff(3327,plain,
% 0.98/1.11 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1361, 3326])).
% 0.98/1.11 tff(3328,plain,
% 0.98/1.11 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3260])).
% 0.98/1.11 tff(3329,plain,
% 0.98/1.11 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3328])).
% 0.98/1.11 tff(3330,plain,
% 0.98/1.11 (~(op(e1, e2) = e0)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[2292, 3329])).
% 0.98/1.11 tff(3331,plain,
% 0.98/1.11 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3266])).
% 0.98/1.11 tff(3332,plain,
% 0.98/1.11 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3331, 666])).
% 0.98/1.11 tff(3333,plain,
% 0.98/1.11 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3332])).
% 0.98/1.11 tff(3334,plain,
% 0.98/1.11 (~(op(e3, e3) = e3)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[571, 3333])).
% 0.98/1.11 tff(3335,plain,
% 0.98/1.11 ((op(e3, e3) = e2) <=> (op(e3, e3) = op(e0, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[1125])).
% 0.98/1.11 tff(3336,plain,
% 0.98/1.11 ((op(e3, e3) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 0.98/1.11 inference(transitivity,[status(thm)],[3335, 659])).
% 0.98/1.11 tff(3337,plain,
% 0.98/1.11 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3336])).
% 0.98/1.11 tff(3338,plain,
% 0.98/1.11 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3337])).
% 0.98/1.11 tff(3339,plain,
% 0.98/1.11 (~(op(e3, e3) = e2)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[1077, 3338])).
% 0.98/1.11 tff(3340,plain,
% 0.98/1.11 (op(e3, e3) = e1),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1071, 3339, 656, 3334])).
% 0.98/1.11 tff(3341,assumption,((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))), introduced(assumption)).
% 0.98/1.11 tff(3342,assumption,((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))), introduced(assumption)).
% 0.98/1.11 tff(3343,plain,
% 0.98/1.11 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[252])).
% 0.98/1.11 tff(3344,plain,
% 0.98/1.11 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3343])).
% 0.98/1.11 tff(3345,plain,
% 0.98/1.11 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3344])).
% 0.98/1.11 tff(3346,plain,
% 0.98/1.11 (~(op(e2, e1) = e0)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[197, 3345])).
% 0.98/1.11 tff(3347,plain,
% 0.98/1.11 (op(e0, e1) = e0),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[292, 84, 3346, 183])).
% 0.98/1.11 tff(3348,plain,
% 0.98/1.11 (op(e0, op(e3, e3)) = op(e0, e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[305])).
% 0.98/1.11 tff(3349,plain,
% 0.98/1.11 (op(op(e0, e1), e1) = op(e0, op(e3, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3347, 306])).
% 0.98/1.11 tff(3350,plain,
% 0.98/1.11 (op(op(e0, e1), e1) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[3349, 3348, 3347])).
% 0.98/1.11 tff(3351,plain,
% 0.98/1.11 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2650, 3350])).
% 0.98/1.11 tff(3352,plain,
% 0.98/1.11 (op(e1, e0) = e0),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1830, 84, 80, 1947])).
% 0.98/1.11 tff(3353,plain,
% 0.98/1.11 (op(e1, e0) = op(e2, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3352, 252])).
% 0.98/1.11 tff(3354,plain,
% 0.98/1.11 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3353])).
% 0.98/1.11 tff(3355,plain,
% 0.98/1.11 (op(e1, op(e1, e0)) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[3354, 256, 3352])).
% 0.98/1.11 tff(3356,plain,
% 0.98/1.11 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1836, 3355])).
% 0.98/1.11 tff(3357,plain,
% 0.98/1.11 ($false),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1459, 3356, 3351, 1275, 3342, 1358, 1304, 1936, 2421, 1347, 1926, 1363, 3341])).
% 0.98/1.11 tff(3358,plain,((op(e1, e1) = e0) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e2, e3) = e0)) | (~(op(e3, e3) = e1)) | (op(e1, e3) = e0) | (op(e1, e2) = e0) | (op(e3, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.11 tff(3359,plain,
% 0.98/1.11 (op(e1, e1) = e0),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[3358, 3327, 1275, 3325, 1261, 3319, 3310, 3306, 3304, 3301, 3264, 3255, 3340, 80, 3330, 183])).
% 0.98/1.11 tff(3360,plain,
% 0.98/1.11 (op(e1, e2) = op(e1, op(e0, e3))),
% 0.98/1.11 inference(symmetry,[status(thm)],[3321])).
% 0.98/1.11 tff(3361,plain,
% 0.98/1.11 ((op(e1, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3360])).
% 0.98/1.11 tff(3362,plain,
% 0.98/1.11 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = e1)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3361])).
% 0.98/1.11 tff(3363,plain,
% 0.98/1.11 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e2) = e1))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3362])).
% 0.98/1.11 tff(3364,plain,
% 0.98/1.11 (~(op(e1, e2) = e1)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[652, 3363])).
% 0.98/1.11 tff(3365,plain,
% 0.98/1.11 (e1 = op(e3, e3)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3340])).
% 0.98/1.11 tff(3366,plain,
% 0.98/1.11 (op(e1, e1) = op(e2, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3359, 3257])).
% 0.98/1.11 tff(3367,plain,
% 0.98/1.11 ((op(e1, e1) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3366, 3365])).
% 0.98/1.11 tff(3368,plain,
% 0.98/1.11 ((op(e2, e3) = op(e3, e3)) <=> (op(e1, e1) = e1)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3367])).
% 0.98/1.11 tff(3369,plain,
% 0.98/1.11 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e1, e1) = e1))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3368])).
% 0.98/1.11 tff(3370,plain,
% 0.98/1.11 (~(op(e1, e1) = e1)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[368, 3369])).
% 0.98/1.11 tff(3371,plain,
% 0.98/1.11 (op(e1, e0) = e1),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[954, 3370, 87, 3364])).
% 0.98/1.11 tff(3372,plain,
% 0.98/1.11 (op(e1, op(e1, e0)) = op(e1, e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3371])).
% 0.98/1.11 tff(3373,plain,
% 0.98/1.11 (op(e1, op(e1, e0)) = e0),
% 0.98/1.11 inference(transitivity,[status(thm)],[3372, 3359])).
% 0.98/1.11 tff(3374,plain,
% 0.98/1.11 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1836, 3373])).
% 0.98/1.11 tff(3375,plain,
% 0.98/1.11 (op(e2, e1) = op(e0, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3316, 1125])).
% 0.98/1.11 tff(3376,plain,
% 0.98/1.11 ((op(e2, e1) = e1) <=> (op(e0, e3) = e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3375])).
% 0.98/1.11 tff(3377,plain,
% 0.98/1.11 ((op(e0, e3) = e1) <=> (op(e2, e1) = e1)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3376])).
% 0.98/1.11 tff(3378,plain,
% 0.98/1.11 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e1) = e1))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3377])).
% 0.98/1.11 tff(3379,plain,
% 0.98/1.11 (~(op(e2, e1) = e1)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[121, 3378])).
% 0.98/1.11 tff(3380,plain,
% 0.98/1.11 (op(e0, e1) = e1),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1252, 3370, 2826, 3379])).
% 0.98/1.11 tff(3381,plain,
% 0.98/1.11 (op(e0, op(e3, e3)) = op(e0, e1)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3340])).
% 0.98/1.11 tff(3382,plain,
% 0.98/1.11 (op(e0, e1) = op(e3, e3)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3380, 3365])).
% 0.98/1.11 tff(3383,plain,
% 0.98/1.11 (op(e0, op(e0, e1)) = op(e0, op(e3, e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3382])).
% 0.98/1.11 tff(3384,plain,
% 0.98/1.11 (op(e0, op(e0, e1)) = e1),
% 0.98/1.11 inference(transitivity,[status(thm)],[3383, 3381, 3380])).
% 0.98/1.11 tff(3385,plain,
% 0.98/1.11 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[2449, 3384])).
% 0.98/1.11 tff(3386,plain,
% 0.98/1.11 ($false),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[1459, 3385, 3374, 1275, 3327, 3325, 1261, 3319, 3310, 3306, 3304, 3301, 3264])).
% 0.98/1.11 tff(3387,plain,((op(e0, e3) = e0) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e3, e1) = e1) | (op(e1, e3) = e1) | (op(e1, e3) = e0) | (op(e3, e1) = e0) | (op(e0, e3) = e3) | (op(e0, e1) = e3) | (op(e2, e1) = e3) | (op(e0, e3) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, e3) = e0) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e0, e3)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.11 tff(3388,plain,
% 0.98/1.11 (op(e0, e3) = e0),
% 0.98/1.11 inference(unit_resolution,[status(thm)],[3387, 3254, 3251, 3231, 80, 3246, 661, 3241, 3238, 121, 466, 656, 651, 652])).
% 0.98/1.11 tff(3389,plain,
% 0.98/1.11 (e0 = op(e0, e3)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3388])).
% 0.98/1.11 tff(3390,plain,
% 0.98/1.11 (e0 = op(e3, e0)),
% 0.98/1.11 inference(transitivity,[status(thm)],[3389, 467])).
% 0.98/1.11 tff(3391,plain,
% 0.98/1.11 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3390])).
% 0.98/1.11 tff(3392,plain,
% 0.98/1.11 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.98/1.11 inference(symmetry,[status(thm)],[3391])).
% 0.98/1.11 tff(3393,plain,
% 0.98/1.11 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3392])).
% 0.98/1.11 tff(3394,plain,
% 0.98/1.11 (~(op(e1, e0) = e0)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[410, 3393])).
% 0.98/1.11 tff(3395,plain,
% 0.98/1.11 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3232])).
% 0.98/1.11 tff(3396,plain,
% 0.98/1.11 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 0.98/1.11 inference(monotonicity,[status(thm)],[3395])).
% 0.98/1.11 tff(3397,plain,
% 0.98/1.11 (~(op(e1, e0) = e3)),
% 0.98/1.11 inference(modus_ponens,[status(thm)],[110, 3396])).
% 0.98/1.12 tff(3398,plain,
% 0.98/1.12 (op(e1, e0) = op(e1, op(e0, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3389])).
% 0.98/1.12 tff(3399,plain,
% 0.98/1.12 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3398])).
% 0.98/1.12 tff(3400,plain,
% 0.98/1.12 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3399])).
% 0.98/1.12 tff(3401,plain,
% 0.98/1.12 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3400])).
% 0.98/1.12 tff(3402,plain,
% 0.98/1.12 (~(op(e1, e0) = e1)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[652, 3401])).
% 0.98/1.12 tff(3403,plain,
% 0.98/1.12 (op(e1, e0) = e2),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[728, 3402, 3397, 3394])).
% 0.98/1.12 tff(3404,plain,
% 0.98/1.12 (e2 = op(e1, e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3403])).
% 0.98/1.12 tff(3405,plain,
% 0.98/1.12 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3404])).
% 0.98/1.12 tff(3406,plain,
% 0.98/1.12 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3405])).
% 0.98/1.12 tff(3407,plain,
% 0.98/1.12 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3406])).
% 0.98/1.12 tff(3408,plain,
% 0.98/1.12 (~(op(e0, e0) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[2471, 3407])).
% 0.98/1.12 tff(3409,plain,
% 0.98/1.12 ((op(e0, e0) = e0) <=> (op(e0, e0) = op(e0, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3389])).
% 0.98/1.12 tff(3410,plain,
% 0.98/1.12 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3409])).
% 0.98/1.12 tff(3411,plain,
% 0.98/1.12 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3410])).
% 0.98/1.12 tff(3412,plain,
% 0.98/1.12 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = op(e0, e3)))),
% 0.98/1.12 inference(rewrite,[status(thm)],[])).
% 0.98/1.12 tff(3413,plain,
% 0.98/1.12 (~(op(e0, e0) = op(e0, e3))),
% 0.98/1.12 inference(and_elim,[status(thm)],[54])).
% 0.98/1.12 tff(3414,plain,
% 0.98/1.12 (~(op(e0, e0) = op(e0, e3))),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3413, 3412])).
% 0.98/1.12 tff(3415,plain,
% 0.98/1.12 (~(op(e0, e0) = e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3414, 3411])).
% 0.98/1.12 tff(3416,plain,
% 0.98/1.12 (op(e0, op(e0, e3)) = op(e0, e0)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3388])).
% 0.98/1.12 tff(3417,plain,
% 0.98/1.12 (op(e0, e0) = op(e0, op(e0, e3))),
% 0.98/1.12 inference(symmetry,[status(thm)],[3416])).
% 0.98/1.12 tff(3418,plain,
% 0.98/1.12 ((op(e0, e0) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3417])).
% 0.98/1.12 tff(3419,plain,
% 0.98/1.12 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e0) = e3)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3418])).
% 0.98/1.12 tff(3420,plain,
% 0.98/1.12 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e3)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3232])).
% 0.98/1.12 tff(3421,plain,
% 0.98/1.12 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3420])).
% 0.98/1.12 tff(3422,plain,
% 0.98/1.12 (~(op(e1, e2) = e3)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[1850, 3421])).
% 0.98/1.12 tff(3423,plain,
% 0.98/1.12 ((e3 = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.98/1.12 inference(commutativity,[status(thm)],[])).
% 0.98/1.12 tff(3424,plain,
% 0.98/1.12 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3235])).
% 0.98/1.12 tff(3425,plain,
% 0.98/1.12 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3424, 3423])).
% 0.98/1.12 tff(3426,plain,
% 0.98/1.12 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3425])).
% 0.98/1.12 tff(3427,plain,
% 0.98/1.12 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e3, e2)))),
% 0.98/1.12 inference(rewrite,[status(thm)],[])).
% 0.98/1.12 tff(3428,plain,
% 0.98/1.12 (~(op(e3, e1) = op(e3, e2))),
% 0.98/1.12 inference(and_elim,[status(thm)],[35])).
% 0.98/1.12 tff(3429,plain,
% 0.98/1.12 (~(op(e3, e1) = op(e3, e2))),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3428, 3427])).
% 0.98/1.12 tff(3430,plain,
% 0.98/1.12 (~(op(e3, e2) = e3)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3429, 3426])).
% 0.98/1.12 tff(3431,plain,
% 0.98/1.12 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3390])).
% 0.98/1.12 tff(3432,plain,
% 0.98/1.12 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3431])).
% 0.98/1.12 tff(3433,plain,
% 0.98/1.12 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3432])).
% 0.98/1.12 tff(3434,plain,
% 0.98/1.12 (~(op(e2, e0) = e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[747, 3433])).
% 0.98/1.12 tff(3435,plain,
% 0.98/1.12 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3389])).
% 0.98/1.12 tff(3436,plain,
% 0.98/1.12 ((op(e2, e3) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3435, 925])).
% 0.98/1.12 tff(3437,plain,
% 0.98/1.12 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3436])).
% 0.98/1.12 tff(3438,plain,
% 0.98/1.12 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3437])).
% 0.98/1.12 tff(3439,plain,
% 0.98/1.12 (~(op(e2, e3) = e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[964, 3438])).
% 0.98/1.12 tff(3440,plain,
% 0.98/1.12 (op(op(e1, e0), e1) = op(e2, e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3403])).
% 0.98/1.12 tff(3441,plain,
% 0.98/1.12 (op(e2, e1) = op(op(e1, e0), e1)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3440])).
% 0.98/1.12 tff(3442,plain,
% 0.98/1.12 ((op(e2, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3441])).
% 0.98/1.12 tff(3443,plain,
% 0.98/1.12 ((op(op(e1, e0), e1) = e0) <=> (op(e2, e1) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3442])).
% 0.98/1.12 tff(3444,plain,
% 0.98/1.12 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3232])).
% 0.98/1.12 tff(3445,plain,
% 0.98/1.12 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3444, 112])).
% 0.98/1.12 tff(3446,plain,
% 0.98/1.12 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3445])).
% 0.98/1.12 tff(3447,plain,
% 0.98/1.12 (~(op(e2, e3) = e3)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[118, 3446])).
% 0.98/1.12 tff(3448,plain,
% 0.98/1.12 (op(e2, op(e0, e3)) = op(e2, e0)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3388])).
% 0.98/1.12 tff(3449,plain,
% 0.98/1.12 (op(e2, e0) = op(e2, op(e0, e3))),
% 0.98/1.12 inference(symmetry,[status(thm)],[3448])).
% 0.98/1.12 tff(3450,plain,
% 0.98/1.12 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3449])).
% 0.98/1.12 tff(3451,plain,
% 0.98/1.12 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3450])).
% 0.98/1.12 tff(3452,plain,
% 0.98/1.12 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e0) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3451])).
% 0.98/1.12 tff(3453,plain,
% 0.98/1.12 (~(op(e2, e0) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[651, 3452])).
% 0.98/1.12 tff(3454,plain,
% 0.98/1.12 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[772])).
% 0.98/1.12 tff(3455,plain,
% 0.98/1.12 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3454])).
% 0.98/1.12 tff(3456,plain,
% 0.98/1.12 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3455])).
% 0.98/1.12 tff(3457,plain,
% 0.98/1.12 (~(op(e0, e1) = e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[818, 3456])).
% 0.98/1.12 tff(3458,plain,
% 0.98/1.12 (op(e2, e1) = e0),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[292, 84, 3457, 183])).
% 0.98/1.12 tff(3459,plain,
% 0.98/1.12 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[1366])).
% 0.98/1.12 tff(3460,plain,
% 0.98/1.12 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3459])).
% 0.98/1.12 tff(3461,plain,
% 0.98/1.12 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3460])).
% 0.98/1.12 tff(3462,plain,
% 0.98/1.12 (~(op(e1, e0) = e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[410, 3461])).
% 0.98/1.12 tff(3463,plain,
% 0.98/1.12 (op(e1, e0) = e2),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[728, 929, 2168, 3462])).
% 0.98/1.12 tff(3464,plain,
% 0.98/1.12 (e2 = op(e1, e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3463])).
% 0.98/1.12 tff(3465,plain,
% 0.98/1.12 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3464])).
% 0.98/1.12 tff(3466,plain,
% 0.98/1.12 ((op(e1, e1) = e2) <=> (op(e1, e0) = op(e1, e1))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3465, 710])).
% 0.98/1.12 tff(3467,plain,
% 0.98/1.12 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3466])).
% 0.98/1.12 tff(3468,plain,
% 0.98/1.12 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3467])).
% 0.98/1.12 tff(3469,plain,
% 0.98/1.12 (~(op(e1, e1) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[737, 3468])).
% 0.98/1.12 tff(3470,plain,
% 0.98/1.12 (op(e1, e1) = e1),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[630, 84, 1291, 3469])).
% 0.98/1.12 tff(3471,plain,
% 0.98/1.12 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3470])).
% 0.98/1.12 tff(3472,plain,
% 0.98/1.12 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3471])).
% 0.98/1.12 tff(3473,plain,
% 0.98/1.12 (~(op(e0, e1) = e1)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[792, 3472])).
% 0.98/1.12 tff(3474,plain,
% 0.98/1.12 (op(e2, e1) = op(e3, e0)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3458, 772, 467])).
% 0.98/1.12 tff(3475,plain,
% 0.98/1.12 ((op(e2, e1) = e2) <=> (op(e3, e0) = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3474, 3464])).
% 0.98/1.12 tff(3476,plain,
% 0.98/1.12 ((op(e2, e1) = e2) <=> (op(e1, e0) = op(e3, e0))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3475, 2294])).
% 0.98/1.12 tff(3477,plain,
% 0.98/1.12 ((op(e1, e0) = op(e3, e0)) <=> (op(e2, e1) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3476])).
% 0.98/1.12 tff(3478,plain,
% 0.98/1.12 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e2, e1) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3477])).
% 0.98/1.12 tff(3479,plain,
% 0.98/1.12 (~(op(e2, e1) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[410, 3478])).
% 0.98/1.12 tff(3480,plain,
% 0.98/1.12 (op(e0, e1) = e2),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[829, 3473, 2527, 3457])).
% 0.98/1.12 tff(3481,plain,
% 0.98/1.12 (op(e1, op(e1, e0)) = op(e1, e2)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3463])).
% 0.98/1.12 tff(3482,plain,
% 0.98/1.12 (op(e1, e2) = op(e1, op(e1, e0))),
% 0.98/1.12 inference(symmetry,[status(thm)],[3481])).
% 0.98/1.12 tff(3483,plain,
% 0.98/1.12 ((op(e1, e2) = e0) <=> (op(e1, op(e1, e0)) = e0)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3482])).
% 0.98/1.12 tff(3484,plain,
% 0.98/1.12 (op(e1, e2) = e0),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1830, 84, 80, 3462])).
% 0.98/1.12 tff(3485,plain,
% 0.98/1.12 (op(e1, op(e1, e0)) = e0),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 0.98/1.12 tff(3486,plain,
% 0.98/1.12 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1836, 3485])).
% 0.98/1.12 tff(3487,plain,
% 0.98/1.12 (op(e1, e2) = op(e0, e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3484, 772])).
% 0.98/1.12 tff(3488,plain,
% 0.98/1.12 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3487])).
% 0.98/1.12 tff(3489,plain,
% 0.98/1.12 (op(e1, op(e1, e2)) = e2),
% 0.98/1.12 inference(transitivity,[status(thm)],[3488, 777, 3463])).
% 0.98/1.12 tff(3490,plain,
% 0.98/1.12 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2377, 3489])).
% 0.98/1.12 tff(3491,plain,
% 0.98/1.12 ((e2 = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.98/1.12 inference(commutativity,[status(thm)],[])).
% 0.98/1.12 tff(3492,assumption,(op(e0, e1) = e2), introduced(assumption)).
% 0.98/1.12 tff(3493,plain,
% 0.98/1.12 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3492])).
% 0.98/1.12 tff(3494,plain,
% 0.98/1.12 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3493, 3491])).
% 0.98/1.12 tff(3495,plain,
% 0.98/1.12 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3494])).
% 0.98/1.12 tff(3496,plain,
% 0.98/1.12 (~(op(e0, e2) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[2102, 3495])).
% 0.98/1.12 tff(3497,plain,
% 0.98/1.12 ((e3 = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.98/1.12 inference(commutativity,[status(thm)],[])).
% 0.98/1.12 tff(3498,plain,
% 0.98/1.12 ((op(e2, e2) = e2) <=> (e3 = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3273, 975])).
% 0.98/1.12 tff(3499,plain,
% 0.98/1.12 ((op(e2, e2) = e2) <=> (op(e1, e0) = e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3498, 3497])).
% 0.98/1.12 tff(3500,plain,
% 0.98/1.12 ((op(e1, e0) = e3) <=> (op(e2, e2) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3499])).
% 0.98/1.12 tff(3501,plain,
% 0.98/1.12 ((~(op(e1, e0) = e3)) <=> (~(op(e2, e2) = e2))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3500])).
% 0.98/1.12 tff(3502,plain,
% 0.98/1.12 (~(op(e2, e2) = e2)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[2168, 3501])).
% 0.98/1.12 tff(3503,plain,
% 0.98/1.12 (op(e3, e2) = e2),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1151, 3502, 1313, 3496])).
% 0.98/1.12 tff(3504,plain,
% 0.98/1.12 (op(e3, e2) = op(e1, e0)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3503, 975])).
% 0.98/1.12 tff(3505,plain,
% 0.98/1.12 (op(e3, op(e3, e2)) = op(e3, op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3504])).
% 0.98/1.12 tff(3506,plain,
% 0.98/1.12 (op(e3, op(e3, e2)) = e2),
% 0.98/1.12 inference(transitivity,[status(thm)],[3505, 1365, 3503])).
% 0.98/1.12 tff(3507,plain,
% 0.98/1.12 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1904, 3506])).
% 0.98/1.12 tff(3508,assumption,(op(e2, e1) = e0), introduced(assumption)).
% 0.98/1.12 tff(3509,plain,
% 0.98/1.12 (op(e2, e0) = e1),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[765, 3272, 982, 983])).
% 0.98/1.12 tff(3510,plain,
% 0.98/1.12 (op(e2, op(e2, e0)) = op(op(e1, e0), e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[975, 3509])).
% 0.98/1.12 tff(3511,plain,
% 0.98/1.12 (op(e2, op(e2, e0)) = e0),
% 0.98/1.12 inference(transitivity,[status(thm)],[3510, 1351, 3508])).
% 0.98/1.12 tff(3512,plain,
% 0.98/1.12 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2653, 3511])).
% 0.98/1.12 tff(3513,plain,
% 0.98/1.12 (op(e0, e1) = op(e1, e0)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3492, 975])).
% 0.98/1.12 tff(3514,plain,
% 0.98/1.12 (op(op(e0, e1), e1) = op(op(e1, e0), e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3513])).
% 0.98/1.12 tff(3515,plain,
% 0.98/1.12 (op(op(e0, e1), e1) = e0),
% 0.98/1.12 inference(transitivity,[status(thm)],[3514, 1351, 3508])).
% 0.98/1.12 tff(3516,plain,
% 0.98/1.12 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2650, 3515])).
% 0.98/1.12 tff(3517,plain,
% 0.98/1.12 (op(op(e2, e1), e1) = op(e0, e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3508])).
% 0.98/1.12 tff(3518,plain,
% 0.98/1.12 ((op(op(e2, e1), e1) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3517, 975])).
% 0.98/1.12 tff(3519,plain,
% 0.98/1.12 ((op(op(e2, e1), e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3518, 595])).
% 0.98/1.12 tff(3520,plain,
% 0.98/1.12 ((op(e1, e0) = op(e0, e1)) <=> (op(op(e2, e1), e1) = e2)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3519])).
% 0.98/1.12 tff(3521,plain,
% 0.98/1.12 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[975])).
% 0.98/1.12 tff(3522,plain,
% 0.98/1.12 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3521, 595])).
% 0.98/1.12 tff(3523,plain,
% 0.98/1.12 ((op(e0, e1) = e2) <=> (op(op(e2, e1), e1) = e2)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3522, 3520])).
% 0.98/1.12 tff(3524,plain,
% 0.98/1.12 (op(op(e2, e1), e1) = e2),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3492, 3523])).
% 0.98/1.12 tff(3525,plain,
% 0.98/1.12 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2371, 3524])).
% 0.98/1.12 tff(3526,plain,
% 0.98/1.12 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3509])).
% 0.98/1.12 tff(3527,plain,
% 0.98/1.12 (e1 = op(e2, e0)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3509])).
% 0.98/1.12 tff(3528,assumption,(~(op(e0, e1) = e1)), introduced(assumption)).
% 0.98/1.12 tff(3529,plain,
% 0.98/1.12 (op(e0, e0) = e3),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2713, 3272, 2410, 2168])).
% 0.98/1.12 tff(3530,plain,
% 0.98/1.12 ((op(e0, e0) = e1) <=> (e3 = e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3529])).
% 0.98/1.12 tff(3531,plain,
% 0.98/1.12 ((op(e0, e0) = e1) <=> (e1 = e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3530, 128])).
% 0.98/1.12 tff(3532,plain,
% 0.98/1.12 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3531])).
% 0.98/1.12 tff(3533,plain,
% 0.98/1.12 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3532])).
% 0.98/1.12 tff(3534,plain,
% 0.98/1.12 (~(op(e0, e0) = e1)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[303, 3533])).
% 0.98/1.12 tff(3535,plain,
% 0.98/1.12 (op(e0, e2) = e1),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[384, 3534, 121, 3528])).
% 0.98/1.12 tff(3536,plain,
% 0.98/1.12 (op(e0, e2) = op(e2, e0)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3535, 3527])).
% 0.98/1.12 tff(3537,plain,
% 0.98/1.12 (op(e0, op(e0, e2)) = op(e0, op(e2, e0))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3536])).
% 0.98/1.12 tff(3538,plain,
% 0.98/1.12 (op(e0, op(e0, e2)) = e2),
% 0.98/1.12 inference(transitivity,[status(thm)],[3537, 3526, 3492])).
% 0.98/1.12 tff(3539,plain,
% 0.98/1.12 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1331, 3538])).
% 0.98/1.12 tff(3540,assumption,(~(op(e2, e1) = e2)), introduced(assumption)).
% 0.98/1.12 tff(3541,plain,
% 0.98/1.12 (op(e2, e3) = e2),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2088, 3502, 982, 3540])).
% 0.98/1.12 tff(3542,plain,
% 0.98/1.12 (op(e2, op(e2, e3)) = op(e2, e2)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3541])).
% 0.98/1.12 tff(3543,plain,
% 0.98/1.12 (op(e2, op(e2, e3)) = e3),
% 0.98/1.12 inference(transitivity,[status(thm)],[3542, 3273])).
% 0.98/1.12 tff(3544,plain,
% 0.98/1.12 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2344, 3543])).
% 0.98/1.12 tff(3545,plain,
% 0.98/1.12 ($false),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1459, 3544, 3539, 1275, 3342, 1358, 1304, 1357, 3525, 3516, 1926, 3512, 3507])).
% 0.98/1.12 tff(3546,plain,((op(e2, e0) = e3) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~(op(e1, e0) = e2)) | (~(op(e0, e1) = e2)) | (op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e0, e3) = e1) | (op(e0, e1) = e1) | (~(op(e2, e1) = e0)) | (op(e1, e0) = e3) | (op(e2, e0) = e0) | (op(e2, e1) = e3) | (op(e2, e3) = e3) | (op(e3, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.12 tff(3547,plain,
% 0.98/1.12 (op(e2, e0) = e3),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[3546, 3490, 1362, 1275, 1304, 3486, 2420, 3463, 3480, 982, 3479, 121, 3473, 3458, 2168, 1370, 3271, 124, 665])).
% 0.98/1.12 tff(3548,plain,
% 0.98/1.12 ((op(e2, e0) = e1) <=> (e3 = e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3547])).
% 0.98/1.12 tff(3549,plain,
% 0.98/1.12 ((op(e2, e0) = e1) <=> (e1 = e3)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3548, 128])).
% 0.98/1.12 tff(3550,plain,
% 0.98/1.12 ((e1 = e3) <=> (op(e2, e0) = e1)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3549])).
% 0.98/1.12 tff(3551,plain,
% 0.98/1.12 ((~(e1 = e3)) <=> (~(op(e2, e0) = e1))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3550])).
% 0.98/1.12 tff(3552,plain,
% 0.98/1.12 (~(op(e2, e0) = e1)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[303, 3551])).
% 0.98/1.12 tff(3553,plain,
% 0.98/1.12 (op(e0, e0) = e1),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[1480, 3552, 899, 929])).
% 0.98/1.12 tff(3554,plain,
% 0.98/1.12 (e1 = op(e0, e0)),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[3553, 74])).
% 0.98/1.12 tff(3555,plain,
% 0.98/1.12 (op(e0, op(e0, e0)) = op(e0, e1)),
% 0.98/1.12 inference(monotonicity,[status(thm)],[3553])).
% 0.98/1.12 tff(3556,plain,
% 0.98/1.12 (op(e0, e1) = op(e0, op(e0, e0))),
% 0.98/1.12 inference(symmetry,[status(thm)],[3555])).
% 0.98/1.12 tff(3557,plain,
% 0.98/1.12 (e2 = op(e0, e1)),
% 0.98/1.12 inference(symmetry,[status(thm)],[3480])).
% 0.98/1.12 tff(3558,plain,
% 0.98/1.12 (e2 = op(e0, op(e0, e0))),
% 0.98/1.12 inference(transitivity,[status(thm)],[3557, 3556])).
% 0.98/1.12 tff(3559,plain,
% 0.98/1.12 (op(e0, op(e0, e0)) = op(e1, e0)),
% 0.98/1.12 inference(transitivity,[status(thm)],[3555, 3480, 3464])).
% 0.98/1.12 tff(3560,plain,
% 0.98/1.12 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e0))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3559])).
% 0.98/1.13 tff(3561,plain,
% 0.98/1.13 (op(e0, op(e1, e0)) = op(e0, op(e0, op(e0, e0)))),
% 0.98/1.13 inference(symmetry,[status(thm)],[3560])).
% 0.98/1.13 tff(3562,plain,
% 0.98/1.13 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3463])).
% 0.98/1.13 tff(3563,plain,
% 0.98/1.13 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.98/1.13 inference(symmetry,[status(thm)],[3562])).
% 0.98/1.13 tff(3564,plain,
% 0.98/1.13 ((op(e0, e0) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2428])).
% 0.98/1.13 tff(3565,plain,
% 0.98/1.13 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e0) = e3)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3564])).
% 0.98/1.13 tff(3566,plain,
% 0.98/1.13 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, op(e0, e3)) = e3)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2428, 3547])).
% 0.98/1.13 tff(3567,plain,
% 0.98/1.13 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3566, 3565])).
% 0.98/1.13 tff(3568,plain,
% 0.98/1.13 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3567])).
% 0.98/1.13 tff(3569,plain,
% 0.98/1.13 (~(op(e0, e0) = e3)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[359, 3568])).
% 0.98/1.13 tff(3570,plain,
% 0.98/1.13 (op(e0, e2) = e3),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1495, 3569, 661, 2527])).
% 0.98/1.13 tff(3571,plain,
% 0.98/1.13 (e3 = op(e0, e2)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3570])).
% 0.98/1.13 tff(3572,plain,
% 0.98/1.13 (e3 = op(e0, op(e0, op(e0, e0)))),
% 0.98/1.13 inference(transitivity,[status(thm)],[3571, 3563, 3561])).
% 0.98/1.13 tff(3573,plain,
% 0.98/1.13 ((~(~((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0)))))) <=> ((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3574,plain,
% 0.98/1.13 (((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0)))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3575,plain,
% 0.98/1.13 ((~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0))))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3574])).
% 0.98/1.13 tff(3576,plain,
% 0.98/1.13 ((~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[3575, 3573])).
% 0.98/1.13 tff(3577,plain,
% 0.98/1.13 ((~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3578,plain,
% 0.98/1.13 ((~(((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0))) & (e3 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0))))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3579,axiom,(~(((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0))) & (e3 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax8')).
% 0.98/1.13 tff(3580,plain,
% 0.98/1.13 (~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 0.98/1.13 tff(3581,plain,
% 0.98/1.13 (~((e2 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e3 = op(e0, op(e0, op(e0, e0)))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3580, 3577])).
% 0.98/1.13 tff(3582,plain,
% 0.98/1.13 ((~(e3 = op(e0, op(e0, op(e0, e0))))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(e0, e0)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3581, 3576])).
% 0.98/1.13 tff(3583,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[3582, 3572, 3558, 3554])).
% 0.98/1.13 tff(3584,plain,((op(e1, e1) = e0) | (op(e0, e3) = e3) | (op(e0, e1) = e3) | (op(e1, e0) = e1) | (~(op(e0, e3) = e0)) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e0) = e2) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e3) = e0) | (op(e3, e1) = e0) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(3585,plain,
% 0.98/1.13 (op(e1, e1) = e0),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[3584, 3241, 661, 3402, 3388, 3254, 1261, 3453, 121, 3397, 3238, 3447, 466, 80, 3246, 1291])).
% 0.98/1.13 tff(3586,plain,
% 0.98/1.13 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(op(e1, e0), e1))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3585, 3441])).
% 0.98/1.13 tff(3587,plain,
% 0.98/1.13 ((op(e1, e1) = op(e2, e1)) <=> (op(op(e1, e0), e1) = e0)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3586, 1290])).
% 0.98/1.13 tff(3588,plain,
% 0.98/1.13 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3587, 3443])).
% 0.98/1.13 tff(3589,plain,
% 0.98/1.13 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3588])).
% 0.98/1.13 tff(3590,plain,
% 0.98/1.13 (~(op(e2, e1) = e0)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[225, 3589])).
% 0.98/1.13 tff(3591,plain,
% 0.98/1.13 (op(e2, e2) = e0),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2311, 3590, 3439, 3434])).
% 0.98/1.13 tff(3592,plain,
% 0.98/1.13 (op(e2, e2) = op(e0, e3)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3591, 3389])).
% 0.98/1.13 tff(3593,plain,
% 0.98/1.13 ((op(e2, e2) = e3) <=> (op(e0, e3) = e3)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3592])).
% 0.98/1.13 tff(3594,plain,
% 0.98/1.13 ((op(e0, e3) = e3) <=> (op(e2, e2) = e3)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3593])).
% 0.98/1.13 tff(3595,plain,
% 0.98/1.13 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e2) = e3))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3594])).
% 0.98/1.13 tff(3596,plain,
% 0.98/1.13 (~(op(e2, e2) = e3)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[661, 3595])).
% 0.98/1.13 tff(3597,plain,
% 0.98/1.13 (op(e0, e2) = e3),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2111, 3596, 3430, 3422])).
% 0.98/1.13 tff(3598,plain,
% 0.98/1.13 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e3)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3417, 3597])).
% 0.98/1.13 tff(3599,plain,
% 0.98/1.13 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3598, 3419])).
% 0.98/1.13 tff(3600,plain,
% 0.98/1.13 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3599])).
% 0.98/1.13 tff(3601,plain,
% 0.98/1.13 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = op(e0, e2)))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3602,plain,
% 0.98/1.13 (~(op(e0, e0) = op(e0, e2))),
% 0.98/1.13 inference(and_elim,[status(thm)],[55])).
% 0.98/1.13 tff(3603,plain,
% 0.98/1.13 (~(op(e0, e0) = op(e0, e2))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 0.98/1.13 tff(3604,plain,
% 0.98/1.13 (~(op(e0, e0) = e3)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3603, 3600])).
% 0.98/1.13 tff(3605,plain,
% 0.98/1.13 (((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))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3606,plain,
% 0.98/1.13 ((((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))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3607,plain,
% 0.98/1.13 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3608,plain,
% 0.98/1.13 (((((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))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3607])).
% 0.98/1.13 tff(3609,plain,
% 0.98/1.13 (((((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))),
% 0.98/1.13 inference(transitivity,[status(thm)],[3608, 3606])).
% 0.98/1.13 tff(3610,plain,
% 0.98/1.13 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)),
% 0.98/1.13 inference(and_elim,[status(thm)],[826])).
% 0.98/1.13 tff(3611,plain,
% 0.98/1.13 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 0.98/1.13 tff(3612,plain,
% 0.98/1.13 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3611, 3605])).
% 0.98/1.13 tff(3613,plain,
% 0.98/1.13 (op(e0, e0) = e1),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[3612, 3604, 3415, 3408])).
% 0.98/1.13 tff(3614,plain,
% 0.98/1.13 (e1 = op(e0, e0)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[3613, 74])).
% 0.98/1.13 tff(3615,plain,
% 0.98/1.13 (op(e1, e1) = op(e0, e3)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3585, 3389])).
% 0.98/1.13 tff(3616,plain,
% 0.98/1.13 ((op(e1, e1) = e1) <=> (op(e0, e3) = e1)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3615])).
% 0.98/1.13 tff(3617,plain,
% 0.98/1.13 ((op(e0, e3) = e1) <=> (op(e1, e1) = e1)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3616])).
% 0.98/1.13 tff(3618,plain,
% 0.98/1.13 ((~(op(e0, e3) = e1)) <=> (~(op(e1, e1) = e1))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3617])).
% 0.98/1.13 tff(3619,plain,
% 0.98/1.13 (~(op(e1, e1) = e1)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[121, 3618])).
% 0.98/1.13 tff(3620,plain,
% 0.98/1.13 (op(e1, e2) = e1),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[954, 3619, 3231, 3402])).
% 0.98/1.13 tff(3621,plain,
% 0.98/1.13 (e1 = op(e1, e2)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3620])).
% 0.98/1.13 tff(3622,plain,
% 0.98/1.13 (op(e0, e0) = op(e1, e2)),
% 0.98/1.13 inference(transitivity,[status(thm)],[3613, 3621])).
% 0.98/1.13 tff(3623,plain,
% 0.98/1.13 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3622])).
% 0.98/1.13 tff(3624,plain,
% 0.98/1.13 (op(e0, op(e1, e2)) = op(e0, op(e0, e0))),
% 0.98/1.13 inference(symmetry,[status(thm)],[3623])).
% 0.98/1.13 tff(3625,plain,
% 0.98/1.13 (op(e0, op(e1, e2)) = op(e0, e1)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3620])).
% 0.98/1.13 tff(3626,plain,
% 0.98/1.13 (op(e0, e1) = op(e0, op(e1, e2))),
% 0.98/1.13 inference(symmetry,[status(thm)],[3625])).
% 0.98/1.13 tff(3627,plain,
% 0.98/1.13 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3389])).
% 0.98/1.13 tff(3628,plain,
% 0.98/1.13 ((~(e0 = e2)) <=> (~(op(e0, e3) = e2))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3627])).
% 0.98/1.13 tff(3629,plain,
% 0.98/1.13 (~(op(e0, e3) = e2)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[14, 3628])).
% 0.98/1.13 tff(3630,plain,
% 0.98/1.13 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e0))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3390])).
% 0.98/1.13 tff(3631,plain,
% 0.98/1.13 ((op(e3, e2) = e0) <=> (op(e3, e0) = op(e3, e2))),
% 0.98/1.13 inference(transitivity,[status(thm)],[3630, 1123])).
% 0.98/1.13 tff(3632,plain,
% 0.98/1.13 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3631])).
% 0.98/1.13 tff(3633,plain,
% 0.98/1.13 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3632])).
% 0.98/1.13 tff(3634,plain,
% 0.98/1.13 (~(op(e3, e2) = e0)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1133, 3633])).
% 0.98/1.13 tff(3635,plain,
% 0.98/1.13 ((op(e3, e2) = op(e1, e2)) <=> (op(e1, e2) = op(e3, e2))),
% 0.98/1.13 inference(commutativity,[status(thm)],[])).
% 0.98/1.13 tff(3636,plain,
% 0.98/1.13 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e1, e2))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3621])).
% 0.98/1.13 tff(3637,plain,
% 0.98/1.13 ((op(e3, e2) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 0.98/1.13 inference(transitivity,[status(thm)],[3636, 3635])).
% 0.98/1.13 tff(3638,plain,
% 0.98/1.13 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.98/1.13 inference(symmetry,[status(thm)],[3637])).
% 0.98/1.13 tff(3639,plain,
% 0.98/1.13 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3638])).
% 0.98/1.13 tff(3640,plain,
% 0.98/1.13 (~(op(e3, e2) = e1)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2292, 3639])).
% 0.98/1.13 tff(3641,plain,
% 0.98/1.13 (op(e3, e2) = e2),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1898, 3640, 3634, 3430])).
% 0.98/1.13 tff(3642,plain,
% 0.98/1.13 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3641])).
% 0.98/1.13 tff(3643,plain,
% 0.98/1.13 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[3642])).
% 0.98/1.13 tff(3644,plain,
% 0.98/1.13 (~(op(e0, e2) = e2)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1467, 3643])).
% 0.98/1.13 tff(3645,plain,
% 0.98/1.13 (((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))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(3646,plain,
% 0.98/1.13 ((((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))),
% 1.03/1.13 inference(rewrite,[status(thm)],[])).
% 1.03/1.13 tff(3647,plain,
% 1.03/1.13 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2))),
% 1.03/1.13 inference(rewrite,[status(thm)],[])).
% 1.03/1.13 tff(3648,plain,
% 1.03/1.13 (((((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))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3647])).
% 1.03/1.13 tff(3649,plain,
% 1.03/1.13 (((((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))),
% 1.03/1.13 inference(transitivity,[status(thm)],[3648, 3646])).
% 1.03/1.13 tff(3650,plain,
% 1.03/1.13 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)),
% 1.03/1.13 inference(and_elim,[status(thm)],[379])).
% 1.03/1.13 tff(3651,plain,
% 1.03/1.13 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 1.03/1.13 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 1.03/1.13 tff(3652,plain,
% 1.03/1.13 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 1.03/1.13 inference(modus_ponens,[status(thm)],[3651, 3645])).
% 1.03/1.13 tff(3653,plain,
% 1.03/1.13 (op(e0, e1) = e2),
% 1.03/1.13 inference(unit_resolution,[status(thm)],[3652, 3644, 3629, 3408])).
% 1.03/1.13 tff(3654,plain,
% 1.03/1.13 (e2 = op(e0, e1)),
% 1.03/1.13 inference(symmetry,[status(thm)],[3653])).
% 1.03/1.13 tff(3655,plain,
% 1.03/1.13 (e2 = op(e0, op(e0, e0))),
% 1.03/1.13 inference(transitivity,[status(thm)],[3654, 3626, 3624])).
% 1.03/1.13 tff(3656,plain,
% 1.03/1.13 (op(e0, op(e0, e0)) = op(e1, e0)),
% 1.03/1.13 inference(transitivity,[status(thm)],[3623, 3625, 3653, 3404])).
% 1.03/1.13 tff(3657,plain,
% 1.03/1.13 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e0))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3656])).
% 1.03/1.13 tff(3658,plain,
% 1.03/1.13 (op(e0, op(e1, e0)) = op(e0, op(e0, op(e0, e0)))),
% 1.03/1.13 inference(symmetry,[status(thm)],[3657])).
% 1.03/1.13 tff(3659,plain,
% 1.03/1.13 (op(e0, op(e1, e0)) = op(e0, e2)),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3403])).
% 1.03/1.13 tff(3660,plain,
% 1.03/1.13 (op(e0, e2) = op(e0, op(e1, e0))),
% 1.03/1.13 inference(symmetry,[status(thm)],[3659])).
% 1.03/1.13 tff(3661,plain,
% 1.03/1.13 (e3 = op(e0, e2)),
% 1.03/1.13 inference(symmetry,[status(thm)],[3597])).
% 1.03/1.13 tff(3662,plain,
% 1.03/1.13 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.03/1.13 inference(transitivity,[status(thm)],[3661, 3660, 3658])).
% 1.03/1.13 tff(3663,plain,
% 1.03/1.13 ($false),
% 1.03/1.13 inference(unit_resolution,[status(thm)],[3582, 3662, 3655, 3614])).
% 1.03/1.13 tff(3664,plain,((op(e1, e1) = e3) | (op(e0, e3) = e3) | (op(e0, e3) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e3) = e0) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e0, e3)) = e1) | (op(e3, e3) = e0) | (op(e0, op(e0, e3)) = e0) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.13 tff(3665,plain,
% 1.03/1.13 (op(e1, e1) = e3),
% 1.03/1.13 inference(unit_resolution,[status(thm)],[3664, 656, 121, 466, 80, 651, 652, 661, 649, 650])).
% 1.03/1.13 tff(3666,plain,
% 1.03/1.13 ((op(e1, e1) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.13 tff(3667,plain,
% 1.03/1.13 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.03/1.13 inference(transitivity,[status(thm)],[3666, 3230])).
% 1.03/1.13 tff(3668,plain,
% 1.03/1.13 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3667])).
% 1.03/1.13 tff(3669,plain,
% 1.03/1.13 (~(op(e1, e3) = e3)),
% 1.03/1.13 inference(modus_ponens,[status(thm)],[619, 3668])).
% 1.03/1.13 tff(3670,plain,
% 1.03/1.13 (op(e1, e3) = e1),
% 1.03/1.13 inference(unit_resolution,[status(thm)],[104, 3669, 845, 80])).
% 1.03/1.13 tff(3671,plain,
% 1.03/1.13 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3670])).
% 1.03/1.13 tff(3672,plain,
% 1.03/1.13 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.03/1.13 inference(transitivity,[status(thm)],[3671, 657])).
% 1.03/1.13 tff(3673,plain,
% 1.03/1.13 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3672])).
% 1.03/1.13 tff(3674,plain,
% 1.03/1.13 (~(op(e3, e3) = e1)),
% 1.03/1.13 inference(modus_ponens,[status(thm)],[571, 3673])).
% 1.03/1.13 tff(3675,plain,
% 1.03/1.13 (e3 = op(e1, e1)),
% 1.03/1.13 inference(symmetry,[status(thm)],[3665])).
% 1.03/1.13 tff(3676,plain,
% 1.03/1.13 ((e0 = e3) <=> (e0 = op(e1, e1))),
% 1.03/1.13 inference(monotonicity,[status(thm)],[3675])).
% 1.03/1.13 tff(3677,plain,
% 1.03/1.13 ((e0 = e3) <=> (op(e1, e1) = e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3676, 122])).
% 1.03/1.14 tff(3678,plain,
% 1.03/1.14 ((~(e0 = e3)) <=> (~(op(e1, e1) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3677])).
% 1.03/1.14 tff(3679,plain,
% 1.03/1.14 (~(op(e1, e1) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[181, 3678])).
% 1.03/1.14 tff(3680,plain,
% 1.03/1.14 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.14 tff(3681,plain,
% 1.03/1.14 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3680])).
% 1.03/1.14 tff(3682,plain,
% 1.03/1.14 (~(op(e1, e0) = e3)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[737, 3681])).
% 1.03/1.14 tff(3683,plain,
% 1.03/1.14 ((e2 = e3) <=> (e2 = op(e1, e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3675])).
% 1.03/1.14 tff(3684,plain,
% 1.03/1.14 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3683, 2166])).
% 1.03/1.14 tff(3685,plain,
% 1.03/1.14 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3684])).
% 1.03/1.14 tff(3686,plain,
% 1.03/1.14 (~(op(e1, e1) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[1321, 3685])).
% 1.03/1.14 tff(3687,plain,
% 1.03/1.14 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.14 tff(3688,plain,
% 1.03/1.14 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3687, 1262])).
% 1.03/1.14 tff(3689,plain,
% 1.03/1.14 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3688])).
% 1.03/1.14 tff(3690,plain,
% 1.03/1.14 (~(op(e2, e1) = e3)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[225, 3689])).
% 1.03/1.14 tff(3691,plain,
% 1.03/1.14 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.14 tff(3692,plain,
% 1.03/1.14 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3691])).
% 1.03/1.14 tff(3693,plain,
% 1.03/1.14 (~(op(e0, e1) = e3)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[792, 3692])).
% 1.03/1.14 tff(3694,plain,
% 1.03/1.14 ((op(e1, e1) = e1) <=> (e3 = e1)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.14 tff(3695,plain,
% 1.03/1.14 ((op(e1, e1) = e1) <=> (e1 = e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3694, 128])).
% 1.03/1.14 tff(3696,plain,
% 1.03/1.14 ((e1 = e3) <=> (op(e1, e1) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3695])).
% 1.03/1.14 tff(3697,plain,
% 1.03/1.14 ((~(e1 = e3)) <=> (~(op(e1, e1) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3696])).
% 1.03/1.14 tff(3698,plain,
% 1.03/1.14 (~(op(e1, e1) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[303, 3697])).
% 1.03/1.14 tff(3699,plain,
% 1.03/1.14 (op(e1, e3) = e1),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[104, 1080, 72, 80])).
% 1.03/1.14 tff(3700,plain,
% 1.03/1.14 (e1 = op(e1, e3)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3699])).
% 1.03/1.14 tff(3701,plain,
% 1.03/1.14 (op(e3, e3) = e3),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[480, 124, 661, 1080])).
% 1.03/1.14 tff(3702,plain,
% 1.03/1.14 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3701])).
% 1.03/1.14 tff(3703,plain,
% 1.03/1.14 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3702])).
% 1.03/1.14 tff(3704,plain,
% 1.03/1.14 (~(op(e3, e2) = e3)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[1888, 3703])).
% 1.03/1.14 tff(3705,plain,
% 1.03/1.14 ((op(e3, e3) = e2) <=> (e3 = e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3701])).
% 1.03/1.14 tff(3706,plain,
% 1.03/1.14 ((op(e3, e3) = e2) <=> (e2 = e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3705, 1314])).
% 1.03/1.14 tff(3707,plain,
% 1.03/1.14 ((e2 = e3) <=> (op(e3, e3) = e2)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3706])).
% 1.03/1.14 tff(3708,plain,
% 1.03/1.14 ((~(e2 = e3)) <=> (~(op(e3, e3) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3707])).
% 1.03/1.14 tff(3709,plain,
% 1.03/1.14 (~(op(e3, e3) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[1321, 3708])).
% 1.03/1.14 tff(3710,plain,
% 1.03/1.14 (e1 = op(e1, e3)),
% 1.03/1.14 inference(symmetry,[status(thm)],[132])).
% 1.03/1.14 tff(3711,plain,
% 1.03/1.14 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3710])).
% 1.03/1.14 tff(3712,plain,
% 1.03/1.14 ((op(e2, e3) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.03/1.14 inference(transitivity,[status(thm)],[3711, 1687])).
% 1.03/1.14 tff(3713,plain,
% 1.03/1.14 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3712])).
% 1.03/1.14 tff(3714,plain,
% 1.03/1.14 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3713])).
% 1.03/1.14 tff(3715,plain,
% 1.03/1.14 (~(op(e2, e3) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[118, 3714])).
% 1.03/1.14 tff(3716,plain,
% 1.03/1.14 (op(e0, e3) = e0),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1098, 1063, 80, 656])).
% 1.03/1.14 tff(3717,plain,
% 1.03/1.14 (e0 = op(e0, e3)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3716])).
% 1.03/1.14 tff(3718,plain,
% 1.03/1.14 (e0 = op(e3, e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3717, 467])).
% 1.03/1.14 tff(3719,plain,
% 1.03/1.14 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3718])).
% 1.03/1.14 tff(3720,plain,
% 1.03/1.14 ((op(e3, e1) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 1.03/1.14 inference(transitivity,[status(thm)],[3719, 881])).
% 1.03/1.14 tff(3721,plain,
% 1.03/1.14 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3720])).
% 1.03/1.14 tff(3722,plain,
% 1.03/1.14 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3721])).
% 1.03/1.14 tff(3723,plain,
% 1.03/1.14 (~(op(e3, e1) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[580, 3722])).
% 1.03/1.14 tff(3724,plain,
% 1.03/1.14 (op(e0, e1) = op(e0, op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3710])).
% 1.03/1.14 tff(3725,plain,
% 1.03/1.14 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3724])).
% 1.03/1.14 tff(3726,plain,
% 1.03/1.14 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3725])).
% 1.03/1.14 tff(3727,plain,
% 1.03/1.14 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3724, 3716])).
% 1.03/1.14 tff(3728,plain,
% 1.03/1.14 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3727, 3726])).
% 1.03/1.14 tff(3729,plain,
% 1.03/1.14 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3728])).
% 1.03/1.14 tff(3730,plain,
% 1.03/1.14 (~(op(e0, e1) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[818, 3729])).
% 1.03/1.14 tff(3731,plain,
% 1.03/1.14 (op(e2, e1) = e0),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[292, 3730, 84, 3723])).
% 1.03/1.14 tff(3732,plain,
% 1.03/1.14 (op(e2, e1) = op(e0, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3731, 3717])).
% 1.03/1.14 tff(3733,plain,
% 1.03/1.14 ((op(e2, e1) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3732, 3710])).
% 1.03/1.14 tff(3734,plain,
% 1.03/1.14 ((op(e0, e3) = op(e1, e3)) <=> (op(e2, e1) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3733])).
% 1.03/1.14 tff(3735,plain,
% 1.03/1.14 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e2, e1) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3734])).
% 1.03/1.14 tff(3736,plain,
% 1.03/1.14 (~(op(e2, e1) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[64, 3735])).
% 1.03/1.14 tff(3737,plain,
% 1.03/1.14 (op(e2, e3) = e2),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[206, 1063, 3715, 124])).
% 1.03/1.14 tff(3738,plain,
% 1.03/1.14 (e2 = op(e2, e3)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3737])).
% 1.03/1.14 tff(3739,plain,
% 1.03/1.14 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3718])).
% 1.03/1.14 tff(3740,plain,
% 1.03/1.14 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3739])).
% 1.03/1.14 tff(3741,plain,
% 1.03/1.14 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3740])).
% 1.03/1.14 tff(3742,plain,
% 1.03/1.14 (~(op(e1, e0) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[410, 3741])).
% 1.03/1.14 tff(3743,plain,
% 1.03/1.14 (op(e1, e2) = e0),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1830, 3742, 80, 84])).
% 1.03/1.14 tff(3744,plain,
% 1.03/1.14 (op(e1, e2) = op(e0, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3743, 3717])).
% 1.03/1.14 tff(3745,plain,
% 1.03/1.14 ((op(e1, e2) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3744, 3738])).
% 1.03/1.14 tff(3746,plain,
% 1.03/1.14 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e2) = e2)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3745])).
% 1.03/1.14 tff(3747,plain,
% 1.03/1.14 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e2) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3746])).
% 1.03/1.14 tff(3748,plain,
% 1.03/1.14 (~(op(e1, e2) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[964, 3747])).
% 1.03/1.14 tff(3749,plain,
% 1.03/1.14 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3718])).
% 1.03/1.14 tff(3750,plain,
% 1.03/1.14 ((op(e3, e2) = e0) <=> (op(e3, e0) = op(e3, e2))),
% 1.03/1.14 inference(transitivity,[status(thm)],[3749, 1123])).
% 1.03/1.14 tff(3751,plain,
% 1.03/1.14 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3750])).
% 1.03/1.14 tff(3752,plain,
% 1.03/1.14 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3751])).
% 1.03/1.14 tff(3753,plain,
% 1.03/1.14 (~(op(e3, e2) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[1133, 3752])).
% 1.03/1.14 tff(3754,plain,
% 1.03/1.14 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3717])).
% 1.03/1.14 tff(3755,plain,
% 1.03/1.14 ((e0 = e2) <=> (op(e3, e0) = e2)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3754, 668])).
% 1.03/1.14 tff(3756,plain,
% 1.03/1.14 ((~(e0 = e2)) <=> (~(op(e3, e0) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3755])).
% 1.03/1.14 tff(3757,plain,
% 1.03/1.14 (~(op(e3, e0) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[14, 3756])).
% 1.03/1.14 tff(3758,plain,
% 1.03/1.14 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e3, e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3718])).
% 1.03/1.14 tff(3759,plain,
% 1.03/1.14 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3758])).
% 1.03/1.14 tff(3760,plain,
% 1.03/1.14 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3759])).
% 1.03/1.14 tff(3761,plain,
% 1.03/1.14 (~(op(e2, e0) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[747, 3760])).
% 1.03/1.14 tff(3762,plain,
% 1.03/1.14 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3710])).
% 1.03/1.14 tff(3763,plain,
% 1.03/1.14 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3762])).
% 1.03/1.14 tff(3764,plain,
% 1.03/1.14 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3763])).
% 1.03/1.14 tff(3765,plain,
% 1.03/1.14 (~(op(e1, e0) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[110, 3764])).
% 1.03/1.14 tff(3766,plain,
% 1.03/1.14 (op(e1, e0) = e2),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[728, 3742, 2168, 3765])).
% 1.03/1.14 tff(3767,plain,
% 1.03/1.14 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3716])).
% 1.03/1.14 tff(3768,plain,
% 1.03/1.14 (op(e3, op(e3, e0)) = e0),
% 1.03/1.14 inference(transitivity,[status(thm)],[1343, 3767, 466, 3716])).
% 1.03/1.14 tff(3769,plain,
% 1.03/1.14 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1345, 3768])).
% 1.03/1.14 tff(3770,plain,
% 1.03/1.14 (op(e1, op(e2, e3)) = op(e1, e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3737])).
% 1.03/1.14 tff(3771,plain,
% 1.03/1.14 (op(e1, e0) = op(e2, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3766, 3738])).
% 1.03/1.14 tff(3772,plain,
% 1.03/1.14 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3771])).
% 1.03/1.14 tff(3773,plain,
% 1.03/1.14 (op(e1, op(e1, e0)) = e0),
% 1.03/1.14 inference(transitivity,[status(thm)],[3772, 3770, 3743])).
% 1.03/1.14 tff(3774,plain,
% 1.03/1.14 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1836, 3773])).
% 1.03/1.14 tff(3775,plain,
% 1.03/1.14 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3716])).
% 1.03/1.14 tff(3776,plain,
% 1.03/1.14 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3744])).
% 1.03/1.14 tff(3777,plain,
% 1.03/1.14 (op(e1, op(e1, e2)) = e2),
% 1.03/1.14 inference(transitivity,[status(thm)],[3776, 3775, 3766])).
% 1.03/1.14 tff(3778,plain,
% 1.03/1.14 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[2377, 3777])).
% 1.03/1.14 tff(3779,plain,
% 1.03/1.14 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[920])).
% 1.03/1.14 tff(3780,plain,
% 1.03/1.14 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3779])).
% 1.03/1.14 tff(3781,plain,
% 1.03/1.14 (~(op(e0, e0) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[2471, 3780])).
% 1.03/1.14 tff(3782,plain,
% 1.03/1.14 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[772])).
% 1.03/1.14 tff(3783,plain,
% 1.03/1.14 ((~(e0 = e2)) <=> (~(op(e0, e3) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3782])).
% 1.03/1.14 tff(3784,plain,
% 1.03/1.14 (~(op(e0, e3) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[14, 3783])).
% 1.03/1.14 tff(3785,assumption,(~(op(e1, e2) = e2)), introduced(assumption)).
% 1.03/1.14 tff(3786,assumption,(~(op(e3, e0) = e2)), introduced(assumption)).
% 1.03/1.14 tff(3787,assumption,(op(e2, e3) = e2), introduced(assumption)).
% 1.03/1.14 tff(3788,plain,
% 1.03/1.14 (op(e0, op(e1, e3)) = op(e0, e1)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[132])).
% 1.03/1.14 tff(3789,plain,
% 1.03/1.14 (op(e0, e1) = op(e0, op(e1, e3))),
% 1.03/1.14 inference(symmetry,[status(thm)],[3788])).
% 1.03/1.14 tff(3790,plain,
% 1.03/1.14 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3789])).
% 1.03/1.14 tff(3791,plain,
% 1.03/1.14 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3790])).
% 1.03/1.14 tff(3792,plain,
% 1.03/1.14 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3789, 771])).
% 1.03/1.14 tff(3793,plain,
% 1.03/1.14 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3792, 3791])).
% 1.03/1.14 tff(3794,plain,
% 1.03/1.14 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3793])).
% 1.03/1.14 tff(3795,plain,
% 1.03/1.14 (~(op(e0, e1) = e0)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[818, 3794])).
% 1.03/1.14 tff(3796,plain,
% 1.03/1.14 (op(e2, op(e1, e3)) = op(e2, e1)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[132])).
% 1.03/1.14 tff(3797,plain,
% 1.03/1.14 (e2 = op(e2, e3)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3787])).
% 1.03/1.14 tff(3798,plain,
% 1.03/1.14 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e2, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3797])).
% 1.03/1.14 tff(3799,plain,
% 1.03/1.14 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3798])).
% 1.03/1.14 tff(3800,plain,
% 1.03/1.14 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3799])).
% 1.03/1.14 tff(3801,plain,
% 1.03/1.14 (~(op(e2, e0) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[989, 3800])).
% 1.03/1.14 tff(3802,plain,
% 1.03/1.14 (op(e2, e0) = e1),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[765, 3272, 3801, 983])).
% 1.03/1.14 tff(3803,plain,
% 1.03/1.14 (op(e2, e0) = op(e1, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3802, 3710])).
% 1.03/1.14 tff(3804,plain,
% 1.03/1.14 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3803])).
% 1.03/1.14 tff(3805,plain,
% 1.03/1.14 (op(e2, op(e2, e0)) = e0),
% 1.03/1.14 inference(transitivity,[status(thm)],[3804, 3796, 3508])).
% 1.03/1.14 tff(3806,plain,
% 1.03/1.14 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[2653, 3805])).
% 1.03/1.14 tff(3807,plain,
% 1.03/1.14 ((op(e3, e3) = e1) <=> (op(e3, e3) = op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3710])).
% 1.03/1.14 tff(3808,plain,
% 1.03/1.14 ((op(e3, e3) = e1) <=> (op(e1, e3) = op(e3, e3))),
% 1.03/1.14 inference(transitivity,[status(thm)],[3807, 1659])).
% 1.03/1.14 tff(3809,plain,
% 1.03/1.14 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3808])).
% 1.03/1.14 tff(3810,plain,
% 1.03/1.14 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3809])).
% 1.03/1.14 tff(3811,plain,
% 1.03/1.14 (~(op(e3, e3) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[571, 3810])).
% 1.03/1.14 tff(3812,plain,
% 1.03/1.14 ((e2 = op(e2, op(e0, e3))) <=> (op(e2, op(e0, e3)) = e2)),
% 1.03/1.14 inference(commutativity,[status(thm)],[])).
% 1.03/1.14 tff(3813,plain,
% 1.03/1.14 (op(e2, e0) = op(e2, op(e0, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[772])).
% 1.03/1.14 tff(3814,plain,
% 1.03/1.14 (e1 = op(e2, op(e0, e3))),
% 1.03/1.14 inference(transitivity,[status(thm)],[768, 3813])).
% 1.03/1.14 tff(3815,assumption,(~(op(e3, op(e3, e1)) = e1)), introduced(assumption)).
% 1.03/1.14 tff(3816,plain,
% 1.03/1.14 (op(e3, e2) = e1),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1898, 2386, 85, 1890])).
% 1.03/1.14 tff(3817,plain,
% 1.03/1.14 (op(e3, op(e2, e3)) = op(e3, e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3787])).
% 1.03/1.14 tff(3818,plain,
% 1.03/1.14 (op(e3, e1) = e2),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[2015, 2386, 126, 3786])).
% 1.03/1.14 tff(3819,plain,
% 1.03/1.14 (op(e3, e1) = op(e2, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3818, 3797])).
% 1.03/1.14 tff(3820,plain,
% 1.03/1.14 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3819])).
% 1.03/1.14 tff(3821,plain,
% 1.03/1.14 (op(e3, op(e3, e1)) = e1),
% 1.03/1.14 inference(transitivity,[status(thm)],[3820, 3817, 3816])).
% 1.03/1.14 tff(3822,plain,
% 1.03/1.14 ($false),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[3815, 3821])).
% 1.03/1.14 tff(3823,plain,((op(e3, e2) = e2) | (op(e3, op(e3, e1)) = e1) | (~(op(e2, e3) = e2)) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e3, e2) = e0) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.14 tff(3824,plain,
% 1.03/1.14 (op(e3, e2) = e2),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[3823, 3815, 3787, 126, 3786, 85, 1890])).
% 1.03/1.14 tff(3825,plain,
% 1.03/1.14 ((op(e3, e2) = e1) <=> (e2 = op(e2, op(e0, e3)))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3824, 3814])).
% 1.03/1.14 tff(3826,plain,
% 1.03/1.14 ((op(e3, e2) = e1) <=> (op(e2, op(e0, e3)) = e2)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3825, 3812])).
% 1.03/1.14 tff(3827,plain,
% 1.03/1.14 ((op(e2, op(e0, e3)) = e2) <=> (op(e3, e2) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3826])).
% 1.03/1.14 tff(3828,plain,
% 1.03/1.14 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e3, e2) = e1))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3827])).
% 1.03/1.14 tff(3829,plain,
% 1.03/1.14 (~(op(e3, e2) = e1)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[651, 3828])).
% 1.03/1.14 tff(3830,plain,
% 1.03/1.14 (op(e3, e1) = e1),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[939, 3829, 931, 3811])).
% 1.03/1.14 tff(3831,plain,
% 1.03/1.14 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[132])).
% 1.03/1.14 tff(3832,plain,
% 1.03/1.14 (op(e2, e0) = op(e1, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[767, 3710])).
% 1.03/1.14 tff(3833,plain,
% 1.03/1.14 (op(e3, op(e2, e0)) = op(e3, op(e1, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3832])).
% 1.03/1.14 tff(3834,plain,
% 1.03/1.14 (op(e3, e1) = op(e2, e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3830, 768])).
% 1.03/1.14 tff(3835,plain,
% 1.03/1.14 (op(e3, op(e3, e1)) = op(e3, op(e2, e0))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3834])).
% 1.03/1.14 tff(3836,plain,
% 1.03/1.14 (op(e3, op(e3, e1)) = e1),
% 1.03/1.14 inference(transitivity,[status(thm)],[3835, 3833, 3831, 3830])).
% 1.03/1.14 tff(3837,plain,
% 1.03/1.14 ($false),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[3815, 3836])).
% 1.03/1.14 tff(3838,plain,((op(e3, op(e3, e1)) = e1) | (~(op(e1, e3) = e1)) | (~(op(e2, e0) = e1)) | (op(e3, e0) = e1) | (op(e2, op(e0, e3)) = e2) | (~(op(e0, e3) = e0)) | (~(op(e2, e3) = e2)) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e3, e2) = e0) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.14 tff(3839,plain,
% 1.03/1.14 (op(e3, op(e3, e1)) = e1),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[3838, 3802, 132, 931, 651, 771, 3787, 126, 3786, 85, 1890])).
% 1.03/1.14 tff(3840,plain,
% 1.03/1.14 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[2594, 3839])).
% 1.03/1.14 tff(3841,plain,
% 1.03/1.14 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3813])).
% 1.03/1.14 tff(3842,plain,
% 1.03/1.14 (op(e2, e1) = op(e0, e3)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3508, 772])).
% 1.03/1.14 tff(3843,plain,
% 1.03/1.14 (op(e2, op(e2, e1)) = op(e2, op(e0, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3842])).
% 1.03/1.14 tff(3844,plain,
% 1.03/1.14 (op(e2, op(e2, e1)) = op(e2, e0)),
% 1.03/1.14 inference(transitivity,[status(thm)],[3843, 3841])).
% 1.03/1.14 tff(3845,plain,
% 1.03/1.14 ((op(e2, op(e2, e1)) = e1) <=> (op(e2, e0) = e1)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3844])).
% 1.03/1.14 tff(3846,plain,
% 1.03/1.14 ((op(e2, e0) = e1) <=> (op(e2, op(e2, e1)) = e1)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3845])).
% 1.03/1.14 tff(3847,plain,
% 1.03/1.14 (op(e2, op(e2, e1)) = e1),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[3802, 3846])).
% 1.03/1.14 tff(3848,plain,
% 1.03/1.14 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1355, 3847])).
% 1.03/1.14 tff(3849,assumption,(~(op(e0, e1) = e0)), introduced(assumption)).
% 1.03/1.14 tff(3850,plain,
% 1.03/1.14 ((op(e2, e2) = e2) <=> (op(e2, e2) = op(e2, e3))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3797])).
% 1.03/1.14 tff(3851,plain,
% 1.03/1.14 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.03/1.14 inference(symmetry,[status(thm)],[3850])).
% 1.03/1.14 tff(3852,plain,
% 1.03/1.14 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3851])).
% 1.03/1.14 tff(3853,plain,
% 1.03/1.14 (~(op(e2, e2) = e2)),
% 1.03/1.14 inference(modus_ponens,[status(thm)],[515, 3852])).
% 1.03/1.14 tff(3854,plain,
% 1.03/1.14 (op(e0, e2) = e2),
% 1.03/1.14 inference(unit_resolution,[status(thm)],[1151, 2386, 3853, 3785])).
% 1.03/1.14 tff(3855,plain,
% 1.03/1.14 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 1.03/1.14 inference(monotonicity,[status(thm)],[3854])).
% 1.03/1.15 tff(3856,plain,
% 1.03/1.15 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3855])).
% 1.03/1.15 tff(3857,plain,
% 1.03/1.15 (~(op(e0, e1) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[2102, 3856])).
% 1.03/1.15 tff(3858,plain,
% 1.03/1.15 (op(e0, e1) = e1),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[829, 3857, 2527, 3849])).
% 1.03/1.15 tff(3859,plain,
% 1.03/1.15 (op(e0, op(e2, e0)) = op(e0, op(e1, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3832])).
% 1.03/1.15 tff(3860,plain,
% 1.03/1.15 (op(e0, e1) = op(e2, e0)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3858, 768])).
% 1.03/1.15 tff(3861,plain,
% 1.03/1.15 (op(e0, op(e0, e1)) = op(e0, op(e2, e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3860])).
% 1.03/1.15 tff(3862,plain,
% 1.03/1.15 (op(e0, op(e0, e1)) = e1),
% 1.03/1.15 inference(transitivity,[status(thm)],[3861, 3859, 3788, 3858])).
% 1.03/1.15 tff(3863,plain,
% 1.03/1.15 (op(e3, e2) = op(e2, e0)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3816, 768])).
% 1.03/1.15 tff(3864,plain,
% 1.03/1.15 (op(e3, op(e3, e2)) = op(e3, op(e2, e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3863])).
% 1.03/1.15 tff(3865,plain,
% 1.03/1.15 (op(e3, op(e3, e2)) = e2),
% 1.03/1.15 inference(transitivity,[status(thm)],[3864, 3833, 3831, 3818])).
% 1.03/1.15 tff(3866,plain,
% 1.03/1.15 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1904, 3865])).
% 1.03/1.15 tff(3867,plain,
% 1.03/1.15 (op(op(e2, e3), e3) = op(e2, e3)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3787])).
% 1.03/1.15 tff(3868,plain,
% 1.03/1.15 (op(op(e2, e3), e3) = e2),
% 1.03/1.15 inference(transitivity,[status(thm)],[3867, 3787])).
% 1.03/1.15 tff(3869,plain,
% 1.03/1.15 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1288, 3868])).
% 1.03/1.15 tff(3870,plain,
% 1.03/1.15 (op(e0, op(e2, e3)) = op(e0, e2)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3787])).
% 1.03/1.15 tff(3871,plain,
% 1.03/1.15 (op(e0, e2) = op(e2, e3)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3854, 3797])).
% 1.03/1.15 tff(3872,plain,
% 1.03/1.15 (op(e0, op(e0, e2)) = op(e0, op(e2, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3871])).
% 1.03/1.15 tff(3873,plain,
% 1.03/1.15 (op(e0, op(e0, e2)) = e2),
% 1.03/1.15 inference(transitivity,[status(thm)],[3872, 3870, 3854])).
% 1.03/1.15 tff(3874,plain,
% 1.03/1.15 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1331, 3873])).
% 1.03/1.15 tff(3875,plain,
% 1.03/1.15 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1459, 3874, 3869, 3342, 1358, 1304, 1357, 1936, 1275, 1926, 2421, 3866])).
% 1.03/1.15 tff(3876,plain,
% 1.03/1.15 (~(op(e0, op(e0, e1)) = e1)),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[2449, 3875])).
% 1.03/1.15 tff(3877,plain,
% 1.03/1.15 ($false),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3876, 3862])).
% 1.03/1.15 tff(3878,plain,((op(e3, e2) = e2) | (~(op(e1, e3) = e1)) | (~(op(e2, e0) = e1)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (op(e0, e1) = e3) | (op(e0, e1) = e0) | (~(op(e2, e3) = e2)) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e3, e2) = e0) | (op(e3, e2) = e3) | (op(e1, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.15 tff(3879,plain,
% 1.03/1.15 (op(e3, e2) = e2),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3878, 3802, 132, 1362, 1358, 1304, 1357, 3848, 3840, 1926, 3806, 2527, 3795, 3787, 126, 3786, 85, 1890, 3785])).
% 1.03/1.15 tff(3880,plain,
% 1.03/1.15 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3879])).
% 1.03/1.15 tff(3881,plain,
% 1.03/1.15 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3880])).
% 1.03/1.15 tff(3882,plain,
% 1.03/1.15 (~(op(e0, e2) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[1467, 3881])).
% 1.03/1.15 tff(3883,plain,
% 1.03/1.15 (op(e0, e1) = e2),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3652, 3882, 3784, 3781])).
% 1.03/1.15 tff(3884,plain,
% 1.03/1.15 (op(e2, e1) = op(e2, op(e1, e3))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3796])).
% 1.03/1.15 tff(3885,plain,
% 1.03/1.15 ((op(e2, e1) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3884])).
% 1.03/1.15 tff(3886,plain,
% 1.03/1.15 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e1) = e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3885])).
% 1.03/1.15 tff(3887,plain,
% 1.03/1.15 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e1) = op(e2, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3796, 3797])).
% 1.03/1.15 tff(3888,plain,
% 1.03/1.15 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, op(e1, e3)) = e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3887])).
% 1.03/1.15 tff(3889,plain,
% 1.03/1.15 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3888, 3886])).
% 1.03/1.15 tff(3890,plain,
% 1.03/1.15 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3889])).
% 1.03/1.15 tff(3891,plain,
% 1.03/1.15 (~(op(e2, e1) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[197, 3890])).
% 1.03/1.15 tff(3892,plain,
% 1.03/1.15 (op(e0, e1) = e1),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3546, 3883, 1362, 1358, 1304, 1357, 1926, 920, 3272, 3801, 3891, 121, 3840, 3508, 2168, 983, 3271, 124, 2410])).
% 1.03/1.15 tff(3893,plain,
% 1.03/1.15 (e1 = op(e0, e1)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3892])).
% 1.03/1.15 tff(3894,plain,
% 1.03/1.15 (op(e2, op(e0, e3)) = e2),
% 1.03/1.15 inference(transitivity,[status(thm)],[3841, 3802, 3893, 3883])).
% 1.03/1.15 tff(3895,plain,
% 1.03/1.15 ($false),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[651, 3894])).
% 1.03/1.15 tff(3896,plain,((op(e2, e0) = e3) | (op(e2, op(e0, e3)) = e2) | (~(op(e0, e3) = e0)) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~(op(e1, e0) = e2)) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e1, e0) = e3) | (op(e2, e0) = e0) | (op(e2, e1) = e3) | (op(e2, e3) = e3) | (op(e3, e0) = e3) | (~(op(e1, e3) = e1)) | (op(e0, e1) = e3) | (~(op(e2, e3) = e2)) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e3, e2) = e0) | (op(e3, e2) = e3) | (op(e1, e2) = e2) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.15 tff(3897,plain,
% 1.03/1.15 (op(e2, e0) = e3),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3896, 3716, 651, 3778, 1304, 3774, 3769, 3766, 121, 3731, 2168, 3761, 3271, 124, 2410, 132, 2527, 3737, 126, 3757, 3753, 1890, 3748, 899])).
% 1.03/1.15 tff(3898,plain,
% 1.03/1.15 ((op(e2, e0) = e1) <=> (e3 = op(e1, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3897, 3710])).
% 1.03/1.15 tff(3899,plain,
% 1.03/1.15 ((op(e2, e0) = e1) <=> (op(e1, e3) = e3)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3898, 3230])).
% 1.03/1.15 tff(3900,plain,
% 1.03/1.15 ((op(e1, e3) = e3) <=> (op(e2, e0) = e1)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3899])).
% 1.03/1.15 tff(3901,plain,
% 1.03/1.15 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e0) = e1))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3900])).
% 1.03/1.15 tff(3902,plain,
% 1.03/1.15 (~(op(e2, e0) = e1)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[1080, 3901])).
% 1.03/1.15 tff(3903,plain,
% 1.03/1.15 (op(e2, e2) = e1),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[345, 3902, 3736, 3715])).
% 1.03/1.15 tff(3904,plain,
% 1.03/1.15 (e1 = op(e2, e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[3903, 317])).
% 1.03/1.15 tff(3905,plain,
% 1.03/1.15 (op(e0, e0) = e1),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1480, 3902, 899, 3765])).
% 1.03/1.15 tff(3906,plain,
% 1.03/1.15 (e1 = op(e0, e0)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3905])).
% 1.03/1.15 tff(3907,plain,
% 1.03/1.15 (op(e2, e2) = op(e0, e0)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3903, 3906])).
% 1.03/1.15 tff(3908,plain,
% 1.03/1.15 (op(e2, op(e2, e2)) = op(e2, op(e0, e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3907])).
% 1.03/1.15 tff(3909,plain,
% 1.03/1.15 (op(e2, op(e0, e0)) = op(e2, op(e2, e2))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3908])).
% 1.03/1.15 tff(3910,plain,
% 1.03/1.15 (op(e0, e0) = op(e1, e3)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3905, 3710])).
% 1.03/1.15 tff(3911,plain,
% 1.03/1.15 (op(e2, op(e0, e0)) = op(e2, op(e1, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3910])).
% 1.03/1.15 tff(3912,plain,
% 1.03/1.15 (op(e2, op(e1, e3)) = op(e2, op(e0, e0))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3911])).
% 1.03/1.15 tff(3913,plain,
% 1.03/1.15 (e0 = op(e2, e1)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3731])).
% 1.03/1.15 tff(3914,plain,
% 1.03/1.15 (e0 = op(e2, op(e2, e2))),
% 1.03/1.15 inference(transitivity,[status(thm)],[3913, 3884, 3912, 3909])).
% 1.03/1.15 tff(3915,plain,
% 1.03/1.15 (op(e2, op(e2, e2)) = op(e0, e3)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3908, 3911, 3796, 3731, 3717])).
% 1.03/1.15 tff(3916,plain,
% 1.03/1.15 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e0, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3915])).
% 1.03/1.15 tff(3917,plain,
% 1.03/1.15 (op(e2, op(e0, e3)) = op(e2, op(e2, op(e2, e2)))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3916])).
% 1.03/1.15 tff(3918,plain,
% 1.03/1.15 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3716])).
% 1.03/1.15 tff(3919,plain,
% 1.03/1.15 (op(e2, e0) = op(e2, op(e0, e3))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3918])).
% 1.03/1.15 tff(3920,plain,
% 1.03/1.15 (e3 = op(e2, e0)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3897])).
% 1.03/1.15 tff(3921,plain,
% 1.03/1.15 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.03/1.15 inference(transitivity,[status(thm)],[3920, 3919, 3917])).
% 1.03/1.15 tff(3922,plain,
% 1.03/1.15 ($false),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1648, 3921, 3914, 3904])).
% 1.03/1.15 tff(3923,plain,((op(e2, e3) = e0) | (~(op(e1, e3) = e1)) | (op(e1, e3) = e3) | (op(e2, op(e0, e3)) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3) | (op(e3, e0) = e3) | (op(e0, e1) = e3) | (op(e3, e3) = e2) | (op(e3, e2) = e3) | (op(e1, e1) = e0) | (op(e1, e3) = e0) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.15 tff(3924,plain,
% 1.03/1.15 (op(e2, e3) = e0),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[3923, 124, 1080, 651, 1304, 121, 2168, 3271, 3699, 665, 2527, 3709, 3704, 84, 80, 466, 656])).
% 1.03/1.15 tff(3925,plain,
% 1.03/1.15 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e0)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.15 tff(3926,plain,
% 1.03/1.15 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3925])).
% 1.03/1.15 tff(3927,plain,
% 1.03/1.15 (~(op(e0, e3) = e0)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[964, 3926])).
% 1.03/1.15 tff(3928,plain,
% 1.03/1.15 (op(e0, e3) = e2),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[687, 3927, 121, 661])).
% 1.03/1.15 tff(3929,plain,
% 1.03/1.15 (e2 = op(e0, e3)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3928])).
% 1.03/1.15 tff(3930,plain,
% 1.03/1.15 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3929])).
% 1.03/1.15 tff(3931,plain,
% 1.03/1.15 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3930])).
% 1.03/1.15 tff(3932,plain,
% 1.03/1.15 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3931])).
% 1.03/1.15 tff(3933,plain,
% 1.03/1.15 (~(op(e0, e1) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[818, 3932])).
% 1.03/1.15 tff(3934,plain,
% 1.03/1.15 (e2 = op(e3, e0)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3929, 467])).
% 1.03/1.15 tff(3935,plain,
% 1.03/1.15 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e3, e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3934])).
% 1.03/1.15 tff(3936,plain,
% 1.03/1.15 ((op(e3, e1) = e2) <=> (op(e3, e0) = op(e3, e1))),
% 1.03/1.15 inference(transitivity,[status(thm)],[3935, 881])).
% 1.03/1.15 tff(3937,plain,
% 1.03/1.15 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3936])).
% 1.03/1.15 tff(3938,plain,
% 1.03/1.15 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3937])).
% 1.03/1.15 tff(3939,plain,
% 1.03/1.15 (~(op(e3, e1) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[580, 3938])).
% 1.03/1.15 tff(3940,plain,
% 1.03/1.15 (op(e2, e1) = e2),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[1993, 3939, 3933, 68])).
% 1.03/1.15 tff(3941,plain,
% 1.03/1.15 (op(e2, e1) = op(e0, e3)),
% 1.03/1.15 inference(transitivity,[status(thm)],[3940, 3929])).
% 1.03/1.15 tff(3942,plain,
% 1.03/1.15 ((op(e2, e1) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3941, 3700])).
% 1.03/1.15 tff(3943,plain,
% 1.03/1.15 ((op(e0, e3) = op(e1, e3)) <=> (op(e2, e1) = e1)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3942])).
% 1.03/1.15 tff(3944,plain,
% 1.03/1.15 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e2, e1) = e1))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3943])).
% 1.03/1.15 tff(3945,plain,
% 1.03/1.15 (~(op(e2, e1) = e1)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[64, 3944])).
% 1.03/1.15 tff(3946,plain,
% 1.03/1.15 (e0 = op(e2, e3)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3924])).
% 1.03/1.15 tff(3947,plain,
% 1.03/1.15 (op(e0, op(e0, e3)) = op(op(e2, e3), e2)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3946, 3928])).
% 1.03/1.15 tff(3948,plain,
% 1.03/1.15 (op(op(e2, e3), e2) = op(e0, op(e0, e3))),
% 1.03/1.15 inference(symmetry,[status(thm)],[3947])).
% 1.03/1.15 tff(3949,plain,
% 1.03/1.15 (op(op(e2, e3), e2) = op(e0, e2)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.15 tff(3950,plain,
% 1.03/1.15 (op(e0, e2) = op(op(e2, e3), e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3949])).
% 1.03/1.15 tff(3951,plain,
% 1.03/1.15 (op(e0, e2) = op(e0, op(e0, e3))),
% 1.03/1.15 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.03/1.15 tff(3952,plain,
% 1.03/1.15 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3951])).
% 1.03/1.15 tff(3953,plain,
% 1.03/1.15 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3952])).
% 1.03/1.15 tff(3954,plain,
% 1.03/1.15 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(e0, e2) = e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3953])).
% 1.03/1.15 tff(3955,plain,
% 1.03/1.15 (~(op(e0, e2) = e0)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[649, 3954])).
% 1.03/1.15 tff(3956,plain,
% 1.03/1.15 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3700])).
% 1.03/1.15 tff(3957,plain,
% 1.03/1.15 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3956])).
% 1.03/1.15 tff(3958,plain,
% 1.03/1.15 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3957])).
% 1.03/1.15 tff(3959,plain,
% 1.03/1.15 (~(op(e1, e0) = e1)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[110, 3958])).
% 1.03/1.15 tff(3960,plain,
% 1.03/1.15 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e3, e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3934])).
% 1.03/1.15 tff(3961,plain,
% 1.03/1.15 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 1.03/1.15 inference(symmetry,[status(thm)],[3960])).
% 1.03/1.15 tff(3962,plain,
% 1.03/1.15 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3961])).
% 1.03/1.15 tff(3963,plain,
% 1.03/1.15 (~(op(e1, e0) = e2)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[410, 3962])).
% 1.03/1.15 tff(3964,plain,
% 1.03/1.15 (op(e1, e0) = e0),
% 1.03/1.15 inference(unit_resolution,[status(thm)],[728, 3963, 2168, 3959])).
% 1.03/1.15 tff(3965,plain,
% 1.03/1.15 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3964])).
% 1.03/1.15 tff(3966,plain,
% 1.03/1.15 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3965])).
% 1.03/1.15 tff(3967,plain,
% 1.03/1.15 (~(op(e0, e0) = e0)),
% 1.03/1.15 inference(modus_ponens,[status(thm)],[2471, 3966])).
% 1.03/1.15 tff(3968,plain,
% 1.03/1.15 (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 1.03/1.15 inference(rewrite,[status(thm)],[])).
% 1.03/1.15 tff(3969,plain,
% 1.03/1.15 ((((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 1.03/1.15 inference(rewrite,[status(thm)],[])).
% 1.03/1.15 tff(3970,plain,
% 1.03/1.15 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0))),
% 1.03/1.15 inference(rewrite,[status(thm)],[])).
% 1.03/1.15 tff(3971,plain,
% 1.03/1.15 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0))),
% 1.03/1.15 inference(monotonicity,[status(thm)],[3970])).
% 1.03/1.15 tff(3972,plain,
% 1.03/1.15 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 1.03/1.15 inference(transitivity,[status(thm)],[3971, 3969])).
% 1.03/1.15 tff(3973,plain,
% 1.03/1.15 (((((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))),
% 1.03/1.16 inference(and_elim,[status(thm)],[381])).
% 1.03/1.16 tff(3974,plain,
% 1.03/1.16 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)),
% 1.03/1.16 inference(and_elim,[status(thm)],[3973])).
% 1.03/1.16 tff(3975,plain,
% 1.03/1.16 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[3974, 3972])).
% 1.03/1.16 tff(3976,plain,
% 1.03/1.16 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[3975, 3968])).
% 1.03/1.16 tff(3977,plain,
% 1.03/1.16 (op(e0, e1) = e0),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[3976, 3967, 3927, 3955])).
% 1.03/1.16 tff(3978,plain,
% 1.03/1.16 (op(e0, e1) = op(e2, e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[3977, 3946])).
% 1.03/1.16 tff(3979,plain,
% 1.03/1.16 ((op(e0, e1) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3978, 3700])).
% 1.03/1.16 tff(3980,plain,
% 1.03/1.16 ((op(e0, e1) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.03/1.16 inference(transitivity,[status(thm)],[3979, 1687])).
% 1.03/1.16 tff(3981,plain,
% 1.03/1.16 ((op(e1, e3) = op(e2, e3)) <=> (op(e0, e1) = e1)),
% 1.03/1.16 inference(symmetry,[status(thm)],[3980])).
% 1.03/1.16 tff(3982,plain,
% 1.03/1.16 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e0, e1) = e1))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3981])).
% 1.03/1.16 tff(3983,plain,
% 1.03/1.16 (~(op(e0, e1) = e1)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[118, 3982])).
% 1.03/1.16 tff(3984,plain,
% 1.03/1.16 (op(e3, e1) = e1),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1252, 3983, 3945, 1266])).
% 1.03/1.16 tff(3985,plain,
% 1.03/1.16 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3699])).
% 1.03/1.16 tff(3986,plain,
% 1.03/1.16 (op(e3, e1) = op(e1, e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[3984, 3700])).
% 1.03/1.16 tff(3987,plain,
% 1.03/1.16 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3986])).
% 1.03/1.16 tff(3988,plain,
% 1.03/1.16 (op(e3, op(e3, e1)) = e1),
% 1.03/1.16 inference(transitivity,[status(thm)],[3987, 3985, 3984])).
% 1.03/1.16 tff(3989,plain,
% 1.03/1.16 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.16 tff(3990,plain,
% 1.03/1.16 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3946])).
% 1.03/1.16 tff(3991,plain,
% 1.03/1.16 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[3990])).
% 1.03/1.16 tff(3992,plain,
% 1.03/1.16 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3991])).
% 1.03/1.16 tff(3993,plain,
% 1.03/1.16 (~(op(e2, e2) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[515, 3992])).
% 1.03/1.16 tff(3994,plain,
% 1.03/1.16 ((op(e1, e0) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3964])).
% 1.03/1.16 tff(3995,plain,
% 1.03/1.16 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 1.03/1.16 inference(transitivity,[status(thm)],[3994, 67])).
% 1.03/1.16 tff(3996,plain,
% 1.03/1.16 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3995])).
% 1.03/1.16 tff(3997,plain,
% 1.03/1.16 (~(op(e1, e2) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[1312, 3996])).
% 1.03/1.16 tff(3998,plain,
% 1.03/1.16 (op(e3, e2) = e0),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[973, 3997, 3993, 3955])).
% 1.03/1.16 tff(3999,plain,
% 1.03/1.16 (op(e3, e2) = op(e2, e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[3998, 3946])).
% 1.03/1.16 tff(4000,plain,
% 1.03/1.16 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3999])).
% 1.03/1.16 tff(4001,plain,
% 1.03/1.16 (op(e3, op(e3, e2)) = e2),
% 1.03/1.16 inference(transitivity,[status(thm)],[4000, 3989, 466, 3928])).
% 1.03/1.16 tff(4002,plain,
% 1.03/1.16 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1904, 4001])).
% 1.03/1.16 tff(4003,plain,
% 1.03/1.16 (op(op(e0, e3), e3) = op(e2, e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3928])).
% 1.03/1.16 tff(4004,plain,
% 1.03/1.16 (op(e2, op(e2, e3)) = op(e2, e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.16 tff(4005,plain,
% 1.03/1.16 (op(e2, e0) = op(e2, op(e2, e3))),
% 1.03/1.16 inference(symmetry,[status(thm)],[4004])).
% 1.03/1.16 tff(4006,plain,
% 1.03/1.16 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4005])).
% 1.03/1.16 tff(4007,plain,
% 1.03/1.16 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4006])).
% 1.03/1.16 tff(4008,plain,
% 1.03/1.16 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4004, 3934])).
% 1.03/1.16 tff(4009,plain,
% 1.03/1.16 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, op(e2, e3)) = e2)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4008])).
% 1.03/1.16 tff(4010,plain,
% 1.03/1.16 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4009, 4007])).
% 1.03/1.16 tff(4011,plain,
% 1.03/1.16 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4010])).
% 1.03/1.16 tff(4012,plain,
% 1.03/1.16 (~(op(e2, e0) = e2)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[747, 4011])).
% 1.03/1.16 tff(4013,plain,
% 1.03/1.16 (op(e2, e0) = e3),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[3293, 4012, 3924, 3928, 3271, 124])).
% 1.03/1.16 tff(4014,plain,
% 1.03/1.16 (op(e2, op(e2, e0)) = op(op(e0, e3), e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3929, 4013])).
% 1.03/1.16 tff(4015,plain,
% 1.03/1.16 (op(e2, op(e2, e0)) = e0),
% 1.03/1.16 inference(transitivity,[status(thm)],[4014, 4003, 3924])).
% 1.03/1.16 tff(4016,plain,
% 1.03/1.16 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2653, 4015])).
% 1.03/1.16 tff(4017,plain,
% 1.03/1.16 (op(op(e3, e0), e0) = op(op(e0, e3), e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[466])).
% 1.03/1.16 tff(4018,plain,
% 1.03/1.16 ((op(op(e3, e0), e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4017])).
% 1.03/1.16 tff(4019,plain,
% 1.03/1.16 ((op(op(e0, e3), e0) = e3) <=> (op(op(e3, e0), e0) = e3)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4018])).
% 1.03/1.16 tff(4020,plain,
% 1.03/1.16 (op(op(e0, e3), e0) = op(e2, op(e2, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3928, 3946])).
% 1.03/1.16 tff(4021,plain,
% 1.03/1.16 (op(e2, op(e2, e3)) = op(op(e0, e3), e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4020])).
% 1.03/1.16 tff(4022,plain,
% 1.03/1.16 ((op(e2, op(e2, e3)) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4021])).
% 1.03/1.16 tff(4023,plain,
% 1.03/1.16 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4005])).
% 1.03/1.16 tff(4024,plain,
% 1.03/1.16 ((op(e2, e0) = e3) <=> (op(op(e3, e0), e0) = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4023, 4022, 4019])).
% 1.03/1.16 tff(4025,plain,
% 1.03/1.16 (op(op(e3, e0), e0) = e3),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[4013, 4024])).
% 1.03/1.16 tff(4026,plain,
% 1.03/1.16 (((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))) | (~(op(op(e3, e0), e0) = e3))),
% 1.03/1.16 inference(tautology,[status(thm)],[])).
% 1.03/1.16 tff(4027,plain,
% 1.03/1.16 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[4026, 4025])).
% 1.03/1.16 tff(4028,plain,
% 1.03/1.16 ((op(e2, e0) = e1) <=> (e3 = op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4013, 3700])).
% 1.03/1.16 tff(4029,plain,
% 1.03/1.16 ((op(e2, e0) = e1) <=> (op(e1, e3) = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4028, 3230])).
% 1.03/1.16 tff(4030,plain,
% 1.03/1.16 ((op(e1, e3) = e3) <=> (op(e2, e0) = e1)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4029])).
% 1.03/1.16 tff(4031,plain,
% 1.03/1.16 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e0) = e1))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4030])).
% 1.03/1.16 tff(4032,plain,
% 1.03/1.16 (~(op(e2, e0) = e1)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[1080, 4031])).
% 1.03/1.16 tff(4033,plain,
% 1.03/1.16 (op(e0, e0) = e1),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1480, 4032, 899, 3959])).
% 1.03/1.16 tff(4034,plain,
% 1.03/1.16 (op(e0, op(e0, e1)) = op(e0, e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3977])).
% 1.03/1.16 tff(4035,plain,
% 1.03/1.16 (op(e0, op(e0, e1)) = e1),
% 1.03/1.16 inference(transitivity,[status(thm)],[4034, 4033])).
% 1.03/1.16 tff(4036,plain,
% 1.03/1.16 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2449, 4035])).
% 1.03/1.16 tff(4037,plain,
% 1.03/1.16 (op(e2, op(e1, e3)) = op(e2, e1)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3699])).
% 1.03/1.16 tff(4038,plain,
% 1.03/1.16 (op(op(e2, e1), e1) = op(e2, op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3940, 3700])).
% 1.03/1.16 tff(4039,plain,
% 1.03/1.16 (op(op(e2, e1), e1) = e2),
% 1.03/1.16 inference(transitivity,[status(thm)],[4038, 4037, 3940])).
% 1.03/1.16 tff(4040,plain,
% 1.03/1.16 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2371, 4039])).
% 1.03/1.16 tff(4041,plain,
% 1.03/1.16 (op(e1, op(e2, e3)) = op(e1, e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.16 tff(4042,plain,
% 1.03/1.16 (op(e1, e0) = op(e2, e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[3964, 3946])).
% 1.03/1.16 tff(4043,plain,
% 1.03/1.16 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4042])).
% 1.03/1.16 tff(4044,plain,
% 1.03/1.16 (op(e1, op(e1, e0)) = e0),
% 1.03/1.16 inference(transitivity,[status(thm)],[4043, 4041, 3964])).
% 1.03/1.16 tff(4045,plain,
% 1.03/1.16 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1836, 4044])).
% 1.03/1.16 tff(4046,plain,
% 1.03/1.16 (op(e1, e2) = e2),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2285, 3963, 72, 68])).
% 1.03/1.16 tff(4047,plain,
% 1.03/1.16 (op(e1, op(e0, e3)) = op(e1, e2)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3928])).
% 1.03/1.16 tff(4048,plain,
% 1.03/1.16 (op(e1, e2) = op(e0, e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4046, 3929])).
% 1.03/1.16 tff(4049,plain,
% 1.03/1.16 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4048])).
% 1.03/1.16 tff(4050,plain,
% 1.03/1.16 (op(e1, op(e1, e2)) = e2),
% 1.03/1.16 inference(transitivity,[status(thm)],[4049, 4047, 4046])).
% 1.03/1.16 tff(4051,plain,
% 1.03/1.16 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2377, 4050])).
% 1.03/1.16 tff(4052,plain,
% 1.03/1.16 (op(op(e0, e3), e3) = e0),
% 1.03/1.16 inference(transitivity,[status(thm)],[4003, 3924])).
% 1.03/1.16 tff(4053,plain,
% 1.03/1.16 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1361, 4052])).
% 1.03/1.16 tff(4054,plain,
% 1.03/1.16 (op(op(e2, e3), e3) = op(e0, e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3924])).
% 1.03/1.16 tff(4055,plain,
% 1.03/1.16 ((op(op(e2, e3), e3) = e2) <=> (op(e0, e3) = e2)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4054])).
% 1.03/1.16 tff(4056,plain,
% 1.03/1.16 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4055])).
% 1.03/1.16 tff(4057,plain,
% 1.03/1.16 (op(op(e2, e3), e3) = e2),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[3928, 4056])).
% 1.03/1.16 tff(4058,plain,
% 1.03/1.16 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1288, 4057])).
% 1.03/1.16 tff(4059,plain,
% 1.03/1.16 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4013])).
% 1.03/1.16 tff(4060,plain,
% 1.03/1.16 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4059])).
% 1.03/1.16 tff(4061,plain,
% 1.03/1.16 (~(op(e0, e0) = e3)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[359, 4060])).
% 1.03/1.16 tff(4062,plain,
% 1.03/1.16 (op(e0, e2) = e3),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1495, 4061, 661, 2527])).
% 1.03/1.16 tff(4063,plain,
% 1.03/1.16 (op(e0, op(e0, e2)) = op(op(e2, e3), e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3946, 4062])).
% 1.03/1.16 tff(4064,plain,
% 1.03/1.16 (op(e0, op(e0, e2)) = e2),
% 1.03/1.16 inference(transitivity,[status(thm)],[4063, 4054, 3928])).
% 1.03/1.16 tff(4065,plain,
% 1.03/1.16 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1331, 4064])).
% 1.03/1.16 tff(4066,plain,
% 1.03/1.16 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1459, 4065, 4058, 4053, 4051, 1304, 4045, 4040, 4036, 4027, 4016, 4002])).
% 1.03/1.16 tff(4067,plain,
% 1.03/1.16 (~(op(e3, op(e3, e1)) = e1)),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2594, 4066])).
% 1.03/1.16 tff(4068,plain,
% 1.03/1.16 ($false),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[4067, 3988])).
% 1.03/1.16 tff(4069,plain,((op(e2, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e1) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e3) = e3) | (op(e0, e1) = e3) | (op(e1, e3) = e3) | (op(e2, e1) = e3) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e0) = e3) | (op(e0, op(e0, e3)) = e0) | (op(e0, e3) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e1, e1) = e0) | (op(e1, e3) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.16 tff(4070,plain,
% 1.03/1.16 (op(e2, e3) = e3),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[4069, 3698, 1261, 466, 661, 3693, 3669, 3690, 3686, 845, 3682, 649, 121, 651, 3679, 80, 656])).
% 1.03/1.16 tff(4071,plain,
% 1.03/1.16 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4070])).
% 1.03/1.16 tff(4072,plain,
% 1.03/1.16 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4071, 666])).
% 1.03/1.16 tff(4073,plain,
% 1.03/1.16 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4072])).
% 1.03/1.16 tff(4074,plain,
% 1.03/1.16 (~(op(e3, e3) = e3)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[368, 4073])).
% 1.03/1.16 tff(4075,plain,
% 1.03/1.16 (op(e3, e3) = e2),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1071, 4074, 656, 3674])).
% 1.03/1.16 tff(4076,plain,
% 1.03/1.16 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3665])).
% 1.03/1.16 tff(4077,plain,
% 1.03/1.16 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4076, 396])).
% 1.03/1.16 tff(4078,plain,
% 1.03/1.16 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4077])).
% 1.03/1.16 tff(4079,plain,
% 1.03/1.16 (~(op(e3, e1) = e3)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[945, 4078])).
% 1.03/1.16 tff(4080,plain,
% 1.03/1.16 (op(e3, e2) = e3),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[422, 4074, 665, 4079])).
% 1.03/1.16 tff(4081,plain,
% 1.03/1.16 (op(e3, op(e3, e2)) = op(e3, e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4080])).
% 1.03/1.16 tff(4082,plain,
% 1.03/1.16 (op(e3, op(e3, e2)) = e2),
% 1.03/1.16 inference(transitivity,[status(thm)],[4081, 4075])).
% 1.03/1.16 tff(4083,plain,
% 1.03/1.16 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1904, 4082])).
% 1.03/1.16 tff(4084,plain,
% 1.03/1.16 ((op(e2, e3) = e0) <=> (e3 = e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4070])).
% 1.03/1.16 tff(4085,plain,
% 1.03/1.16 ((op(e2, e3) = e0) <=> (e0 = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4084, 159])).
% 1.03/1.16 tff(4086,plain,
% 1.03/1.16 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4085])).
% 1.03/1.16 tff(4087,plain,
% 1.03/1.16 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4086])).
% 1.03/1.16 tff(4088,plain,
% 1.03/1.16 (~(op(e2, e3) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[181, 4087])).
% 1.03/1.16 tff(4089,plain,
% 1.03/1.16 (op(e0, e3) = e0),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1098, 4088, 80, 656])).
% 1.03/1.16 tff(4090,plain,
% 1.03/1.16 (e0 = op(e0, e3)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4089])).
% 1.03/1.16 tff(4091,plain,
% 1.03/1.16 (e0 = op(e3, e0)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4090, 467])).
% 1.03/1.16 tff(4092,plain,
% 1.03/1.16 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4091])).
% 1.03/1.16 tff(4093,plain,
% 1.03/1.16 ((op(e3, e1) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 1.03/1.16 inference(transitivity,[status(thm)],[4092, 881])).
% 1.03/1.16 tff(4094,plain,
% 1.03/1.16 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4093])).
% 1.03/1.16 tff(4095,plain,
% 1.03/1.16 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4094])).
% 1.03/1.16 tff(4096,plain,
% 1.03/1.16 (~(op(e3, e1) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[580, 4095])).
% 1.03/1.16 tff(4097,plain,
% 1.03/1.16 (op(e0, op(e1, e3)) = op(e0, e1)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3670])).
% 1.03/1.16 tff(4098,plain,
% 1.03/1.16 (op(e0, e1) = op(e0, op(e1, e3))),
% 1.03/1.16 inference(symmetry,[status(thm)],[4097])).
% 1.03/1.16 tff(4099,plain,
% 1.03/1.16 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4098])).
% 1.03/1.16 tff(4100,plain,
% 1.03/1.16 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4099])).
% 1.03/1.16 tff(4101,plain,
% 1.03/1.16 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4097, 4090])).
% 1.03/1.16 tff(4102,plain,
% 1.03/1.16 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4101])).
% 1.03/1.16 tff(4103,plain,
% 1.03/1.16 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4102, 4100])).
% 1.03/1.16 tff(4104,plain,
% 1.03/1.16 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4103])).
% 1.03/1.16 tff(4105,plain,
% 1.03/1.16 (~(op(e0, e1) = e0)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[818, 4104])).
% 1.03/1.16 tff(4106,plain,
% 1.03/1.16 (op(e2, e1) = e0),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[292, 4105, 3679, 4096])).
% 1.03/1.16 tff(4107,plain,
% 1.03/1.16 (op(e2, op(e1, e3)) = op(e2, e1)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[3670])).
% 1.03/1.16 tff(4108,plain,
% 1.03/1.16 (e1 = op(e1, e3)),
% 1.03/1.16 inference(symmetry,[status(thm)],[3670])).
% 1.03/1.16 tff(4109,plain,
% 1.03/1.16 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4108])).
% 1.03/1.16 tff(4110,plain,
% 1.03/1.16 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4109])).
% 1.03/1.16 tff(4111,plain,
% 1.03/1.16 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4110])).
% 1.03/1.16 tff(4112,plain,
% 1.03/1.16 (~(op(e1, e0) = e1)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[110, 4111])).
% 1.03/1.16 tff(4113,plain,
% 1.03/1.16 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4070])).
% 1.03/1.16 tff(4114,plain,
% 1.03/1.16 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4113])).
% 1.03/1.16 tff(4115,plain,
% 1.03/1.16 (~(op(e2, e0) = e3)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[989, 4114])).
% 1.03/1.16 tff(4116,plain,
% 1.03/1.16 (op(e0, e0) = e3),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[2713, 4115, 665, 3682])).
% 1.03/1.16 tff(4117,plain,
% 1.03/1.16 ((op(e0, e0) = e1) <=> (e3 = op(e1, e3))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4116, 4108])).
% 1.03/1.16 tff(4118,plain,
% 1.03/1.16 ((op(e0, e0) = e1) <=> (op(e1, e3) = e3)),
% 1.03/1.16 inference(transitivity,[status(thm)],[4117, 3230])).
% 1.03/1.16 tff(4119,plain,
% 1.03/1.16 ((op(e1, e3) = e3) <=> (op(e0, e0) = e1)),
% 1.03/1.16 inference(symmetry,[status(thm)],[4118])).
% 1.03/1.16 tff(4120,plain,
% 1.03/1.16 ((~(op(e1, e3) = e3)) <=> (~(op(e0, e0) = e1))),
% 1.03/1.16 inference(monotonicity,[status(thm)],[4119])).
% 1.03/1.16 tff(4121,plain,
% 1.03/1.16 (~(op(e0, e0) = e1)),
% 1.03/1.16 inference(modus_ponens,[status(thm)],[3669, 4120])).
% 1.03/1.16 tff(4122,plain,
% 1.03/1.16 (op(e2, e0) = e1),
% 1.03/1.16 inference(unit_resolution,[status(thm)],[1480, 4121, 899, 4112])).
% 1.03/1.17 tff(4123,plain,
% 1.03/1.17 (op(e2, e0) = op(e1, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4122, 4108])).
% 1.03/1.17 tff(4124,plain,
% 1.03/1.17 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4123])).
% 1.03/1.17 tff(4125,plain,
% 1.03/1.17 (op(e2, op(e2, e0)) = e0),
% 1.03/1.17 inference(transitivity,[status(thm)],[4124, 4107, 4106])).
% 1.03/1.17 tff(4126,plain,
% 1.03/1.17 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2653, 4125])).
% 1.03/1.17 tff(4127,plain,
% 1.03/1.17 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4089])).
% 1.03/1.17 tff(4128,plain,
% 1.03/1.17 (op(e3, op(e3, e0)) = e0),
% 1.03/1.17 inference(transitivity,[status(thm)],[1343, 4127, 466, 4089])).
% 1.03/1.17 tff(4129,plain,
% 1.03/1.17 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1345, 4128])).
% 1.03/1.17 tff(4130,plain,
% 1.03/1.17 (e2 = op(e3, e3)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4075])).
% 1.03/1.17 tff(4131,plain,
% 1.03/1.17 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e3, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4130])).
% 1.03/1.17 tff(4132,plain,
% 1.03/1.17 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4131])).
% 1.03/1.17 tff(4133,plain,
% 1.03/1.17 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4132])).
% 1.03/1.17 tff(4134,plain,
% 1.03/1.17 (~(op(e3, e1) = e2)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[437, 4133])).
% 1.03/1.17 tff(4135,plain,
% 1.03/1.17 (op(e3, e1) = e1),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[446, 4096, 4079, 4134])).
% 1.03/1.17 tff(4136,plain,
% 1.03/1.17 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[3670])).
% 1.03/1.17 tff(4137,plain,
% 1.03/1.17 (op(e3, e1) = op(e1, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4135, 4108])).
% 1.03/1.17 tff(4138,plain,
% 1.03/1.17 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4137])).
% 1.03/1.17 tff(4139,plain,
% 1.03/1.17 (op(e3, op(e3, e1)) = e1),
% 1.03/1.17 inference(transitivity,[status(thm)],[4138, 4136, 4135])).
% 1.03/1.17 tff(4140,plain,
% 1.03/1.17 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2594, 4139])).
% 1.03/1.17 tff(4141,plain,
% 1.03/1.17 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4089])).
% 1.03/1.17 tff(4142,plain,
% 1.03/1.17 (op(e2, e1) = op(e0, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4106, 4090])).
% 1.03/1.17 tff(4143,plain,
% 1.03/1.17 (op(e2, op(e2, e1)) = op(e2, op(e0, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4142])).
% 1.03/1.17 tff(4144,plain,
% 1.03/1.17 (op(e2, op(e2, e1)) = e1),
% 1.03/1.17 inference(transitivity,[status(thm)],[4143, 4141, 4122])).
% 1.03/1.17 tff(4145,plain,
% 1.03/1.17 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1355, 4144])).
% 1.03/1.17 tff(4146,plain,
% 1.03/1.17 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e3, e0))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4091])).
% 1.03/1.17 tff(4147,plain,
% 1.03/1.17 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4146])).
% 1.03/1.17 tff(4148,plain,
% 1.03/1.17 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4147])).
% 1.03/1.17 tff(4149,plain,
% 1.03/1.17 (~(op(e1, e0) = e0)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[410, 4148])).
% 1.03/1.17 tff(4150,plain,
% 1.03/1.17 (op(e1, e2) = e0),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1830, 4149, 80, 3679])).
% 1.03/1.17 tff(4151,plain,
% 1.03/1.17 (op(e1, op(e3, e3)) = op(e1, e2)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4075])).
% 1.03/1.17 tff(4152,plain,
% 1.03/1.17 (op(e2, e0) = op(e2, op(e0, e3))),
% 1.03/1.17 inference(symmetry,[status(thm)],[4141])).
% 1.03/1.17 tff(4153,plain,
% 1.03/1.17 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4152])).
% 1.03/1.17 tff(4154,plain,
% 1.03/1.17 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4153])).
% 1.03/1.17 tff(4155,plain,
% 1.03/1.17 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e0) = e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4154])).
% 1.03/1.17 tff(4156,plain,
% 1.03/1.17 (~(op(e2, e0) = e2)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[651, 4155])).
% 1.03/1.17 tff(4157,plain,
% 1.03/1.17 ((op(e0, e0) = e2) <=> (e3 = op(e3, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4116, 4130])).
% 1.03/1.17 tff(4158,plain,
% 1.03/1.17 ((op(e0, e0) = e2) <=> (op(e3, e3) = e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4157, 666])).
% 1.03/1.17 tff(4159,plain,
% 1.03/1.17 ((op(e3, e3) = e3) <=> (op(e0, e0) = e2)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4158])).
% 1.03/1.17 tff(4160,plain,
% 1.03/1.17 ((~(op(e3, e3) = e3)) <=> (~(op(e0, e0) = e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4159])).
% 1.03/1.17 tff(4161,plain,
% 1.03/1.17 (~(op(e0, e0) = e2)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[4074, 4160])).
% 1.03/1.17 tff(4162,plain,
% 1.03/1.17 ((~(op(e0, e3) = e2)) <=> (~(op(e3, e0) = e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[668])).
% 1.03/1.17 tff(4163,plain,
% 1.03/1.17 (~(op(e0, e3) = e2)),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[860, 4080, 650])).
% 1.03/1.17 tff(4164,plain,
% 1.03/1.17 (~(op(e3, e0) = e2)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 1.03/1.17 tff(4165,plain,
% 1.03/1.17 (op(e1, e0) = e2),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[589, 4164, 4161, 4156])).
% 1.03/1.17 tff(4166,plain,
% 1.03/1.17 (op(e1, e0) = op(e3, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4165, 4130])).
% 1.03/1.17 tff(4167,plain,
% 1.03/1.17 (op(e1, op(e1, e0)) = op(e1, op(e3, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4166])).
% 1.03/1.17 tff(4168,plain,
% 1.03/1.17 (op(e1, op(e1, e0)) = e0),
% 1.03/1.17 inference(transitivity,[status(thm)],[4167, 4151, 4150])).
% 1.03/1.17 tff(4169,plain,
% 1.03/1.17 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1836, 4168])).
% 1.03/1.17 tff(4170,plain,
% 1.03/1.17 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4089])).
% 1.03/1.17 tff(4171,plain,
% 1.03/1.17 (op(e1, e2) = op(e0, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4150, 4090])).
% 1.03/1.17 tff(4172,plain,
% 1.03/1.17 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4171])).
% 1.03/1.17 tff(4173,plain,
% 1.03/1.17 (op(e1, op(e1, e2)) = e2),
% 1.03/1.17 inference(transitivity,[status(thm)],[4172, 4170, 4165])).
% 1.03/1.17 tff(4174,plain,
% 1.03/1.17 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2377, 4173])).
% 1.03/1.17 tff(4175,plain,
% 1.03/1.17 (op(op(e0, e3), e3) = op(e0, e3)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4089])).
% 1.03/1.17 tff(4176,plain,
% 1.03/1.17 (op(op(e0, e3), e3) = e0),
% 1.03/1.17 inference(transitivity,[status(thm)],[4175, 4089])).
% 1.03/1.17 tff(4177,plain,
% 1.03/1.17 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1361, 4176])).
% 1.03/1.17 tff(4178,plain,
% 1.03/1.17 (op(e2, op(e2, e3)) = op(e2, e3)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4070])).
% 1.03/1.17 tff(4179,plain,
% 1.03/1.17 (op(e2, op(e2, e3)) = e3),
% 1.03/1.17 inference(transitivity,[status(thm)],[4178, 4070])).
% 1.03/1.17 tff(4180,plain,
% 1.03/1.17 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2344, 4179])).
% 1.03/1.17 tff(4181,plain,
% 1.03/1.17 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4135])).
% 1.03/1.17 tff(4182,plain,
% 1.03/1.17 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4181])).
% 1.03/1.17 tff(4183,plain,
% 1.03/1.17 (~(op(e0, e1) = e1)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[3046, 4182])).
% 1.03/1.17 tff(4184,plain,
% 1.03/1.17 (op(e0, e2) = e1),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[384, 4183, 121, 4121])).
% 1.03/1.17 tff(4185,plain,
% 1.03/1.17 (op(e0, op(e3, e3)) = op(e0, e2)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4075])).
% 1.03/1.17 tff(4186,plain,
% 1.03/1.17 (op(e0, e1) = e2),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[829, 4183, 3693, 4105])).
% 1.03/1.17 tff(4187,plain,
% 1.03/1.17 (op(e0, e1) = op(e3, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4186, 4130])).
% 1.03/1.17 tff(4188,plain,
% 1.03/1.17 (op(e0, op(e0, e1)) = op(e0, op(e3, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4187])).
% 1.03/1.17 tff(4189,plain,
% 1.03/1.17 (op(e0, op(e0, e1)) = e1),
% 1.03/1.17 inference(transitivity,[status(thm)],[4188, 4185, 4184])).
% 1.03/1.17 tff(4190,plain,
% 1.03/1.17 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2449, 4189])).
% 1.03/1.17 tff(4191,plain,
% 1.03/1.17 (op(e0, e2) = op(e1, e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4184, 4108])).
% 1.03/1.17 tff(4192,plain,
% 1.03/1.17 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4191])).
% 1.03/1.17 tff(4193,plain,
% 1.03/1.17 (op(e0, op(e0, e2)) = e2),
% 1.03/1.17 inference(transitivity,[status(thm)],[4192, 4097, 4186])).
% 1.03/1.17 tff(4194,plain,
% 1.03/1.17 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1331, 4193])).
% 1.03/1.17 tff(4195,plain,
% 1.03/1.17 ($false),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1459, 4194, 4190, 4180, 4177, 4174, 1261, 4169, 4145, 4140, 4129, 4126, 4083])).
% 1.03/1.17 tff(4196,plain,((op(e3, e3) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e2, op(e0, e3)) = e2) | (~(op(e3, e0) = op(e0, e3))) | (op(e3, op(e0, e3)) = e3) | (op(e0, e3) = e3) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.17 tff(4197,plain,
% 1.03/1.17 (op(e1, e3) = e0),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[4196, 3229, 121, 651, 466, 650, 661, 649, 652])).
% 1.03/1.17 tff(4198,plain,
% 1.03/1.17 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4197])).
% 1.03/1.17 tff(4199,plain,
% 1.03/1.17 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4198, 86])).
% 1.03/1.17 tff(4200,plain,
% 1.03/1.17 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4199])).
% 1.03/1.17 tff(4201,plain,
% 1.03/1.17 (~(op(e2, e3) = e0)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[118, 4200])).
% 1.03/1.17 tff(4202,plain,
% 1.03/1.17 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4197])).
% 1.03/1.17 tff(4203,plain,
% 1.03/1.17 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4202])).
% 1.03/1.17 tff(4204,plain,
% 1.03/1.17 (~(op(e0, e3) = e0)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[64, 4203])).
% 1.03/1.17 tff(4205,plain,
% 1.03/1.17 (op(e1, op(e1, e3)) = e3),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[1156, 4204, 651, 121, 3221, 466, 661, 3229, 4201])).
% 1.03/1.17 tff(4206,plain,
% 1.03/1.17 (e0 = op(e1, e3)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4197])).
% 1.03/1.17 tff(4207,plain,
% 1.03/1.17 (op(e1, e0) = op(e1, op(e1, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4206])).
% 1.03/1.17 tff(4208,plain,
% 1.03/1.17 (op(e1, e0) = e3),
% 1.03/1.17 inference(transitivity,[status(thm)],[4207, 4205])).
% 1.03/1.17 tff(4209,plain,
% 1.03/1.17 ((op(e1, e0) = e1) <=> (e3 = e1)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4208])).
% 1.03/1.17 tff(4210,plain,
% 1.03/1.17 ((op(e1, e0) = e1) <=> (e1 = e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4209, 128])).
% 1.03/1.17 tff(4211,plain,
% 1.03/1.17 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4210])).
% 1.03/1.17 tff(4212,plain,
% 1.03/1.17 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4211])).
% 1.03/1.17 tff(4213,plain,
% 1.03/1.17 (~(op(e1, e0) = e1)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[303, 4212])).
% 1.03/1.17 tff(4214,plain,
% 1.03/1.17 (op(e0, e3) = e2),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[687, 4204, 121, 661])).
% 1.03/1.17 tff(4215,plain,
% 1.03/1.17 (op(e0, op(e0, e3)) = op(e0, e2)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4214])).
% 1.03/1.17 tff(4216,plain,
% 1.03/1.17 (op(e0, e2) = op(e0, op(e0, e3))),
% 1.03/1.17 inference(symmetry,[status(thm)],[4215])).
% 1.03/1.17 tff(4217,plain,
% 1.03/1.17 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4216])).
% 1.03/1.17 tff(4218,plain,
% 1.03/1.17 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4217])).
% 1.03/1.17 tff(4219,plain,
% 1.03/1.17 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(e0, e2) = e0))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4218])).
% 1.03/1.17 tff(4220,plain,
% 1.03/1.17 (~(op(e0, e2) = e0)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[649, 4219])).
% 1.03/1.17 tff(4221,plain,
% 1.03/1.17 ((e3 = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.03/1.17 inference(commutativity,[status(thm)],[])).
% 1.03/1.17 tff(4222,plain,
% 1.03/1.17 (op(e0, e1) = e3),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2763, 4197, 121, 1261, 661, 466, 3229, 651, 649, 650])).
% 1.03/1.17 tff(4223,plain,
% 1.03/1.17 ((op(e0, e1) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4222])).
% 1.03/1.17 tff(4224,plain,
% 1.03/1.17 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.03/1.17 inference(transitivity,[status(thm)],[4223, 4221])).
% 1.03/1.17 tff(4225,plain,
% 1.03/1.17 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4224])).
% 1.03/1.17 tff(4226,plain,
% 1.03/1.17 (~(op(e0, e2) = e3)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[2102, 4225])).
% 1.03/1.17 tff(4227,plain,
% 1.03/1.17 (e2 = op(e0, e3)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4214])).
% 1.03/1.17 tff(4228,plain,
% 1.03/1.17 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4227])).
% 1.03/1.17 tff(4229,plain,
% 1.03/1.17 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4228])).
% 1.03/1.17 tff(4230,plain,
% 1.03/1.17 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4229])).
% 1.03/1.17 tff(4231,plain,
% 1.03/1.17 (~(op(e0, e2) = e2)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[918, 4230])).
% 1.03/1.17 tff(4232,plain,
% 1.03/1.17 (op(e0, e2) = e1),
% 1.03/1.17 inference(unit_resolution,[status(thm)],[2745, 4231, 4226, 4220])).
% 1.03/1.17 tff(4233,plain,
% 1.03/1.17 (e1 = op(e0, e2)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4232])).
% 1.03/1.17 tff(4234,plain,
% 1.03/1.17 ((op(e0, e0) = e1) <=> (op(e0, e0) = op(e0, e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4233])).
% 1.03/1.17 tff(4235,plain,
% 1.03/1.17 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4234])).
% 1.03/1.17 tff(4236,plain,
% 1.03/1.17 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e1))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4235])).
% 1.03/1.17 tff(4237,plain,
% 1.03/1.17 (~(op(e0, e0) = e1)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[3603, 4236])).
% 1.03/1.17 tff(4238,plain,
% 1.03/1.17 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4233])).
% 1.03/1.17 tff(4239,plain,
% 1.03/1.17 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e1)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4238])).
% 1.03/1.17 tff(4240,plain,
% 1.03/1.17 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4197])).
% 1.03/1.17 tff(4241,plain,
% 1.03/1.17 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 1.03/1.17 inference(symmetry,[status(thm)],[4240])).
% 1.03/1.17 tff(4242,plain,
% 1.03/1.17 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 1.03/1.17 inference(monotonicity,[status(thm)],[4241])).
% 1.03/1.17 tff(4243,plain,
% 1.03/1.17 (~(op(e1, e3) = e1)),
% 1.03/1.17 inference(modus_ponens,[status(thm)],[26, 4242])).
% 1.03/1.17 tff(4244,plain,
% 1.03/1.17 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4222])).
% 1.07/1.17 tff(4245,plain,
% 1.07/1.17 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4244, 396])).
% 1.07/1.17 tff(4246,plain,
% 1.07/1.17 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4245])).
% 1.07/1.17 tff(4247,plain,
% 1.07/1.17 (~(op(e3, e1) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[3046, 4246])).
% 1.07/1.17 tff(4248,plain,
% 1.07/1.17 (~(op(e3, e2) = e3)),
% 1.07/1.17 inference(unit_resolution,[status(thm)],[860, 4214, 650])).
% 1.07/1.17 tff(4249,plain,
% 1.07/1.17 (op(e3, e3) = e3),
% 1.07/1.17 inference(unit_resolution,[status(thm)],[422, 4248, 665, 4247])).
% 1.07/1.17 tff(4250,plain,
% 1.07/1.17 ((op(e3, e3) = e1) <=> (e3 = e1)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4249])).
% 1.07/1.17 tff(4251,plain,
% 1.07/1.17 ((op(e3, e3) = e1) <=> (e1 = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4250, 128])).
% 1.07/1.17 tff(4252,plain,
% 1.07/1.17 ((e1 = e3) <=> (op(e3, e3) = e1)),
% 1.07/1.17 inference(symmetry,[status(thm)],[4251])).
% 1.07/1.17 tff(4253,plain,
% 1.07/1.17 ((~(e1 = e3)) <=> (~(op(e3, e3) = e1))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4252])).
% 1.07/1.17 tff(4254,plain,
% 1.07/1.17 (~(op(e3, e3) = e1)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[303, 4253])).
% 1.07/1.17 tff(4255,plain,
% 1.07/1.17 (op(e2, e3) = e1),
% 1.07/1.17 inference(unit_resolution,[status(thm)],[151, 4254, 121, 4243])).
% 1.07/1.17 tff(4256,plain,
% 1.07/1.17 (op(e2, e3) = op(e0, e2)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4255, 4233])).
% 1.07/1.17 tff(4257,plain,
% 1.07/1.17 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4256])).
% 1.07/1.17 tff(4258,plain,
% 1.07/1.17 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4257, 4239])).
% 1.07/1.17 tff(4259,plain,
% 1.07/1.17 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4258])).
% 1.07/1.17 tff(4260,plain,
% 1.07/1.17 (~(op(e2, e0) = e1)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[989, 4259])).
% 1.07/1.17 tff(4261,plain,
% 1.07/1.17 ($false),
% 1.07/1.17 inference(unit_resolution,[status(thm)],[1480, 4260, 4237, 899, 4213])).
% 1.07/1.17 tff(4262,plain,((op(e0, e3) = e3) | (op(e0, e3) = e1) | (op(e0, op(e0, e3)) = e0) | (op(e3, op(e0, e3)) = e3) | (op(e2, op(e0, e3)) = e2) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, op(e0, e3)) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.17 tff(4263,plain,
% 1.07/1.17 (op(e0, e3) = e3),
% 1.07/1.17 inference(unit_resolution,[status(thm)],[4262, 121, 649, 650, 651, 466, 652])).
% 1.07/1.17 tff(4264,plain,
% 1.07/1.17 (op(e3, e0) = e3),
% 1.07/1.17 inference(transitivity,[status(thm)],[466, 4263])).
% 1.07/1.17 tff(4265,plain,
% 1.07/1.17 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4264])).
% 1.07/1.17 tff(4266,plain,
% 1.07/1.17 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4265])).
% 1.07/1.17 tff(4267,plain,
% 1.07/1.17 (~(op(e1, e0) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[410, 4266])).
% 1.07/1.17 tff(4268,plain,
% 1.07/1.17 ((op(e0, e3) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.17 tff(4269,plain,
% 1.07/1.17 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4268, 3230])).
% 1.07/1.17 tff(4270,plain,
% 1.07/1.17 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4269])).
% 1.07/1.17 tff(4271,plain,
% 1.07/1.17 (~(op(e1, e3) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[64, 4270])).
% 1.07/1.17 tff(4272,plain,
% 1.07/1.17 (e3 = op(e0, e3)),
% 1.07/1.17 inference(symmetry,[status(thm)],[4263])).
% 1.07/1.17 tff(4273,plain,
% 1.07/1.17 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e0, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4272])).
% 1.07/1.17 tff(4274,plain,
% 1.07/1.17 ((op(e3, e3) = e3) <=> (op(e0, e3) = op(e3, e3))),
% 1.07/1.17 inference(transitivity,[status(thm)],[4273, 659])).
% 1.07/1.17 tff(4275,plain,
% 1.07/1.17 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.07/1.17 inference(symmetry,[status(thm)],[4274])).
% 1.07/1.17 tff(4276,plain,
% 1.07/1.17 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4275])).
% 1.07/1.17 tff(4277,plain,
% 1.07/1.17 (~(op(e3, e3) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[1077, 4276])).
% 1.07/1.17 tff(4278,plain,
% 1.07/1.17 ((op(e0, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.17 tff(4279,plain,
% 1.07/1.17 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4278, 112])).
% 1.07/1.17 tff(4280,plain,
% 1.07/1.17 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4279])).
% 1.07/1.17 tff(4281,plain,
% 1.07/1.17 (~(op(e2, e3) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[964, 4280])).
% 1.07/1.17 tff(4282,plain,
% 1.07/1.17 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4264])).
% 1.07/1.17 tff(4283,plain,
% 1.07/1.17 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4282, 3423])).
% 1.07/1.17 tff(4284,plain,
% 1.07/1.17 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4283])).
% 1.07/1.17 tff(4285,plain,
% 1.07/1.17 (~(op(e3, e2) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[1133, 4284])).
% 1.07/1.17 tff(4286,plain,
% 1.07/1.17 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.17 tff(4287,plain,
% 1.07/1.17 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4286])).
% 1.07/1.17 tff(4288,plain,
% 1.07/1.17 (~(op(e0, e2) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[918, 4287])).
% 1.07/1.17 tff(4289,plain,
% 1.07/1.17 ((e2 = e3) <=> (e2 = op(e0, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4272])).
% 1.07/1.17 tff(4290,plain,
% 1.07/1.17 ((e2 = e3) <=> (op(e0, e3) = e2)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4289, 1681])).
% 1.07/1.17 tff(4291,plain,
% 1.07/1.17 ((e2 = e3) <=> (op(e3, e0) = e2)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4290, 668])).
% 1.07/1.17 tff(4292,plain,
% 1.07/1.17 ((~(e2 = e3)) <=> (~(op(e3, e0) = e2))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4291])).
% 1.07/1.17 tff(4293,plain,
% 1.07/1.17 (~(op(e3, e0) = e2)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[1321, 4292])).
% 1.07/1.17 tff(4294,plain,
% 1.07/1.17 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4264])).
% 1.07/1.17 tff(4295,plain,
% 1.07/1.17 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4294])).
% 1.07/1.17 tff(4296,plain,
% 1.07/1.17 (~(op(e2, e0) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[747, 4295])).
% 1.07/1.17 tff(4297,plain,
% 1.07/1.17 ((e0 = e3) <=> (e0 = op(e0, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4272])).
% 1.07/1.17 tff(4298,plain,
% 1.07/1.17 ((e0 = e3) <=> (op(e0, e3) = e0)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4297, 1079])).
% 1.07/1.17 tff(4299,plain,
% 1.07/1.17 ((~(e0 = e3)) <=> (~(op(e0, e3) = e0))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4298])).
% 1.07/1.17 tff(4300,plain,
% 1.07/1.17 (~(op(e0, e3) = e0)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[181, 4299])).
% 1.07/1.17 tff(4301,plain,
% 1.07/1.17 ((~(e2 = e3)) <=> (~(op(e0, e3) = e2))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4290])).
% 1.07/1.17 tff(4302,plain,
% 1.07/1.17 (~(op(e0, e3) = e2)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[1321, 4301])).
% 1.07/1.17 tff(4303,plain,
% 1.07/1.17 (op(e2, e3) = op(e2, op(e0, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4272])).
% 1.07/1.17 tff(4304,plain,
% 1.07/1.17 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4303])).
% 1.07/1.17 tff(4305,plain,
% 1.07/1.17 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 1.07/1.17 inference(symmetry,[status(thm)],[4304])).
% 1.07/1.17 tff(4306,plain,
% 1.07/1.17 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e3) = e2))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4305])).
% 1.07/1.17 tff(4307,plain,
% 1.07/1.17 (~(op(e2, e3) = e2)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[651, 4306])).
% 1.07/1.17 tff(4308,plain,
% 1.07/1.17 ((op(e3, e0) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4264])).
% 1.07/1.17 tff(4309,plain,
% 1.07/1.17 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.07/1.17 inference(transitivity,[status(thm)],[4308, 396])).
% 1.07/1.17 tff(4310,plain,
% 1.07/1.17 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4309])).
% 1.07/1.17 tff(4311,plain,
% 1.07/1.17 (~(op(e3, e1) = e3)),
% 1.07/1.17 inference(modus_ponens,[status(thm)],[580, 4310])).
% 1.07/1.17 tff(4312,plain,
% 1.07/1.17 (op(e1, e3) = op(e1, op(e0, e3))),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4272])).
% 1.07/1.17 tff(4313,plain,
% 1.07/1.17 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.07/1.17 inference(monotonicity,[status(thm)],[4312])).
% 1.07/1.17 tff(4314,plain,
% 1.07/1.17 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e1)),
% 1.07/1.17 inference(symmetry,[status(thm)],[4313])).
% 1.07/1.17 tff(4315,plain,
% 1.07/1.17 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e3) = e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4314])).
% 1.07/1.18 tff(4316,plain,
% 1.07/1.18 (~(op(e1, e3) = e1)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[652, 4315])).
% 1.07/1.18 tff(4317,plain,
% 1.07/1.18 (op(op(e0, e3), e0) = op(e3, e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.18 tff(4318,plain,
% 1.07/1.18 (op(op(e0, e3), e0) = e3),
% 1.07/1.18 inference(transitivity,[status(thm)],[4317, 466, 4263])).
% 1.07/1.18 tff(4319,plain,
% 1.07/1.18 (op(op(e3, e0), e0) = e3),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[4318, 4019])).
% 1.07/1.18 tff(4320,plain,
% 1.07/1.18 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[4026, 4319])).
% 1.07/1.18 tff(4321,plain,
% 1.07/1.18 (op(e0, op(e0, e3)) = op(e0, e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.18 tff(4322,plain,
% 1.07/1.18 (op(e0, op(e0, e3)) = e3),
% 1.07/1.18 inference(transitivity,[status(thm)],[4321, 4263])).
% 1.07/1.18 tff(4323,plain,
% 1.07/1.18 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1938, 4322])).
% 1.07/1.18 tff(4324,plain,
% 1.07/1.18 (op(e1, e3) = e2),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[104, 80, 1080, 87])).
% 1.07/1.18 tff(4325,plain,
% 1.07/1.18 (op(e3, e3) = e1),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1071, 656, 468, 1880])).
% 1.07/1.18 tff(4326,plain,
% 1.07/1.18 (e1 = op(e3, e3)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[4325, 658])).
% 1.07/1.18 tff(4327,plain,
% 1.07/1.18 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4325])).
% 1.07/1.18 tff(4328,plain,
% 1.07/1.18 ((e2 = op(e3, op(e3, e3))) <=> (op(e1, e3) = op(e3, e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[265, 4327])).
% 1.07/1.18 tff(4329,plain,
% 1.07/1.18 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = op(e1, e3))),
% 1.07/1.18 inference(transitivity,[status(thm)],[4328, 1674])).
% 1.07/1.18 tff(4330,plain,
% 1.07/1.18 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e3, op(e3, e3)))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4329])).
% 1.07/1.18 tff(4331,plain,
% 1.07/1.18 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.07/1.18 inference(transitivity,[status(thm)],[1972, 4330])).
% 1.07/1.18 tff(4332,plain,
% 1.07/1.18 (op(e2, e3) = e0),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1105, 656, 121, 313, 1087, 79])).
% 1.07/1.18 tff(4333,plain,
% 1.07/1.18 (e0 = op(e2, e3)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4332])).
% 1.07/1.18 tff(4334,plain,
% 1.07/1.18 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4333])).
% 1.07/1.18 tff(4335,plain,
% 1.07/1.18 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4334])).
% 1.07/1.18 tff(4336,plain,
% 1.07/1.18 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4335])).
% 1.07/1.18 tff(4337,plain,
% 1.07/1.18 (~(op(e2, e2) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[515, 4336])).
% 1.07/1.18 tff(4338,plain,
% 1.07/1.18 (op(e2, e1) = op(op(e1, e3), e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[265])).
% 1.07/1.18 tff(4339,plain,
% 1.07/1.18 (op(e2, e1) = e3),
% 1.07/1.18 inference(transitivity,[status(thm)],[4338, 313])).
% 1.07/1.18 tff(4340,plain,
% 1.07/1.18 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4339])).
% 1.07/1.18 tff(4341,plain,
% 1.07/1.18 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4340, 502])).
% 1.07/1.18 tff(4342,plain,
% 1.07/1.18 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4341])).
% 1.07/1.18 tff(4343,plain,
% 1.07/1.18 (~(op(e2, e2) = e3)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[508, 4342])).
% 1.07/1.18 tff(4344,plain,
% 1.07/1.18 (~(op(e2, e2) = e1)),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[336, 4332, 313, 4325, 264])).
% 1.07/1.18 tff(4345,plain,
% 1.07/1.18 (op(e2, e2) = e2),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[524, 4344, 4343, 4337])).
% 1.07/1.18 tff(4346,plain,
% 1.07/1.18 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4345])).
% 1.07/1.18 tff(4347,plain,
% 1.07/1.18 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4346, 2234])).
% 1.07/1.18 tff(4348,plain,
% 1.07/1.18 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4347])).
% 1.07/1.18 tff(4349,plain,
% 1.07/1.18 (~(op(e3, e2) = e2)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[1546, 4348])).
% 1.07/1.18 tff(4350,plain,
% 1.07/1.18 (op(e3, e1) = e2),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2015, 4349, 3786, 1880])).
% 1.07/1.18 tff(4351,plain,
% 1.07/1.18 (e2 = op(e3, op(e3, e3))),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[4350, 4331])).
% 1.07/1.18 tff(4352,plain,
% 1.07/1.18 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4327])).
% 1.07/1.18 tff(4353,plain,
% 1.07/1.18 (op(e3, op(e3, e1)) = op(e3, op(e3, op(e3, e3)))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4352])).
% 1.07/1.18 tff(4354,plain,
% 1.07/1.18 (op(e3, e1) = op(e1, e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4350, 265])).
% 1.07/1.18 tff(4355,plain,
% 1.07/1.18 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4354])).
% 1.07/1.18 tff(4356,plain,
% 1.07/1.18 (op(e3, op(e1, e3)) = op(e3, op(e3, e1))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4355])).
% 1.07/1.18 tff(4357,plain,
% 1.07/1.18 (op(e3, e2) = op(e3, op(e1, e3))),
% 1.07/1.18 inference(symmetry,[status(thm)],[1900])).
% 1.07/1.18 tff(4358,plain,
% 1.07/1.18 (e1 = op(e3, e3)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4325])).
% 1.07/1.18 tff(4359,plain,
% 1.07/1.18 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4358])).
% 1.07/1.18 tff(4360,plain,
% 1.07/1.18 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4359])).
% 1.07/1.18 tff(4361,plain,
% 1.07/1.18 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4360])).
% 1.07/1.18 tff(4362,plain,
% 1.07/1.18 (~(op(e3, e2) = e1)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[1888, 4361])).
% 1.07/1.18 tff(4363,plain,
% 1.07/1.18 (op(e3, e2) = e0),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1898, 4349, 1890, 4362])).
% 1.07/1.18 tff(4364,plain,
% 1.07/1.18 (e0 = op(e3, e2)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4363])).
% 1.07/1.18 tff(4365,plain,
% 1.07/1.18 (e0 = op(e3, op(e3, op(e3, e3)))),
% 1.07/1.18 inference(transitivity,[status(thm)],[4364, 4357, 4356, 4353])).
% 1.07/1.18 tff(4366,plain,
% 1.07/1.18 ($false),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2034, 4365, 4351, 4326])).
% 1.07/1.18 tff(4367,plain,((op(e3, e3) = e0) | (~(op(e1, e3) = e2)) | (op(e3, e2) = e3) | (op(e3, e0) = e2) | (~(op(op(e1, e3), e1) = e3)) | (op(e3, e3) = e3) | (op(e0, e3) = e1) | (op(e0, e3) = e0) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.18 tff(4368,plain,
% 1.07/1.18 (op(e3, e3) = e0),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[4367, 4324, 1890, 3786, 313, 468, 121, 1087, 79])).
% 1.07/1.18 tff(4369,plain,
% 1.07/1.18 (e0 = op(e3, e3)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4368])).
% 1.07/1.18 tff(4370,plain,
% 1.07/1.18 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4369])).
% 1.07/1.18 tff(4371,plain,
% 1.07/1.18 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4370])).
% 1.07/1.18 tff(4372,plain,
% 1.07/1.18 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4371])).
% 1.07/1.18 tff(4373,plain,
% 1.07/1.18 (~(op(e3, e1) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[437, 4372])).
% 1.07/1.18 tff(4374,plain,
% 1.07/1.18 (e2 = op(e1, e3)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4324])).
% 1.07/1.18 tff(4375,plain,
% 1.07/1.18 (op(e2, e1) = op(op(e1, e3), e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4374])).
% 1.07/1.18 tff(4376,plain,
% 1.07/1.18 (op(e2, e1) = e3),
% 1.07/1.18 inference(transitivity,[status(thm)],[4375, 313])).
% 1.07/1.18 tff(4377,plain,
% 1.07/1.18 ((op(e2, e1) = e0) <=> (e3 = e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4376])).
% 1.07/1.18 tff(4378,plain,
% 1.07/1.18 ((op(e2, e1) = e0) <=> (e0 = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4377, 159])).
% 1.07/1.18 tff(4379,plain,
% 1.07/1.18 ((e0 = e3) <=> (op(e2, e1) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4378])).
% 1.07/1.18 tff(4380,plain,
% 1.07/1.18 ((~(e0 = e3)) <=> (~(op(e2, e1) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4379])).
% 1.07/1.18 tff(4381,plain,
% 1.07/1.18 (~(op(e2, e1) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[181, 4380])).
% 1.07/1.18 tff(4382,assumption,(~(op(e2, e3) = e2)), introduced(assumption)).
% 1.07/1.18 tff(4383,plain,
% 1.07/1.18 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4369])).
% 1.07/1.18 tff(4384,plain,
% 1.07/1.18 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4383])).
% 1.07/1.18 tff(4385,plain,
% 1.07/1.18 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4384])).
% 1.07/1.18 tff(4386,plain,
% 1.07/1.18 (~(op(e2, e3) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[368, 4385])).
% 1.07/1.18 tff(4387,plain,
% 1.07/1.18 (op(e2, e3) = e1),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[206, 4386, 4382, 124])).
% 1.07/1.18 tff(4388,plain,
% 1.07/1.18 (op(e0, op(e2, e3)) = op(e0, e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4387])).
% 1.07/1.18 tff(4389,plain,
% 1.07/1.18 (op(e0, e1) = op(e0, op(e2, e3))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4388])).
% 1.07/1.18 tff(4390,plain,
% 1.07/1.18 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4389])).
% 1.07/1.18 tff(4391,plain,
% 1.07/1.18 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4390])).
% 1.07/1.18 tff(4392,plain,
% 1.07/1.18 ((op(e2, e1) = e2) <=> (e3 = op(e1, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4376, 4374])).
% 1.07/1.18 tff(4393,plain,
% 1.07/1.18 ((op(e2, e1) = e2) <=> (op(e1, e3) = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4392, 3230])).
% 1.07/1.18 tff(4394,plain,
% 1.07/1.18 ((op(e1, e3) = e3) <=> (op(e2, e1) = e2)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4393])).
% 1.07/1.18 tff(4395,plain,
% 1.07/1.18 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e1) = e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4394])).
% 1.07/1.18 tff(4396,plain,
% 1.07/1.18 (~(op(e2, e1) = e2)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[1080, 4395])).
% 1.07/1.18 tff(4397,plain,
% 1.07/1.18 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4374])).
% 1.07/1.18 tff(4398,plain,
% 1.07/1.18 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4397])).
% 1.07/1.18 tff(4399,plain,
% 1.07/1.18 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4398])).
% 1.07/1.18 tff(4400,plain,
% 1.07/1.18 (~(op(e1, e1) = e2)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[619, 4399])).
% 1.07/1.18 tff(4401,plain,
% 1.07/1.18 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4374])).
% 1.07/1.18 tff(4402,plain,
% 1.07/1.18 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4401])).
% 1.07/1.18 tff(4403,plain,
% 1.07/1.18 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4376])).
% 1.07/1.18 tff(4404,plain,
% 1.07/1.18 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4403])).
% 1.07/1.18 tff(4405,plain,
% 1.07/1.18 (~(op(e1, e1) = e3)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[225, 4404])).
% 1.07/1.18 tff(4406,plain,
% 1.07/1.18 (op(e1, e2) = e3),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[247, 4405, 1080, 2168])).
% 1.07/1.18 tff(4407,plain,
% 1.07/1.18 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4406])).
% 1.07/1.18 tff(4408,plain,
% 1.07/1.18 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4407, 159])).
% 1.07/1.18 tff(4409,plain,
% 1.07/1.18 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4408])).
% 1.07/1.18 tff(4410,plain,
% 1.07/1.18 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4409])).
% 1.07/1.18 tff(4411,plain,
% 1.07/1.18 (~(op(e1, e2) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[181, 4410])).
% 1.07/1.18 tff(4412,assumption,(~(op(e0, e2) = e3)), introduced(assumption)).
% 1.07/1.18 tff(4413,plain,
% 1.07/1.18 (op(e1, op(e1, e3)) = op(e1, e2)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4324])).
% 1.07/1.18 tff(4414,plain,
% 1.07/1.18 (op(e1, e2) = op(e1, op(e1, e3))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4413])).
% 1.07/1.18 tff(4415,plain,
% 1.07/1.18 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4414])).
% 1.07/1.18 tff(4416,plain,
% 1.07/1.18 ((op(e1, op(e1, e3)) = e1) <=> (op(e1, e2) = e1)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4415])).
% 1.07/1.18 tff(4417,plain,
% 1.07/1.18 (op(e1, op(e1, e3)) = e3),
% 1.07/1.18 inference(transitivity,[status(thm)],[4413, 4406])).
% 1.07/1.18 tff(4418,plain,
% 1.07/1.18 ((op(e1, op(e1, e3)) = e1) <=> (e3 = e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4417])).
% 1.07/1.18 tff(4419,plain,
% 1.07/1.18 ((op(e1, op(e1, e3)) = e1) <=> (e1 = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4418, 128])).
% 1.07/1.18 tff(4420,plain,
% 1.07/1.18 ((e1 = e3) <=> (op(e1, op(e1, e3)) = e1)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4419])).
% 1.07/1.18 tff(4421,plain,
% 1.07/1.18 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4420, 4416])).
% 1.07/1.18 tff(4422,plain,
% 1.07/1.18 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4421])).
% 1.07/1.18 tff(4423,plain,
% 1.07/1.18 (~(op(e1, e2) = e1)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[303, 4422])).
% 1.07/1.18 tff(4424,plain,
% 1.07/1.18 ((op(e2, e1) = e1) <=> (e3 = e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4376])).
% 1.07/1.18 tff(4425,plain,
% 1.07/1.18 ((op(e2, e1) = e1) <=> (e1 = e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4424, 128])).
% 1.07/1.18 tff(4426,plain,
% 1.07/1.18 ((e1 = e3) <=> (op(e2, e1) = e1)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4425])).
% 1.07/1.18 tff(4427,plain,
% 1.07/1.18 ((~(e1 = e3)) <=> (~(op(e2, e1) = e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4426])).
% 1.07/1.18 tff(4428,plain,
% 1.07/1.18 (~(op(e2, e1) = e1)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[303, 4427])).
% 1.07/1.18 tff(4429,plain,
% 1.07/1.18 (op(op(e1, e3), e3) = op(e2, e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4324])).
% 1.07/1.18 tff(4430,plain,
% 1.07/1.18 (op(e2, op(e2, e1)) = op(op(e1, e3), e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4374, 4376])).
% 1.07/1.18 tff(4431,plain,
% 1.07/1.18 (op(e2, op(e2, e1)) = op(e2, e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4430, 4429])).
% 1.07/1.18 tff(4432,plain,
% 1.07/1.18 ((op(e2, op(e2, e1)) = e1) <=> (op(e2, e3) = e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4431])).
% 1.07/1.18 tff(4433,plain,
% 1.07/1.18 ((op(e2, e3) = e1) <=> (op(e2, op(e2, e1)) = e1)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4432])).
% 1.07/1.18 tff(4434,plain,
% 1.07/1.18 (op(e2, op(e2, e1)) = e1),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[4387, 4433])).
% 1.07/1.18 tff(4435,plain,
% 1.07/1.18 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1355, 4434])).
% 1.07/1.18 tff(4436,plain,
% 1.07/1.18 (op(e1, op(e1, e2)) = op(e1, e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4406])).
% 1.07/1.18 tff(4437,plain,
% 1.07/1.18 (op(e1, op(e1, e2)) = e2),
% 1.07/1.18 inference(transitivity,[status(thm)],[4436, 4324])).
% 1.07/1.18 tff(4438,plain,
% 1.07/1.18 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2377, 4437])).
% 1.07/1.18 tff(4439,plain,
% 1.07/1.18 ((op(e1, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[264])).
% 1.07/1.18 tff(4440,plain,
% 1.07/1.18 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4439, 565])).
% 1.07/1.18 tff(4441,plain,
% 1.07/1.18 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4440])).
% 1.07/1.18 tff(4442,plain,
% 1.07/1.18 (~(op(e3, e3) = e2)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[571, 4441])).
% 1.07/1.18 tff(4443,plain,
% 1.07/1.18 (op(e3, e1) = e2),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2015, 2386, 3786, 4442])).
% 1.07/1.18 tff(4444,plain,
% 1.07/1.18 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4443])).
% 1.07/1.18 tff(4445,plain,
% 1.07/1.18 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4444])).
% 1.07/1.18 tff(4446,plain,
% 1.07/1.18 (~(op(e0, e1) = e2)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[3046, 4445])).
% 1.07/1.18 tff(4447,plain,
% 1.07/1.18 (op(e0, op(e2, e3)) = op(e0, e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[2684])).
% 1.07/1.18 tff(4448,plain,
% 1.07/1.18 (op(e0, e1) = op(e0, op(e2, e3))),
% 1.07/1.18 inference(symmetry,[status(thm)],[4447])).
% 1.07/1.18 tff(4449,plain,
% 1.07/1.18 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4448])).
% 1.07/1.18 tff(4450,plain,
% 1.07/1.18 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4449])).
% 1.07/1.18 tff(4451,plain,
% 1.07/1.18 (e0 = op(e3, e3)),
% 1.07/1.18 inference(symmetry,[status(thm)],[3066])).
% 1.07/1.18 tff(4452,plain,
% 1.07/1.18 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4451])).
% 1.07/1.18 tff(4453,plain,
% 1.07/1.18 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4452])).
% 1.07/1.18 tff(4454,plain,
% 1.07/1.18 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4453])).
% 1.07/1.18 tff(4455,plain,
% 1.07/1.18 (~(op(e3, e2) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[1888, 4454])).
% 1.07/1.18 tff(4456,plain,
% 1.07/1.18 (op(e3, e2) = e1),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1898, 2386, 1890, 4455])).
% 1.07/1.18 tff(4457,plain,
% 1.07/1.18 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e1)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4456])).
% 1.07/1.18 tff(4458,plain,
% 1.07/1.18 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e1))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4457])).
% 1.07/1.18 tff(4459,plain,
% 1.07/1.18 (~(op(e0, e2) = e1)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[1467, 4458])).
% 1.07/1.18 tff(4460,plain,
% 1.07/1.18 (op(e3, e2) = op(e2, e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4456, 2685])).
% 1.07/1.18 tff(4461,plain,
% 1.07/1.18 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4460])).
% 1.07/1.18 tff(4462,plain,
% 1.07/1.18 (op(e3, op(e3, e2)) = e2),
% 1.07/1.18 inference(transitivity,[status(thm)],[4461, 2832, 4443])).
% 1.07/1.18 tff(4463,plain,
% 1.07/1.18 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1904, 4462])).
% 1.07/1.18 tff(4464,plain,
% 1.07/1.18 (op(e3, e1) = op(e1, e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4443, 265])).
% 1.07/1.18 tff(4465,plain,
% 1.07/1.18 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4464])).
% 1.07/1.18 tff(4466,plain,
% 1.07/1.18 (op(e3, op(e3, e1)) = e1),
% 1.07/1.18 inference(transitivity,[status(thm)],[4465, 1900, 4456])).
% 1.07/1.18 tff(4467,plain,
% 1.07/1.18 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2594, 4466])).
% 1.07/1.18 tff(4468,plain,
% 1.07/1.18 (op(e1, op(e3, e3)) = op(e1, e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[3066])).
% 1.07/1.18 tff(4469,plain,
% 1.07/1.18 (op(e1, e0) = op(e3, e3)),
% 1.07/1.18 inference(transitivity,[status(thm)],[3352, 4451])).
% 1.07/1.18 tff(4470,plain,
% 1.07/1.18 (op(e1, op(e1, e0)) = op(e1, op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4469])).
% 1.07/1.18 tff(4471,plain,
% 1.07/1.18 (op(e1, op(e1, e0)) = e0),
% 1.07/1.18 inference(transitivity,[status(thm)],[4470, 4468, 3352])).
% 1.07/1.18 tff(4472,plain,
% 1.07/1.18 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1836, 4471])).
% 1.07/1.18 tff(4473,plain,
% 1.07/1.18 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4451])).
% 1.07/1.18 tff(4474,plain,
% 1.07/1.18 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4473])).
% 1.07/1.18 tff(4475,plain,
% 1.07/1.18 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4474])).
% 1.07/1.18 tff(4476,plain,
% 1.07/1.18 (~(op(e3, e1) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[437, 4475])).
% 1.07/1.18 tff(4477,plain,
% 1.07/1.18 (op(e0, e1) = e0),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[292, 84, 2559, 4476])).
% 1.07/1.18 tff(4478,plain,
% 1.07/1.18 (op(op(e0, e1), e1) = op(e0, op(e2, e3))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4477, 2685])).
% 1.07/1.18 tff(4479,plain,
% 1.07/1.18 (op(op(e0, e1), e1) = e0),
% 1.07/1.18 inference(transitivity,[status(thm)],[4478, 4447, 4477])).
% 1.07/1.18 tff(4480,plain,
% 1.07/1.18 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2650, 4479])).
% 1.07/1.18 tff(4481,plain,
% 1.07/1.18 (op(op(e2, e3), e3) = op(e1, e3)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[2684])).
% 1.07/1.18 tff(4482,plain,
% 1.07/1.18 (op(op(e2, e3), e3) = e2),
% 1.07/1.18 inference(transitivity,[status(thm)],[4481, 264])).
% 1.07/1.18 tff(4483,plain,
% 1.07/1.18 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[1288, 4482])).
% 1.07/1.18 tff(4484,assumption,(~(op(e0, e2) = e1)), introduced(assumption)).
% 1.07/1.18 tff(4485,plain,
% 1.07/1.18 (op(e0, e2) = op(e0, op(e1, e3))),
% 1.07/1.18 inference(symmetry,[status(thm)],[1927])).
% 1.07/1.18 tff(4486,plain,
% 1.07/1.18 ((op(e0, e2) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4485])).
% 1.07/1.18 tff(4487,plain,
% 1.07/1.18 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.07/1.18 inference(symmetry,[status(thm)],[4486])).
% 1.07/1.18 tff(4488,plain,
% 1.07/1.18 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, op(e1, e3)))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4477, 4485])).
% 1.07/1.18 tff(4489,plain,
% 1.07/1.18 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4488, 653])).
% 1.07/1.18 tff(4490,plain,
% 1.07/1.18 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 1.07/1.18 inference(transitivity,[status(thm)],[4489, 4487])).
% 1.07/1.18 tff(4491,plain,
% 1.07/1.18 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 1.07/1.18 inference(monotonicity,[status(thm)],[4490])).
% 1.07/1.18 tff(4492,plain,
% 1.07/1.18 (~(op(e0, e2) = e0)),
% 1.07/1.18 inference(modus_ponens,[status(thm)],[2102, 4491])).
% 1.07/1.18 tff(4493,plain,
% 1.07/1.18 (op(e0, e2) = e2),
% 1.07/1.18 inference(unit_resolution,[status(thm)],[2745, 4492, 4412, 4484])).
% 1.07/1.19 tff(4494,plain,
% 1.07/1.19 (op(e0, e2) = op(e1, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4493, 265])).
% 1.07/1.19 tff(4495,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4494])).
% 1.07/1.19 tff(4496,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = e2),
% 1.07/1.19 inference(transitivity,[status(thm)],[4495, 1927, 4493])).
% 1.07/1.19 tff(4497,plain,
% 1.07/1.19 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1331, 4496])).
% 1.07/1.19 tff(4498,plain,
% 1.07/1.19 (op(e2, e2) = e0),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[973, 4492, 1947, 4455])).
% 1.07/1.19 tff(4499,plain,
% 1.07/1.19 ((e0 = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.07/1.19 inference(commutativity,[status(thm)],[])).
% 1.07/1.19 tff(4500,plain,
% 1.07/1.19 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[3352])).
% 1.07/1.19 tff(4501,plain,
% 1.07/1.19 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4500, 4499])).
% 1.07/1.19 tff(4502,plain,
% 1.07/1.19 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4501])).
% 1.07/1.19 tff(4503,plain,
% 1.07/1.19 (~(op(e2, e0) = e0)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[756, 4502])).
% 1.07/1.19 tff(4504,plain,
% 1.07/1.19 (op(e2, e0) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[765, 4503, 3272, 2689])).
% 1.07/1.19 tff(4505,plain,
% 1.07/1.19 (op(e2, op(e2, e0)) = op(e2, e2)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4504])).
% 1.07/1.19 tff(4506,plain,
% 1.07/1.19 (op(e2, op(e2, e0)) = e0),
% 1.07/1.19 inference(transitivity,[status(thm)],[4505, 4498])).
% 1.07/1.19 tff(4507,plain,
% 1.07/1.19 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[2653, 4506])).
% 1.07/1.19 tff(4508,plain,
% 1.07/1.19 ($false),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1459, 4507, 4497, 4483, 3342, 1358, 1304, 4480, 1936, 1275, 1926, 4472, 3341])).
% 1.07/1.19 tff(4509,plain,((op(e1, e1) = e0) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e1, e3) = e2)) | (op(e2, e0) = e3) | (op(e0, e2) = e3) | (op(e0, e2) = e1) | (op(e1, e2) = e0) | (~(op(e3, e3) = e0)) | (~(op(e2, e3) = e1)) | (op(e1, e3) = e0) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.19 tff(4510,plain,
% 1.07/1.19 (op(e1, e1) = e0),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[4509, 4467, 1358, 1304, 1936, 3342, 1926, 4463, 264, 3272, 4412, 4459, 1947, 3066, 2684, 80, 2559])).
% 1.07/1.19 tff(4511,plain,
% 1.07/1.19 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, op(e2, e3)) = e0)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4448, 4510])).
% 1.07/1.19 tff(4512,plain,
% 1.07/1.19 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4511, 4450])).
% 1.07/1.19 tff(4513,plain,
% 1.07/1.19 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4512])).
% 1.07/1.19 tff(4514,plain,
% 1.07/1.19 (~(op(e0, e1) = e0)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[792, 4513])).
% 1.07/1.19 tff(4515,assumption,(~(op(e1, e2) = e1)), introduced(assumption)).
% 1.07/1.19 tff(4516,plain,
% 1.07/1.19 (op(e1, e1) = op(e3, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4510, 4451])).
% 1.07/1.19 tff(4517,plain,
% 1.07/1.19 ((op(e1, e1) = e1) <=> (op(e3, e3) = op(e2, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4516, 2685])).
% 1.07/1.19 tff(4518,plain,
% 1.07/1.19 ((op(e1, e1) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 1.07/1.19 inference(transitivity,[status(thm)],[4517, 2820])).
% 1.07/1.19 tff(4519,plain,
% 1.07/1.19 ((op(e2, e3) = op(e3, e3)) <=> (op(e1, e1) = e1)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4518])).
% 1.07/1.19 tff(4520,plain,
% 1.07/1.19 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e1, e1) = e1))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4519])).
% 1.07/1.19 tff(4521,plain,
% 1.07/1.19 (~(op(e1, e1) = e1)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[368, 4520])).
% 1.07/1.19 tff(4522,plain,
% 1.07/1.19 (op(e1, e0) = e1),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[954, 4521, 87, 4515])).
% 1.07/1.19 tff(4523,plain,
% 1.07/1.19 (op(e1, op(e1, e0)) = op(e1, e1)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4522])).
% 1.07/1.19 tff(4524,plain,
% 1.07/1.19 (op(e1, op(e1, e0)) = e0),
% 1.07/1.19 inference(transitivity,[status(thm)],[4523, 4510])).
% 1.07/1.19 tff(4525,plain,
% 1.07/1.19 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1836, 4524])).
% 1.07/1.19 tff(4526,plain,
% 1.07/1.19 ((op(e3, e1) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4464, 2685])).
% 1.07/1.19 tff(4527,plain,
% 1.07/1.19 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e1) = e1)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4526])).
% 1.07/1.19 tff(4528,plain,
% 1.07/1.19 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e1))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4527])).
% 1.07/1.19 tff(4529,plain,
% 1.07/1.19 (~(op(e3, e1) = e1)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[118, 4528])).
% 1.07/1.19 tff(4530,assumption,(~(op(e2, e1) = e1)), introduced(assumption)).
% 1.07/1.19 tff(4531,plain,
% 1.07/1.19 (op(e0, e1) = e1),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1252, 4521, 4530, 4529])).
% 1.07/1.19 tff(4532,plain,
% 1.07/1.19 (op(e0, e1) = op(e2, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4531, 2685])).
% 1.07/1.19 tff(4533,plain,
% 1.07/1.19 (op(e0, op(e0, e1)) = op(e0, op(e2, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4532])).
% 1.07/1.19 tff(4534,plain,
% 1.07/1.19 (op(e0, op(e0, e1)) = e1),
% 1.07/1.19 inference(transitivity,[status(thm)],[4533, 4447, 4531])).
% 1.07/1.19 tff(4535,plain,
% 1.07/1.19 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[2449, 4534])).
% 1.07/1.19 tff(4536,plain,
% 1.07/1.19 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e1, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[265])).
% 1.07/1.19 tff(4537,plain,
% 1.07/1.19 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4536])).
% 1.07/1.19 tff(4538,plain,
% 1.07/1.19 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4537])).
% 1.07/1.19 tff(4539,plain,
% 1.07/1.19 (~(op(e1, e0) = e2)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[110, 4538])).
% 1.07/1.19 tff(4540,plain,
% 1.07/1.19 (op(e0, e0) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[589, 982, 3786, 4539])).
% 1.07/1.19 tff(4541,plain,
% 1.07/1.19 (op(e0, e0) = op(e1, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4540, 265])).
% 1.07/1.19 tff(4542,plain,
% 1.07/1.19 ((op(e0, e0) = e0) <=> (op(e1, e3) = op(e3, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4541, 4451])).
% 1.07/1.19 tff(4543,plain,
% 1.07/1.19 ((op(e1, e3) = op(e3, e3)) <=> (op(e0, e0) = e0)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4542])).
% 1.07/1.19 tff(4544,plain,
% 1.07/1.19 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e0, e0) = e0))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4543])).
% 1.07/1.19 tff(4545,plain,
% 1.07/1.19 (~(op(e0, e0) = e0)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[571, 4544])).
% 1.07/1.19 tff(4546,plain,
% 1.07/1.19 (op(e0, e2) = e0),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[3976, 4545, 1087, 3849])).
% 1.07/1.19 tff(4547,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = op(e0, e0)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4546])).
% 1.07/1.19 tff(4548,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = e2),
% 1.07/1.19 inference(transitivity,[status(thm)],[4547, 4540])).
% 1.07/1.19 tff(4549,assumption,((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))), introduced(assumption)).
% 1.07/1.19 tff(4550,plain,
% 1.07/1.19 (op(e2, e0) = e0),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[765, 982, 3272, 1349])).
% 1.07/1.19 tff(4551,plain,
% 1.07/1.19 (op(e2, op(e3, e3)) = op(e2, e0)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[3066])).
% 1.07/1.19 tff(4552,plain,
% 1.07/1.19 (op(e2, e0) = op(e3, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4550, 4451])).
% 1.07/1.19 tff(4553,plain,
% 1.07/1.19 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4552])).
% 1.07/1.19 tff(4554,plain,
% 1.07/1.19 (op(e2, op(e2, e0)) = e0),
% 1.07/1.19 inference(transitivity,[status(thm)],[4553, 4551, 4550])).
% 1.07/1.19 tff(4555,plain,
% 1.07/1.19 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[2653, 4554])).
% 1.07/1.19 tff(4556,plain,
% 1.07/1.19 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1459, 4555, 1347, 3342, 1358, 1304, 4549, 1936, 1275, 1926, 1357, 3341])).
% 1.07/1.19 tff(4557,plain,
% 1.07/1.19 (~(op(e0, op(e0, e2)) = e2)),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1331, 4556])).
% 1.07/1.19 tff(4558,plain,
% 1.07/1.19 ($false),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[4557, 4548])).
% 1.07/1.19 tff(4559,plain,((op(e2, e0) = e2) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (op(e0, e3) = e0) | (op(e0, e1) = e0) | (~(op(e3, e3) = e0)) | (~(op(e1, e3) = e2)) | (op(e2, e0) = e3) | (op(e2, e0) = e1) | (op(e3, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.19 tff(4560,plain,
% 1.07/1.19 (op(e2, e0) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[4559, 4535, 3342, 1358, 1304, 4483, 1936, 4467, 1926, 4525, 4463, 1087, 4514, 3066, 264, 3272, 2689, 3786])).
% 1.07/1.19 tff(4561,plain,
% 1.07/1.19 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4560])).
% 1.07/1.19 tff(4562,plain,
% 1.07/1.19 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4561])).
% 1.07/1.19 tff(4563,plain,
% 1.07/1.19 (~(op(e0, e0) = e2)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[359, 4562])).
% 1.07/1.19 tff(4564,plain,
% 1.07/1.19 (op(e0, e2) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[3652, 4563, 79, 4446])).
% 1.07/1.19 tff(4565,plain,
% 1.07/1.19 (op(e0, e2) = op(e1, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4564, 265])).
% 1.07/1.19 tff(4566,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4565])).
% 1.07/1.19 tff(4567,plain,
% 1.07/1.19 (op(e0, op(e0, e2)) = e2),
% 1.07/1.19 inference(transitivity,[status(thm)],[4566, 1927, 4564])).
% 1.07/1.19 tff(4568,plain,
% 1.07/1.19 (op(op(e2, e0), e0) = op(e2, op(e3, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4560, 4451])).
% 1.07/1.19 tff(4569,plain,
% 1.07/1.19 (op(op(e2, e0), e0) = e2),
% 1.07/1.19 inference(transitivity,[status(thm)],[4568, 4551, 4560])).
% 1.07/1.19 tff(4570,plain,
% 1.07/1.19 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1945, 4569])).
% 1.07/1.19 tff(4571,plain,
% 1.07/1.19 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1459, 4570, 4483, 3342, 1358, 1304, 4535, 1936, 4467, 1926, 4525, 4463])).
% 1.07/1.19 tff(4572,plain,
% 1.07/1.19 (~(op(e0, op(e0, e2)) = e2)),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1331, 4571])).
% 1.07/1.19 tff(4573,plain,
% 1.07/1.19 ($false),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[4572, 4567])).
% 1.07/1.19 tff(4574,plain,((op(e3, e2) = e2) | (~(op(e1, e3) = e2)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (op(e0, e3) = e2) | (~(op(e3, e3) = e0)) | (op(e0, e3) = e0) | (op(e2, e0) = e3) | (op(e3, e0) = e2) | (~(op(e2, e3) = e1)) | (op(e2, e1) = e1) | (op(e1, e3) = e1) | (op(e1, e2) = e1) | (op(e0, e2) = e3) | (op(e1, e2) = e0) | (op(e1, e3) = e0) | (op(e2, e1) = e0) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.19 tff(4575,plain,
% 1.07/1.19 (op(e3, e2) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[4574, 4324, 3342, 4438, 1304, 4435, 1926, 79, 4368, 1087, 3272, 3786, 4387, 4428, 87, 4423, 4412, 4411, 80, 4381, 1890])).
% 1.07/1.19 tff(4576,plain,
% 1.07/1.19 (op(e3, e2) = op(e1, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4575, 4374])).
% 1.07/1.19 tff(4577,plain,
% 1.07/1.19 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4576])).
% 1.07/1.19 tff(4578,plain,
% 1.07/1.19 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e2)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4577, 4402])).
% 1.07/1.19 tff(4579,plain,
% 1.07/1.19 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e2))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4578])).
% 1.07/1.19 tff(4580,plain,
% 1.07/1.19 (~(op(e3, e1) = e2)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[3429, 4579])).
% 1.07/1.19 tff(4581,plain,
% 1.07/1.19 (op(e0, e1) = e2),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1993, 4580, 4400, 4396])).
% 1.07/1.19 tff(4582,plain,
% 1.07/1.19 (op(e0, op(e2, e3)) = op(e1, e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4388, 4581, 4374])).
% 1.07/1.19 tff(4583,plain,
% 1.07/1.19 ((op(e0, op(e2, e3)) = e0) <=> (op(e1, e3) = op(e3, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4582, 4369])).
% 1.07/1.19 tff(4584,plain,
% 1.07/1.19 ((op(e1, e3) = op(e3, e3)) <=> (op(e0, op(e2, e3)) = e0)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4583])).
% 1.07/1.19 tff(4585,plain,
% 1.07/1.19 ((op(e1, e3) = op(e3, e3)) <=> (op(e0, e1) = e0)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4584, 4391])).
% 1.07/1.19 tff(4586,plain,
% 1.07/1.19 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e0, e1) = e0))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4585])).
% 1.07/1.19 tff(4587,plain,
% 1.07/1.19 (~(op(e0, e1) = e0)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[571, 4586])).
% 1.07/1.19 tff(4588,plain,
% 1.07/1.19 (op(e1, e1) = e0),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[292, 4587, 4381, 4373])).
% 1.07/1.19 tff(4589,plain,
% 1.07/1.19 (op(e3, e1) = e1),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[446, 4580, 2839, 4373])).
% 1.07/1.19 tff(4590,plain,
% 1.07/1.19 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4589])).
% 1.07/1.19 tff(4591,plain,
% 1.07/1.19 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4590])).
% 1.07/1.19 tff(4592,plain,
% 1.07/1.19 (~(op(e1, e1) = e1)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[945, 4591])).
% 1.07/1.19 tff(4593,plain,
% 1.07/1.19 (op(e1, e0) = e1),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[954, 4592, 87, 4423])).
% 1.07/1.19 tff(4594,plain,
% 1.07/1.19 (op(e1, op(e1, e0)) = op(e1, e1)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4593])).
% 1.07/1.19 tff(4595,plain,
% 1.07/1.19 (op(e1, op(e1, e0)) = e0),
% 1.07/1.19 inference(transitivity,[status(thm)],[4594, 4588])).
% 1.07/1.19 tff(4596,plain,
% 1.07/1.19 (op(e3, op(e1, e3)) = op(e3, e2)),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4324])).
% 1.07/1.19 tff(4597,plain,
% 1.07/1.19 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4576])).
% 1.07/1.19 tff(4598,plain,
% 1.07/1.19 (op(e3, op(e3, e2)) = e2),
% 1.07/1.19 inference(transitivity,[status(thm)],[4597, 4596, 4575])).
% 1.07/1.19 tff(4599,plain,
% 1.07/1.19 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.07/1.19 inference(unit_resolution,[status(thm)],[1904, 4598])).
% 1.07/1.19 tff(4600,plain,
% 1.07/1.19 (e1 = op(e2, e3)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4387])).
% 1.07/1.19 tff(4601,plain,
% 1.07/1.19 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e2, e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4600])).
% 1.07/1.19 tff(4602,plain,
% 1.07/1.19 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 1.07/1.19 inference(symmetry,[status(thm)],[4601])).
% 1.07/1.19 tff(4603,plain,
% 1.07/1.19 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4602])).
% 1.07/1.19 tff(4604,plain,
% 1.07/1.19 (~(op(e2, e2) = e1)),
% 1.07/1.19 inference(modus_ponens,[status(thm)],[515, 4603])).
% 1.07/1.19 tff(4605,plain,
% 1.07/1.19 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4376])).
% 1.07/1.19 tff(4606,plain,
% 1.07/1.19 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.07/1.19 inference(transitivity,[status(thm)],[4605, 502])).
% 1.07/1.19 tff(4607,plain,
% 1.07/1.19 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.07/1.19 inference(monotonicity,[status(thm)],[4606])).
% 1.07/1.19 tff(4608,plain,
% 1.07/1.19 (~(op(e2, e2) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[508, 4607])).
% 1.07/1.20 tff(4609,plain,
% 1.07/1.20 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4575])).
% 1.07/1.20 tff(4610,plain,
% 1.07/1.20 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4609])).
% 1.07/1.20 tff(4611,plain,
% 1.07/1.20 (~(op(e2, e2) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[1546, 4610])).
% 1.07/1.20 tff(4612,plain,
% 1.07/1.20 (op(e2, e2) = e0),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[524, 4611, 4608, 4604])).
% 1.07/1.20 tff(4613,plain,
% 1.07/1.20 (op(e2, e0) = e2),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[2088, 4611, 4382, 4396])).
% 1.07/1.20 tff(4614,plain,
% 1.07/1.20 (op(e2, op(e2, e0)) = op(e2, e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4613])).
% 1.07/1.20 tff(4615,plain,
% 1.07/1.20 (op(e2, op(e2, e0)) = e0),
% 1.07/1.20 inference(transitivity,[status(thm)],[4614, 4612])).
% 1.07/1.20 tff(4616,plain,
% 1.07/1.20 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[2653, 4615])).
% 1.07/1.20 tff(4617,plain,
% 1.07/1.20 (op(e3, op(e2, e3)) = op(e3, e1)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4387])).
% 1.07/1.20 tff(4618,plain,
% 1.07/1.20 (op(e3, e1) = op(e2, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4589, 4600])).
% 1.07/1.20 tff(4619,plain,
% 1.07/1.20 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4618])).
% 1.07/1.20 tff(4620,plain,
% 1.07/1.20 (op(e3, op(e3, e1)) = e1),
% 1.07/1.20 inference(transitivity,[status(thm)],[4619, 4617, 4589])).
% 1.07/1.20 tff(4621,plain,
% 1.07/1.20 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[2594, 4620])).
% 1.07/1.20 tff(4622,plain,
% 1.07/1.20 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4600])).
% 1.07/1.20 tff(4623,plain,
% 1.07/1.20 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4622])).
% 1.07/1.20 tff(4624,plain,
% 1.07/1.20 ((op(e3, e2) = op(e2, e3)) <=> (op(e1, e3) = op(e2, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4576])).
% 1.07/1.20 tff(4625,plain,
% 1.07/1.20 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e2) = op(e2, e3))),
% 1.07/1.20 inference(symmetry,[status(thm)],[4624])).
% 1.07/1.20 tff(4626,plain,
% 1.07/1.20 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4625, 4623])).
% 1.07/1.20 tff(4627,plain,
% 1.07/1.20 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e2) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4626])).
% 1.07/1.20 tff(4628,plain,
% 1.07/1.20 (~(op(e3, e2) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[118, 4627])).
% 1.07/1.20 tff(4629,plain,
% 1.07/1.20 (op(e0, e2) = e1),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1613, 4628, 4423, 4604])).
% 1.07/1.20 tff(4630,plain,
% 1.07/1.20 (op(e0, op(e1, e3)) = op(e0, e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4324])).
% 1.07/1.20 tff(4631,plain,
% 1.07/1.20 (op(e0, e1) = op(e1, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4581, 4374])).
% 1.07/1.20 tff(4632,plain,
% 1.07/1.20 (op(e0, op(e0, e1)) = op(e0, op(e1, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4631])).
% 1.07/1.20 tff(4633,plain,
% 1.07/1.20 (op(e0, op(e0, e1)) = e1),
% 1.07/1.20 inference(transitivity,[status(thm)],[4632, 4630, 4629])).
% 1.07/1.20 tff(4634,plain,
% 1.07/1.20 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[2449, 4633])).
% 1.07/1.20 tff(4635,plain,
% 1.07/1.20 (op(op(e2, e3), e3) = op(e1, e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4387])).
% 1.07/1.20 tff(4636,plain,
% 1.07/1.20 (op(op(e2, e3), e3) = e2),
% 1.07/1.20 inference(transitivity,[status(thm)],[4635, 4324])).
% 1.07/1.20 tff(4637,plain,
% 1.07/1.20 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1288, 4636])).
% 1.07/1.20 tff(4638,plain,
% 1.07/1.20 (op(e0, e2) = op(e2, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4629, 4600])).
% 1.07/1.20 tff(4639,plain,
% 1.07/1.20 (op(e0, op(e0, e2)) = op(e0, op(e2, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4638])).
% 1.07/1.20 tff(4640,plain,
% 1.07/1.20 (op(e0, op(e0, e2)) = e2),
% 1.07/1.20 inference(transitivity,[status(thm)],[4639, 4388, 4581])).
% 1.07/1.20 tff(4641,plain,
% 1.07/1.20 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1331, 4640])).
% 1.07/1.20 tff(4642,plain,
% 1.07/1.20 (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1459, 4641, 4637, 3342, 4438, 1304, 4634, 4435, 4621, 1926, 4616, 4599])).
% 1.07/1.20 tff(4643,plain,
% 1.07/1.20 (~(op(e1, op(e1, e0)) = e0)),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1836, 4642])).
% 1.07/1.20 tff(4644,plain,
% 1.07/1.20 ($false),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4643, 4595])).
% 1.07/1.20 tff(4645,plain,((op(e1, e3) = e0) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (op(e1, e3) = e1) | (op(e3, e1) = e3) | (op(e2, e3) = e2) | (op(e0, e3) = e2) | (op(e0, e3) = e0) | (op(e2, e0) = e3) | (op(e3, e0) = e2) | (op(e0, e2) = e3) | (op(e3, e2) = e3) | (~(op(op(e1, e3), e1) = e3)) | (op(e2, e3) = e3) | (op(e3, e3) = e3) | (op(e0, e3) = e1) | (op(e1, e3) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.20 tff(4646,plain,
% 1.07/1.20 (op(e1, e3) = e0),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4645, 4323, 1261, 4320, 4316, 4311, 4307, 4302, 4300, 4296, 4293, 4288, 4285, 3221, 4281, 4277, 121, 4271, 4267])).
% 1.07/1.20 tff(4647,plain,
% 1.07/1.20 (e0 = op(e1, e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4646])).
% 1.07/1.20 tff(4648,plain,
% 1.07/1.20 (op(e0, e1) = op(op(e1, e3), e1)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4647])).
% 1.07/1.20 tff(4649,plain,
% 1.07/1.20 (op(e0, e1) = e3),
% 1.07/1.20 inference(transitivity,[status(thm)],[4648, 3221])).
% 1.07/1.20 tff(4650,plain,
% 1.07/1.20 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4263])).
% 1.07/1.20 tff(4651,plain,
% 1.07/1.20 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4650])).
% 1.07/1.20 tff(4652,plain,
% 1.07/1.20 (~(op(e0, e1) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[818, 4651])).
% 1.07/1.20 tff(4653,plain,
% 1.07/1.20 ($false),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4652, 4649])).
% 1.07/1.20 tff(4654,plain,((op(e0, e3) = e1) | (~(op(e3, e0) = op(e0, e3))) | (op(e2, op(e0, e3)) = e2) | (op(e1, op(e0, e3)) = e1) | (op(e0, op(e0, e3)) = e0) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.20 tff(4655,plain,
% 1.07/1.20 (op(e0, e3) = e1),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4654, 648, 646, 644, 642, 640])).
% 1.07/1.20 tff(4656,plain,
% 1.07/1.20 (e1 = op(e0, e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4655])).
% 1.07/1.20 tff(4657,plain,
% 1.07/1.20 (op(e3, e1) = op(e3, op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4656])).
% 1.07/1.20 tff(4658,plain,
% 1.07/1.20 (op(e3, op(e0, e3)) = op(e3, e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4657])).
% 1.07/1.20 tff(4659,plain,
% 1.07/1.20 (op(e0, e1) = op(e0, op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4656])).
% 1.07/1.20 tff(4660,plain,
% 1.07/1.20 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4659])).
% 1.07/1.20 tff(4661,plain,
% 1.07/1.20 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4660])).
% 1.07/1.20 tff(4662,plain,
% 1.07/1.20 ((~(op(e0, op(e0, e3)) = e0)) <=> (~(op(e0, e1) = e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4661])).
% 1.07/1.20 tff(4663,plain,
% 1.07/1.20 (~(op(e0, e1) = e0)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[642, 4662])).
% 1.07/1.20 tff(4664,plain,
% 1.07/1.20 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1260, 644, 648, 646])).
% 1.07/1.20 tff(4665,plain,
% 1.07/1.20 ((op(e3, e1) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4657])).
% 1.07/1.20 tff(4666,plain,
% 1.07/1.20 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e1) = e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4665])).
% 1.07/1.20 tff(4667,plain,
% 1.07/1.20 ((~(op(e3, op(e0, e3)) = e3)) <=> (~(op(e3, e1) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4666])).
% 1.07/1.20 tff(4668,plain,
% 1.07/1.20 (~(op(e3, e1) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[640, 4667])).
% 1.07/1.20 tff(4669,plain,
% 1.07/1.20 (op(e2, op(e0, e3)) = op(e2, e1)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4655])).
% 1.07/1.20 tff(4670,plain,
% 1.07/1.20 (op(e2, e1) = op(e2, op(e0, e3))),
% 1.07/1.20 inference(symmetry,[status(thm)],[4669])).
% 1.07/1.20 tff(4671,plain,
% 1.07/1.20 ((op(e2, e1) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4670])).
% 1.07/1.20 tff(4672,plain,
% 1.07/1.20 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e1) = e2)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4671])).
% 1.07/1.20 tff(4673,plain,
% 1.07/1.20 ((~(op(e2, op(e0, e3)) = e2)) <=> (~(op(e2, e1) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4672])).
% 1.07/1.20 tff(4674,plain,
% 1.07/1.20 (~(op(e2, e1) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[646, 4673])).
% 1.07/1.20 tff(4675,plain,
% 1.07/1.20 (op(e1, e1) = op(e1, op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4656])).
% 1.07/1.20 tff(4676,plain,
% 1.07/1.20 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4675])).
% 1.07/1.20 tff(4677,plain,
% 1.07/1.20 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e1) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4676])).
% 1.07/1.20 tff(4678,plain,
% 1.07/1.20 ((~(op(e1, op(e0, e3)) = e1)) <=> (~(op(e1, e1) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4677])).
% 1.07/1.20 tff(4679,plain,
% 1.07/1.20 (~(op(e1, e1) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[644, 4678])).
% 1.07/1.20 tff(4680,plain,
% 1.07/1.20 ((op(e0, e2) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e2))),
% 1.07/1.20 inference(commutativity,[status(thm)],[])).
% 1.07/1.20 tff(4681,plain,
% 1.07/1.20 (e1 = op(e0, e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[19])).
% 1.07/1.20 tff(4682,plain,
% 1.07/1.20 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4683,plain,
% 1.07/1.20 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4682])).
% 1.07/1.20 tff(4684,plain,
% 1.07/1.20 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4683])).
% 1.07/1.20 tff(4685,plain,
% 1.07/1.20 (~(op(e0, e1) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[818, 4684])).
% 1.07/1.20 tff(4686,plain,
% 1.07/1.20 (e1 = op(e3, e0)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4681, 467])).
% 1.07/1.20 tff(4687,plain,
% 1.07/1.20 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4686])).
% 1.07/1.20 tff(4688,plain,
% 1.07/1.20 ((op(e3, e1) = e1) <=> (op(e3, e0) = op(e3, e1))),
% 1.07/1.20 inference(transitivity,[status(thm)],[4687, 881])).
% 1.07/1.20 tff(4689,plain,
% 1.07/1.20 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4688])).
% 1.07/1.20 tff(4690,plain,
% 1.07/1.20 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4689])).
% 1.07/1.20 tff(4691,plain,
% 1.07/1.20 (~(op(e3, e1) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[580, 4690])).
% 1.07/1.20 tff(4692,plain,
% 1.07/1.20 (op(e2, e1) = e1),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1252, 1266, 4691, 4685])).
% 1.07/1.20 tff(4693,plain,
% 1.07/1.20 (op(e2, e1) = op(e0, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4692, 4681])).
% 1.07/1.20 tff(4694,plain,
% 1.07/1.20 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4693])).
% 1.07/1.20 tff(4695,plain,
% 1.07/1.20 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4694])).
% 1.07/1.20 tff(4696,plain,
% 1.07/1.20 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4695])).
% 1.07/1.20 tff(4697,plain,
% 1.07/1.20 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4698,plain,
% 1.07/1.20 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4697])).
% 1.07/1.20 tff(4699,plain,
% 1.07/1.20 (~(op(e0, e3) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[303, 4698])).
% 1.07/1.20 tff(4700,plain,
% 1.07/1.20 (~(op(e2, e1) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[4699, 4696])).
% 1.07/1.20 tff(4701,plain,
% 1.07/1.20 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e3, e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4686])).
% 1.07/1.20 tff(4702,plain,
% 1.07/1.20 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4701])).
% 1.07/1.20 tff(4703,plain,
% 1.07/1.20 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4702])).
% 1.07/1.20 tff(4704,plain,
% 1.07/1.20 (~(op(e1, e0) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[410, 4703])).
% 1.07/1.20 tff(4705,plain,
% 1.07/1.20 ((op(e1, e3) = e1) <=> (op(e1, e3) = op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4706,plain,
% 1.07/1.20 ((op(e1, e3) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.07/1.20 inference(transitivity,[status(thm)],[4705, 654])).
% 1.07/1.20 tff(4707,plain,
% 1.07/1.20 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4706])).
% 1.07/1.20 tff(4708,plain,
% 1.07/1.20 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4707])).
% 1.07/1.20 tff(4709,plain,
% 1.07/1.20 (~(op(e1, e3) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[64, 4708])).
% 1.07/1.20 tff(4710,plain,
% 1.07/1.20 (op(e1, e2) = e1),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[954, 1266, 4709, 4704])).
% 1.07/1.20 tff(4711,plain,
% 1.07/1.20 (op(e1, e2) = op(e0, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4710, 4681])).
% 1.07/1.20 tff(4712,plain,
% 1.07/1.20 ((op(e1, e2) = e2) <=> (op(e0, e3) = e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4711])).
% 1.07/1.20 tff(4713,plain,
% 1.07/1.20 ((op(e0, e3) = e2) <=> (op(e1, e2) = e2)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4712])).
% 1.07/1.20 tff(4714,plain,
% 1.07/1.20 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e2) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4713])).
% 1.07/1.20 tff(4715,plain,
% 1.07/1.20 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4716,plain,
% 1.07/1.20 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4715])).
% 1.07/1.20 tff(4717,plain,
% 1.07/1.20 (~(op(e0, e3) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[708, 4716])).
% 1.07/1.20 tff(4718,plain,
% 1.07/1.20 (~(op(e1, e2) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[4717, 4714])).
% 1.07/1.20 tff(4719,plain,
% 1.07/1.20 ((op(e2, e1) = e0) <=> (op(e0, e3) = e0)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4693])).
% 1.07/1.20 tff(4720,plain,
% 1.07/1.20 ((op(e0, e3) = e0) <=> (op(e2, e1) = e0)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4719])).
% 1.07/1.20 tff(4721,plain,
% 1.07/1.20 ((~(op(e0, e3) = e0)) <=> (~(op(e2, e1) = e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4720])).
% 1.07/1.20 tff(4722,plain,
% 1.07/1.20 ((e0 = e1) <=> (e0 = op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4723,plain,
% 1.07/1.20 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4722, 1079])).
% 1.07/1.20 tff(4724,plain,
% 1.07/1.20 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4723])).
% 1.07/1.20 tff(4725,plain,
% 1.07/1.20 (~(op(e0, e3) = e0)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[26, 4724])).
% 1.07/1.20 tff(4726,plain,
% 1.07/1.20 (~(op(e2, e1) = e0)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[4725, 4721])).
% 1.07/1.20 tff(4727,plain,
% 1.07/1.20 (op(e3, e1) = e0),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[292, 2639, 3849, 4726])).
% 1.07/1.20 tff(4728,plain,
% 1.07/1.20 (op(e1, e0) = op(op(e0, e3), e0)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4729,plain,
% 1.07/1.20 (op(op(e0, e3), e0) = op(e1, e0)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4728])).
% 1.07/1.20 tff(4730,plain,
% 1.07/1.20 (op(e1, op(e1, e3)) = op(op(e0, e3), e0)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681, 1219])).
% 1.07/1.20 tff(4731,assumption,(op(e3, e1) = e0), introduced(assumption)).
% 1.07/1.20 tff(4732,plain,
% 1.07/1.20 (op(e3, e1) = op(e1, e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4731, 2909])).
% 1.07/1.20 tff(4733,plain,
% 1.07/1.20 (op(e1, op(e3, e1)) = op(e1, op(e1, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4732])).
% 1.07/1.20 tff(4734,plain,
% 1.07/1.20 (e0 = op(e3, e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4731])).
% 1.07/1.20 tff(4735,plain,
% 1.07/1.20 (op(op(e0, e3), e3) = op(e1, e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[19])).
% 1.07/1.20 tff(4736,plain,
% 1.07/1.20 (op(e1, e1) = e3),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[1730, 2527, 3271, 2839])).
% 1.07/1.20 tff(4737,plain,
% 1.07/1.20 (op(e1, op(e1, e1)) = op(op(e0, e3), e3)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681, 4736])).
% 1.07/1.20 tff(4738,plain,
% 1.07/1.20 (op(e1, op(e1, e1)) = op(e3, e1)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4737, 4735, 1219, 4734])).
% 1.07/1.20 tff(4739,plain,
% 1.07/1.20 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e3, e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4738])).
% 1.07/1.20 tff(4740,plain,
% 1.07/1.20 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4739, 4733, 4730, 4729])).
% 1.07/1.20 tff(4741,plain,
% 1.07/1.20 (op(e0, e1) = e2),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[829, 2527, 4685, 3849])).
% 1.07/1.20 tff(4742,plain,
% 1.07/1.20 (e2 = op(e0, e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4741])).
% 1.07/1.20 tff(4743,plain,
% 1.07/1.20 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e0, e1) = op(e1, e0))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4742, 4740])).
% 1.07/1.20 tff(4744,plain,
% 1.07/1.20 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = op(e0, e1))),
% 1.07/1.20 inference(transitivity,[status(thm)],[4743, 595])).
% 1.07/1.20 tff(4745,plain,
% 1.07/1.20 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e1, op(e1, op(e1, e1))))),
% 1.07/1.20 inference(symmetry,[status(thm)],[4744])).
% 1.07/1.20 tff(4746,plain,
% 1.07/1.20 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4742])).
% 1.07/1.20 tff(4747,plain,
% 1.07/1.20 ((op(e1, e0) = e2) <=> (e2 = op(e1, op(e1, op(e1, e1))))),
% 1.07/1.20 inference(transitivity,[status(thm)],[4746, 4745])).
% 1.07/1.20 tff(4748,plain,
% 1.07/1.20 ((e0 = e2) <=> (op(e1, e3) = e2)),
% 1.07/1.20 inference(monotonicity,[status(thm)],[2909])).
% 1.07/1.20 tff(4749,plain,
% 1.07/1.20 ((~(e0 = e2)) <=> (~(op(e1, e3) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4748])).
% 1.07/1.20 tff(4750,plain,
% 1.07/1.20 (~(op(e1, e3) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[14, 4749])).
% 1.07/1.20 tff(4751,plain,
% 1.07/1.20 ((op(e0, e1) = op(e1, e1)) <=> (e2 = op(e1, e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4741])).
% 1.07/1.20 tff(4752,plain,
% 1.07/1.20 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4751, 2166])).
% 1.07/1.20 tff(4753,plain,
% 1.07/1.20 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4752])).
% 1.07/1.20 tff(4754,plain,
% 1.07/1.20 (~(op(e1, e1) = e2)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[792, 4753])).
% 1.07/1.20 tff(4755,plain,
% 1.07/1.20 (op(e1, e0) = e2),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[2285, 4754, 3785, 4750])).
% 1.07/1.20 tff(4756,plain,
% 1.07/1.20 (e2 = op(e1, op(e1, op(e1, e1)))),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[4755, 4747])).
% 1.07/1.20 tff(4757,plain,
% 1.07/1.20 (e3 = op(e1, e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[4736, 1740])).
% 1.07/1.20 tff(4758,plain,
% 1.07/1.20 (op(op(e0, e3), e3) = op(e1, op(e1, e1))),
% 1.07/1.20 inference(symmetry,[status(thm)],[4737])).
% 1.07/1.20 tff(4759,plain,
% 1.07/1.20 (op(e1, e3) = op(op(e0, e3), e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4735])).
% 1.07/1.20 tff(4760,plain,
% 1.07/1.20 (e0 = op(e1, op(e1, e1))),
% 1.07/1.20 inference(transitivity,[status(thm)],[2909, 4759, 4758])).
% 1.07/1.20 tff(4761,plain,
% 1.07/1.20 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[3009, 4760, 4757])).
% 1.07/1.20 tff(4762,plain,
% 1.07/1.20 ($false),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4761, 4756])).
% 1.07/1.20 tff(4763,plain,((op(e0, e1) = e3) | (~(op(e1, e3) = e0)) | (~(op(e3, e1) = e0)) | (~(op(e0, e3) = e1)) | (op(e1, e2) = e2) | (op(e2, e1) = e3) | (op(e3, e1) = e3) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.20 tff(4764,plain,
% 1.07/1.20 (op(e0, e1) = e3),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[4763, 1219, 4727, 19, 4718, 4700, 2839, 3849])).
% 1.07/1.20 tff(4765,plain,
% 1.07/1.20 (e3 = op(e0, e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4764])).
% 1.07/1.20 tff(4766,plain,
% 1.07/1.20 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e0, e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4765])).
% 1.07/1.20 tff(4767,plain,
% 1.07/1.20 ((op(e0, e2) = e3) <=> (op(e0, e1) = op(e0, e2))),
% 1.07/1.20 inference(transitivity,[status(thm)],[4766, 4680])).
% 1.07/1.20 tff(4768,plain,
% 1.07/1.20 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4767])).
% 1.07/1.20 tff(4769,plain,
% 1.07/1.20 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4768])).
% 1.07/1.20 tff(4770,plain,
% 1.07/1.20 (~(op(e0, e2) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[2102, 4769])).
% 1.07/1.20 tff(4771,plain,
% 1.07/1.20 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.20 tff(4772,plain,
% 1.07/1.20 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.07/1.20 inference(symmetry,[status(thm)],[4771])).
% 1.07/1.20 tff(4773,plain,
% 1.07/1.20 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4772])).
% 1.07/1.20 tff(4774,plain,
% 1.07/1.20 (~(op(e0, e2) = e1)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[918, 4773])).
% 1.07/1.20 tff(4775,plain,
% 1.07/1.20 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4764])).
% 1.07/1.20 tff(4776,plain,
% 1.07/1.20 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 1.07/1.20 inference(transitivity,[status(thm)],[4775, 1112])).
% 1.07/1.20 tff(4777,plain,
% 1.07/1.20 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 1.07/1.20 inference(monotonicity,[status(thm)],[4776])).
% 1.07/1.20 tff(4778,plain,
% 1.07/1.20 (~(op(e1, e1) = e3)),
% 1.07/1.20 inference(modus_ponens,[status(thm)],[792, 4777])).
% 1.07/1.20 tff(4779,plain,
% 1.07/1.20 (op(e1, e1) = e2),
% 1.07/1.20 inference(unit_resolution,[status(thm)],[630, 4778, 1266, 2639])).
% 1.07/1.21 tff(4780,plain,
% 1.07/1.21 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[2909])).
% 1.07/1.21 tff(4781,plain,
% 1.07/1.21 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4780])).
% 1.07/1.21 tff(4782,plain,
% 1.07/1.21 (~(op(e1, e3) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[181, 4781])).
% 1.07/1.21 tff(4783,plain,
% 1.07/1.21 ((op(e1, e2) = e3) <=> (op(e0, e3) = e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4711])).
% 1.07/1.21 tff(4784,plain,
% 1.07/1.21 ((op(e0, e3) = e3) <=> (op(e1, e2) = e3)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4783])).
% 1.07/1.21 tff(4785,plain,
% 1.07/1.21 ((~(op(e0, e3) = e3)) <=> (~(op(e1, e2) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4784])).
% 1.07/1.21 tff(4786,plain,
% 1.07/1.21 (~(op(e1, e2) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[4699, 4785])).
% 1.07/1.21 tff(4787,plain,
% 1.07/1.21 (op(e1, e0) = e3),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[247, 4778, 4786, 4782])).
% 1.07/1.21 tff(4788,plain,
% 1.07/1.21 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4787])).
% 1.07/1.21 tff(4789,plain,
% 1.07/1.21 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4788, 660])).
% 1.07/1.21 tff(4790,plain,
% 1.07/1.21 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4789])).
% 1.07/1.21 tff(4791,plain,
% 1.07/1.21 (~(op(e2, e0) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[756, 4790])).
% 1.07/1.21 tff(4792,plain,
% 1.07/1.21 ((e1 = e3) <=> (op(e3, e0) = e3)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4697, 663])).
% 1.07/1.21 tff(4793,plain,
% 1.07/1.21 ((~(e1 = e3)) <=> (~(op(e3, e0) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4792])).
% 1.07/1.21 tff(4794,plain,
% 1.07/1.21 (~(op(e3, e0) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[303, 4793])).
% 1.07/1.21 tff(4795,plain,
% 1.07/1.21 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4686])).
% 1.07/1.21 tff(4796,plain,
% 1.07/1.21 ((op(e3, e2) = e1) <=> (op(e3, e0) = op(e3, e2))),
% 1.07/1.21 inference(transitivity,[status(thm)],[4795, 1123])).
% 1.07/1.21 tff(4797,plain,
% 1.07/1.21 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4796])).
% 1.07/1.21 tff(4798,plain,
% 1.07/1.21 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4797])).
% 1.07/1.21 tff(4799,plain,
% 1.07/1.21 (~(op(e3, e2) = e1)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[1133, 4798])).
% 1.07/1.21 tff(4800,plain,
% 1.07/1.21 ((op(e1, e2) = e0) <=> (op(e0, e3) = e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4711])).
% 1.07/1.21 tff(4801,plain,
% 1.07/1.21 ((op(e0, e3) = e0) <=> (op(e1, e2) = e0)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4800])).
% 1.07/1.21 tff(4802,plain,
% 1.07/1.21 ((~(op(e0, e3) = e0)) <=> (~(op(e1, e2) = e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4801])).
% 1.07/1.21 tff(4803,plain,
% 1.07/1.21 (~(op(e1, e2) = e0)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[4725, 4802])).
% 1.07/1.21 tff(4804,plain,
% 1.07/1.21 (op(e3, op(e0, e3)) = op(e3, op(e3, e0))),
% 1.07/1.21 inference(symmetry,[status(thm)],[1343])).
% 1.07/1.21 tff(4805,plain,
% 1.07/1.21 (op(e3, e1) = op(e3, op(e0, e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.21 tff(4806,plain,
% 1.07/1.21 (op(e3, e1) = op(e3, op(e3, e0))),
% 1.07/1.21 inference(transitivity,[status(thm)],[4805, 4804])).
% 1.07/1.21 tff(4807,plain,
% 1.07/1.21 ((op(e3, e1) = e0) <=> (op(e3, op(e3, e0)) = e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4806])).
% 1.07/1.21 tff(4808,plain,
% 1.07/1.21 (op(e3, op(e3, e0)) = e0),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[4727, 4807])).
% 1.07/1.21 tff(4809,plain,
% 1.07/1.21 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1345, 4808])).
% 1.07/1.21 tff(4810,plain,
% 1.07/1.21 (op(e3, op(e3, e1)) = op(e3, e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4731])).
% 1.07/1.21 tff(4811,plain,
% 1.07/1.21 (op(e3, op(e3, e1)) = e1),
% 1.07/1.21 inference(transitivity,[status(thm)],[4810, 466, 19])).
% 1.07/1.21 tff(4812,plain,
% 1.07/1.21 ($false),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[3815, 4811])).
% 1.07/1.21 tff(4813,plain,((~(op(e3, e1) = e0)) | (op(e3, op(e3, e1)) = e1) | (~(op(e0, e3) = e1)) | (~(op(e3, e0) = op(e0, e3)))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.21 tff(4814,plain,
% 1.07/1.21 (op(e3, op(e3, e1)) = e1),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4813, 4727, 19, 466])).
% 1.07/1.21 tff(4815,plain,
% 1.07/1.21 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2594, 4814])).
% 1.07/1.21 tff(4816,plain,
% 1.07/1.21 (op(e2, op(e0, e3)) = op(e2, e1)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[19])).
% 1.07/1.21 tff(4817,plain,
% 1.07/1.21 (op(e2, op(e2, e1)) = op(e2, op(e0, e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4693])).
% 1.07/1.21 tff(4818,plain,
% 1.07/1.21 (op(e2, op(e2, e1)) = e1),
% 1.07/1.21 inference(transitivity,[status(thm)],[4817, 4816, 4692])).
% 1.07/1.21 tff(4819,plain,
% 1.07/1.21 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1355, 4818])).
% 1.07/1.21 tff(4820,plain,
% 1.07/1.21 (op(op(e1, e3), e3) = e1),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1223, 1219, 19])).
% 1.07/1.21 tff(4821,plain,
% 1.07/1.21 (op(e3, e1) = op(e1, e3)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4727, 2909])).
% 1.07/1.21 tff(4822,plain,
% 1.07/1.21 (op(op(e3, e1), e3) = op(op(e1, e3), e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4821])).
% 1.07/1.21 tff(4823,plain,
% 1.07/1.21 (e0 = op(e3, e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4727])).
% 1.07/1.21 tff(4824,plain,
% 1.07/1.21 (op(e0, op(e0, e1)) = op(op(e3, e1), e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4823, 4764])).
% 1.07/1.21 tff(4825,plain,
% 1.07/1.21 (op(e0, op(e0, e1)) = e1),
% 1.07/1.21 inference(transitivity,[status(thm)],[4824, 4822, 4820])).
% 1.07/1.21 tff(4826,plain,
% 1.07/1.21 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2449, 4825])).
% 1.07/1.21 tff(4827,plain,
% 1.07/1.21 (op(op(e1, e2), e2) = op(e1, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4710])).
% 1.07/1.21 tff(4828,plain,
% 1.07/1.21 (op(op(e1, e2), e2) = e1),
% 1.07/1.21 inference(transitivity,[status(thm)],[4827, 4710])).
% 1.07/1.21 tff(4829,plain,
% 1.07/1.21 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1335, 4828])).
% 1.07/1.21 tff(4830,plain,
% 1.07/1.21 ((op(e1, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4759])).
% 1.07/1.21 tff(4831,plain,
% 1.07/1.21 (op(op(e0, e3), e3) = e0),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[1219, 4830])).
% 1.07/1.21 tff(4832,plain,
% 1.07/1.21 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1361, 4831])).
% 1.07/1.21 tff(4833,plain,
% 1.07/1.21 (op(e1, op(e0, e1)) = op(op(e0, e3), e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4681, 4764])).
% 1.07/1.21 tff(4834,plain,
% 1.07/1.21 (op(e1, e0) = op(e0, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4787, 4765])).
% 1.07/1.21 tff(4835,plain,
% 1.07/1.21 (op(e1, op(e1, e0)) = op(e1, op(e0, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4834])).
% 1.07/1.21 tff(4836,plain,
% 1.07/1.21 (op(e1, op(e1, e0)) = e0),
% 1.07/1.21 inference(transitivity,[status(thm)],[4835, 4833, 4735, 1219])).
% 1.07/1.21 tff(4837,plain,
% 1.07/1.21 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1836, 4836])).
% 1.07/1.21 tff(4838,plain,
% 1.07/1.21 ((e2 = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.07/1.21 inference(commutativity,[status(thm)],[])).
% 1.07/1.21 tff(4839,assumption,(op(e0, e1) = e3), introduced(assumption)).
% 1.07/1.21 tff(4840,plain,
% 1.07/1.21 (e3 = op(e0, e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4839])).
% 1.07/1.21 tff(4841,plain,
% 1.07/1.21 ((e2 = e3) <=> (e2 = op(e0, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4840])).
% 1.07/1.21 tff(4842,plain,
% 1.07/1.21 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4841, 4838])).
% 1.07/1.21 tff(4843,plain,
% 1.07/1.21 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4842])).
% 1.07/1.21 tff(4844,plain,
% 1.07/1.21 (~(op(e0, e1) = e2)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[1321, 4843])).
% 1.07/1.21 tff(4845,plain,
% 1.07/1.21 ((op(e3, e2) = op(e3, e1)) <=> (op(e3, e1) = op(e3, e2))),
% 1.07/1.21 inference(commutativity,[status(thm)],[])).
% 1.07/1.21 tff(4846,plain,
% 1.07/1.21 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4734])).
% 1.07/1.21 tff(4847,plain,
% 1.07/1.21 ((op(e3, e2) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 1.07/1.21 inference(transitivity,[status(thm)],[4846, 4845])).
% 1.07/1.21 tff(4848,plain,
% 1.07/1.21 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4847])).
% 1.07/1.21 tff(4849,plain,
% 1.07/1.21 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4848])).
% 1.07/1.21 tff(4850,plain,
% 1.07/1.21 (~(op(e3, e2) = e0)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[3429, 4849])).
% 1.07/1.21 tff(4851,plain,
% 1.07/1.21 (op(e3, e2) = e2),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1898, 1890, 930, 4850])).
% 1.07/1.21 tff(4852,plain,
% 1.07/1.21 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4851])).
% 1.07/1.21 tff(4853,plain,
% 1.07/1.21 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4852])).
% 1.07/1.21 tff(4854,plain,
% 1.07/1.21 (~(op(e0, e2) = e2)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[1467, 4853])).
% 1.07/1.21 tff(4855,plain,
% 1.07/1.21 (op(e0, e0) = e2),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[3652, 4854, 79, 4844])).
% 1.07/1.21 tff(4856,plain,
% 1.07/1.21 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e0, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4840])).
% 1.07/1.21 tff(4857,plain,
% 1.07/1.21 ((op(e0, e2) = e3) <=> (op(e0, e1) = op(e0, e2))),
% 1.07/1.21 inference(transitivity,[status(thm)],[4856, 4680])).
% 1.07/1.21 tff(4858,plain,
% 1.07/1.21 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4857])).
% 1.07/1.21 tff(4859,plain,
% 1.07/1.21 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4858])).
% 1.07/1.21 tff(4860,plain,
% 1.07/1.21 (~(op(e0, e2) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[2102, 4859])).
% 1.07/1.21 tff(4861,plain,
% 1.07/1.21 (op(e2, e2) = e3),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2111, 1890, 75, 4860])).
% 1.07/1.21 tff(4862,plain,
% 1.07/1.21 (op(e2, e2) = op(e0, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4861, 4840])).
% 1.07/1.21 tff(4863,plain,
% 1.07/1.21 ((op(e2, e2) = e0) <=> (op(e0, e1) = op(e3, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4862, 4734])).
% 1.07/1.21 tff(4864,plain,
% 1.07/1.21 ((op(e0, e1) = op(e3, e1)) <=> (op(e2, e2) = e0)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4863])).
% 1.07/1.21 tff(4865,plain,
% 1.07/1.21 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e2, e2) = e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4864])).
% 1.07/1.21 tff(4866,plain,
% 1.07/1.21 (~(op(e2, e2) = e0)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[3046, 4865])).
% 1.07/1.21 tff(4867,plain,
% 1.07/1.21 (op(e0, e2) = e0),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[973, 4866, 1947, 4850])).
% 1.07/1.21 tff(4868,plain,
% 1.07/1.21 (op(e0, op(e0, e2)) = op(e0, e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4867])).
% 1.07/1.21 tff(4869,plain,
% 1.07/1.21 (op(e0, op(e0, e2)) = e2),
% 1.07/1.21 inference(transitivity,[status(thm)],[4868, 4855])).
% 1.07/1.21 tff(4870,plain,
% 1.07/1.21 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1331, 4869])).
% 1.07/1.21 tff(4871,plain,
% 1.07/1.21 (op(e3, op(e1, e1)) = op(e3, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[2891])).
% 1.07/1.21 tff(4872,plain,
% 1.07/1.21 (e2 = op(e1, e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[2891])).
% 1.07/1.21 tff(4873,plain,
% 1.07/1.21 (op(e3, e2) = op(e1, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4851, 4872])).
% 1.07/1.21 tff(4874,plain,
% 1.07/1.21 (op(e3, op(e3, e2)) = op(e3, op(e1, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4873])).
% 1.07/1.21 tff(4875,plain,
% 1.07/1.21 (op(e3, op(e3, e2)) = e2),
% 1.07/1.21 inference(transitivity,[status(thm)],[4874, 4871, 4851])).
% 1.07/1.21 tff(4876,plain,
% 1.07/1.21 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1904, 4875])).
% 1.07/1.21 tff(4877,plain,
% 1.07/1.21 (op(e3, e3) = e3),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[422, 1890, 2410, 2839])).
% 1.07/1.21 tff(4878,plain,
% 1.07/1.21 (op(e3, e3) = op(e0, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4877, 4840])).
% 1.07/1.21 tff(4879,plain,
% 1.07/1.21 ((op(e3, e3) = e2) <=> (op(e0, e1) = op(e1, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4878, 4872])).
% 1.07/1.21 tff(4880,plain,
% 1.07/1.21 ((op(e0, e1) = op(e1, e1)) <=> (op(e3, e3) = e2)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4879])).
% 1.07/1.21 tff(4881,plain,
% 1.07/1.21 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e3, e3) = e2))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4880])).
% 1.07/1.21 tff(4882,plain,
% 1.07/1.21 (~(op(e3, e3) = e2)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[792, 4881])).
% 1.07/1.21 tff(4883,plain,
% 1.07/1.21 (op(e2, e3) = e2),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2786, 4882, 79, 4750])).
% 1.07/1.21 tff(4884,plain,
% 1.07/1.21 (op(e2, op(e2, e3)) = op(e2, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4883])).
% 1.07/1.21 tff(4885,plain,
% 1.07/1.21 (op(e2, op(e2, e3)) = e3),
% 1.07/1.21 inference(transitivity,[status(thm)],[4884, 4861])).
% 1.07/1.21 tff(4886,plain,
% 1.07/1.21 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2344, 4885])).
% 1.07/1.21 tff(4887,plain,
% 1.07/1.21 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e1, e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[2909])).
% 1.07/1.21 tff(4888,plain,
% 1.07/1.21 ((op(e2, e3) = e0) <=> (op(e1, e3) = op(e2, e3))),
% 1.07/1.21 inference(transitivity,[status(thm)],[4887, 1687])).
% 1.07/1.21 tff(4889,plain,
% 1.07/1.21 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4888])).
% 1.07/1.21 tff(4890,plain,
% 1.07/1.21 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4889])).
% 1.07/1.21 tff(4891,plain,
% 1.07/1.21 (~(op(e2, e3) = e0)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[118, 4890])).
% 1.07/1.21 tff(4892,plain,
% 1.07/1.21 (op(e2, e0) = e0),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2311, 4866, 2559, 4891])).
% 1.07/1.21 tff(4893,plain,
% 1.07/1.21 (op(e2, op(e1, e3)) = op(e2, e0)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[1219])).
% 1.07/1.21 tff(4894,plain,
% 1.07/1.21 (op(e2, op(e3, e1)) = op(e2, op(e1, e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4732])).
% 1.07/1.21 tff(4895,plain,
% 1.07/1.21 (op(e2, e0) = op(e3, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4892, 4734])).
% 1.07/1.21 tff(4896,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = op(e2, op(e3, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4895])).
% 1.07/1.21 tff(4897,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = e0),
% 1.07/1.21 inference(transitivity,[status(thm)],[4896, 4894, 4893, 4892])).
% 1.07/1.21 tff(4898,plain,
% 1.07/1.21 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2653, 4897])).
% 1.07/1.21 tff(4899,plain,
% 1.07/1.21 ($false),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1459, 4898, 4886, 1357, 3342, 1358, 1304, 4549, 1936, 1275, 1926, 4876, 4870])).
% 1.07/1.21 tff(4900,plain,((op(e3, e2) = e3) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~(op(e1, e3) = e0)) | (~(op(e3, e1) = e0)) | (op(e0, e3) = e2) | (op(e1, e2) = e0) | (op(e2, e1) = e0) | (~(op(e1, e1) = e2)) | (~(op(e0, e1) = e3)) | (op(e3, e2) = e1) | (op(e1, e2) = e3) | (op(e3, e0) = e3) | (op(e3, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.21 tff(4901,plain,
% 1.07/1.21 (op(e3, e2) = e3),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4900, 4837, 4832, 4829, 1304, 4826, 4819, 4815, 4809, 1219, 4727, 4717, 4803, 4726, 4779, 4764, 4799, 4786, 4794, 2839])).
% 1.07/1.21 tff(4902,plain,
% 1.07/1.21 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4901])).
% 1.07/1.21 tff(4903,plain,
% 1.07/1.21 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4902])).
% 1.07/1.21 tff(4904,plain,
% 1.07/1.21 (~(op(e2, e2) = e3)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[1546, 4903])).
% 1.07/1.21 tff(4905,plain,
% 1.07/1.21 (op(e2, e3) = e3),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1559, 4904, 4700, 4791])).
% 1.07/1.21 tff(4906,plain,
% 1.07/1.21 (op(e2, op(e0, e1)) = op(e2, e3)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4764])).
% 1.07/1.21 tff(4907,plain,
% 1.07/1.21 (op(e2, e3) = op(e0, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4905, 4765])).
% 1.07/1.21 tff(4908,plain,
% 1.07/1.21 (op(e2, op(e2, e3)) = op(e2, op(e0, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4907])).
% 1.07/1.21 tff(4909,plain,
% 1.07/1.21 (op(e2, op(e2, e3)) = e3),
% 1.07/1.21 inference(transitivity,[status(thm)],[4908, 4906, 4905])).
% 1.07/1.21 tff(4910,plain,
% 1.07/1.21 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2344, 4909])).
% 1.07/1.21 tff(4911,plain,
% 1.07/1.21 (op(e3, op(e1, e1)) = op(e3, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4779])).
% 1.07/1.21 tff(4912,plain,
% 1.07/1.21 (e2 = op(e1, e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4779])).
% 1.07/1.21 tff(4913,plain,
% 1.07/1.21 (op(op(e3, e2), e2) = op(e3, op(e1, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4901, 4912])).
% 1.07/1.21 tff(4914,plain,
% 1.07/1.21 (op(op(e3, e2), e2) = e3),
% 1.07/1.21 inference(transitivity,[status(thm)],[4913, 4911, 4901])).
% 1.07/1.21 tff(4915,plain,
% 1.07/1.21 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1339, 4914])).
% 1.07/1.21 tff(4916,plain,
% 1.07/1.21 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e3, e0))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4686])).
% 1.07/1.21 tff(4917,plain,
% 1.07/1.21 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e1)),
% 1.07/1.21 inference(symmetry,[status(thm)],[4916])).
% 1.07/1.21 tff(4918,plain,
% 1.07/1.21 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4917])).
% 1.07/1.21 tff(4919,plain,
% 1.07/1.21 (~(op(e2, e0) = e1)),
% 1.07/1.21 inference(modus_ponens,[status(thm)],[747, 4918])).
% 1.07/1.21 tff(4920,assumption,(~(op(e2, op(e2, e0)) = e0)), introduced(assumption)).
% 1.07/1.21 tff(4921,assumption,(op(e2, e0) = e0), introduced(assumption)).
% 1.07/1.21 tff(4922,plain,
% 1.07/1.21 (op(e2, e0) = op(e3, e1)),
% 1.07/1.21 inference(transitivity,[status(thm)],[4921, 4734])).
% 1.07/1.21 tff(4923,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = op(e2, op(e3, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4922])).
% 1.07/1.21 tff(4924,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = e0),
% 1.07/1.21 inference(transitivity,[status(thm)],[4923, 4894, 4893, 4921])).
% 1.07/1.21 tff(4925,plain,
% 1.07/1.21 ($false),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4920, 4924])).
% 1.07/1.21 tff(4926,plain,((~(op(e2, e0) = e0)) | (op(e2, op(e2, e0)) = e0) | (~(op(e1, e3) = e0)) | (~(op(e3, e1) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.21 tff(4927,plain,
% 1.07/1.21 (~(op(e2, e0) = e0)),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4926, 4920, 1219, 4731])).
% 1.07/1.21 tff(4928,plain,
% 1.07/1.21 (op(e2, e2) = e0),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2311, 4927, 2559, 4891])).
% 1.07/1.21 tff(4929,plain,
% 1.07/1.21 (op(e2, e0) = e2),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[765, 4927, 3272, 1349])).
% 1.07/1.21 tff(4930,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = op(e2, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4929])).
% 1.07/1.21 tff(4931,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = e0),
% 1.07/1.21 inference(transitivity,[status(thm)],[4930, 4928])).
% 1.07/1.21 tff(4932,plain,
% 1.07/1.21 ($false),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4920, 4931])).
% 1.07/1.21 tff(4933,plain,((op(e2, op(e2, e0)) = e0) | (op(e2, e0) = e3) | (op(e2, e0) = e1) | (op(e2, e1) = e0) | (~(op(e1, e3) = e0)) | (~(op(e3, e1) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.21 tff(4934,plain,
% 1.07/1.21 (op(e2, op(e2, e0)) = e0),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4933, 4791, 4919, 4726, 1219, 4727])).
% 1.07/1.21 tff(4935,plain,
% 1.07/1.21 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[2653, 4934])).
% 1.07/1.21 tff(4936,plain,
% 1.07/1.21 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1459, 4935, 4837, 4832, 4829, 1304, 4826, 4819, 4815, 4809, 4915, 4910])).
% 1.07/1.21 tff(4937,plain,
% 1.07/1.21 (~(op(op(e0, e2), e2) = e0)),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[1956, 4936])).
% 1.07/1.21 tff(4938,assumption,(op(e0, e2) = e0), introduced(assumption)).
% 1.07/1.21 tff(4939,plain,
% 1.07/1.21 (op(e0, op(e1, e1)) = op(e0, e2)),
% 1.07/1.21 inference(monotonicity,[status(thm)],[2891])).
% 1.07/1.21 tff(4940,plain,
% 1.07/1.21 (op(op(e0, e2), e2) = op(e0, op(e1, e1))),
% 1.07/1.21 inference(monotonicity,[status(thm)],[4938, 4872])).
% 1.07/1.21 tff(4941,plain,
% 1.07/1.21 (op(op(e0, e2), e2) = e0),
% 1.07/1.21 inference(transitivity,[status(thm)],[4940, 4939, 4938])).
% 1.07/1.21 tff(4942,assumption,(~(op(op(e0, e2), e2) = e0)), introduced(assumption)).
% 1.07/1.21 tff(4943,plain,
% 1.07/1.21 ($false),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4942, 4941])).
% 1.07/1.21 tff(4944,plain,((~(op(e0, e2) = e0)) | (op(op(e0, e2), e2) = e0) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.21 tff(4945,plain,
% 1.07/1.21 (~(op(e0, e2) = e0)),
% 1.07/1.21 inference(unit_resolution,[status(thm)],[4944, 4937, 4779])).
% 1.07/1.21 tff(4946,plain,
% 1.07/1.21 (op(e0, e2) = e2),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2745, 4945, 4774, 4770])).
% 1.07/1.22 tff(4947,plain,
% 1.07/1.22 (op(e0, op(e1, e1)) = op(e0, e2)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4779])).
% 1.07/1.22 tff(4948,plain,
% 1.07/1.22 (op(e0, e2) = op(e1, e1)),
% 1.07/1.22 inference(transitivity,[status(thm)],[4946, 4912])).
% 1.07/1.22 tff(4949,plain,
% 1.07/1.22 (op(e0, op(e0, e2)) = op(e0, op(e1, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4948])).
% 1.07/1.22 tff(4950,plain,
% 1.07/1.22 (op(e0, op(e0, e2)) = e2),
% 1.07/1.22 inference(transitivity,[status(thm)],[4949, 4947, 4946])).
% 1.07/1.22 tff(4951,plain,
% 1.07/1.22 (~(op(e0, op(e0, e2)) = e2)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1331, 4936])).
% 1.07/1.22 tff(4952,plain,
% 1.07/1.22 ($false),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[4951, 4950])).
% 1.07/1.22 tff(4953,plain,((~(op(e1, e3) = e0)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e3, e1) = e3) | (~(op(e0, e3) = e1)) | (op(e1, e1) = e1) | (op(e0, e1) = e0) | (~(op(e3, e0) = op(e0, e3)))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.22 tff(4954,plain,
% 1.07/1.22 (~(op(e1, e3) = e0)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[4953, 4664, 4668, 4655, 4679, 4663, 648])).
% 1.07/1.22 tff(4955,plain,
% 1.07/1.22 (op(e2, e3) = e0),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1098, 80, 4725, 656])).
% 1.07/1.22 tff(4956,plain,
% 1.07/1.22 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4955])).
% 1.07/1.22 tff(4957,plain,
% 1.07/1.22 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4956])).
% 1.07/1.22 tff(4958,plain,
% 1.07/1.22 (~(op(e2, e2) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[515, 4957])).
% 1.07/1.22 tff(4959,plain,
% 1.07/1.22 ((e0 = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.07/1.22 inference(commutativity,[status(thm)],[])).
% 1.07/1.22 tff(4960,assumption,(op(e1, e1) = e3), introduced(assumption)).
% 1.07/1.22 tff(4961,plain,
% 1.07/1.22 ((op(e1, e1) = e0) <=> (e3 = e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4960])).
% 1.07/1.22 tff(4962,plain,
% 1.07/1.22 ((op(e1, e1) = e0) <=> (e0 = e3)),
% 1.07/1.22 inference(transitivity,[status(thm)],[4961, 159])).
% 1.07/1.22 tff(4963,plain,
% 1.07/1.22 ((e0 = e3) <=> (op(e1, e1) = e0)),
% 1.07/1.22 inference(symmetry,[status(thm)],[4962])).
% 1.07/1.22 tff(4964,plain,
% 1.07/1.22 ((~(e0 = e3)) <=> (~(op(e1, e1) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4963])).
% 1.07/1.22 tff(4965,plain,
% 1.07/1.22 (~(op(e1, e1) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[181, 4964])).
% 1.07/1.22 tff(4966,plain,
% 1.07/1.22 (op(e3, e1) = e0),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[292, 4965, 3849, 2559])).
% 1.07/1.22 tff(4967,plain,
% 1.07/1.22 ((op(e3, e1) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4966])).
% 1.07/1.22 tff(4968,plain,
% 1.07/1.22 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.07/1.22 inference(transitivity,[status(thm)],[4967, 4959])).
% 1.07/1.22 tff(4969,plain,
% 1.07/1.22 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4968])).
% 1.07/1.22 tff(4970,plain,
% 1.07/1.22 (~(op(e3, e2) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[3429, 4969])).
% 1.07/1.22 tff(4971,plain,
% 1.07/1.22 (e3 = op(e1, e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[4960])).
% 1.07/1.22 tff(4972,plain,
% 1.07/1.22 (op(e0, op(e0, e3)) = op(e0, e1)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[19])).
% 1.07/1.22 tff(4973,plain,
% 1.07/1.22 (op(e0, e1) = op(e0, op(e0, e3))),
% 1.07/1.22 inference(symmetry,[status(thm)],[4972])).
% 1.07/1.22 tff(4974,plain,
% 1.07/1.22 ((op(e0, e1) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4973])).
% 1.07/1.22 tff(4975,plain,
% 1.07/1.22 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e1) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[4974])).
% 1.07/1.22 tff(4976,plain,
% 1.07/1.22 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4972, 4971])).
% 1.07/1.22 tff(4977,plain,
% 1.07/1.22 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, op(e0, e3)) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[4976])).
% 1.07/1.22 tff(4978,plain,
% 1.07/1.22 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.07/1.22 inference(transitivity,[status(thm)],[4977, 4975])).
% 1.07/1.22 tff(4979,plain,
% 1.07/1.22 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4978])).
% 1.07/1.22 tff(4980,plain,
% 1.07/1.22 (~(op(e0, e1) = e3)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[792, 4979])).
% 1.07/1.22 tff(4981,plain,
% 1.07/1.22 (op(e0, e0) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1495, 2527, 4699, 4412])).
% 1.07/1.22 tff(4982,plain,
% 1.07/1.22 (op(e0, op(e0, e0)) = op(e0, e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4981])).
% 1.07/1.22 tff(4983,plain,
% 1.07/1.22 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4982])).
% 1.07/1.22 tff(4984,plain,
% 1.07/1.22 (op(e0, op(e0, e3)) = op(e0, op(e0, op(e0, e0)))),
% 1.07/1.22 inference(symmetry,[status(thm)],[4983])).
% 1.07/1.22 tff(4985,plain,
% 1.07/1.22 (e2 = op(e0, op(e0, op(e0, e0)))),
% 1.07/1.22 inference(transitivity,[status(thm)],[4742, 4973, 4984])).
% 1.07/1.22 tff(4986,plain,
% 1.07/1.22 (e3 = op(e0, e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[4981, 71])).
% 1.07/1.22 tff(4987,plain,
% 1.07/1.22 (op(e0, e3) = op(e0, op(e0, e0))),
% 1.07/1.22 inference(symmetry,[status(thm)],[4982])).
% 1.07/1.22 tff(4988,plain,
% 1.07/1.22 (e1 = op(e0, op(e0, e0))),
% 1.07/1.22 inference(transitivity,[status(thm)],[4681, 4987])).
% 1.07/1.22 tff(4989,plain,
% 1.07/1.22 ((~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0)))))))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0))))))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(4990,plain,
% 1.07/1.22 (((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0)))))))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(4991,plain,
% 1.07/1.22 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0))))))))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4990])).
% 1.07/1.22 tff(4992,plain,
% 1.07/1.22 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0))))))),
% 1.07/1.22 inference(transitivity,[status(thm)],[4991, 4989])).
% 1.07/1.22 tff(4993,plain,
% 1.07/1.22 ((~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(4994,plain,
% 1.07/1.22 ((~(((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(4995,axiom,(~(((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0))) & (e2 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax7')).
% 1.07/1.22 tff(4996,plain,
% 1.07/1.22 (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[4995, 4994])).
% 1.07/1.22 tff(4997,plain,
% 1.07/1.22 (~((e1 = op(e0, op(e0, e0))) & (e3 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[4996, 4993])).
% 1.07/1.22 tff(4998,plain,
% 1.07/1.22 ((~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, op(e0, e0)))))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[4997, 4992])).
% 1.07/1.22 tff(4999,plain,
% 1.07/1.22 ($false),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[4998, 4988, 4986, 4985])).
% 1.07/1.22 tff(5000,plain,((op(e0, e1) = e3) | (~(op(e0, e3) = e1)) | (op(e0, e2) = e3) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.22 tff(5001,plain,
% 1.07/1.22 (op(e0, e2) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[5000, 4980, 19, 3849])).
% 1.07/1.22 tff(5002,plain,
% 1.07/1.22 (op(e0, e2) = op(e1, e1)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5001, 4971])).
% 1.07/1.22 tff(5003,plain,
% 1.07/1.22 ((op(e0, e2) = e0) <=> (op(e1, e1) = e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5002])).
% 1.07/1.22 tff(5004,plain,
% 1.07/1.22 ((op(e1, e1) = e0) <=> (op(e0, e2) = e0)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5003])).
% 1.07/1.22 tff(5005,plain,
% 1.07/1.22 ((~(op(e1, e1) = e0)) <=> (~(op(e0, e2) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5004])).
% 1.07/1.22 tff(5006,plain,
% 1.07/1.22 (~(op(e0, e2) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[4965, 5005])).
% 1.07/1.22 tff(5007,plain,
% 1.07/1.22 ($false),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[973, 5006, 4970, 1947, 17])).
% 1.07/1.22 tff(5008,plain,((~(op(e1, e1) = e3)) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (~(op(e0, e3) = e1)) | (op(e0, e1) = e0) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.22 tff(5009,plain,
% 1.07/1.22 (~(op(e1, e1) = e3)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[5008, 4958, 4803, 19, 3849, 4726])).
% 1.07/1.22 tff(5010,plain,
% 1.07/1.22 (op(e0, e1) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1730, 5009, 4700, 2839])).
% 1.07/1.22 tff(5011,plain,
% 1.07/1.22 (e3 = op(e0, e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5010])).
% 1.07/1.22 tff(5012,plain,
% 1.07/1.22 ((e2 = e3) <=> (e2 = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5011])).
% 1.07/1.22 tff(5013,plain,
% 1.07/1.22 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5012, 4838])).
% 1.07/1.22 tff(5014,plain,
% 1.07/1.22 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5013])).
% 1.07/1.22 tff(5015,plain,
% 1.07/1.22 (~(op(e0, e1) = e2)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[1321, 5014])).
% 1.07/1.22 tff(5016,plain,
% 1.07/1.22 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[251])).
% 1.07/1.22 tff(5017,plain,
% 1.07/1.22 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5016])).
% 1.07/1.22 tff(5018,plain,
% 1.07/1.22 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5017])).
% 1.07/1.22 tff(5019,plain,
% 1.07/1.22 (~(op(e2, e3) = e2)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[14, 5018])).
% 1.07/1.22 tff(5020,plain,
% 1.07/1.22 ((op(e1, e3) = op(e1, e1)) <=> (op(e1, e1) = op(e1, e3))),
% 1.07/1.22 inference(commutativity,[status(thm)],[])).
% 1.07/1.22 tff(5021,plain,
% 1.07/1.22 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[251])).
% 1.07/1.22 tff(5022,plain,
% 1.07/1.22 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5021])).
% 1.07/1.22 tff(5023,plain,
% 1.07/1.22 (~(op(e2, e2) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[515, 5022])).
% 1.07/1.22 tff(5024,plain,
% 1.07/1.22 (~(op(e1, e1) = e3)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[5008, 5023, 4803, 19, 3849, 4726])).
% 1.07/1.22 tff(5025,plain,
% 1.07/1.22 (op(e1, e1) = e2),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[630, 84, 1266, 5024])).
% 1.07/1.22 tff(5026,plain,
% 1.07/1.22 (e2 = op(e1, e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5025])).
% 1.07/1.22 tff(5027,plain,
% 1.07/1.22 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e1, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5026])).
% 1.07/1.22 tff(5028,plain,
% 1.07/1.22 ((op(e1, e3) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 1.07/1.22 inference(transitivity,[status(thm)],[5027, 5020])).
% 1.07/1.22 tff(5029,plain,
% 1.07/1.22 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5028])).
% 1.07/1.22 tff(5030,plain,
% 1.07/1.22 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5029])).
% 1.07/1.22 tff(5031,plain,
% 1.07/1.22 (~(op(e1, e3) = e2)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[619, 5030])).
% 1.07/1.22 tff(5032,plain,
% 1.07/1.22 (op(e3, e3) = e2),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2786, 5031, 4717, 5019])).
% 1.07/1.22 tff(5033,plain,
% 1.07/1.22 ((op(e1, e1) = op(e0, e1)) <=> (op(e0, e1) = op(e1, e1))),
% 1.07/1.22 inference(commutativity,[status(thm)],[])).
% 1.07/1.22 tff(5034,plain,
% 1.07/1.22 (op(e0, e1) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1730, 5024, 4700, 2839])).
% 1.07/1.22 tff(5035,plain,
% 1.07/1.22 (e3 = op(e0, e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5034])).
% 1.07/1.22 tff(5036,plain,
% 1.07/1.22 (op(e3, e3) = op(e1, e1)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5032, 5026])).
% 1.07/1.22 tff(5037,plain,
% 1.07/1.22 ((op(e3, e3) = e3) <=> (op(e1, e1) = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5036, 5035])).
% 1.07/1.22 tff(5038,plain,
% 1.07/1.22 ((op(e3, e3) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 1.07/1.22 inference(transitivity,[status(thm)],[5037, 5033])).
% 1.07/1.22 tff(5039,plain,
% 1.07/1.22 ((op(e0, e1) = op(e1, e1)) <=> (op(e3, e3) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5038])).
% 1.07/1.22 tff(5040,plain,
% 1.07/1.22 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e3, e3) = e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5039])).
% 1.07/1.22 tff(5041,plain,
% 1.07/1.22 (~(op(e3, e3) = e3)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[792, 5040])).
% 1.07/1.22 tff(5042,plain,
% 1.07/1.22 (op(e3, e2) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[422, 5041, 4794, 2839])).
% 1.07/1.22 tff(5043,plain,
% 1.07/1.22 (op(e3, op(e3, e2)) = op(e3, e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5042])).
% 1.07/1.22 tff(5044,plain,
% 1.07/1.22 (op(e3, op(e3, e2)) = e2),
% 1.07/1.22 inference(transitivity,[status(thm)],[5043, 5032])).
% 1.07/1.22 tff(5045,plain,
% 1.07/1.22 ((op(e0, e0) = e1) <=> (op(e0, e0) = op(e0, e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.22 tff(5046,plain,
% 1.07/1.22 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5045])).
% 1.07/1.22 tff(5047,plain,
% 1.07/1.22 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5046])).
% 1.07/1.22 tff(5048,plain,
% 1.07/1.22 (~(op(e0, e0) = e1)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[3414, 5047])).
% 1.07/1.22 tff(5049,plain,
% 1.07/1.22 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5035])).
% 1.07/1.22 tff(5050,plain,
% 1.07/1.22 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5049])).
% 1.07/1.22 tff(5051,plain,
% 1.07/1.22 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5050])).
% 1.07/1.22 tff(5052,plain,
% 1.07/1.22 (~(op(e0, e0) = e3)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[811, 5051])).
% 1.07/1.22 tff(5053,plain,
% 1.07/1.22 (op(e1, e0) = e0),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1830, 84, 80, 4803])).
% 1.07/1.22 tff(5054,plain,
% 1.07/1.22 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5053])).
% 1.07/1.22 tff(5055,plain,
% 1.07/1.22 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5054])).
% 1.07/1.22 tff(5056,plain,
% 1.07/1.22 (~(op(e0, e0) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[2471, 5055])).
% 1.07/1.22 tff(5057,plain,
% 1.07/1.22 (op(e0, e0) = e2),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[3612, 5056, 5052, 5048])).
% 1.07/1.22 tff(5058,plain,
% 1.07/1.22 (op(e3, e1) = e0),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[292, 84, 3849, 4726])).
% 1.07/1.22 tff(5059,plain,
% 1.07/1.22 (e0 = op(e3, e1)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5058])).
% 1.07/1.22 tff(5060,plain,
% 1.07/1.22 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5059])).
% 1.07/1.22 tff(5061,plain,
% 1.07/1.22 ((op(e3, e2) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 1.07/1.22 inference(transitivity,[status(thm)],[5060, 4845])).
% 1.07/1.22 tff(5062,plain,
% 1.07/1.22 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5061])).
% 1.07/1.22 tff(5063,plain,
% 1.07/1.22 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5062])).
% 1.07/1.22 tff(5064,plain,
% 1.07/1.22 (~(op(e3, e2) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[3429, 5063])).
% 1.07/1.22 tff(5065,plain,
% 1.07/1.22 (op(e0, e2) = e0),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[973, 5064, 4803, 5023])).
% 1.07/1.22 tff(5066,plain,
% 1.07/1.22 (op(e0, op(e0, e2)) = op(e0, e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5065])).
% 1.07/1.22 tff(5067,plain,
% 1.07/1.22 (op(e0, op(e0, e2)) = e2),
% 1.07/1.22 inference(transitivity,[status(thm)],[5066, 5057])).
% 1.07/1.22 tff(5068,plain,
% 1.07/1.22 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1331, 5067])).
% 1.07/1.22 tff(5069,plain,
% 1.07/1.22 (op(op(e0, e3), e0) = op(e1, e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[19])).
% 1.07/1.22 tff(5070,plain,
% 1.07/1.22 (op(e1, op(e3, e1)) = op(op(e0, e3), e0)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4681, 5058])).
% 1.07/1.22 tff(5071,plain,
% 1.07/1.22 (op(e1, e0) = op(e3, e1)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5053, 5059])).
% 1.07/1.22 tff(5072,plain,
% 1.07/1.22 (op(e1, op(e1, e0)) = op(e1, op(e3, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5071])).
% 1.07/1.22 tff(5073,plain,
% 1.07/1.22 (op(e1, op(e1, e0)) = e0),
% 1.07/1.22 inference(transitivity,[status(thm)],[5072, 5070, 5069, 5053])).
% 1.07/1.22 tff(5074,plain,
% 1.07/1.22 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1836, 5073])).
% 1.07/1.22 tff(5075,plain,
% 1.07/1.22 ((op(e1, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 1.07/1.22 inference(transitivity,[status(thm)],[4830, 1758])).
% 1.07/1.22 tff(5076,plain,
% 1.07/1.22 ((~(op(e1, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5075])).
% 1.07/1.22 tff(5077,plain,
% 1.07/1.22 (~(op(op(e3, e0), e3) = e0)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[80, 5076])).
% 1.07/1.22 tff(5078,plain,
% 1.07/1.22 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1764, 5077])).
% 1.07/1.22 tff(5079,plain,
% 1.07/1.22 (op(e3, op(e3, e1)) = e1),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[4813, 5058, 19, 466])).
% 1.07/1.22 tff(5080,plain,
% 1.07/1.22 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2594, 5079])).
% 1.07/1.22 tff(5081,plain,
% 1.07/1.22 (op(e0, op(e0, e1)) = op(e0, e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5034])).
% 1.07/1.22 tff(5082,plain,
% 1.07/1.22 (op(e0, op(e0, e1)) = e1),
% 1.07/1.22 inference(transitivity,[status(thm)],[5081, 19])).
% 1.07/1.22 tff(5083,plain,
% 1.07/1.22 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2449, 5082])).
% 1.07/1.22 tff(5084,plain,
% 1.07/1.22 (op(e0, e1) = op(e0, op(e0, e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.22 tff(5085,plain,
% 1.07/1.22 ((op(e0, e1) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5084])).
% 1.07/1.22 tff(5086,plain,
% 1.07/1.22 (op(e0, op(e0, e3)) = e3),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[5034, 5085])).
% 1.07/1.22 tff(5087,plain,
% 1.07/1.22 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1938, 5086])).
% 1.07/1.22 tff(5088,plain,
% 1.07/1.22 (op(op(e2, e3), e2) = op(e0, e2)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[251])).
% 1.07/1.22 tff(5089,plain,
% 1.07/1.22 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e2) = e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5088])).
% 1.07/1.22 tff(5090,plain,
% 1.07/1.22 ((op(e0, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5089])).
% 1.07/1.22 tff(5091,plain,
% 1.07/1.22 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5035])).
% 1.07/1.22 tff(5092,plain,
% 1.07/1.22 ((op(e0, e2) = e3) <=> (op(e0, e1) = op(e0, e2))),
% 1.07/1.22 inference(transitivity,[status(thm)],[5091, 4680])).
% 1.07/1.22 tff(5093,plain,
% 1.07/1.22 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5092])).
% 1.07/1.22 tff(5094,plain,
% 1.07/1.22 ((op(e0, e1) = op(e0, e2)) <=> (op(op(e2, e3), e2) = e3)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5093, 5090])).
% 1.07/1.22 tff(5095,plain,
% 1.07/1.22 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5094])).
% 1.07/1.22 tff(5096,plain,
% 1.07/1.22 (~(op(op(e2, e3), e2) = e3)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[2102, 5095])).
% 1.07/1.22 tff(5097,plain,
% 1.07/1.22 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1934, 5096])).
% 1.07/1.22 tff(5098,plain,
% 1.07/1.22 (op(e2, op(e0, e1)) = op(e2, e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5034])).
% 1.07/1.22 tff(5099,plain,
% 1.07/1.22 (op(e1, e0) = op(op(e0, e3), e0)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5069])).
% 1.07/1.22 tff(5100,plain,
% 1.07/1.22 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5099])).
% 1.07/1.22 tff(5101,plain,
% 1.07/1.22 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5100])).
% 1.07/1.22 tff(5102,plain,
% 1.07/1.22 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5069, 5035])).
% 1.07/1.22 tff(5103,plain,
% 1.07/1.22 ((op(e1, e0) = op(e0, e1)) <=> (op(op(e0, e3), e0) = e3)),
% 1.07/1.22 inference(symmetry,[status(thm)],[5102])).
% 1.07/1.22 tff(5104,plain,
% 1.07/1.22 ((op(e3, e1) = op(e0, e1)) <=> (op(e0, e1) = op(e3, e1))),
% 1.07/1.22 inference(commutativity,[status(thm)],[])).
% 1.07/1.22 tff(5105,plain,
% 1.07/1.22 ((op(e1, e0) = op(e0, e1)) <=> (op(e3, e1) = op(e0, e1))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5071])).
% 1.07/1.22 tff(5106,plain,
% 1.07/1.22 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e3, e1))),
% 1.07/1.22 inference(transitivity,[status(thm)],[5105, 5104])).
% 1.07/1.22 tff(5107,plain,
% 1.07/1.22 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e0) = op(e0, e1))),
% 1.07/1.22 inference(symmetry,[status(thm)],[5106])).
% 1.07/1.22 tff(5108,plain,
% 1.07/1.22 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e0) = e3)),
% 1.07/1.22 inference(transitivity,[status(thm)],[5107, 5103, 5101])).
% 1.07/1.22 tff(5109,plain,
% 1.07/1.22 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e0) = e3))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[5108])).
% 1.07/1.22 tff(5110,plain,
% 1.07/1.22 (~(op(e1, e0) = e3)),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[3046, 5109])).
% 1.07/1.22 tff(5111,plain,
% 1.07/1.22 (op(e2, e0) = e3),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2713, 5110, 4794, 5052])).
% 1.07/1.22 tff(5112,plain,
% 1.07/1.22 (op(e2, e0) = op(e0, e1)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5111, 5035])).
% 1.07/1.23 tff(5113,plain,
% 1.07/1.23 (op(e2, op(e2, e0)) = op(e2, op(e0, e1))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5112])).
% 1.07/1.23 tff(5114,plain,
% 1.07/1.23 (op(e2, op(e2, e0)) = e0),
% 1.07/1.23 inference(transitivity,[status(thm)],[5113, 5098, 251])).
% 1.07/1.23 tff(5115,plain,
% 1.07/1.23 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2653, 5114])).
% 1.07/1.23 tff(5116,plain,
% 1.07/1.23 (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1459, 5115, 5097, 5087, 4829, 1304, 5083, 4819, 5080, 5078, 5074, 5068])).
% 1.07/1.23 tff(5117,plain,
% 1.07/1.23 (~(op(e3, op(e3, e2)) = e2)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1904, 5116])).
% 1.07/1.23 tff(5118,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5117, 5044])).
% 1.07/1.23 tff(5119,plain,((op(e1, e1) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e3, e1) = e3) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e1)) | (~(op(e3, e0) = op(e0, e3))) | (op(e1, e3) = e0) | (op(e0, e1) = e0) | (op(e1, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(5120,plain,
% 1.07/1.23 (op(e1, e1) = e0),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5119, 4955, 2839, 1304, 19, 466, 80, 3849, 1266])).
% 1.07/1.23 tff(5121,plain,
% 1.07/1.23 (e0 = op(e1, e1)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5120])).
% 1.07/1.23 tff(5122,plain,
% 1.07/1.23 ((e0 = e2) <=> (op(e1, e1) = e2)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5121])).
% 1.07/1.23 tff(5123,plain,
% 1.07/1.23 ((~(e0 = e2)) <=> (~(op(e1, e1) = e2))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5122])).
% 1.07/1.23 tff(5124,plain,
% 1.07/1.23 (~(op(e1, e1) = e2)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[14, 5123])).
% 1.07/1.23 tff(5125,plain,
% 1.07/1.23 (op(e3, e1) = e2),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1993, 5124, 5015, 3540])).
% 1.07/1.23 tff(5126,plain,
% 1.07/1.23 (e2 = op(e3, e1)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5125])).
% 1.07/1.23 tff(5127,plain,
% 1.07/1.23 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[4955])).
% 1.07/1.23 tff(5128,plain,
% 1.07/1.23 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5127])).
% 1.07/1.23 tff(5129,plain,
% 1.07/1.23 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5128])).
% 1.07/1.23 tff(5130,plain,
% 1.07/1.23 (~(op(e2, e3) = e2)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[14, 5129])).
% 1.07/1.23 tff(5131,plain,
% 1.07/1.23 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5125])).
% 1.07/1.23 tff(5132,plain,
% 1.07/1.23 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5131, 565])).
% 1.07/1.23 tff(5133,plain,
% 1.07/1.23 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5132])).
% 1.07/1.23 tff(5134,plain,
% 1.07/1.23 (~(op(e3, e3) = e2)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[437, 5133])).
% 1.07/1.23 tff(5135,plain,
% 1.07/1.23 (op(e1, e3) = e2),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2786, 5134, 4717, 5130])).
% 1.07/1.23 tff(5136,plain,
% 1.07/1.23 (op(e1, e1) = e0),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[630, 1291, 1266, 1971])).
% 1.07/1.23 tff(5137,plain,
% 1.07/1.23 (e0 = op(e1, e1)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5136, 123])).
% 1.07/1.23 tff(5138,plain,
% 1.07/1.23 (op(e1, op(e1, e1)) = op(op(e0, e3), e0)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[4681, 5136])).
% 1.07/1.23 tff(5139,plain,
% 1.07/1.23 (op(op(e0, e3), e0) = op(e1, op(e1, e1))),
% 1.07/1.23 inference(symmetry,[status(thm)],[5138])).
% 1.07/1.23 tff(5140,plain,
% 1.07/1.23 (op(e1, e0) = e3),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[247, 1291, 75, 1080])).
% 1.07/1.23 tff(5141,plain,
% 1.07/1.23 (e3 = op(e1, e0)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5140])).
% 1.07/1.23 tff(5142,plain,
% 1.07/1.23 (e3 = op(e1, op(e1, e1))),
% 1.07/1.23 inference(transitivity,[status(thm)],[5141, 5099, 5139])).
% 1.07/1.23 tff(5143,plain,
% 1.07/1.23 (op(e1, op(e1, e1)) = e3),
% 1.07/1.23 inference(transitivity,[status(thm)],[5138, 5069, 5140])).
% 1.07/1.23 tff(5144,plain,
% 1.07/1.23 (op(e1, op(e1, op(e1, e1))) = op(op(e0, e3), e3)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[4681, 5143])).
% 1.07/1.23 tff(5145,plain,
% 1.07/1.23 (op(op(e0, e3), e3) = op(e1, op(e1, op(e1, e1)))),
% 1.07/1.23 inference(symmetry,[status(thm)],[5144])).
% 1.07/1.23 tff(5146,plain,
% 1.07/1.23 (op(e1, e3) = op(op(e0, e3), e3)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[4681])).
% 1.07/1.23 tff(5147,plain,
% 1.07/1.23 (e2 = op(e1, op(e1, op(e1, e1)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[265, 5146, 5145])).
% 1.07/1.23 tff(5148,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[276, 5147, 5142, 5137])).
% 1.07/1.23 tff(5149,plain,((op(e1, e1) = e3) | (~(op(e1, e3) = e2)) | (~(op(e0, e3) = e1)) | (op(e1, e1) = e1) | (op(e1, e2) = e3) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(5150,plain,
% 1.07/1.23 (op(e1, e3) = e3),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5149, 5135, 19, 1266, 4786, 5009])).
% 1.07/1.23 tff(5151,plain,
% 1.07/1.23 (e3 = op(e1, e3)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5150])).
% 1.07/1.23 tff(5152,plain,
% 1.07/1.23 (op(e0, e1) = op(e3, e1)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5010, 5151, 5135, 5126])).
% 1.07/1.23 tff(5153,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[3046, 5152])).
% 1.07/1.23 tff(5154,plain,((op(e1, e3) = e0) | (~(op(e0, e3) = e1)) | (op(e1, e1) = e1) | (op(e2, e1) = e2) | (op(e3, e1) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, e1) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(5155,plain,
% 1.07/1.23 (op(e3, e3) = e0),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5154, 4954, 4679, 4674, 4668, 4664, 648, 4663, 4655])).
% 1.07/1.23 tff(5156,plain,
% 1.07/1.23 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5155])).
% 1.07/1.23 tff(5157,plain,
% 1.07/1.23 (op(e3, op(e3, e3)) = op(e0, e3)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5156, 648])).
% 1.07/1.23 tff(5158,plain,
% 1.07/1.23 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e0, e3))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5157])).
% 1.07/1.23 tff(5159,plain,
% 1.07/1.23 (op(e3, op(e3, op(e3, e3))) = op(e3, e1)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5158, 4658])).
% 1.07/1.23 tff(5160,plain,
% 1.07/1.23 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e1))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5159])).
% 1.07/1.23 tff(5161,plain,
% 1.07/1.23 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e1) = e2)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5160, 637])).
% 1.07/1.23 tff(5162,plain,
% 1.07/1.23 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, op(e3, e3))))),
% 1.07/1.23 inference(symmetry,[status(thm)],[5161])).
% 1.07/1.23 tff(5163,plain,
% 1.07/1.23 (op(e0, e3) = op(e3, e0)),
% 1.07/1.23 inference(symmetry,[status(thm)],[648])).
% 1.07/1.23 tff(5164,plain,
% 1.07/1.23 (e1 = op(e3, e0)),
% 1.07/1.23 inference(transitivity,[status(thm)],[4656, 5163])).
% 1.07/1.23 tff(5165,plain,
% 1.07/1.23 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e0))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5164])).
% 1.07/1.23 tff(5166,plain,
% 1.07/1.23 ((op(e3, e1) = e1) <=> (op(e3, e0) = op(e3, e1))),
% 1.07/1.23 inference(transitivity,[status(thm)],[5165, 881])).
% 1.07/1.23 tff(5167,plain,
% 1.07/1.23 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5166])).
% 1.07/1.23 tff(5168,plain,
% 1.07/1.23 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5167])).
% 1.07/1.23 tff(5169,plain,
% 1.07/1.23 (~(op(e3, e1) = e1)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[580, 5168])).
% 1.07/1.23 tff(5170,plain,
% 1.07/1.23 (op(e3, op(e3, e0)) = op(e3, op(e0, e3))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[648])).
% 1.07/1.23 tff(5171,plain,
% 1.07/1.23 (op(e3, op(e0, e3)) = op(e3, op(e3, e0))),
% 1.07/1.23 inference(symmetry,[status(thm)],[5170])).
% 1.07/1.23 tff(5172,plain,
% 1.07/1.23 (op(e3, e1) = op(e3, op(e3, e0))),
% 1.07/1.23 inference(transitivity,[status(thm)],[4657, 5171])).
% 1.07/1.23 tff(5173,plain,
% 1.07/1.23 ((op(e3, e1) = e0) <=> (op(e3, op(e3, e0)) = e0)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5172])).
% 1.07/1.23 tff(5174,plain,
% 1.07/1.23 ((op(e3, op(e3, e0)) = e0) <=> (op(e3, e1) = e0)),
% 1.07/1.23 inference(symmetry,[status(thm)],[5173])).
% 1.07/1.23 tff(5175,plain,
% 1.07/1.23 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, op(e3, e0)) = e0)),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5172, 5155])).
% 1.07/1.23 tff(5176,plain,
% 1.07/1.23 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 1.07/1.23 inference(transitivity,[status(thm)],[5175, 5174])).
% 1.07/1.23 tff(5177,plain,
% 1.07/1.23 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5176])).
% 1.07/1.23 tff(5178,plain,
% 1.07/1.23 (~(op(e3, e1) = e0)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[437, 5177])).
% 1.07/1.23 tff(5179,plain,
% 1.07/1.23 (op(e3, e1) = e2),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[446, 5178, 4668, 5169])).
% 1.07/1.23 tff(5180,plain,
% 1.07/1.23 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5179, 5162])).
% 1.07/1.23 tff(5181,plain,
% 1.07/1.23 (e0 = op(e3, e3)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5155, 3078])).
% 1.07/1.23 tff(5182,plain,
% 1.07/1.23 (op(e3, e0) = op(e3, op(e3, e3))),
% 1.07/1.23 inference(symmetry,[status(thm)],[5156])).
% 1.07/1.23 tff(5183,plain,
% 1.07/1.23 (e1 = op(e3, op(e3, e3))),
% 1.07/1.23 inference(transitivity,[status(thm)],[4656, 5163, 5182])).
% 1.07/1.23 tff(5184,plain,
% 1.07/1.23 ((~(~((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3)))))) <=> ((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5185,plain,
% 1.07/1.23 (((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3)))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5186,plain,
% 1.07/1.23 ((~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[5185])).
% 1.07/1.23 tff(5187,plain,
% 1.07/1.23 ((~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[5186, 5184])).
% 1.07/1.23 tff(5188,plain,
% 1.07/1.23 ((~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5189,plain,
% 1.07/1.23 ((~(((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(5190,axiom,(~(((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3))) & (e2 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax26')).
% 1.07/1.23 tff(5191,plain,
% 1.07/1.23 (~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 1.07/1.23 tff(5192,plain,
% 1.07/1.23 (~((e1 = op(e3, op(e3, e3))) & (e0 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5191, 5188])).
% 1.07/1.23 tff(5193,plain,
% 1.07/1.23 ((~(e2 = op(e3, op(e3, op(e3, e3))))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(e3, e3)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[5192, 5187])).
% 1.07/1.23 tff(5194,plain,
% 1.07/1.23 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5193, 5183, 5181])).
% 1.07/1.23 tff(5195,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[5194, 5180])).
% 1.07/1.23 tff(5196,plain,((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(5197,plain,
% 1.07/1.23 (((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)))) <=> ((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5198,plain,
% 1.14/1.24 (((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3))) <=> (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5199,plain,
% 1.14/1.24 (((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) <=> (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5200,plain,
% 1.14/1.24 (((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) <=> (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5201,plain,
% 1.14/1.24 (((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) <=> (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5202,plain,
% 1.14/1.24 (((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) <=> (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5203,plain,
% 1.14/1.24 (((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) <=> (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5204,plain,
% 1.14/1.24 (((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) <=> (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5205,plain,
% 1.14/1.24 (((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) <=> (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5206,plain,
% 1.14/1.24 (((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) <=> (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5207,plain,
% 1.14/1.24 (((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) <=> (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5208,plain,
% 1.14/1.24 (((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) <=> (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5209,plain,
% 1.14/1.24 (((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) <=> (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5210,plain,
% 1.14/1.24 (((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) <=> (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)))),
% 1.14/1.24 inference(rewrite,[status(thm)],[])).
% 1.14/1.24 tff(5211,plain,
% 1.14/1.24 (((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) <=> (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)))),
% 1.14/1.25 inference(rewrite,[status(thm)],[])).
% 1.14/1.25 tff(5212,plain,
% 1.14/1.25 (((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) <=> (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)))),
% 1.14/1.25 inference(rewrite,[status(thm)],[])).
% 1.14/1.25 tff(5213,plain,
% 1.14/1.25 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) <=> (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)))),
% 1.14/1.25 inference(rewrite,[status(thm)],[])).
% 1.14/1.25 tff(5214,plain,
% 1.14/1.25 ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))) <=> ((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))))),
% 1.14/1.25 inference(monotonicity,[status(thm)],[5213, 5212, 5211, 5210, 5209, 5208, 5207, 5206, 5205, 5204, 5203, 5202, 5201, 5200, 5199, 5198])).
% 1.14/1.25 tff(5215,plain,
% 1.14/1.25 ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))) <=> ((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))))),
% 1.14/1.25 inference(transitivity,[status(thm)],[5214, 5197])).
% 1.14/1.25 tff(5216,plain,
% 1.14/1.25 ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3))))),
% 1.16/1.26 inference(rewrite,[status(thm)],[])).
% 1.16/1.26 tff(5217,plain,
% 1.16/1.26 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3)))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3))))),
% 1.16/1.26 inference(rewrite,[status(thm)],[])).
% 1.16/1.26 tff(5218,plain,
% 1.16/1.26 ((((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3))) <=> ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.16/1.26 inference(rewrite,[status(thm)],[])).
% 1.16/1.26 tff(5219,plain,
% 1.16/1.26 ((((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) <=> ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5220,plain,
% 1.16/1.27 ((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) <=> ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5221,plain,
% 1.16/1.27 (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) <=> (((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2)))),
% 1.16/1.27 inference(monotonicity,[status(thm)],[5220])).
% 1.16/1.27 tff(5222,plain,
% 1.16/1.27 (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) <=> ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)))),
% 1.16/1.27 inference(transitivity,[status(thm)],[5221, 5219])).
% 1.16/1.27 tff(5223,plain,
% 1.16/1.27 ((((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3))) <=> (((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.16/1.27 inference(monotonicity,[status(thm)],[5222])).
% 1.16/1.27 tff(5224,plain,
% 1.16/1.27 ((((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3))) <=> ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.16/1.27 inference(transitivity,[status(thm)],[5223, 5218])).
% 1.16/1.27 tff(5225,plain,
% 1.16/1.27 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3)))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5226,plain,
% 1.16/1.27 ((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3))) <=> ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3)))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5227,plain,
% 1.16/1.27 ((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) <=> ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5228,plain,
% 1.16/1.27 ((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) <=> ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)))),
% 1.16/1.27 inference(rewrite,[status(thm)],[])).
% 1.16/1.27 tff(5229,plain,
% 1.16/1.27 (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) <=> (((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2)))),
% 1.16/1.27 inference(monotonicity,[status(thm)],[5228])).
% 1.16/1.27 tff(5230,plain,
% 1.16/1.27 (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) <=> ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)))),
% 1.16/1.27 inference(transitivity,[status(thm)],[5229, 5227])).
% 1.16/1.27 tff(5231,plain,
% 1.16/1.27 ((((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3))) <=> (((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))),
% 1.16/1.27 inference(monotonicity,[status(thm)],[5230])).
% 1.16/1.27 tff(5232,plain,
% 1.16/1.27 ((((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3))) <=> ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3)))),
% 1.16/1.28 inference(transitivity,[status(thm)],[5231, 5226])).
% 1.16/1.28 tff(5233,plain,
% 1.16/1.28 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3)))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))))),
% 1.16/1.28 inference(rewrite,[status(thm)],[])).
% 1.16/1.28 tff(5234,plain,
% 1.16/1.28 ((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3))) <=> ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3)))),
% 1.16/1.28 inference(rewrite,[status(thm)],[])).
% 1.16/1.28 tff(5235,plain,
% 1.16/1.28 ((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) <=> ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)))),
% 1.16/1.28 inference(rewrite,[status(thm)],[])).
% 1.16/1.28 tff(5236,plain,
% 1.16/1.28 ((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) <=> ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)))),
% 1.16/1.28 inference(rewrite,[status(thm)],[])).
% 1.16/1.28 tff(5237,plain,
% 1.16/1.28 (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) <=> (((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2)))),
% 1.16/1.28 inference(monotonicity,[status(thm)],[5236])).
% 1.16/1.28 tff(5238,plain,
% 1.16/1.28 (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) <=> ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)))),
% 1.16/1.28 inference(transitivity,[status(thm)],[5237, 5235])).
% 1.16/1.28 tff(5239,plain,
% 1.16/1.28 ((((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3))) <=> (((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))),
% 1.16/1.28 inference(monotonicity,[status(thm)],[5238])).
% 1.16/1.28 tff(5240,plain,
% 1.16/1.28 ((((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3))) <=> ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3)))),
% 1.16/1.28 inference(transitivity,[status(thm)],[5239, 5234])).
% 1.16/1.28 tff(5241,plain,
% 1.16/1.28 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3)))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5242,plain,
% 1.16/1.29 ((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3))) <=> ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5243,plain,
% 1.16/1.29 ((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) <=> ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5244,plain,
% 1.16/1.29 ((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) <=> ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5245,plain,
% 1.16/1.29 (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) <=> (((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2)))),
% 1.16/1.29 inference(monotonicity,[status(thm)],[5244])).
% 1.16/1.29 tff(5246,plain,
% 1.16/1.29 (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) <=> ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)))),
% 1.16/1.29 inference(transitivity,[status(thm)],[5245, 5243])).
% 1.16/1.29 tff(5247,plain,
% 1.16/1.29 ((((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3))) <=> (((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))),
% 1.16/1.29 inference(monotonicity,[status(thm)],[5246])).
% 1.16/1.29 tff(5248,plain,
% 1.16/1.29 ((((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3))) <=> ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3)))),
% 1.16/1.29 inference(transitivity,[status(thm)],[5247, 5242])).
% 1.16/1.29 tff(5249,plain,
% 1.16/1.29 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3)))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5250,plain,
% 1.16/1.29 ((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3))) <=> ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5251,plain,
% 1.16/1.29 ((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) <=> ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5252,plain,
% 1.16/1.29 ((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) <=> ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)))),
% 1.16/1.29 inference(rewrite,[status(thm)],[])).
% 1.16/1.29 tff(5253,plain,
% 1.16/1.29 (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) <=> (((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2)))),
% 1.16/1.29 inference(monotonicity,[status(thm)],[5252])).
% 1.16/1.29 tff(5254,plain,
% 1.16/1.29 (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) <=> ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)))),
% 1.16/1.29 inference(transitivity,[status(thm)],[5253, 5251])).
% 1.16/1.29 tff(5255,plain,
% 1.16/1.29 ((((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3))) <=> (((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))),
% 1.16/1.29 inference(monotonicity,[status(thm)],[5254])).
% 1.16/1.29 tff(5256,plain,
% 1.16/1.29 ((((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3))) <=> ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3)))),
% 1.16/1.29 inference(transitivity,[status(thm)],[5255, 5250])).
% 1.16/1.29 tff(5257,plain,
% 1.16/1.29 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3)))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5258,plain,
% 1.16/1.30 ((((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3))) <=> ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5259,plain,
% 1.16/1.30 ((((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) <=> ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5260,plain,
% 1.16/1.30 ((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) <=> ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5261,plain,
% 1.16/1.30 (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) <=> (((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2)))),
% 1.16/1.30 inference(monotonicity,[status(thm)],[5260])).
% 1.16/1.30 tff(5262,plain,
% 1.16/1.30 (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) <=> ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)))),
% 1.16/1.30 inference(transitivity,[status(thm)],[5261, 5259])).
% 1.16/1.30 tff(5263,plain,
% 1.16/1.30 ((((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3))) <=> (((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))),
% 1.16/1.30 inference(monotonicity,[status(thm)],[5262])).
% 1.16/1.30 tff(5264,plain,
% 1.16/1.30 ((((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3))) <=> ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3)))),
% 1.16/1.30 inference(transitivity,[status(thm)],[5263, 5258])).
% 1.16/1.30 tff(5265,plain,
% 1.16/1.30 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3)))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5266,plain,
% 1.16/1.30 ((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3))) <=> ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5267,plain,
% 1.16/1.30 ((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) <=> ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5268,plain,
% 1.16/1.30 ((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) <=> ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)))),
% 1.16/1.30 inference(rewrite,[status(thm)],[])).
% 1.16/1.30 tff(5269,plain,
% 1.16/1.30 (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) <=> (((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2)))),
% 1.16/1.31 inference(monotonicity,[status(thm)],[5268])).
% 1.16/1.31 tff(5270,plain,
% 1.16/1.31 (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) <=> ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)))),
% 1.16/1.31 inference(transitivity,[status(thm)],[5269, 5267])).
% 1.16/1.31 tff(5271,plain,
% 1.16/1.31 ((((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3))) <=> (((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))),
% 1.16/1.31 inference(monotonicity,[status(thm)],[5270])).
% 1.16/1.31 tff(5272,plain,
% 1.16/1.31 ((((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3))) <=> ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3)))),
% 1.16/1.31 inference(transitivity,[status(thm)],[5271, 5266])).
% 1.16/1.31 tff(5273,plain,
% 1.16/1.31 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3)))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))))),
% 1.16/1.31 inference(rewrite,[status(thm)],[])).
% 1.16/1.31 tff(5274,plain,
% 1.16/1.31 ((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3))) <=> ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3)))),
% 1.16/1.31 inference(rewrite,[status(thm)],[])).
% 1.16/1.31 tff(5275,plain,
% 1.16/1.31 ((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) <=> ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)))),
% 1.16/1.31 inference(rewrite,[status(thm)],[])).
% 1.16/1.31 tff(5276,plain,
% 1.16/1.31 ((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) <=> ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)))),
% 1.16/1.31 inference(rewrite,[status(thm)],[])).
% 1.16/1.31 tff(5277,plain,
% 1.16/1.31 (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) <=> (((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2)))),
% 1.16/1.31 inference(monotonicity,[status(thm)],[5276])).
% 1.16/1.31 tff(5278,plain,
% 1.16/1.31 (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) <=> ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)))),
% 1.16/1.31 inference(transitivity,[status(thm)],[5277, 5275])).
% 1.16/1.31 tff(5279,plain,
% 1.16/1.31 ((((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3))) <=> (((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))),
% 1.16/1.31 inference(monotonicity,[status(thm)],[5278])).
% 1.16/1.31 tff(5280,plain,
% 1.16/1.31 ((((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3))) <=> ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3)))),
% 1.16/1.31 inference(transitivity,[status(thm)],[5279, 5274])).
% 1.16/1.31 tff(5281,plain,
% 1.16/1.31 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3)))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(5282,plain,
% 1.16/1.32 ((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3))) <=> ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3)))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(5283,plain,
% 1.16/1.32 ((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) <=> ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(5284,plain,
% 1.16/1.32 ((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) <=> ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(5285,plain,
% 1.16/1.32 (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) <=> (((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2)))),
% 1.16/1.32 inference(monotonicity,[status(thm)],[5284])).
% 1.16/1.32 tff(5286,plain,
% 1.16/1.32 (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) <=> ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)))),
% 1.16/1.32 inference(transitivity,[status(thm)],[5285, 5283])).
% 1.16/1.32 tff(5287,plain,
% 1.16/1.32 ((((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3))) <=> (((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))),
% 1.16/1.32 inference(monotonicity,[status(thm)],[5286])).
% 1.16/1.32 tff(5288,plain,
% 1.16/1.32 ((((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3))) <=> ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3)))),
% 1.16/1.32 inference(transitivity,[status(thm)],[5287, 5282])).
% 1.16/1.32 tff(5289,plain,
% 1.16/1.32 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3)))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5290,plain,
% 1.22/1.32 ((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3))) <=> ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5291,plain,
% 1.22/1.32 ((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) <=> ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5292,plain,
% 1.22/1.32 ((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) <=> ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5293,plain,
% 1.22/1.32 (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) <=> (((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2)))),
% 1.22/1.32 inference(monotonicity,[status(thm)],[5292])).
% 1.22/1.32 tff(5294,plain,
% 1.22/1.32 (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) <=> ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)))),
% 1.22/1.32 inference(transitivity,[status(thm)],[5293, 5291])).
% 1.22/1.32 tff(5295,plain,
% 1.22/1.32 ((((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3))) <=> (((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))),
% 1.22/1.32 inference(monotonicity,[status(thm)],[5294])).
% 1.22/1.32 tff(5296,plain,
% 1.22/1.32 ((((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3))) <=> ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3)))),
% 1.22/1.32 inference(transitivity,[status(thm)],[5295, 5290])).
% 1.22/1.32 tff(5297,plain,
% 1.22/1.32 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3)))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5298,plain,
% 1.22/1.32 ((((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3))) <=> ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5299,plain,
% 1.22/1.32 ((((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) <=> ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5300,plain,
% 1.22/1.32 ((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) <=> ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)))),
% 1.22/1.32 inference(rewrite,[status(thm)],[])).
% 1.22/1.32 tff(5301,plain,
% 1.22/1.32 (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) <=> (((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2)))),
% 1.22/1.32 inference(monotonicity,[status(thm)],[5300])).
% 1.22/1.32 tff(5302,plain,
% 1.22/1.32 (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) <=> ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)))),
% 1.22/1.32 inference(transitivity,[status(thm)],[5301, 5299])).
% 1.22/1.32 tff(5303,plain,
% 1.22/1.32 ((((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3))) <=> (((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))),
% 1.22/1.32 inference(monotonicity,[status(thm)],[5302])).
% 1.22/1.32 tff(5304,plain,
% 1.22/1.32 ((((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3))) <=> ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3)))),
% 1.22/1.32 inference(transitivity,[status(thm)],[5303, 5298])).
% 1.22/1.32 tff(5305,plain,
% 1.22/1.32 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3)))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5306,plain,
% 1.22/1.33 ((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3))) <=> ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5307,plain,
% 1.22/1.33 ((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) <=> ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5308,plain,
% 1.22/1.33 ((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) <=> ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5309,plain,
% 1.22/1.33 (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) <=> (((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2)))),
% 1.22/1.33 inference(monotonicity,[status(thm)],[5308])).
% 1.22/1.33 tff(5310,plain,
% 1.22/1.33 (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) <=> ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)))),
% 1.22/1.33 inference(transitivity,[status(thm)],[5309, 5307])).
% 1.22/1.33 tff(5311,plain,
% 1.22/1.33 ((((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3))) <=> (((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))),
% 1.22/1.33 inference(monotonicity,[status(thm)],[5310])).
% 1.22/1.33 tff(5312,plain,
% 1.22/1.33 ((((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3))) <=> ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3)))),
% 1.22/1.33 inference(transitivity,[status(thm)],[5311, 5306])).
% 1.22/1.33 tff(5313,plain,
% 1.22/1.33 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3)))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5314,plain,
% 1.22/1.33 ((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3))) <=> ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5315,plain,
% 1.22/1.33 ((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) <=> ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5316,plain,
% 1.22/1.33 ((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) <=> ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5317,plain,
% 1.22/1.33 (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) <=> (((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2)))),
% 1.22/1.33 inference(monotonicity,[status(thm)],[5316])).
% 1.22/1.33 tff(5318,plain,
% 1.22/1.33 (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) <=> ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)))),
% 1.22/1.33 inference(transitivity,[status(thm)],[5317, 5315])).
% 1.22/1.33 tff(5319,plain,
% 1.22/1.33 ((((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3))) <=> (((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))),
% 1.22/1.33 inference(monotonicity,[status(thm)],[5318])).
% 1.22/1.33 tff(5320,plain,
% 1.22/1.33 ((((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3))) <=> ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3)))),
% 1.22/1.33 inference(transitivity,[status(thm)],[5319, 5314])).
% 1.22/1.33 tff(5321,plain,
% 1.22/1.33 (((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3)))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5322,plain,
% 1.22/1.33 ((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3))) <=> ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3)))),
% 1.22/1.33 inference(rewrite,[status(thm)],[])).
% 1.22/1.33 tff(5323,plain,
% 1.22/1.33 ((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) <=> ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)))),
% 1.22/1.34 inference(rewrite,[status(thm)],[])).
% 1.22/1.34 tff(5324,plain,
% 1.22/1.34 ((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) <=> ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)))),
% 1.22/1.34 inference(rewrite,[status(thm)],[])).
% 1.22/1.34 tff(5325,plain,
% 1.22/1.34 (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) <=> (((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2)))),
% 1.22/1.34 inference(monotonicity,[status(thm)],[5324])).
% 1.22/1.34 tff(5326,plain,
% 1.22/1.34 (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) <=> ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)))),
% 1.22/1.34 inference(transitivity,[status(thm)],[5325, 5323])).
% 1.22/1.34 tff(5327,plain,
% 1.22/1.34 ((((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3))) <=> (((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))),
% 1.22/1.34 inference(monotonicity,[status(thm)],[5326])).
% 1.22/1.34 tff(5328,plain,
% 1.22/1.34 ((((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3))) <=> ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3)))),
% 1.22/1.34 inference(transitivity,[status(thm)],[5327, 5322])).
% 1.22/1.34 tff(5329,plain,
% 1.22/1.34 (((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))))),
% 1.22/1.34 inference(rewrite,[status(thm)],[])).
% 1.22/1.34 tff(5330,plain,
% 1.22/1.34 ((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3)))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))))),
% 1.22/1.34 inference(monotonicity,[status(thm)],[5329, 5328])).
% 1.22/1.34 tff(5331,plain,
% 1.22/1.34 ((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))))),
% 1.22/1.34 inference(transitivity,[status(thm)],[5330, 5321])).
% 1.22/1.34 tff(5332,plain,
% 1.22/1.34 (((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3)))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))))),
% 1.22/1.34 inference(monotonicity,[status(thm)],[5331, 5320])).
% 1.22/1.34 tff(5333,plain,
% 1.22/1.34 (((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))))),
% 1.22/1.34 inference(transitivity,[status(thm)],[5332, 5313])).
% 1.22/1.34 tff(5334,plain,
% 1.22/1.34 ((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3)))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))))),
% 1.22/1.35 inference(monotonicity,[status(thm)],[5333, 5312])).
% 1.22/1.35 tff(5335,plain,
% 1.22/1.35 ((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))))),
% 1.22/1.35 inference(transitivity,[status(thm)],[5334, 5305])).
% 1.22/1.35 tff(5336,plain,
% 1.22/1.35 (((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3)))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))))),
% 1.22/1.35 inference(monotonicity,[status(thm)],[5335, 5304])).
% 1.22/1.35 tff(5337,plain,
% 1.22/1.35 (((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))))),
% 1.22/1.35 inference(transitivity,[status(thm)],[5336, 5297])).
% 1.22/1.35 tff(5338,plain,
% 1.22/1.35 ((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3)))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))))),
% 1.22/1.35 inference(monotonicity,[status(thm)],[5337, 5296])).
% 1.22/1.35 tff(5339,plain,
% 1.22/1.35 ((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))))),
% 1.22/1.36 inference(transitivity,[status(thm)],[5338, 5289])).
% 1.22/1.36 tff(5340,plain,
% 1.22/1.36 (((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3)))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))))),
% 1.26/1.36 inference(monotonicity,[status(thm)],[5339, 5288])).
% 1.26/1.36 tff(5341,plain,
% 1.26/1.36 (((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))))),
% 1.26/1.36 inference(transitivity,[status(thm)],[5340, 5281])).
% 1.26/1.36 tff(5342,plain,
% 1.26/1.36 ((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3)))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))))),
% 1.26/1.36 inference(monotonicity,[status(thm)],[5341, 5280])).
% 1.26/1.36 tff(5343,plain,
% 1.26/1.36 ((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))))),
% 1.26/1.37 inference(transitivity,[status(thm)],[5342, 5273])).
% 1.26/1.37 tff(5344,plain,
% 1.26/1.37 (((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3)))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))))),
% 1.26/1.37 inference(monotonicity,[status(thm)],[5343, 5272])).
% 1.26/1.37 tff(5345,plain,
% 1.26/1.37 (((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))))),
% 1.26/1.37 inference(transitivity,[status(thm)],[5344, 5265])).
% 1.26/1.37 tff(5346,plain,
% 1.26/1.37 ((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3)))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))))),
% 1.26/1.38 inference(monotonicity,[status(thm)],[5345, 5264])).
% 1.26/1.38 tff(5347,plain,
% 1.26/1.38 ((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))))),
% 1.26/1.38 inference(transitivity,[status(thm)],[5346, 5257])).
% 1.26/1.38 tff(5348,plain,
% 1.26/1.38 (((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3)))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))))),
% 1.26/1.39 inference(monotonicity,[status(thm)],[5347, 5256])).
% 1.26/1.39 tff(5349,plain,
% 1.26/1.39 (((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))))),
% 1.26/1.39 inference(transitivity,[status(thm)],[5348, 5249])).
% 1.26/1.39 tff(5350,plain,
% 1.26/1.39 ((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3)))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))))),
% 1.26/1.40 inference(monotonicity,[status(thm)],[5349, 5248])).
% 1.26/1.40 tff(5351,plain,
% 1.26/1.40 ((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))))),
% 1.26/1.40 inference(transitivity,[status(thm)],[5350, 5241])).
% 1.26/1.40 tff(5352,plain,
% 1.26/1.40 (((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3)))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))))),
% 1.26/1.41 inference(monotonicity,[status(thm)],[5351, 5240])).
% 1.26/1.41 tff(5353,plain,
% 1.26/1.41 (((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))))),
% 1.26/1.41 inference(transitivity,[status(thm)],[5352, 5233])).
% 1.26/1.41 tff(5354,plain,
% 1.26/1.41 ((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3)))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))))),
% 1.26/1.41 inference(monotonicity,[status(thm)],[5353, 5232])).
% 1.26/1.41 tff(5355,plain,
% 1.26/1.41 ((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))))),
% 1.26/1.42 inference(transitivity,[status(thm)],[5354, 5225])).
% 1.26/1.42 tff(5356,plain,
% 1.26/1.42 (((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) | (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3)))) <=> ((((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3)))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3))))),
% 1.26/1.43 inference(monotonicity,[status(thm)],[5355, 5224])).
% 1.26/1.43 tff(5357,plain,
% 1.26/1.43 (((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) | (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3)))) <=> (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3))))),
% 1.33/1.43 inference(transitivity,[status(thm)],[5356, 5217])).
% 1.33/1.43 tff(5358,plain,
% 1.33/1.43 ((((((((((((((((((((op(e0, e0) = op(e0, e0)) & (~(op(e0, op(e0, e0)) = e0))) & (~(op(e1, op(e0, e0)) = e1))) & (~(op(e2, op(e0, e0)) = e2))) & (~(op(e3, op(e0, e0)) = e3))) | (((((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0))) & (~(op(e1, op(e0, e1)) = e1))) & (~(op(e2, op(e0, e1)) = e2))) & (~(op(e3, op(e0, e1)) = e3)))) | (((((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0))) & (~(op(e1, op(e0, e2)) = e1))) & (~(op(e2, op(e0, e2)) = e2))) & (~(op(e3, op(e0, e2)) = e3)))) | (((((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0))) & (~(op(e1, op(e0, e3)) = e1))) & (~(op(e2, op(e0, e3)) = e2))) & (~(op(e3, op(e0, e3)) = e3)))) | (((((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0))) & (~(op(e1, op(e1, e0)) = e1))) & (~(op(e2, op(e1, e0)) = e2))) & (~(op(e3, op(e1, e0)) = e3)))) | (((((op(e1, e1) = op(e1, e1)) & (~(op(e0, op(e1, e1)) = e0))) & (~(op(e1, op(e1, e1)) = e1))) & (~(op(e2, op(e1, e1)) = e2))) & (~(op(e3, op(e1, e1)) = e3)))) | (((((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0))) & (~(op(e1, op(e1, e2)) = e1))) & (~(op(e2, op(e1, e2)) = e2))) & (~(op(e3, op(e1, e2)) = e3)))) | (((((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0))) & (~(op(e1, op(e1, e3)) = e1))) & (~(op(e2, op(e1, e3)) = e2))) & (~(op(e3, op(e1, e3)) = e3)))) | (((((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0))) & (~(op(e1, op(e2, e0)) = e1))) & (~(op(e2, op(e2, e0)) = e2))) & (~(op(e3, op(e2, e0)) = e3)))) | (((((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0))) & (~(op(e1, op(e2, e1)) = e1))) & (~(op(e2, op(e2, e1)) = e2))) & (~(op(e3, op(e2, e1)) = e3)))) | (((((op(e2, e2) = op(e2, e2)) & (~(op(e0, op(e2, e2)) = e0))) & (~(op(e1, op(e2, e2)) = e1))) & (~(op(e2, op(e2, e2)) = e2))) & (~(op(e3, op(e2, e2)) = e3)))) | (((((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0))) & (~(op(e1, op(e2, e3)) = e1))) & (~(op(e2, op(e2, e3)) = e2))) & (~(op(e3, op(e2, e3)) = e3)))) | (((((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0))) & (~(op(e1, op(e3, e0)) = e1))) & (~(op(e2, op(e3, e0)) = e2))) & (~(op(e3, op(e3, e0)) = e3)))) | (((((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0))) & (~(op(e1, op(e3, e1)) = e1))) & (~(op(e2, op(e3, e1)) = e2))) & (~(op(e3, op(e3, e1)) = e3)))) | (((((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0))) & (~(op(e1, op(e3, e2)) = e1))) & (~(op(e2, op(e3, e2)) = e2))) & (~(op(e3, op(e3, e2)) = e3)))) | (((((op(e3, e3) = op(e3, e3)) & (~(op(e0, op(e3, e3)) = e0))) & (~(op(e1, op(e3, e3)) = e1))) & (~(op(e2, op(e3, e3)) = e2))) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.43 inference(and_elim,[status(thm)],[1450])).
% 1.33/1.43 tff(5359,plain,
% 1.33/1.43 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.44 inference(modus_ponens,[status(thm)],[5358, 5357])).
% 1.33/1.44 tff(5360,plain,
% 1.33/1.44 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.44 inference(modus_ponens,[status(thm)],[5359, 5216])).
% 1.33/1.44 tff(5361,plain,
% 1.33/1.44 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.44 inference(modus_ponens,[status(thm)],[5360, 5216])).
% 1.33/1.44 tff(5362,plain,
% 1.33/1.44 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.45 inference(modus_ponens,[status(thm)],[5361, 5216])).
% 1.33/1.45 tff(5363,plain,
% 1.33/1.45 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.45 inference(modus_ponens,[status(thm)],[5362, 5216])).
% 1.33/1.45 tff(5364,plain,
% 1.33/1.45 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.45 inference(modus_ponens,[status(thm)],[5363, 5216])).
% 1.33/1.45 tff(5365,plain,
% 1.33/1.45 (((~(op(e0, op(e0, e0)) = e0)) & (~(op(e1, op(e0, e0)) = e1)) & (~(op(e2, op(e0, e0)) = e2)) & (~(op(e3, op(e0, e0)) = e3))) | ((op(e1, e0) = op(e0, e1)) & (~(op(e0, op(e0, e1)) = e0)) & (~(op(e1, op(e0, e1)) = e1)) & (~(op(e2, op(e0, e1)) = e2)) & (~(op(e3, op(e0, e1)) = e3))) | ((op(e2, e0) = op(e0, e2)) & (~(op(e0, op(e0, e2)) = e0)) & (~(op(e1, op(e0, e2)) = e1)) & (~(op(e2, op(e0, e2)) = e2)) & (~(op(e3, op(e0, e2)) = e3))) | ((op(e3, e0) = op(e0, e3)) & (~(op(e0, op(e0, e3)) = e0)) & (~(op(e1, op(e0, e3)) = e1)) & (~(op(e2, op(e0, e3)) = e2)) & (~(op(e3, op(e0, e3)) = e3))) | ((op(e0, e1) = op(e1, e0)) & (~(op(e0, op(e1, e0)) = e0)) & (~(op(e1, op(e1, e0)) = e1)) & (~(op(e2, op(e1, e0)) = e2)) & (~(op(e3, op(e1, e0)) = e3))) | ((~(op(e0, op(e1, e1)) = e0)) & (~(op(e1, op(e1, e1)) = e1)) & (~(op(e2, op(e1, e1)) = e2)) & (~(op(e3, op(e1, e1)) = e3))) | ((op(e2, e1) = op(e1, e2)) & (~(op(e0, op(e1, e2)) = e0)) & (~(op(e1, op(e1, e2)) = e1)) & (~(op(e2, op(e1, e2)) = e2)) & (~(op(e3, op(e1, e2)) = e3))) | ((op(e3, e1) = op(e1, e3)) & (~(op(e0, op(e1, e3)) = e0)) & (~(op(e1, op(e1, e3)) = e1)) & (~(op(e2, op(e1, e3)) = e2)) & (~(op(e3, op(e1, e3)) = e3))) | ((op(e0, e2) = op(e2, e0)) & (~(op(e0, op(e2, e0)) = e0)) & (~(op(e1, op(e2, e0)) = e1)) & (~(op(e2, op(e2, e0)) = e2)) & (~(op(e3, op(e2, e0)) = e3))) | ((op(e1, e2) = op(e2, e1)) & (~(op(e0, op(e2, e1)) = e0)) & (~(op(e1, op(e2, e1)) = e1)) & (~(op(e2, op(e2, e1)) = e2)) & (~(op(e3, op(e2, e1)) = e3))) | ((~(op(e0, op(e2, e2)) = e0)) & (~(op(e1, op(e2, e2)) = e1)) & (~(op(e2, op(e2, e2)) = e2)) & (~(op(e3, op(e2, e2)) = e3))) | ((op(e3, e2) = op(e2, e3)) & (~(op(e0, op(e2, e3)) = e0)) & (~(op(e1, op(e2, e3)) = e1)) & (~(op(e2, op(e2, e3)) = e2)) & (~(op(e3, op(e2, e3)) = e3))) | ((op(e0, e3) = op(e3, e0)) & (~(op(e0, op(e3, e0)) = e0)) & (~(op(e1, op(e3, e0)) = e1)) & (~(op(e2, op(e3, e0)) = e2)) & (~(op(e3, op(e3, e0)) = e3))) | ((op(e1, e3) = op(e3, e1)) & (~(op(e0, op(e3, e1)) = e0)) & (~(op(e1, op(e3, e1)) = e1)) & (~(op(e2, op(e3, e1)) = e2)) & (~(op(e3, op(e3, e1)) = e3))) | ((op(e2, e3) = op(e3, e2)) & (~(op(e0, op(e3, e2)) = e0)) & (~(op(e1, op(e3, e2)) = e1)) & (~(op(e2, op(e3, e2)) = e2)) & (~(op(e3, op(e3, e2)) = e3))) | ((~(op(e0, op(e3, e3)) = e0)) & (~(op(e1, op(e3, e3)) = e1)) & (~(op(e2, op(e3, e3)) = e2)) & (~(op(e3, op(e3, e3)) = e3)))),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5364, 5216])).
% 1.33/1.46 tff(5366,plain,
% 1.33/1.46 ((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)))),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5365, 5215])).
% 1.33/1.46 tff(5367,plain,
% 1.33/1.46 ((~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)))),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5366, 5196])).
% 1.33/1.46 tff(5368,plain,
% 1.33/1.46 (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5367, 636, 614, 610, 594, 558, 554, 548, 540, 529, 501, 497, 451, 431, 393])).
% 1.33/1.46 tff(5369,plain,
% 1.33/1.46 (((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)) | (~(op(e0, op(e0, e2)) = e0))),
% 1.33/1.46 inference(tautology,[status(thm)],[])).
% 1.33/1.46 tff(5370,plain,
% 1.33/1.46 (~(op(e0, op(e0, e2)) = e0)),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5369, 5368])).
% 1.33/1.46 tff(5371,plain,
% 1.33/1.46 ($false),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5370, 388])).
% 1.33/1.46 tff(5372,plain,(((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e0, e3) = e1) | (op(e3, e1) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.46 tff(5373,plain,
% 1.33/1.46 (op(e3, e1) = e0),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5372, 129, 121, 80])).
% 1.33/1.46 tff(5374,plain,
% 1.33/1.46 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e0)),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5373])).
% 1.33/1.46 tff(5375,plain,
% 1.33/1.46 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e0))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5374])).
% 1.33/1.46 tff(5376,plain,
% 1.33/1.46 (~(op(e3, e0) = e0)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[580, 5375])).
% 1.33/1.46 tff(5377,plain,
% 1.33/1.46 ((e2 = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 1.33/1.46 inference(commutativity,[status(thm)],[])).
% 1.33/1.46 tff(5378,plain,
% 1.33/1.46 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.33/1.46 inference(monotonicity,[status(thm)],[152])).
% 1.33/1.46 tff(5379,plain,
% 1.33/1.46 (op(e3, op(e3, e3)) = e0),
% 1.33/1.46 inference(transitivity,[status(thm)],[5378, 5373])).
% 1.33/1.46 tff(5380,plain,
% 1.33/1.46 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5379])).
% 1.33/1.46 tff(5381,plain,
% 1.33/1.46 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5380])).
% 1.33/1.46 tff(5382,plain,
% 1.33/1.46 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 1.33/1.46 inference(transitivity,[status(thm)],[5381, 5377])).
% 1.33/1.46 tff(5383,plain,
% 1.33/1.46 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5382])).
% 1.33/1.46 tff(5384,plain,
% 1.33/1.46 (e1 = op(e3, e3)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[152, 658])).
% 1.33/1.46 tff(5385,plain,
% 1.33/1.46 (op(e3, e1) = op(e3, op(e3, e3))),
% 1.33/1.46 inference(symmetry,[status(thm)],[5378])).
% 1.33/1.46 tff(5386,plain,
% 1.33/1.46 (e0 = op(e3, e1)),
% 1.33/1.46 inference(symmetry,[status(thm)],[5373])).
% 1.33/1.46 tff(5387,plain,
% 1.33/1.46 (e0 = op(e3, op(e3, e3))),
% 1.33/1.46 inference(transitivity,[status(thm)],[5386, 5385])).
% 1.33/1.46 tff(5388,plain,
% 1.33/1.46 ((~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3)))))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5389,plain,
% 1.33/1.46 (((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3)))))))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5390,plain,
% 1.33/1.46 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3))))))))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5389])).
% 1.33/1.46 tff(5391,plain,
% 1.33/1.46 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.33/1.46 inference(transitivity,[status(thm)],[5390, 5388])).
% 1.33/1.46 tff(5392,plain,
% 1.33/1.46 ((~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5393,plain,
% 1.33/1.46 ((~(((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3))))))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5394,axiom,(~(((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3))) & (e2 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax24')).
% 1.33/1.46 tff(5395,plain,
% 1.33/1.46 (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5394, 5393])).
% 1.33/1.46 tff(5396,plain,
% 1.33/1.46 (~((e0 = op(e3, op(e3, e3))) & (e1 = op(e3, e3)) & (e2 = op(e3, op(e3, op(e3, e3)))))),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5395, 5392])).
% 1.33/1.46 tff(5397,plain,
% 1.33/1.46 ((~(e0 = op(e3, op(e3, e3)))) | (~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, op(e3, e3)))))),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5396, 5391])).
% 1.33/1.46 tff(5398,plain,
% 1.33/1.46 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5397, 5387, 5384])).
% 1.33/1.46 tff(5399,plain,
% 1.33/1.46 (~(op(e3, e0) = e2)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5398, 5383])).
% 1.33/1.46 tff(5400,plain,
% 1.33/1.46 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 1.33/1.46 inference(monotonicity,[status(thm)],[152])).
% 1.33/1.46 tff(5401,plain,
% 1.33/1.46 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 1.33/1.46 inference(symmetry,[status(thm)],[5400])).
% 1.33/1.46 tff(5402,plain,
% 1.33/1.46 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5401])).
% 1.33/1.46 tff(5403,plain,
% 1.33/1.46 (~(op(e3, e3) = e3)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[303, 5402])).
% 1.33/1.46 tff(5404,plain,
% 1.33/1.46 (op(e0, e3) = e3),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[480, 5403, 124, 170])).
% 1.33/1.46 tff(5405,plain,
% 1.33/1.46 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5404])).
% 1.33/1.46 tff(5406,plain,
% 1.33/1.46 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5405])).
% 1.33/1.46 tff(5407,plain,
% 1.33/1.46 (op(e1, e3) = e2),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[104, 138, 80, 170])).
% 1.33/1.46 tff(5408,plain,
% 1.33/1.46 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5407])).
% 1.33/1.46 tff(5409,plain,
% 1.33/1.46 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.33/1.46 inference(transitivity,[status(thm)],[5408, 120])).
% 1.33/1.46 tff(5410,plain,
% 1.33/1.46 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5409])).
% 1.33/1.46 tff(5411,plain,
% 1.33/1.46 (~(op(e2, e3) = e2)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[118, 5410])).
% 1.33/1.46 tff(5412,plain,
% 1.33/1.46 (op(e2, e3) = e0),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[206, 5411, 76, 124])).
% 1.33/1.46 tff(5413,plain,
% 1.33/1.46 (~(op(e3, e0) = op(e0, e3))),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[493, 5412, 163, 161, 138, 5403])).
% 1.33/1.46 tff(5414,plain,
% 1.33/1.46 (~(op(e3, e0) = e3)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5413, 5406])).
% 1.33/1.46 tff(5415,plain,
% 1.33/1.46 (((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))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5416,plain,
% 1.33/1.46 ((((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))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5417,plain,
% 1.33/1.46 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2))),
% 1.33/1.46 inference(rewrite,[status(thm)],[])).
% 1.33/1.46 tff(5418,plain,
% 1.33/1.46 (((((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))),
% 1.33/1.46 inference(monotonicity,[status(thm)],[5417])).
% 1.33/1.46 tff(5419,plain,
% 1.33/1.46 (((((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))),
% 1.33/1.46 inference(transitivity,[status(thm)],[5418, 5416])).
% 1.33/1.46 tff(5420,plain,
% 1.33/1.46 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)),
% 1.33/1.46 inference(and_elim,[status(thm)],[96])).
% 1.33/1.46 tff(5421,plain,
% 1.33/1.46 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5420, 5419])).
% 1.33/1.46 tff(5422,plain,
% 1.33/1.46 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 1.33/1.46 inference(modus_ponens,[status(thm)],[5421, 5415])).
% 1.33/1.46 tff(5423,plain,
% 1.33/1.46 ($false),
% 1.33/1.46 inference(unit_resolution,[status(thm)],[5422, 5414, 5399, 5376, 158])).
% 1.33/1.46 tff(5424,plain,(((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e1, e3) = e0) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.47 tff(5425,plain,
% 1.33/1.47 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5424, 124, 76, 80, 121])).
% 1.33/1.47 tff(5426,plain,
% 1.33/1.47 (op(e1, e3) = e1),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[104, 1080, 80, 72])).
% 1.33/1.47 tff(5427,plain,
% 1.33/1.47 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5426])).
% 1.33/1.47 tff(5428,plain,
% 1.33/1.47 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5427, 657])).
% 1.33/1.47 tff(5429,plain,
% 1.33/1.47 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5428])).
% 1.33/1.47 tff(5430,plain,
% 1.33/1.47 (~(op(e3, e3) = e1)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[571, 5429])).
% 1.33/1.47 tff(5431,plain,
% 1.33/1.47 (op(e2, e3) = e2),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[2786, 126, 72, 79])).
% 1.33/1.47 tff(5432,plain,
% 1.33/1.47 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5431])).
% 1.33/1.47 tff(5433,plain,
% 1.33/1.47 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5432, 1])).
% 1.33/1.47 tff(5434,plain,
% 1.33/1.47 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 1.33/1.47 inference(symmetry,[status(thm)],[5433])).
% 1.33/1.47 tff(5435,plain,
% 1.33/1.47 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5434])).
% 1.33/1.47 tff(5436,plain,
% 1.33/1.47 (~(op(e2, e3) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[14, 5435])).
% 1.33/1.47 tff(5437,plain,
% 1.33/1.47 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5426])).
% 1.33/1.47 tff(5438,plain,
% 1.33/1.47 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5437])).
% 1.33/1.47 tff(5439,plain,
% 1.33/1.47 (~(op(e1, e0) = e1)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[110, 5438])).
% 1.33/1.47 tff(5440,plain,
% 1.33/1.47 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5431])).
% 1.33/1.47 tff(5441,plain,
% 1.33/1.47 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5440])).
% 1.33/1.47 tff(5442,plain,
% 1.33/1.47 (~(op(e2, e0) = e2)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[989, 5441])).
% 1.33/1.47 tff(5443,plain,
% 1.33/1.47 ((op(e2, e1) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5444,plain,
% 1.33/1.47 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5443, 86])).
% 1.33/1.47 tff(5445,plain,
% 1.33/1.47 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5444])).
% 1.33/1.47 tff(5446,plain,
% 1.33/1.47 (~(op(e2, e3) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[197, 5445])).
% 1.33/1.47 tff(5447,plain,
% 1.33/1.47 (op(e0, e3) = e0),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1098, 656, 5446, 80])).
% 1.33/1.47 tff(5448,plain,
% 1.33/1.47 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5447])).
% 1.33/1.47 tff(5449,plain,
% 1.33/1.47 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5448])).
% 1.33/1.47 tff(5450,plain,
% 1.33/1.47 (~(op(e0, e0) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[3414, 5449])).
% 1.33/1.47 tff(5451,plain,
% 1.33/1.47 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5447])).
% 1.33/1.47 tff(5452,plain,
% 1.33/1.47 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5451])).
% 1.33/1.47 tff(5453,plain,
% 1.33/1.47 (~(op(e0, e2) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[918, 5452])).
% 1.33/1.47 tff(5454,plain,
% 1.33/1.47 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5455,plain,
% 1.33/1.47 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5454])).
% 1.33/1.47 tff(5456,plain,
% 1.33/1.47 (~(op(e1, e1) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[225, 5455])).
% 1.33/1.47 tff(5457,assumption,(~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))), introduced(assumption)).
% 1.33/1.47 tff(5458,plain,
% 1.33/1.47 (~(op(op(e0, e3), e3) = e0)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1361, 5457])).
% 1.33/1.47 tff(5459,assumption,(~(op(op(e0, e3), e3) = e0)), introduced(assumption)).
% 1.33/1.47 tff(5460,plain,
% 1.33/1.47 ($false),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5459, 1360])).
% 1.33/1.47 tff(5461,plain,((~(op(e0, e3) = e0)) | (op(op(e0, e3), e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.47 tff(5462,plain,
% 1.33/1.47 (~(op(e0, e3) = e0)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5461, 5458])).
% 1.33/1.47 tff(5463,plain,
% 1.33/1.47 (op(e0, e3) = e3),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[687, 5462, 121, 79])).
% 1.33/1.47 tff(5464,plain,
% 1.33/1.47 (op(e0, op(e0, e3)) = op(e0, e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5463])).
% 1.33/1.47 tff(5465,plain,
% 1.33/1.47 (op(e0, op(e0, e3)) = e3),
% 1.33/1.47 inference(transitivity,[status(thm)],[5464, 5463])).
% 1.33/1.47 tff(5466,plain,
% 1.33/1.47 (~(op(e0, op(e0, e3)) = e3)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1938, 5457])).
% 1.33/1.47 tff(5467,plain,
% 1.33/1.47 ($false),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5466, 5465])).
% 1.33/1.47 tff(5468,plain,(((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))) | (op(e0, e3) = e1) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.47 tff(5469,plain,
% 1.33/1.47 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5468, 79, 121])).
% 1.33/1.47 tff(5470,plain,
% 1.33/1.47 ((e0 = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.33/1.47 inference(commutativity,[status(thm)],[])).
% 1.33/1.47 tff(5471,plain,
% 1.33/1.47 ((op(e2, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5472,plain,
% 1.33/1.47 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5471, 5470])).
% 1.33/1.47 tff(5473,plain,
% 1.33/1.47 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5472])).
% 1.33/1.47 tff(5474,plain,
% 1.33/1.47 (~(op(e3, e1) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[402, 5473])).
% 1.33/1.47 tff(5475,plain,
% 1.33/1.47 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5372, 5474, 121, 80])).
% 1.33/1.47 tff(5476,plain,
% 1.33/1.47 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5477,plain,
% 1.33/1.47 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5476])).
% 1.33/1.47 tff(5478,plain,
% 1.33/1.47 (~(op(e0, e1) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[606, 5477])).
% 1.33/1.47 tff(5479,plain,
% 1.33/1.47 (op(e1, e3) = e3),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[104, 87, 80, 72])).
% 1.33/1.47 tff(5480,plain,
% 1.33/1.47 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5479])).
% 1.33/1.47 tff(5481,plain,
% 1.33/1.47 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5480, 112])).
% 1.33/1.47 tff(5482,plain,
% 1.33/1.47 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5481])).
% 1.33/1.47 tff(5483,plain,
% 1.33/1.47 (~(op(e2, e3) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[118, 5482])).
% 1.33/1.47 tff(5484,plain,
% 1.33/1.47 ((op(e2, e1) = e3) <=> (e0 = e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5485,plain,
% 1.33/1.47 ((e0 = e3) <=> (op(e2, e1) = e3)),
% 1.33/1.47 inference(symmetry,[status(thm)],[5484])).
% 1.33/1.47 tff(5486,plain,
% 1.33/1.47 ((~(e0 = e3)) <=> (~(op(e2, e1) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5485])).
% 1.33/1.47 tff(5487,plain,
% 1.33/1.47 (~(op(e2, e1) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[181, 5486])).
% 1.33/1.47 tff(5488,plain,
% 1.33/1.47 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5479])).
% 1.33/1.47 tff(5489,plain,
% 1.33/1.47 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5488])).
% 1.33/1.47 tff(5490,plain,
% 1.33/1.47 (~(op(e1, e2) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[1850, 5489])).
% 1.33/1.47 tff(5491,plain,
% 1.33/1.47 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5479])).
% 1.33/1.47 tff(5492,plain,
% 1.33/1.47 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5491])).
% 1.33/1.47 tff(5493,plain,
% 1.33/1.47 (~(op(e1, e1) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[619, 5492])).
% 1.33/1.47 tff(5494,plain,
% 1.33/1.47 (op(e3, e1) = e3),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1730, 5493, 5487, 2527])).
% 1.33/1.47 tff(5495,plain,
% 1.33/1.47 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5494])).
% 1.33/1.47 tff(5496,plain,
% 1.33/1.47 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5495, 3423])).
% 1.33/1.47 tff(5497,plain,
% 1.33/1.47 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5496])).
% 1.33/1.47 tff(5498,plain,
% 1.33/1.47 (~(op(e3, e2) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[3429, 5497])).
% 1.33/1.47 tff(5499,plain,
% 1.33/1.47 (op(e0, op(e1, e3)) = op(e0, e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5479])).
% 1.33/1.47 tff(5500,plain,
% 1.33/1.47 (op(e0, op(e1, e3)) = e0),
% 1.33/1.47 inference(transitivity,[status(thm)],[5499, 771])).
% 1.33/1.47 tff(5501,plain,
% 1.33/1.47 (((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)) | (~(op(e0, op(e1, e3)) = e0))),
% 1.33/1.47 inference(tautology,[status(thm)],[])).
% 1.33/1.47 tff(5502,plain,
% 1.33/1.47 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5501, 5500])).
% 1.33/1.47 tff(5503,plain,
% 1.33/1.47 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5479])).
% 1.33/1.47 tff(5504,plain,
% 1.33/1.47 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5503])).
% 1.33/1.47 tff(5505,plain,
% 1.33/1.47 (~(op(e1, e0) = e3)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[110, 5504])).
% 1.33/1.47 tff(5506,plain,
% 1.33/1.47 (op(e1, e1) = e1),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[630, 68, 5456, 1291])).
% 1.33/1.47 tff(5507,plain,
% 1.33/1.47 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5506])).
% 1.33/1.47 tff(5508,plain,
% 1.33/1.47 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5507])).
% 1.33/1.47 tff(5509,plain,
% 1.33/1.47 (~(op(e1, e0) = e1)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[737, 5508])).
% 1.33/1.47 tff(5510,plain,
% 1.33/1.47 (op(e3, e1) = e3),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1730, 1291, 5487, 2527])).
% 1.33/1.47 tff(5511,assumption,((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)), introduced(assumption)).
% 1.33/1.47 tff(5512,plain,
% 1.33/1.47 ((op(e2, e1) = e2) <=> (e0 = e2)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5513,plain,
% 1.33/1.47 ((e0 = e2) <=> (op(e2, e1) = e2)),
% 1.33/1.47 inference(symmetry,[status(thm)],[5512])).
% 1.33/1.47 tff(5514,plain,
% 1.33/1.47 ((~(e0 = e2)) <=> (~(op(e2, e1) = e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5513])).
% 1.33/1.47 tff(5515,plain,
% 1.33/1.47 (~(op(e2, e1) = e2)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[14, 5514])).
% 1.33/1.47 tff(5516,plain,
% 1.33/1.47 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5510])).
% 1.33/1.47 tff(5517,plain,
% 1.33/1.47 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5516, 1314])).
% 1.33/1.47 tff(5518,plain,
% 1.33/1.47 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 1.33/1.47 inference(symmetry,[status(thm)],[5517])).
% 1.33/1.47 tff(5519,plain,
% 1.33/1.47 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5518])).
% 1.33/1.47 tff(5520,plain,
% 1.33/1.47 (~(op(e3, e1) = e2)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[1321, 5519])).
% 1.33/1.47 tff(5521,plain,
% 1.33/1.47 (op(e0, e1) = e2),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1993, 68, 5520, 5515])).
% 1.33/1.47 tff(5522,plain,
% 1.33/1.47 ((e1 = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.33/1.47 inference(commutativity,[status(thm)],[])).
% 1.33/1.47 tff(5523,assumption,(op(e1, e1) = e1), introduced(assumption)).
% 1.33/1.47 tff(5524,plain,
% 1.33/1.47 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5523])).
% 1.33/1.47 tff(5525,plain,
% 1.33/1.47 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5524, 5522])).
% 1.33/1.47 tff(5526,plain,
% 1.33/1.47 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5525])).
% 1.33/1.47 tff(5527,plain,
% 1.33/1.47 (~(op(e1, e2) = e1)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[1604, 5526])).
% 1.33/1.47 tff(5528,assumption,(~(op(e3, e0) = op(e0, e3))), introduced(assumption)).
% 1.33/1.47 tff(5529,plain,
% 1.33/1.47 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[771])).
% 1.33/1.47 tff(5530,plain,
% 1.33/1.47 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5529, 3077])).
% 1.33/1.47 tff(5531,plain,
% 1.33/1.47 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5530])).
% 1.33/1.47 tff(5532,plain,
% 1.33/1.47 (~(op(e3, e3) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[1077, 5531])).
% 1.33/1.47 tff(5533,plain,
% 1.33/1.47 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[772])).
% 1.33/1.47 tff(5534,plain,
% 1.33/1.47 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.33/1.47 inference(symmetry,[status(thm)],[5533])).
% 1.33/1.47 tff(5535,plain,
% 1.33/1.47 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5534])).
% 1.33/1.47 tff(5536,plain,
% 1.33/1.47 (~(op(e3, e0) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[5528, 5535])).
% 1.33/1.47 tff(5537,plain,
% 1.33/1.47 ($false),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1916, 5536, 5532, 183, 85])).
% 1.33/1.47 tff(5538,plain,((~(op(e0, e3) = e0)) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e0) = op(e0, e3))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.47 tff(5539,plain,
% 1.33/1.47 (op(e3, e2) = e0),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[5538, 5528, 5474, 771])).
% 1.33/1.47 tff(5540,plain,
% 1.33/1.47 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5539])).
% 1.33/1.47 tff(5541,plain,
% 1.33/1.47 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5540])).
% 1.33/1.47 tff(5542,plain,
% 1.33/1.47 (~(op(e1, e2) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[2292, 5541])).
% 1.33/1.47 tff(5543,plain,
% 1.33/1.47 (op(e1, e2) = e2),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[1859, 5542, 5527, 75])).
% 1.33/1.47 tff(5544,plain,
% 1.33/1.47 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5543])).
% 1.33/1.47 tff(5545,plain,
% 1.33/1.47 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5544, 81])).
% 1.33/1.47 tff(5546,plain,
% 1.33/1.47 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5545])).
% 1.33/1.47 tff(5547,plain,
% 1.33/1.47 (~(op(e2, e2) = e2)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[1273, 5546])).
% 1.33/1.47 tff(5548,assumption,(~(op(e2, e2) = e2)), introduced(assumption)).
% 1.33/1.47 tff(5549,plain,
% 1.33/1.47 ((op(e2, e1) = op(e2, e2)) <=> (e0 = op(e2, e2))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.33/1.47 tff(5550,plain,
% 1.33/1.47 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 1.33/1.47 inference(transitivity,[status(thm)],[5549, 994])).
% 1.33/1.47 tff(5551,plain,
% 1.33/1.47 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 1.33/1.47 inference(monotonicity,[status(thm)],[5550])).
% 1.33/1.47 tff(5552,plain,
% 1.33/1.47 (~(op(e2, e2) = e0)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[508, 5551])).
% 1.33/1.47 tff(5553,plain,
% 1.33/1.47 (op(e2, e2) = e1),
% 1.33/1.47 inference(unit_resolution,[status(thm)],[524, 2431, 5552, 5548])).
% 1.33/1.47 tff(5554,plain,
% 1.33/1.47 (e1 = op(e2, e2)),
% 1.33/1.47 inference(modus_ponens,[status(thm)],[5553, 317])).
% 1.33/1.47 tff(5555,plain,
% 1.33/1.47 (e2 = op(e0, e1)),
% 1.33/1.47 inference(symmetry,[status(thm)],[3492])).
% 1.37/1.47 tff(5556,plain,
% 1.37/1.47 (op(e2, op(e2, e2)) = op(op(e0, e1), e1)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5555, 5553])).
% 1.37/1.47 tff(5557,plain,
% 1.37/1.47 (op(op(e0, e1), e1) = op(e2, op(e2, e2))),
% 1.37/1.47 inference(symmetry,[status(thm)],[5556])).
% 1.37/1.47 tff(5558,plain,
% 1.37/1.47 (op(op(e0, e1), e1) = op(e2, e1)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[3492])).
% 1.37/1.47 tff(5559,plain,
% 1.37/1.47 (op(e2, e1) = op(op(e0, e1), e1)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5558])).
% 1.37/1.47 tff(5560,plain,
% 1.37/1.47 (e0 = op(e2, e1)),
% 1.37/1.47 inference(symmetry,[status(thm)],[3508])).
% 1.37/1.47 tff(5561,plain,
% 1.37/1.47 (e0 = op(e2, op(e2, e2))),
% 1.37/1.47 inference(transitivity,[status(thm)],[5560, 5559, 5557])).
% 1.37/1.47 tff(5562,plain,
% 1.37/1.47 (op(e2, op(e2, e2)) = e0),
% 1.37/1.47 inference(transitivity,[status(thm)],[5556, 5558, 3508])).
% 1.37/1.47 tff(5563,plain,
% 1.37/1.47 (op(e2, op(e2, op(e2, e2))) = op(op(e0, e1), e0)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5555, 5562])).
% 1.37/1.47 tff(5564,plain,
% 1.37/1.47 (op(op(e0, e1), e0) = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.47 inference(symmetry,[status(thm)],[5563])).
% 1.37/1.47 tff(5565,plain,
% 1.37/1.47 (op(op(e0, e1), e0) = op(e2, e0)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[3492])).
% 1.37/1.47 tff(5566,plain,
% 1.37/1.47 (op(e2, e0) = op(op(e0, e1), e0)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5565])).
% 1.37/1.47 tff(5567,plain,
% 1.37/1.47 (op(e2, e0) = e3),
% 1.37/1.47 inference(unit_resolution,[status(thm)],[1559, 2431, 5487, 124])).
% 1.37/1.47 tff(5568,plain,
% 1.37/1.47 (e3 = op(e2, e0)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5567])).
% 1.37/1.47 tff(5569,plain,
% 1.37/1.47 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.47 inference(transitivity,[status(thm)],[5568, 5566, 5564])).
% 1.37/1.47 tff(5570,plain,
% 1.37/1.47 ($false),
% 1.37/1.47 inference(unit_resolution,[status(thm)],[1648, 5569, 5561, 5554])).
% 1.37/1.47 tff(5571,plain,((op(e2, e2) = e3) | (~(op(e2, e1) = e0)) | (~(op(e0, e1) = e2)) | (op(e2, e2) = e2) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.47 tff(5572,plain,
% 1.37/1.47 (op(e2, e2) = e3),
% 1.37/1.47 inference(unit_resolution,[status(thm)],[5571, 5547, 3508, 3492, 124])).
% 1.37/1.47 tff(5573,plain,
% 1.37/1.47 (e3 = op(e2, e2)),
% 1.37/1.47 inference(modus_ponens,[status(thm)],[5572, 1796])).
% 1.37/1.47 tff(5574,plain,
% 1.37/1.47 ((e1 = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 1.37/1.47 inference(commutativity,[status(thm)],[])).
% 1.37/1.47 tff(5575,plain,
% 1.37/1.47 (op(e2, op(e2, e2)) = op(e2, e3)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5572])).
% 1.37/1.47 tff(5576,plain,
% 1.37/1.47 ((e1 = op(e2, op(e2, e2))) <=> (e1 = op(e2, e3))),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5575])).
% 1.37/1.47 tff(5577,plain,
% 1.37/1.47 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e3) = e1)),
% 1.37/1.47 inference(transitivity,[status(thm)],[5576, 5574])).
% 1.37/1.47 tff(5578,plain,
% 1.37/1.47 ((op(e2, e3) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 1.37/1.47 inference(symmetry,[status(thm)],[5577])).
% 1.37/1.47 tff(5579,plain,
% 1.37/1.47 ((op(e2, e1) = e1) <=> (e0 = e1)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.47 tff(5580,plain,
% 1.37/1.47 ((e0 = e1) <=> (op(e2, e1) = e1)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5579])).
% 1.37/1.47 tff(5581,plain,
% 1.37/1.47 ((~(e0 = e1)) <=> (~(op(e2, e1) = e1))),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5580])).
% 1.37/1.47 tff(5582,plain,
% 1.37/1.47 (~(op(e2, e1) = e1)),
% 1.37/1.47 inference(modus_ponens,[status(thm)],[26, 5581])).
% 1.37/1.47 tff(5583,plain,
% 1.37/1.47 ((op(e2, e2) = e1) <=> (e3 = e1)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5572])).
% 1.37/1.47 tff(5584,plain,
% 1.37/1.47 ((op(e2, e2) = e1) <=> (e1 = e3)),
% 1.37/1.47 inference(transitivity,[status(thm)],[5583, 128])).
% 1.37/1.47 tff(5585,plain,
% 1.37/1.47 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5584])).
% 1.37/1.47 tff(5586,plain,
% 1.37/1.47 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5585])).
% 1.37/1.47 tff(5587,plain,
% 1.37/1.47 (~(op(e2, e2) = e1)),
% 1.37/1.47 inference(modus_ponens,[status(thm)],[303, 5586])).
% 1.37/1.47 tff(5588,plain,
% 1.37/1.47 ((op(e0, e3) = e3) <=> (e0 = e3)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[771])).
% 1.37/1.47 tff(5589,plain,
% 1.37/1.47 ((e0 = e3) <=> (op(e0, e3) = e3)),
% 1.37/1.47 inference(symmetry,[status(thm)],[5588])).
% 1.37/1.47 tff(5590,plain,
% 1.37/1.47 ((~(e0 = e3)) <=> (~(op(e0, e3) = e3))),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5589])).
% 1.37/1.47 tff(5591,plain,
% 1.37/1.47 (~(op(e0, e3) = e3)),
% 1.37/1.47 inference(modus_ponens,[status(thm)],[181, 5590])).
% 1.37/1.47 tff(5592,plain,
% 1.37/1.47 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.37/1.47 inference(monotonicity,[status(thm)],[5572])).
% 1.37/1.47 tff(5593,plain,
% 1.37/1.47 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5592])).
% 1.37/1.48 tff(5594,plain,
% 1.37/1.48 (~(op(e0, e2) = e3)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[2736, 5593])).
% 1.37/1.48 tff(5595,plain,
% 1.37/1.48 (op(e0, e0) = e3),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[1495, 5594, 2527, 5591])).
% 1.37/1.48 tff(5596,plain,
% 1.37/1.48 (op(e0, op(e0, e0)) = op(e0, e3)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5595])).
% 1.37/1.48 tff(5597,plain,
% 1.37/1.48 (op(e0, op(e0, e0)) = e0),
% 1.37/1.48 inference(transitivity,[status(thm)],[5596, 771])).
% 1.37/1.48 tff(5598,plain,
% 1.37/1.48 (((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)) | (~(op(e0, op(e0, e0)) = e0))),
% 1.37/1.48 inference(tautology,[status(thm)],[])).
% 1.37/1.48 tff(5599,plain,
% 1.37/1.48 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[5598, 5597])).
% 1.37/1.48 tff(5600,plain,
% 1.37/1.48 ((op(e3, e2) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5539])).
% 1.37/1.48 tff(5601,plain,
% 1.37/1.48 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.37/1.48 inference(transitivity,[status(thm)],[5600, 86])).
% 1.37/1.48 tff(5602,plain,
% 1.37/1.48 ((op(e2, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.37/1.48 inference(symmetry,[status(thm)],[5601])).
% 1.37/1.48 tff(5603,plain,
% 1.37/1.48 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.37/1.48 inference(transitivity,[status(thm)],[5602, 395])).
% 1.37/1.48 tff(5604,plain,
% 1.37/1.48 ((~(op(e2, e3) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5603])).
% 1.37/1.48 tff(5605,plain,
% 1.37/1.48 (~(op(e2, e3) = op(e3, e2))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5446, 5604])).
% 1.37/1.48 tff(5606,plain,
% 1.37/1.48 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[430, 5605])).
% 1.37/1.48 tff(5607,assumption,(op(e3, e1) = e3), introduced(assumption)).
% 1.37/1.48 tff(5608,plain,
% 1.37/1.48 (op(e0, op(e3, e1)) = op(e0, e3)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5607])).
% 1.37/1.48 tff(5609,plain,
% 1.37/1.48 (op(e0, op(e3, e1)) = e0),
% 1.37/1.48 inference(transitivity,[status(thm)],[5608, 771])).
% 1.37/1.48 tff(5610,plain,
% 1.37/1.48 (((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)) | (~(op(e0, op(e3, e1)) = e0))),
% 1.37/1.48 inference(tautology,[status(thm)],[])).
% 1.37/1.48 tff(5611,plain,
% 1.37/1.48 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[5610, 5609])).
% 1.37/1.48 tff(5612,plain,
% 1.37/1.48 (~(op(e0, e3) = op(e3, e0))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5528, 454])).
% 1.37/1.48 tff(5613,plain,
% 1.37/1.48 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[496, 5612])).
% 1.37/1.48 tff(5614,plain,
% 1.37/1.48 ((~(op(e2, e3) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5602])).
% 1.37/1.48 tff(5615,plain,
% 1.37/1.48 (~(op(e3, e2) = op(e2, e3))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5446, 5614])).
% 1.37/1.48 tff(5616,plain,
% 1.37/1.48 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[500, 5615])).
% 1.37/1.48 tff(5617,plain,
% 1.37/1.48 (op(e0, op(e2, e2)) = op(e0, e3)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5572])).
% 1.37/1.48 tff(5618,plain,
% 1.37/1.48 (op(e0, op(e2, e2)) = e0),
% 1.37/1.48 inference(transitivity,[status(thm)],[5617, 771])).
% 1.37/1.48 tff(5619,plain,
% 1.37/1.48 (((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)) | (~(op(e0, op(e2, e2)) = e0))),
% 1.37/1.48 inference(tautology,[status(thm)],[])).
% 1.37/1.48 tff(5620,plain,
% 1.37/1.48 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[5619, 5618])).
% 1.37/1.48 tff(5621,plain,
% 1.37/1.48 ((op(e2, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.48 tff(5622,plain,
% 1.37/1.48 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 1.37/1.48 inference(transitivity,[status(thm)],[5621, 67])).
% 1.37/1.48 tff(5623,plain,
% 1.37/1.48 ((op(e1, e2) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 1.37/1.48 inference(symmetry,[status(thm)],[5622])).
% 1.37/1.48 tff(5624,plain,
% 1.37/1.48 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 1.37/1.48 inference(transitivity,[status(thm)],[5540, 5623, 531])).
% 1.37/1.48 tff(5625,plain,
% 1.37/1.48 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5624])).
% 1.37/1.48 tff(5626,plain,
% 1.37/1.48 (~(op(e1, e2) = op(e2, e1))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[2292, 5625])).
% 1.37/1.48 tff(5627,plain,
% 1.37/1.48 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[539, 5626])).
% 1.37/1.48 tff(5628,plain,
% 1.37/1.48 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5539])).
% 1.37/1.48 tff(5629,plain,
% 1.37/1.48 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 1.37/1.48 inference(symmetry,[status(thm)],[5628])).
% 1.37/1.48 tff(5630,plain,
% 1.37/1.48 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5629])).
% 1.37/1.48 tff(5631,plain,
% 1.37/1.48 (~(op(e3, e2) = e1)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[26, 5630])).
% 1.37/1.48 tff(5632,plain,
% 1.37/1.48 (op(e0, e2) = e1),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[1613, 5587, 5527, 5631])).
% 1.37/1.48 tff(5633,plain,
% 1.37/1.48 (op(e3, op(e0, e2)) = op(e3, e1)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5632])).
% 1.37/1.48 tff(5634,plain,
% 1.37/1.48 (op(e3, op(e0, e2)) = e3),
% 1.37/1.48 inference(transitivity,[status(thm)],[5633, 5607])).
% 1.37/1.48 tff(5635,plain,
% 1.37/1.48 (((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)) | (~(op(e3, op(e0, e2)) = e3))),
% 1.37/1.48 inference(tautology,[status(thm)],[])).
% 1.37/1.48 tff(5636,plain,
% 1.37/1.48 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[5635, 5634])).
% 1.37/1.48 tff(5637,plain,
% 1.37/1.48 ((e0 = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 1.37/1.48 inference(commutativity,[status(thm)],[])).
% 1.37/1.48 tff(5638,plain,
% 1.37/1.48 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[771])).
% 1.37/1.48 tff(5639,plain,
% 1.37/1.48 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5638])).
% 1.37/1.48 tff(5640,plain,
% 1.37/1.48 (~(op(e0, e0) = e0)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[3414, 5639])).
% 1.37/1.48 tff(5641,plain,
% 1.37/1.48 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e0)),
% 1.37/1.48 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.48 tff(5642,plain,
% 1.37/1.48 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e0))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5641])).
% 1.37/1.48 tff(5643,plain,
% 1.37/1.48 (~(op(e2, e0) = e0)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[1966, 5642])).
% 1.37/1.48 tff(5644,plain,
% 1.37/1.48 (((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))),
% 1.37/1.48 inference(rewrite,[status(thm)],[])).
% 1.37/1.48 tff(5645,plain,
% 1.37/1.48 ((((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))),
% 1.37/1.48 inference(rewrite,[status(thm)],[])).
% 1.37/1.48 tff(5646,plain,
% 1.37/1.48 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) <=> ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0))),
% 1.37/1.48 inference(rewrite,[status(thm)],[])).
% 1.37/1.48 tff(5647,plain,
% 1.37/1.48 (((((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))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5646])).
% 1.37/1.48 tff(5648,plain,
% 1.37/1.48 (((((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))),
% 1.37/1.48 inference(transitivity,[status(thm)],[5647, 5645])).
% 1.37/1.48 tff(5649,plain,
% 1.37/1.48 ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0)),
% 1.37/1.48 inference(and_elim,[status(thm)],[3973])).
% 1.37/1.48 tff(5650,plain,
% 1.37/1.48 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5649, 5648])).
% 1.37/1.48 tff(5651,plain,
% 1.37/1.48 ((op(e0, e0) = e0) | (op(e1, e0) = e0) | (op(e2, e0) = e0) | (op(e3, e0) = e0)),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5650, 5644])).
% 1.37/1.48 tff(5652,plain,
% 1.37/1.48 (op(e1, e0) = e0),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[5651, 5536, 5643, 5640])).
% 1.37/1.48 tff(5653,plain,
% 1.37/1.48 ((op(e1, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5652])).
% 1.37/1.48 tff(5654,plain,
% 1.37/1.48 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 1.37/1.48 inference(transitivity,[status(thm)],[5653, 5637])).
% 1.37/1.48 tff(5655,plain,
% 1.37/1.48 ((op(e0, e1) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 1.37/1.48 inference(symmetry,[status(thm)],[5654])).
% 1.37/1.48 tff(5656,plain,
% 1.37/1.48 ((~(op(e0, e1) = e0)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5655])).
% 1.37/1.48 tff(5657,plain,
% 1.37/1.48 (~(op(e1, e0) = op(e0, e1))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5478, 5656])).
% 1.37/1.48 tff(5658,plain,
% 1.37/1.48 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[613, 5657])).
% 1.37/1.48 tff(5659,plain,
% 1.37/1.48 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e1) = op(e1, e2))),
% 1.37/1.48 inference(transitivity,[status(thm)],[5540, 5623])).
% 1.37/1.48 tff(5660,plain,
% 1.37/1.48 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5659])).
% 1.37/1.48 tff(5661,plain,
% 1.37/1.48 (~(op(e2, e1) = op(e1, e2))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[2292, 5660])).
% 1.37/1.48 tff(5662,plain,
% 1.37/1.48 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[557, 5661])).
% 1.37/1.48 tff(5663,plain,
% 1.37/1.48 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e1, e0))),
% 1.37/1.48 inference(transitivity,[status(thm)],[5655, 596])).
% 1.37/1.48 tff(5664,plain,
% 1.37/1.48 ((~(op(e0, e1) = e0)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.37/1.48 inference(monotonicity,[status(thm)],[5663])).
% 1.37/1.48 tff(5665,plain,
% 1.37/1.48 (~(op(e0, e1) = op(e1, e0))),
% 1.37/1.48 inference(modus_ponens,[status(thm)],[5478, 5664])).
% 1.37/1.48 tff(5666,plain,
% 1.37/1.48 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.37/1.48 inference(unit_resolution,[status(thm)],[609, 5665])).
% 1.37/1.48 tff(5667,assumption,((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5668,assumption,((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5669,assumption,((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5670,assumption,((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5671,assumption,((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5672,assumption,((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5673,assumption,((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5674,assumption,((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)), introduced(assumption)).
% 1.37/1.48 tff(5675,assumption,((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)), introduced(assumption)).
% 1.37/1.49 tff(5676,plain,
% 1.37/1.49 (op(e1, op(e1, e1)) = op(e1, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5523])).
% 1.37/1.49 tff(5677,plain,
% 1.37/1.49 (op(e1, op(e1, e1)) = e1),
% 1.37/1.49 inference(transitivity,[status(thm)],[5676, 5523])).
% 1.37/1.49 tff(5678,plain,
% 1.37/1.49 (((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)) | (~(op(e1, op(e1, e1)) = e1))),
% 1.37/1.49 inference(tautology,[status(thm)],[])).
% 1.37/1.49 tff(5679,plain,
% 1.37/1.49 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5678, 5677])).
% 1.37/1.49 tff(5680,assumption,((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)), introduced(assumption)).
% 1.37/1.49 tff(5681,assumption,((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)), introduced(assumption)).
% 1.37/1.49 tff(5682,plain,
% 1.37/1.49 (op(e3, e3) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[151, 76, 121, 87])).
% 1.37/1.49 tff(5683,plain,
% 1.37/1.49 (op(e1, op(e3, e3)) = op(e1, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5682])).
% 1.37/1.49 tff(5684,plain,
% 1.37/1.49 (op(e1, op(e3, e3)) = e1),
% 1.37/1.49 inference(transitivity,[status(thm)],[5683, 5523])).
% 1.37/1.49 tff(5685,plain,
% 1.37/1.49 (((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)) | (~(op(e1, op(e3, e3)) = e1))),
% 1.37/1.49 inference(tautology,[status(thm)],[])).
% 1.37/1.49 tff(5686,plain,
% 1.37/1.49 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5685, 5684])).
% 1.37/1.49 tff(5687,plain,
% 1.37/1.49 (op(e2, e0) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[345, 76, 1348, 4530])).
% 1.37/1.49 tff(5688,plain,
% 1.37/1.49 (op(e1, op(e2, e0)) = op(e1, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5687])).
% 1.37/1.49 tff(5689,plain,
% 1.37/1.49 (op(e1, op(e2, e0)) = e1),
% 1.37/1.49 inference(transitivity,[status(thm)],[5688, 5523])).
% 1.37/1.49 tff(5690,plain,
% 1.37/1.49 (((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)) | (~(op(e1, op(e2, e0)) = e1))),
% 1.37/1.49 inference(tautology,[status(thm)],[])).
% 1.37/1.49 tff(5691,plain,
% 1.37/1.49 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5690, 5689])).
% 1.37/1.49 tff(5692,plain,
% 1.37/1.49 ($false),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5367, 5691, 5686, 5511, 5681, 5680, 5679, 5675, 5674, 5673, 5672, 5671, 5670, 5669, 5668, 5667])).
% 1.37/1.49 tff(5693,plain,((op(e2, e3) = e1) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~(op(e1, e1) = e1)) | (op(e2, e2) = e1) | (op(e2, e1) = e1) | (op(e0, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.49 tff(5694,plain,
% 1.37/1.49 (op(e2, e3) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5693, 5666, 5511, 5662, 5658, 5636, 5627, 5620, 5616, 5613, 5611, 5606, 5599, 5523, 5587, 5582, 121, 87])).
% 1.37/1.49 tff(5695,plain,
% 1.37/1.49 (e1 = op(e2, op(e2, e2))),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[5694, 5578])).
% 1.37/1.49 tff(5696,plain,
% 1.37/1.49 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5575])).
% 1.37/1.49 tff(5697,plain,
% 1.37/1.49 (op(e2, op(e2, e3)) = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.49 inference(symmetry,[status(thm)],[5696])).
% 1.37/1.49 tff(5698,plain,
% 1.37/1.49 (e1 = op(e0, e2)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5632])).
% 1.37/1.49 tff(5699,plain,
% 1.37/1.49 (op(e2, e3) = op(e0, e2)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5694, 5698])).
% 1.37/1.49 tff(5700,plain,
% 1.37/1.49 (op(e2, op(e2, e3)) = op(e2, op(e0, e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5699])).
% 1.37/1.49 tff(5701,plain,
% 1.37/1.49 (op(e2, op(e0, e2)) = op(e2, op(e2, e3))),
% 1.37/1.49 inference(symmetry,[status(thm)],[5700])).
% 1.37/1.49 tff(5702,plain,
% 1.37/1.49 (op(e2, op(e0, e2)) = op(op(e0, e1), e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5555, 5632])).
% 1.37/1.49 tff(5703,plain,
% 1.37/1.49 (op(op(e0, e1), e1) = op(e2, op(e0, e2))),
% 1.37/1.49 inference(symmetry,[status(thm)],[5702])).
% 1.37/1.49 tff(5704,plain,
% 1.37/1.49 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.49 inference(transitivity,[status(thm)],[5560, 5559, 5703, 5701, 5697])).
% 1.37/1.49 tff(5705,plain,
% 1.37/1.49 ($false),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2952, 5704, 5695, 5573])).
% 1.37/1.49 tff(5706,plain,((op(e3, e0) = op(e0, e3)) | (~(op(e2, e1) = e0)) | (~(op(e0, e1) = e2)) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~(op(e1, e1) = e1)) | (op(e0, e3) = e1) | (op(e1, e3) = e1) | (~(op(e0, e3) = e0)) | (~(op(e3, e1) = e3)) | (op(e0, e1) = e3) | (op(e2, e3) = e3) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.49 tff(5707,plain,
% 1.37/1.49 (op(e3, e0) = op(e0, e3)),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5706, 5521, 3508, 5511, 5506, 121, 87, 771, 5510, 2527, 124, 75])).
% 1.37/1.49 tff(5708,plain,
% 1.37/1.49 (op(e3, e0) = e0),
% 1.37/1.49 inference(transitivity,[status(thm)],[5707, 771])).
% 1.37/1.49 tff(5709,plain,
% 1.37/1.49 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5708])).
% 1.37/1.49 tff(5710,plain,
% 1.37/1.49 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5709])).
% 1.37/1.49 tff(5711,plain,
% 1.37/1.49 (~(op(e1, e0) = e0)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[410, 5710])).
% 1.37/1.49 tff(5712,plain,
% 1.37/1.49 (e2 = op(e0, e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5521])).
% 1.37/1.49 tff(5713,plain,
% 1.37/1.49 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5712])).
% 1.37/1.49 tff(5714,plain,
% 1.37/1.49 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5713])).
% 1.37/1.49 tff(5715,plain,
% 1.37/1.49 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[2418])).
% 1.37/1.49 tff(5716,plain,
% 1.37/1.49 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5715])).
% 1.37/1.49 tff(5717,plain,
% 1.37/1.49 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5510])).
% 1.37/1.49 tff(5718,plain,
% 1.37/1.49 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, op(e0, e3)) = e3)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5717, 5716])).
% 1.37/1.49 tff(5719,plain,
% 1.37/1.49 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5718])).
% 1.37/1.49 tff(5720,plain,
% 1.37/1.49 (~(op(e3, op(e0, e3)) = e3)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[580, 5719])).
% 1.37/1.49 tff(5721,plain,
% 1.37/1.49 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e0) = e0)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[1469])).
% 1.37/1.49 tff(5722,plain,
% 1.37/1.49 ((op(e0, e0) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5721])).
% 1.37/1.49 tff(5723,plain,
% 1.37/1.49 ((~(op(e0, e0) = e0)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5722])).
% 1.37/1.49 tff(5724,plain,
% 1.37/1.49 (~(op(e0, op(e0, e3)) = e0)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[5640, 5723])).
% 1.37/1.49 tff(5725,plain,
% 1.37/1.49 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[2179])).
% 1.37/1.49 tff(5726,plain,
% 1.37/1.49 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5725])).
% 1.37/1.49 tff(5727,plain,
% 1.37/1.49 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, op(e0, e3)) = e1)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5507, 5726])).
% 1.37/1.49 tff(5728,plain,
% 1.37/1.49 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5727])).
% 1.37/1.49 tff(5729,plain,
% 1.37/1.49 (~(op(e1, op(e0, e3)) = e1)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[737, 5728])).
% 1.37/1.49 tff(5730,plain,
% 1.37/1.49 (op(e2, op(e0, e3)) = e2),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[4654, 5707, 121, 5729, 5724, 5720])).
% 1.37/1.49 tff(5731,plain,
% 1.37/1.49 (op(e2, e0) = op(e0, e1)),
% 1.37/1.49 inference(transitivity,[status(thm)],[3813, 5730, 5712])).
% 1.37/1.49 tff(5732,plain,
% 1.37/1.49 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5731])).
% 1.37/1.49 tff(5733,plain,
% 1.37/1.49 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5732, 5714])).
% 1.37/1.49 tff(5734,plain,
% 1.37/1.49 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5733])).
% 1.37/1.49 tff(5735,plain,
% 1.37/1.49 (~(op(e1, e0) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[756, 5734])).
% 1.37/1.49 tff(5736,plain,
% 1.37/1.49 ($false),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[728, 5735, 5711, 2168, 5509])).
% 1.37/1.49 tff(5737,plain,((op(e1, e1) = e2) | (op(e1, e0) = e3) | (~(op(e0, e3) = e0)) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (op(e1, e3) = e1) | (op(e0, e1) = e3) | (op(e2, e3) = e3) | (op(e1, e2) = e3) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.49 tff(5738,plain,
% 1.37/1.49 (op(e1, e1) = e2),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5737, 5505, 771, 121, 3508, 5502, 87, 2527, 5483, 5490, 5493])).
% 1.37/1.49 tff(5739,plain,
% 1.37/1.49 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5738])).
% 1.37/1.49 tff(5740,plain,
% 1.37/1.49 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5739])).
% 1.37/1.49 tff(5741,plain,
% 1.37/1.49 (~(op(e1, e0) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[737, 5740])).
% 1.37/1.49 tff(5742,plain,
% 1.37/1.49 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5494])).
% 1.37/1.49 tff(5743,plain,
% 1.37/1.49 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5742, 1314])).
% 1.37/1.49 tff(5744,plain,
% 1.37/1.49 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5743])).
% 1.37/1.49 tff(5745,plain,
% 1.37/1.49 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5744])).
% 1.37/1.49 tff(5746,plain,
% 1.37/1.49 (~(op(e3, e1) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[1321, 5745])).
% 1.37/1.49 tff(5747,plain,
% 1.37/1.49 (op(op(e3, e1), e1) = op(e3, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5494])).
% 1.37/1.49 tff(5748,plain,
% 1.37/1.49 (op(op(e3, e1), e1) = e3),
% 1.37/1.49 inference(transitivity,[status(thm)],[5747, 5494])).
% 1.37/1.49 tff(5749,plain,
% 1.37/1.49 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2416, 5748])).
% 1.37/1.49 tff(5750,plain,
% 1.37/1.49 ((op(e3, e1) = e1) <=> (e3 = e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5494])).
% 1.37/1.49 tff(5751,plain,
% 1.37/1.49 ((op(e3, e1) = e1) <=> (e1 = e3)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5750, 128])).
% 1.37/1.49 tff(5752,plain,
% 1.37/1.49 ((e1 = e3) <=> (op(e3, e1) = e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5751])).
% 1.37/1.49 tff(5753,plain,
% 1.37/1.49 ((~(e1 = e3)) <=> (~(op(e3, e1) = e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5752])).
% 1.37/1.49 tff(5754,plain,
% 1.37/1.49 (~(op(e3, e1) = e1)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[303, 5753])).
% 1.37/1.49 tff(5755,plain,
% 1.37/1.49 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[2891])).
% 1.37/1.49 tff(5756,plain,
% 1.37/1.49 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5755, 69])).
% 1.37/1.49 tff(5757,plain,
% 1.37/1.49 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5756])).
% 1.37/1.49 tff(5758,plain,
% 1.37/1.49 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5757])).
% 1.37/1.49 tff(5759,plain,
% 1.37/1.49 (~(op(e1, e1) = e1)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[708, 5758])).
% 1.37/1.49 tff(5760,plain,
% 1.37/1.49 (op(e0, e1) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[1252, 5759, 5582, 2826])).
% 1.37/1.49 tff(5761,plain,
% 1.37/1.49 (e1 = op(e0, e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5760])).
% 1.37/1.49 tff(5762,plain,
% 1.37/1.49 ((e2 = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 1.37/1.49 inference(commutativity,[status(thm)],[])).
% 1.37/1.49 tff(5763,plain,
% 1.37/1.49 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[2891])).
% 1.37/1.49 tff(5764,plain,
% 1.37/1.49 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5763, 5762])).
% 1.37/1.49 tff(5765,plain,
% 1.37/1.49 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5764])).
% 1.37/1.49 tff(5766,plain,
% 1.37/1.49 (~(op(e1, e2) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[1604, 5765])).
% 1.37/1.49 tff(5767,plain,
% 1.37/1.49 (op(e1, e2) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[1859, 5542, 5766, 75])).
% 1.37/1.49 tff(5768,plain,
% 1.37/1.49 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5767])).
% 1.37/1.49 tff(5769,plain,
% 1.37/1.49 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5768, 316])).
% 1.37/1.49 tff(5770,plain,
% 1.37/1.49 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5769])).
% 1.37/1.49 tff(5771,plain,
% 1.37/1.49 (~(op(e2, e2) = e1)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[1273, 5770])).
% 1.37/1.49 tff(5772,plain,
% 1.37/1.49 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[2891])).
% 1.37/1.49 tff(5773,plain,
% 1.37/1.49 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5772])).
% 1.37/1.49 tff(5774,plain,
% 1.37/1.49 (~(op(e0, e1) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[792, 5773])).
% 1.37/1.49 tff(5775,plain,
% 1.37/1.49 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5539])).
% 1.37/1.49 tff(5776,plain,
% 1.37/1.49 (op(op(e3, e2), e3) = e0),
% 1.37/1.49 inference(transitivity,[status(thm)],[5775, 771])).
% 1.37/1.49 tff(5777,plain,
% 1.37/1.49 ((op(op(e3, e2), e3) = e2) <=> (e0 = e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5776])).
% 1.37/1.49 tff(5778,plain,
% 1.37/1.49 ((e0 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5777])).
% 1.37/1.49 tff(5779,plain,
% 1.37/1.49 ((~(e0 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5778])).
% 1.37/1.49 tff(5780,plain,
% 1.37/1.49 (~(op(op(e3, e2), e3) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[14, 5779])).
% 1.37/1.49 tff(5781,plain,
% 1.37/1.49 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2408, 5780])).
% 1.37/1.49 tff(5782,plain,
% 1.37/1.49 (op(e1, op(e1, e2)) = op(e1, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5767])).
% 1.37/1.49 tff(5783,plain,
% 1.37/1.49 (op(e1, op(e1, e2)) = e2),
% 1.37/1.49 inference(transitivity,[status(thm)],[5782, 2891])).
% 1.37/1.49 tff(5784,plain,
% 1.37/1.49 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2377, 5783])).
% 1.37/1.49 tff(5785,plain,
% 1.37/1.49 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[771])).
% 1.37/1.49 tff(5786,plain,
% 1.37/1.49 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5785])).
% 1.37/1.49 tff(5787,plain,
% 1.37/1.49 (~(op(e3, e0) = e0)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[5528, 5786])).
% 1.37/1.49 tff(5788,plain,
% 1.37/1.49 (op(e1, e0) = e0),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5651, 5787, 5643, 5640])).
% 1.37/1.49 tff(5789,plain,
% 1.37/1.49 (op(op(e0, e1), e0) = op(e1, e0)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5760])).
% 1.37/1.49 tff(5790,plain,
% 1.37/1.49 (op(e1, op(e1, e0)) = op(op(e0, e1), e0)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5761, 5788])).
% 1.37/1.49 tff(5791,plain,
% 1.37/1.49 (op(e1, op(e1, e0)) = e0),
% 1.37/1.49 inference(transitivity,[status(thm)],[5790, 5789, 5788])).
% 1.37/1.49 tff(5792,plain,
% 1.37/1.49 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[1836, 5791])).
% 1.37/1.49 tff(5793,plain,
% 1.37/1.49 (op(e2, e3) = e2),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[206, 76, 5446, 124])).
% 1.37/1.49 tff(5794,plain,
% 1.37/1.49 (op(op(e2, e3), e3) = op(e2, e3)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5793])).
% 1.37/1.49 tff(5795,plain,
% 1.37/1.49 (op(op(e2, e3), e3) = e2),
% 1.37/1.49 inference(transitivity,[status(thm)],[5794, 5793])).
% 1.37/1.49 tff(5796,plain,
% 1.37/1.49 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[1288, 5795])).
% 1.37/1.49 tff(5797,plain,
% 1.37/1.49 (op(op(e2, e1), e2) = op(e0, e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.49 tff(5798,plain,
% 1.37/1.49 ((op(op(e2, e1), e2) = e1) <=> (op(e0, e2) = e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5797])).
% 1.37/1.49 tff(5799,plain,
% 1.37/1.49 ((op(e0, e2) = e1) <=> (op(op(e2, e1), e2) = e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5798])).
% 1.37/1.49 tff(5800,assumption,(op(e0, e1) = e1), introduced(assumption)).
% 1.37/1.49 tff(5801,plain,
% 1.37/1.49 (e1 = op(e0, e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5800])).
% 1.37/1.49 tff(5802,plain,
% 1.37/1.49 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5801])).
% 1.37/1.49 tff(5803,plain,
% 1.37/1.49 ((op(e0, e2) = e1) <=> (op(e0, e1) = op(e0, e2))),
% 1.37/1.49 inference(transitivity,[status(thm)],[5802, 4680])).
% 1.37/1.49 tff(5804,plain,
% 1.37/1.49 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5803])).
% 1.37/1.49 tff(5805,plain,
% 1.37/1.49 ((op(e0, e1) = op(e0, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5804, 5799])).
% 1.37/1.49 tff(5806,plain,
% 1.37/1.49 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5805])).
% 1.37/1.49 tff(5807,plain,
% 1.37/1.49 (~(op(op(e2, e1), e2) = e1)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[2102, 5806])).
% 1.37/1.49 tff(5808,plain,
% 1.37/1.49 (((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))) | (op(op(e2, e1), e2) = e1)),
% 1.37/1.49 inference(tautology,[status(thm)],[])).
% 1.37/1.49 tff(5809,plain,
% 1.37/1.49 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[5808, 5807])).
% 1.37/1.49 tff(5810,plain,
% 1.37/1.49 (op(e2, op(e0, e1)) = op(e2, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5800])).
% 1.37/1.49 tff(5811,plain,
% 1.37/1.49 (op(e2, e0) = e1),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[345, 76, 1348, 5582])).
% 1.37/1.49 tff(5812,plain,
% 1.37/1.49 (op(e2, e0) = op(e0, e1)),
% 1.37/1.49 inference(transitivity,[status(thm)],[5811, 5801])).
% 1.37/1.49 tff(5813,plain,
% 1.37/1.49 (op(e2, op(e2, e0)) = op(e2, op(e0, e1))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5812])).
% 1.37/1.49 tff(5814,plain,
% 1.37/1.49 (op(e2, op(e2, e0)) = e0),
% 1.37/1.49 inference(transitivity,[status(thm)],[5813, 5810, 3508])).
% 1.37/1.49 tff(5815,plain,
% 1.37/1.49 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2653, 5814])).
% 1.37/1.49 tff(5816,plain,
% 1.37/1.49 (op(e0, op(e0, e1)) = op(e0, e1)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5800])).
% 1.37/1.49 tff(5817,plain,
% 1.37/1.49 (op(e0, op(e0, e1)) = e1),
% 1.37/1.49 inference(transitivity,[status(thm)],[5816, 5800])).
% 1.37/1.49 tff(5818,plain,
% 1.37/1.49 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.37/1.49 inference(unit_resolution,[status(thm)],[2449, 5817])).
% 1.37/1.49 tff(5819,assumption,(op(e3, e2) = e0), introduced(assumption)).
% 1.37/1.49 tff(5820,plain,
% 1.37/1.49 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5819])).
% 1.37/1.49 tff(5821,plain,
% 1.37/1.49 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 1.37/1.49 inference(symmetry,[status(thm)],[5820])).
% 1.37/1.49 tff(5822,plain,
% 1.37/1.49 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 1.37/1.49 inference(monotonicity,[status(thm)],[5821])).
% 1.37/1.49 tff(5823,plain,
% 1.37/1.49 (~(op(e3, e2) = e2)),
% 1.37/1.49 inference(modus_ponens,[status(thm)],[14, 5822])).
% 1.37/1.50 tff(5824,plain,
% 1.37/1.50 (op(e3, e3) = op(e0, e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5682, 5801])).
% 1.37/1.50 tff(5825,plain,
% 1.37/1.50 ((op(e3, e3) = e2) <=> (op(e0, e1) = e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5824])).
% 1.37/1.50 tff(5826,plain,
% 1.37/1.50 ((op(e0, e1) = e2) <=> (op(e3, e3) = e2)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5825])).
% 1.37/1.50 tff(5827,plain,
% 1.37/1.50 ((~(op(e0, e1) = e2)) <=> (~(op(e3, e3) = e2))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5826])).
% 1.37/1.50 tff(5828,assumption,(~(op(e0, e1) = e2)), introduced(assumption)).
% 1.37/1.50 tff(5829,plain,
% 1.37/1.50 (~(op(e3, e3) = e2)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 1.37/1.50 tff(5830,plain,
% 1.37/1.50 (op(e3, e0) = e2),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[2015, 5829, 82, 5823])).
% 1.37/1.50 tff(5831,plain,
% 1.37/1.50 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5830])).
% 1.37/1.50 tff(5832,plain,
% 1.37/1.50 (op(e3, op(e3, e0)) = e0),
% 1.37/1.50 inference(transitivity,[status(thm)],[5831, 5819])).
% 1.37/1.50 tff(5833,plain,
% 1.37/1.50 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1345, 5832])).
% 1.37/1.50 tff(5834,plain,
% 1.37/1.50 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5793])).
% 1.37/1.50 tff(5835,plain,
% 1.37/1.50 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5834])).
% 1.37/1.50 tff(5836,plain,
% 1.37/1.50 (~(op(e2, e2) = e2)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[515, 5835])).
% 1.37/1.50 tff(5837,plain,
% 1.37/1.50 (op(e0, e2) = e2),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1151, 5836, 3785, 5823])).
% 1.37/1.50 tff(5838,plain,
% 1.37/1.50 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5837])).
% 1.37/1.50 tff(5839,plain,
% 1.37/1.50 (op(e0, op(e0, e2)) = e2),
% 1.37/1.50 inference(transitivity,[status(thm)],[5838, 5837])).
% 1.37/1.50 tff(5840,plain,
% 1.37/1.50 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1331, 5839])).
% 1.37/1.50 tff(5841,plain,
% 1.37/1.50 ($false),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1459, 5840, 5833, 1357, 5818, 3342, 1304, 5815, 5809, 1358, 1275, 3341, 5796])).
% 1.37/1.50 tff(5842,plain,((op(e2, e3) = e1) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e3, e2) = e0)) | (op(e1, e2) = e2) | (op(e3, e1) = e2) | (~(op(e2, e1) = e0)) | (~(op(e0, e1) = e1)) | (op(e0, e1) = e2) | (op(e2, e2) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.50 tff(5843,plain,
% 1.37/1.50 (op(e2, e3) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[5842, 5792, 5469, 1304, 5784, 1275, 5781, 5539, 5766, 82, 3508, 5760, 5774, 5771, 124, 121, 87])).
% 1.37/1.50 tff(5844,plain,
% 1.37/1.50 (op(e2, e3) = op(e0, e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5843, 5761])).
% 1.37/1.50 tff(5845,plain,
% 1.37/1.50 ((op(e2, e3) = e2) <=> (op(e0, e1) = e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5844])).
% 1.37/1.50 tff(5846,plain,
% 1.37/1.50 ((op(e0, e1) = e2) <=> (op(e2, e3) = e2)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5845])).
% 1.37/1.50 tff(5847,plain,
% 1.37/1.50 ((~(op(e0, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5846])).
% 1.37/1.50 tff(5848,plain,
% 1.37/1.50 (~(op(e2, e3) = e2)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5774, 5847])).
% 1.37/1.50 tff(5849,plain,
% 1.37/1.50 (op(e3, e3) = e2),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[2786, 5848, 72, 79])).
% 1.37/1.50 tff(5850,plain,
% 1.37/1.50 (e2 = op(e3, e3)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5849, 2811])).
% 1.37/1.50 tff(5851,plain,
% 1.37/1.50 (op(e3, op(e3, e3)) = op(e3, e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5849])).
% 1.37/1.50 tff(5852,plain,
% 1.37/1.50 (op(e3, e2) = op(e3, op(e3, e3))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5851])).
% 1.37/1.50 tff(5853,plain,
% 1.37/1.50 (e0 = op(e3, e2)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5539])).
% 1.37/1.50 tff(5854,plain,
% 1.37/1.50 (e0 = op(e3, op(e3, e3))),
% 1.37/1.50 inference(transitivity,[status(thm)],[5853, 5852])).
% 1.37/1.50 tff(5855,plain,
% 1.37/1.50 (op(e3, op(e3, e3)) = e0),
% 1.37/1.50 inference(transitivity,[status(thm)],[5851, 5539])).
% 1.37/1.50 tff(5856,plain,
% 1.37/1.50 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5855])).
% 1.37/1.50 tff(5857,plain,
% 1.37/1.50 (op(e3, e0) = op(e3, op(e3, op(e3, e3)))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5856])).
% 1.37/1.50 tff(5858,plain,
% 1.37/1.50 ((op(e3, e2) = e1) <=> (e0 = op(e0, e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5539, 5761])).
% 1.37/1.50 tff(5859,plain,
% 1.37/1.50 ((op(e3, e2) = e1) <=> (op(e0, e1) = e0)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5858, 5637])).
% 1.37/1.50 tff(5860,plain,
% 1.37/1.50 ((op(e0, e1) = e0) <=> (op(e3, e2) = e1)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5859])).
% 1.37/1.50 tff(5861,plain,
% 1.37/1.50 ((~(op(e0, e1) = e0)) <=> (~(op(e3, e2) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5860])).
% 1.37/1.50 tff(5862,plain,
% 1.37/1.50 (~(op(e3, e2) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5478, 5861])).
% 1.37/1.50 tff(5863,plain,
% 1.37/1.50 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5843])).
% 1.37/1.50 tff(5864,plain,
% 1.37/1.50 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5863, 657])).
% 1.37/1.50 tff(5865,plain,
% 1.37/1.50 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5864])).
% 1.37/1.50 tff(5866,plain,
% 1.37/1.50 (~(op(e3, e3) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[368, 5865])).
% 1.37/1.50 tff(5867,plain,
% 1.37/1.50 (op(e3, e0) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[939, 5866, 2826, 5862])).
% 1.37/1.50 tff(5868,plain,
% 1.37/1.50 (e1 = op(e3, e0)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5867])).
% 1.37/1.50 tff(5869,plain,
% 1.37/1.50 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.37/1.50 inference(transitivity,[status(thm)],[5868, 5857])).
% 1.37/1.50 tff(5870,plain,
% 1.37/1.50 ((~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3)))))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3))))))),
% 1.37/1.50 inference(rewrite,[status(thm)],[])).
% 1.37/1.50 tff(5871,plain,
% 1.37/1.50 (((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))) <=> (~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3)))))))),
% 1.37/1.50 inference(rewrite,[status(thm)],[])).
% 1.37/1.50 tff(5872,plain,
% 1.37/1.50 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~(~((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3))))))))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5871])).
% 1.37/1.50 tff(5873,plain,
% 1.37/1.50 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3))))))),
% 1.37/1.50 inference(transitivity,[status(thm)],[5872, 5870])).
% 1.37/1.50 tff(5874,plain,
% 1.37/1.50 ((~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))))),
% 1.37/1.50 inference(rewrite,[status(thm)],[])).
% 1.37/1.50 tff(5875,plain,
% 1.37/1.50 ((~(((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(e3, op(e3, op(e3, e3)))))) <=> (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3))))))),
% 1.37/1.50 inference(rewrite,[status(thm)],[])).
% 1.37/1.50 tff(5876,axiom,(~(((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3))) & (e1 = op(e3, op(e3, op(e3, e3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax25')).
% 1.37/1.50 tff(5877,plain,
% 1.37/1.50 (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5876, 5875])).
% 1.37/1.50 tff(5878,plain,
% 1.37/1.50 (~((e0 = op(e3, op(e3, e3))) & (e2 = op(e3, e3)) & (e1 = op(e3, op(e3, op(e3, e3)))))),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5877, 5874])).
% 1.37/1.50 tff(5879,plain,
% 1.37/1.50 ((~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, op(e3, e3)))))),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5878, 5873])).
% 1.37/1.50 tff(5880,plain,
% 1.37/1.50 ($false),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[5879, 5869, 5854, 5850])).
% 1.37/1.50 tff(5881,plain,((op(e3, e0) = op(e0, e3)) | (op(e3, e1) = e1) | (op(e1, e3) = e2) | (op(e0, e3) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e3, e1) = e2) | (~(op(e2, e1) = e0)) | (op(e2, e3) = e3) | (op(e0, e3) = e1) | (op(e1, e3) = e1) | (~(op(e1, e1) = e2)) | (op(e1, e2) = e3) | (~(op(e0, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.50 tff(5882,plain,
% 1.37/1.50 (op(e3, e0) = op(e0, e3)),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[5881, 5754, 72, 79, 5475, 5749, 5746, 3508, 5483, 121, 87, 5738, 5490, 771])).
% 1.37/1.50 tff(5883,plain,
% 1.37/1.50 (op(e3, e0) = e0),
% 1.37/1.50 inference(transitivity,[status(thm)],[5882, 771])).
% 1.37/1.50 tff(5884,plain,
% 1.37/1.50 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5883])).
% 1.37/1.50 tff(5885,plain,
% 1.37/1.50 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5884])).
% 1.37/1.50 tff(5886,plain,
% 1.37/1.50 (~(op(e1, e0) = e0)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[410, 5885])).
% 1.37/1.50 tff(5887,plain,
% 1.37/1.50 (op(e1, e0) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[728, 5886, 5505, 5741])).
% 1.37/1.50 tff(5888,plain,
% 1.37/1.50 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5738])).
% 1.37/1.50 tff(5889,plain,
% 1.37/1.50 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5888, 69])).
% 1.37/1.50 tff(5890,plain,
% 1.37/1.50 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5889])).
% 1.37/1.50 tff(5891,plain,
% 1.37/1.50 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5890])).
% 1.37/1.50 tff(5892,plain,
% 1.37/1.50 (~(op(e1, e1) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[708, 5891])).
% 1.37/1.50 tff(5893,plain,
% 1.37/1.50 (op(e0, e1) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1252, 5892, 5582, 5754])).
% 1.37/1.50 tff(5894,plain,
% 1.37/1.50 (e1 = op(e0, e1)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5893])).
% 1.37/1.50 tff(5895,plain,
% 1.37/1.50 ((op(e3, e0) = e1) <=> (e0 = op(e0, e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5883, 5894])).
% 1.37/1.50 tff(5896,plain,
% 1.37/1.50 ((op(e3, e0) = e1) <=> (op(e0, e1) = e0)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5895, 5637])).
% 1.37/1.50 tff(5897,plain,
% 1.37/1.50 ((op(e0, e1) = e0) <=> (op(e3, e0) = e1)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5896])).
% 1.37/1.50 tff(5898,plain,
% 1.37/1.50 ((~(op(e0, e1) = e0)) <=> (~(op(e3, e0) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5897])).
% 1.37/1.50 tff(5899,plain,
% 1.37/1.50 (~(op(e3, e0) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5478, 5898])).
% 1.37/1.50 tff(5900,assumption,(op(e1, e0) = e1), introduced(assumption)).
% 1.37/1.50 tff(5901,plain,
% 1.37/1.50 (op(e1, e0) = op(e0, e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5900, 5801])).
% 1.37/1.50 tff(5902,plain,
% 1.37/1.50 (op(e2, op(e1, e0)) = op(e2, op(e0, e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5901])).
% 1.37/1.50 tff(5903,plain,
% 1.37/1.50 (e1 = op(e1, e0)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5900])).
% 1.37/1.50 tff(5904,plain,
% 1.37/1.50 ((op(e1, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5900])).
% 1.37/1.50 tff(5905,plain,
% 1.37/1.50 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5904, 16])).
% 1.37/1.50 tff(5906,plain,
% 1.37/1.50 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5905])).
% 1.37/1.50 tff(5907,plain,
% 1.37/1.50 (~(op(e2, e0) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[756, 5906])).
% 1.37/1.50 tff(5908,plain,
% 1.37/1.50 (op(e2, e2) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[345, 76, 5907, 5582])).
% 1.37/1.50 tff(5909,plain,
% 1.37/1.50 (op(e2, e2) = op(e1, e0)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5908, 5903])).
% 1.37/1.50 tff(5910,plain,
% 1.37/1.50 (op(e2, op(e2, e2)) = op(e2, op(e1, e0))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5909])).
% 1.37/1.50 tff(5911,plain,
% 1.37/1.50 (op(e2, op(e2, e2)) = e0),
% 1.37/1.50 inference(transitivity,[status(thm)],[5910, 5902, 5810, 3508])).
% 1.37/1.50 tff(5912,plain,
% 1.37/1.50 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5911])).
% 1.37/1.50 tff(5913,plain,
% 1.37/1.50 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (e3 = op(e2, e0))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5912])).
% 1.37/1.50 tff(5914,plain,
% 1.37/1.50 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e3)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5913, 660])).
% 1.37/1.50 tff(5915,plain,
% 1.37/1.50 ((op(e2, e0) = e3) <=> (e3 = op(e2, op(e2, op(e2, e2))))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5914])).
% 1.37/1.50 tff(5916,plain,
% 1.37/1.50 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5793])).
% 1.37/1.50 tff(5917,plain,
% 1.37/1.50 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5916])).
% 1.37/1.50 tff(5918,plain,
% 1.37/1.50 (~(op(e2, e0) = e2)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[989, 5917])).
% 1.37/1.50 tff(5919,plain,
% 1.37/1.50 (op(e2, e0) = e3),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[765, 5918, 5907, 5643])).
% 1.37/1.50 tff(5920,plain,
% 1.37/1.50 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5919, 5915])).
% 1.37/1.50 tff(5921,plain,
% 1.37/1.50 (e1 = op(e2, e2)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[5908, 317])).
% 1.37/1.50 tff(5922,plain,
% 1.37/1.50 (op(e2, op(e1, e0)) = op(e2, op(e2, e2))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5910])).
% 1.37/1.50 tff(5923,plain,
% 1.37/1.50 (op(e2, op(e0, e1)) = op(e2, op(e1, e0))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5902])).
% 1.37/1.50 tff(5924,plain,
% 1.37/1.50 (op(e2, e1) = op(e2, op(e0, e1))),
% 1.37/1.50 inference(symmetry,[status(thm)],[5810])).
% 1.37/1.50 tff(5925,plain,
% 1.37/1.50 (e0 = op(e2, op(e2, e2))),
% 1.37/1.50 inference(transitivity,[status(thm)],[5560, 5924, 5923, 5922])).
% 1.37/1.50 tff(5926,plain,
% 1.37/1.50 (~(e3 = op(e2, op(e2, op(e2, e2))))),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1648, 5925, 5921])).
% 1.37/1.50 tff(5927,plain,
% 1.37/1.50 ($false),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[5926, 5920])).
% 1.37/1.50 tff(5928,plain,((op(e2, e3) = e1) | (~(op(e2, e1) = e0)) | (~(op(e0, e1) = e1)) | (~(op(e1, e0) = e1)) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.50 tff(5929,plain,
% 1.37/1.50 (op(e2, e3) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[5928, 5893, 3508, 5887, 5483])).
% 1.37/1.50 tff(5930,plain,
% 1.37/1.50 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5929])).
% 1.37/1.50 tff(5931,plain,
% 1.37/1.50 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5930, 657])).
% 1.37/1.50 tff(5932,plain,
% 1.37/1.50 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5931])).
% 1.37/1.50 tff(5933,plain,
% 1.37/1.50 (~(op(e3, e3) = e1)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[368, 5932])).
% 1.37/1.50 tff(5934,plain,
% 1.37/1.50 (op(e3, e2) = e1),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[939, 5933, 5754, 5899])).
% 1.37/1.50 tff(5935,plain,
% 1.37/1.50 (op(e1, e2) = e0),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1830, 5886, 80, 5456])).
% 1.37/1.50 tff(5936,plain,
% 1.37/1.50 (op(op(e2, e3), e2) = op(e1, e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5929])).
% 1.37/1.50 tff(5937,plain,
% 1.37/1.50 (op(op(e2, e3), e2) = e0),
% 1.37/1.50 inference(transitivity,[status(thm)],[5936, 5935])).
% 1.37/1.50 tff(5938,plain,
% 1.37/1.50 ((op(op(e2, e3), e2) = e3) <=> (e0 = e3)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5937])).
% 1.37/1.50 tff(5939,plain,
% 1.37/1.50 ((e0 = e3) <=> (op(op(e2, e3), e2) = e3)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5938])).
% 1.37/1.50 tff(5940,plain,
% 1.37/1.50 ((~(e0 = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5939])).
% 1.37/1.50 tff(5941,plain,
% 1.37/1.50 (~(op(op(e2, e3), e2) = e3)),
% 1.37/1.50 inference(modus_ponens,[status(thm)],[181, 5940])).
% 1.37/1.50 tff(5942,plain,
% 1.37/1.50 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.37/1.50 inference(unit_resolution,[status(thm)],[1934, 5941])).
% 1.37/1.50 tff(5943,plain,
% 1.37/1.50 (op(op(e3, e2), e3) = op(e1, e3)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5934])).
% 1.37/1.50 tff(5944,plain,
% 1.37/1.50 (op(op(e3, e2), e3) = e3),
% 1.37/1.50 inference(transitivity,[status(thm)],[5943, 5479])).
% 1.37/1.50 tff(5945,plain,
% 1.37/1.50 ((op(op(e3, e2), e3) = e2) <=> (e3 = e2)),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5944])).
% 1.37/1.50 tff(5946,plain,
% 1.37/1.50 ((op(op(e3, e2), e3) = e2) <=> (e2 = e3)),
% 1.37/1.50 inference(transitivity,[status(thm)],[5945, 1314])).
% 1.37/1.50 tff(5947,plain,
% 1.37/1.50 ((e2 = e3) <=> (op(op(e3, e2), e3) = e2)),
% 1.37/1.50 inference(symmetry,[status(thm)],[5946])).
% 1.37/1.50 tff(5948,plain,
% 1.37/1.50 ((~(e2 = e3)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.50 inference(monotonicity,[status(thm)],[5947])).
% 1.37/1.50 tff(5949,plain,
% 1.37/1.50 (~(op(op(e3, e2), e3) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1321, 5948])).
% 1.37/1.51 tff(5950,plain,
% 1.37/1.51 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2408, 5949])).
% 1.37/1.51 tff(5951,plain,
% 1.37/1.51 (e1 = op(e1, e0)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5887])).
% 1.37/1.51 tff(5952,plain,
% 1.37/1.51 (op(e0, op(e0, e1)) = op(e0, e1)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5893])).
% 1.37/1.51 tff(5953,plain,
% 1.37/1.51 (op(op(e1, e2), e1) = op(e0, op(e0, e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5935, 5894])).
% 1.37/1.51 tff(5954,plain,
% 1.37/1.51 (op(op(e1, e2), e1) = op(e1, e0)),
% 1.37/1.51 inference(transitivity,[status(thm)],[5953, 5952, 5893, 5951])).
% 1.37/1.51 tff(5955,plain,
% 1.37/1.51 ((op(op(e1, e2), e1) = e2) <=> (op(e1, e0) = e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5954])).
% 1.37/1.51 tff(5956,plain,
% 1.37/1.51 ((op(e1, e0) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5955])).
% 1.37/1.51 tff(5957,plain,
% 1.37/1.51 ((~(op(e1, e0) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5956])).
% 1.37/1.51 tff(5958,plain,
% 1.37/1.51 (~(op(op(e1, e2), e1) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[5741, 5957])).
% 1.37/1.51 tff(5959,plain,
% 1.37/1.51 (((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))) | (op(op(e1, e2), e1) = e2)),
% 1.37/1.51 inference(tautology,[status(thm)],[])).
% 1.37/1.51 tff(5960,plain,
% 1.37/1.51 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[5959, 5958])).
% 1.37/1.51 tff(5961,plain,
% 1.37/1.51 ((op(e0, e1) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5893])).
% 1.37/1.51 tff(5962,plain,
% 1.37/1.51 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 1.37/1.51 inference(transitivity,[status(thm)],[5961, 697])).
% 1.37/1.51 tff(5963,plain,
% 1.37/1.51 ((op(e0, e1) = op(e0, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 1.37/1.51 inference(transitivity,[status(thm)],[5962, 5799])).
% 1.37/1.51 tff(5964,plain,
% 1.37/1.51 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5963])).
% 1.37/1.51 tff(5965,plain,
% 1.37/1.51 (~(op(op(e2, e1), e2) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[2102, 5964])).
% 1.37/1.51 tff(5966,plain,
% 1.37/1.51 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[5808, 5965])).
% 1.37/1.51 tff(5967,plain,
% 1.37/1.51 (op(op(e0, e1), e0) = op(e1, e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5893])).
% 1.37/1.51 tff(5968,plain,
% 1.37/1.51 (op(e1, e0) = op(e0, e1)),
% 1.37/1.51 inference(transitivity,[status(thm)],[5887, 5894])).
% 1.37/1.51 tff(5969,plain,
% 1.37/1.51 (op(op(e1, e0), e0) = op(op(e0, e1), e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5968])).
% 1.37/1.51 tff(5970,plain,
% 1.37/1.51 (op(op(e1, e0), e0) = e1),
% 1.37/1.51 inference(transitivity,[status(thm)],[5969, 5967, 5887])).
% 1.37/1.51 tff(5971,plain,
% 1.37/1.51 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[3015, 5970])).
% 1.37/1.51 tff(5972,plain,
% 1.37/1.51 (op(e0, op(e0, e1)) = e1),
% 1.37/1.51 inference(transitivity,[status(thm)],[5952, 5893])).
% 1.37/1.51 tff(5973,plain,
% 1.37/1.51 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2449, 5972])).
% 1.37/1.51 tff(5974,plain,
% 1.37/1.51 (op(e3, e0) = e0),
% 1.37/1.51 inference(transitivity,[status(thm)],[466, 771])).
% 1.37/1.51 tff(5975,plain,
% 1.37/1.51 (op(e3, op(e3, e0)) = op(e3, e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5974])).
% 1.37/1.51 tff(5976,plain,
% 1.37/1.51 (op(e3, op(e3, e0)) = e0),
% 1.37/1.51 inference(transitivity,[status(thm)],[5975, 466, 771])).
% 1.37/1.51 tff(5977,plain,
% 1.37/1.51 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1345, 5976])).
% 1.37/1.51 tff(5978,assumption,(op(e3, e2) = e1), introduced(assumption)).
% 1.37/1.51 tff(5979,plain,
% 1.37/1.51 (op(e2, e0) = e3),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1559, 2431, 3271, 124])).
% 1.37/1.51 tff(5980,plain,
% 1.37/1.51 (op(op(e2, e0), e2) = op(e3, e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5979])).
% 1.37/1.51 tff(5981,plain,
% 1.37/1.51 (op(op(e2, e0), e2) = op(e1, e0)),
% 1.37/1.51 inference(transitivity,[status(thm)],[5980, 5978, 5903])).
% 1.37/1.51 tff(5982,plain,
% 1.37/1.51 ((op(op(e2, e0), e2) = e0) <=> (op(e1, e0) = e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5981])).
% 1.37/1.51 tff(5983,plain,
% 1.37/1.51 ((op(e1, e0) = e0) <=> (op(op(e2, e0), e2) = e0)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5982])).
% 1.37/1.51 tff(5984,plain,
% 1.37/1.51 ((~(op(e1, e0) = e0)) <=> (~(op(op(e2, e0), e2) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5983])).
% 1.37/1.51 tff(5985,plain,
% 1.37/1.51 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5974])).
% 1.37/1.51 tff(5986,plain,
% 1.37/1.51 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5985])).
% 1.37/1.51 tff(5987,plain,
% 1.37/1.51 (~(op(e1, e0) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[410, 5986])).
% 1.37/1.51 tff(5988,plain,
% 1.37/1.51 (~(op(op(e2, e0), e2) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[5987, 5984])).
% 1.37/1.51 tff(5989,plain,
% 1.37/1.51 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1379, 5988])).
% 1.37/1.51 tff(5990,plain,
% 1.37/1.51 (op(e0, e2) = e3),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2111, 2431, 1890, 75])).
% 1.37/1.51 tff(5991,plain,
% 1.37/1.51 (op(op(e0, e2), e0) = op(e3, e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5990])).
% 1.37/1.51 tff(5992,plain,
% 1.37/1.51 (op(op(e0, e2), e0) = e0),
% 1.37/1.51 inference(transitivity,[status(thm)],[5991, 466, 771])).
% 1.37/1.51 tff(5993,plain,
% 1.37/1.51 ((op(op(e0, e2), e0) = e2) <=> (e0 = e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5992])).
% 1.37/1.51 tff(5994,plain,
% 1.37/1.51 ((e0 = e2) <=> (op(op(e0, e2), e0) = e2)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5993])).
% 1.37/1.51 tff(5995,plain,
% 1.37/1.51 ((~(e0 = e2)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5994])).
% 1.37/1.51 tff(5996,plain,
% 1.37/1.51 (~(op(op(e0, e2), e0) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[14, 5995])).
% 1.37/1.51 tff(5997,plain,
% 1.37/1.51 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2446, 5996])).
% 1.37/1.51 tff(5998,plain,
% 1.37/1.51 ($false),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1459, 5997, 5989, 5977, 4549, 3342, 1304, 1357, 1936, 1358, 1275, 3341, 1347])).
% 1.37/1.51 tff(5999,plain,((op(e2, e2) = e3) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e3, e0) = op(e0, e3))) | (~(op(e0, e3) = e0)) | (~(op(e3, e2) = e1)) | (~(op(e1, e0) = e1)) | (op(e3, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.51 tff(6000,plain,
% 1.37/1.51 (op(e2, e2) = e3),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[5999, 5973, 5469, 5475, 5971, 5966, 5960, 5749, 5950, 5942, 5882, 771, 5934, 5887, 5498, 5490, 5487, 5483])).
% 1.37/1.51 tff(6001,plain,
% 1.37/1.51 (e3 = op(e2, e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[6000, 1796])).
% 1.37/1.51 tff(6002,plain,
% 1.37/1.51 (op(e2, op(e2, e2)) = op(e2, e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6000])).
% 1.37/1.51 tff(6003,plain,
% 1.37/1.51 (op(e2, e3) = op(e2, op(e2, e2))),
% 1.37/1.51 inference(symmetry,[status(thm)],[6002])).
% 1.37/1.51 tff(6004,plain,
% 1.37/1.51 (e1 = op(e2, e3)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5929])).
% 1.37/1.51 tff(6005,plain,
% 1.37/1.51 (e1 = op(e2, op(e2, e2))),
% 1.37/1.51 inference(transitivity,[status(thm)],[6004, 6003])).
% 1.37/1.51 tff(6006,plain,
% 1.37/1.51 (op(e2, op(e2, e2)) = op(e1, e0)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6002, 5929, 5951])).
% 1.37/1.51 tff(6007,plain,
% 1.37/1.51 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e1, e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6006])).
% 1.37/1.51 tff(6008,plain,
% 1.37/1.51 (op(e2, op(e1, e0)) = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.51 inference(symmetry,[status(thm)],[6007])).
% 1.37/1.51 tff(6009,plain,
% 1.37/1.51 (op(e2, op(e1, e0)) = op(e2, op(e0, e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5968])).
% 1.37/1.51 tff(6010,plain,
% 1.37/1.51 (op(e2, op(e0, e1)) = op(e2, op(e1, e0))),
% 1.37/1.51 inference(symmetry,[status(thm)],[6009])).
% 1.37/1.51 tff(6011,plain,
% 1.37/1.51 (op(e2, op(e0, e1)) = op(e2, e1)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5893])).
% 1.37/1.51 tff(6012,plain,
% 1.37/1.51 (op(e2, e1) = op(e2, op(e0, e1))),
% 1.37/1.51 inference(symmetry,[status(thm)],[6011])).
% 1.37/1.51 tff(6013,plain,
% 1.37/1.51 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.51 inference(transitivity,[status(thm)],[5560, 6012, 6010, 6008])).
% 1.37/1.51 tff(6014,plain,
% 1.37/1.51 ($false),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2952, 6013, 6005, 6001])).
% 1.37/1.51 tff(6015,plain,((op(e1, e3) = e1) | (~(op(e2, e1) = e0)) | (~(op(e0, e3) = e0)) | (op(e1, e3) = e0) | (op(e1, e3) = e2) | (op(e0, e3) = e2) | (op(e0, e3) = e1) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.51 tff(6016,plain,
% 1.37/1.51 (op(e1, e3) = e1),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[6015, 72, 5447, 80, 3508, 79, 121, 2527])).
% 1.37/1.51 tff(6017,plain,
% 1.37/1.51 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6016])).
% 1.37/1.51 tff(6018,plain,
% 1.37/1.51 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6017])).
% 1.37/1.51 tff(6019,plain,
% 1.37/1.51 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6018])).
% 1.37/1.51 tff(6020,plain,
% 1.37/1.51 (~(op(e1, e3) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[303, 6019])).
% 1.37/1.51 tff(6021,plain,
% 1.37/1.51 ((op(e1, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6016])).
% 1.37/1.51 tff(6022,plain,
% 1.37/1.51 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6021, 5574])).
% 1.37/1.51 tff(6023,plain,
% 1.37/1.51 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6022])).
% 1.37/1.51 tff(6024,plain,
% 1.37/1.51 (~(op(e2, e3) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[118, 6023])).
% 1.37/1.51 tff(6025,plain,
% 1.37/1.51 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[5447])).
% 1.37/1.51 tff(6026,plain,
% 1.37/1.51 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6025])).
% 1.37/1.51 tff(6027,plain,
% 1.37/1.51 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6026])).
% 1.37/1.51 tff(6028,plain,
% 1.37/1.51 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6016])).
% 1.37/1.51 tff(6029,plain,
% 1.37/1.51 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, op(e0, e3)) = e1)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6028, 6027])).
% 1.37/1.51 tff(6030,plain,
% 1.37/1.51 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6029])).
% 1.37/1.51 tff(6031,plain,
% 1.37/1.51 (~(op(e1, op(e0, e3)) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[110, 6030])).
% 1.37/1.51 tff(6032,plain,
% 1.37/1.51 (op(e3, e3) = e3),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[480, 124, 5591, 1080])).
% 1.37/1.51 tff(6033,plain,
% 1.37/1.51 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6032])).
% 1.37/1.51 tff(6034,plain,
% 1.37/1.51 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6033, 5716])).
% 1.37/1.51 tff(6035,plain,
% 1.37/1.51 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6034])).
% 1.37/1.51 tff(6036,plain,
% 1.37/1.51 (~(op(e3, op(e0, e3)) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[157, 6035])).
% 1.37/1.51 tff(6037,plain,
% 1.37/1.51 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[980])).
% 1.37/1.51 tff(6038,plain,
% 1.37/1.51 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6037])).
% 1.37/1.51 tff(6039,plain,
% 1.37/1.51 (op(e2, e3) = e2),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[206, 124, 5446, 76])).
% 1.37/1.51 tff(6040,plain,
% 1.37/1.51 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6039])).
% 1.37/1.51 tff(6041,plain,
% 1.37/1.51 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, op(e0, e3)) = e2)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6040, 6038])).
% 1.37/1.51 tff(6042,plain,
% 1.37/1.51 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6041])).
% 1.37/1.51 tff(6043,plain,
% 1.37/1.51 (~(op(e2, op(e0, e3)) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[989, 6042])).
% 1.37/1.51 tff(6044,plain,
% 1.37/1.51 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6032])).
% 1.37/1.51 tff(6045,plain,
% 1.37/1.51 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6044])).
% 1.37/1.51 tff(6046,plain,
% 1.37/1.51 (~(op(e3, e1) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[437, 6045])).
% 1.37/1.51 tff(6047,plain,
% 1.37/1.51 ((op(e0, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[1869])).
% 1.37/1.51 tff(6048,plain,
% 1.37/1.51 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6047, 666])).
% 1.37/1.51 tff(6049,plain,
% 1.37/1.51 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6048])).
% 1.37/1.51 tff(6050,plain,
% 1.37/1.51 (~(op(e3, e3) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1077, 6049])).
% 1.37/1.51 tff(6051,plain,
% 1.37/1.51 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[1869])).
% 1.37/1.51 tff(6052,plain,
% 1.37/1.51 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6051])).
% 1.37/1.51 tff(6053,plain,
% 1.37/1.51 (~(op(e3, e0) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[5528, 6052])).
% 1.37/1.51 tff(6054,plain,
% 1.37/1.51 ($false),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[422, 6053, 6050, 1890, 2839])).
% 1.37/1.51 tff(6055,plain,((~(op(e0, e3) = e3)) | (op(e3, e2) = e3) | (op(e3, e1) = e3) | (op(e3, e0) = op(e0, e3))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.51 tff(6056,plain,
% 1.37/1.51 (~(op(e0, e3) = e3)),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[6055, 1890, 2839, 5528])).
% 1.37/1.51 tff(6057,plain,
% 1.37/1.51 (op(e1, e1) = e3),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1730, 2839, 5487, 2527])).
% 1.37/1.51 tff(6058,plain,
% 1.37/1.51 ((op(e1, e1) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6057])).
% 1.37/1.51 tff(6059,plain,
% 1.37/1.51 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6058, 3230])).
% 1.37/1.51 tff(6060,plain,
% 1.37/1.51 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6059])).
% 1.37/1.51 tff(6061,plain,
% 1.37/1.51 (~(op(e1, e3) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[619, 6060])).
% 1.37/1.51 tff(6062,plain,
% 1.37/1.51 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6057])).
% 1.37/1.51 tff(6063,plain,
% 1.37/1.51 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6062, 532])).
% 1.37/1.51 tff(6064,plain,
% 1.37/1.51 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6063])).
% 1.37/1.51 tff(6065,plain,
% 1.37/1.51 (~(op(e1, e2) = e3)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1604, 6064])).
% 1.37/1.51 tff(6066,plain,
% 1.37/1.51 (e1 = op(e1, e3)),
% 1.37/1.51 inference(symmetry,[status(thm)],[5426])).
% 1.37/1.51 tff(6067,plain,
% 1.37/1.51 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6066])).
% 1.37/1.51 tff(6068,plain,
% 1.37/1.51 ((op(e2, e3) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.37/1.51 inference(transitivity,[status(thm)],[6067, 1687])).
% 1.37/1.51 tff(6069,plain,
% 1.37/1.51 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6068])).
% 1.37/1.51 tff(6070,plain,
% 1.37/1.51 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6069])).
% 1.37/1.51 tff(6071,plain,
% 1.37/1.51 (~(op(e2, e3) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[118, 6070])).
% 1.37/1.51 tff(6072,plain,
% 1.37/1.51 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6066])).
% 1.37/1.51 tff(6073,plain,
% 1.37/1.51 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6072])).
% 1.37/1.51 tff(6074,plain,
% 1.37/1.51 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6073])).
% 1.37/1.51 tff(6075,plain,
% 1.37/1.51 (~(op(e1, e2) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1850, 6074])).
% 1.37/1.51 tff(6076,plain,
% 1.37/1.51 (op(e0, e3) = e0),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[687, 79, 121, 661])).
% 1.37/1.51 tff(6077,plain,
% 1.37/1.51 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6076])).
% 1.37/1.51 tff(6078,plain,
% 1.37/1.51 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6077, 3077])).
% 1.37/1.51 tff(6079,plain,
% 1.37/1.51 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6078])).
% 1.37/1.51 tff(6080,plain,
% 1.37/1.51 (~(op(e3, e3) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1077, 6079])).
% 1.37/1.51 tff(6081,plain,
% 1.37/1.51 (e0 = op(e0, e3)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6076])).
% 1.37/1.51 tff(6082,plain,
% 1.37/1.51 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6081])).
% 1.37/1.51 tff(6083,plain,
% 1.37/1.51 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6082])).
% 1.37/1.51 tff(6084,plain,
% 1.37/1.51 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6083])).
% 1.37/1.51 tff(6085,plain,
% 1.37/1.51 (~(op(e3, e0) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[5528, 6084])).
% 1.37/1.51 tff(6086,plain,
% 1.37/1.51 (op(e3, e2) = e0),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1916, 6085, 183, 6080])).
% 1.37/1.51 tff(6087,plain,
% 1.37/1.51 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6086])).
% 1.37/1.51 tff(6088,plain,
% 1.37/1.51 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6087])).
% 1.37/1.51 tff(6089,plain,
% 1.37/1.51 (~(op(e1, e2) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[2292, 6088])).
% 1.37/1.51 tff(6090,plain,
% 1.37/1.51 (op(e1, e2) = e2),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[1859, 6089, 6075, 75])).
% 1.37/1.51 tff(6091,plain,
% 1.37/1.51 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6090])).
% 1.37/1.51 tff(6092,plain,
% 1.37/1.51 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6091, 81])).
% 1.37/1.51 tff(6093,plain,
% 1.37/1.51 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6092])).
% 1.37/1.51 tff(6094,plain,
% 1.37/1.51 (~(op(e2, e2) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[1273, 6093])).
% 1.37/1.51 tff(6095,plain,
% 1.37/1.51 ((e0 = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 1.37/1.51 inference(commutativity,[status(thm)],[])).
% 1.37/1.51 tff(6096,plain,
% 1.37/1.51 ((op(e3, e2) = e1) <=> (e0 = op(e1, e3))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6086, 6066])).
% 1.37/1.51 tff(6097,plain,
% 1.37/1.51 ((op(e3, e2) = e1) <=> (op(e1, e3) = e0)),
% 1.37/1.51 inference(transitivity,[status(thm)],[6096, 6095])).
% 1.37/1.51 tff(6098,plain,
% 1.37/1.51 ((op(e1, e3) = e0) <=> (op(e3, e2) = e1)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6097])).
% 1.37/1.51 tff(6099,plain,
% 1.37/1.51 ((~(op(e1, e3) = e0)) <=> (~(op(e3, e2) = e1))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6098])).
% 1.37/1.51 tff(6100,plain,
% 1.37/1.51 (~(op(e3, e2) = e1)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[80, 6099])).
% 1.37/1.51 tff(6101,plain,
% 1.37/1.51 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6076])).
% 1.37/1.51 tff(6102,plain,
% 1.37/1.51 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6101])).
% 1.37/1.51 tff(6103,plain,
% 1.37/1.51 (~(op(e0, e0) = e0)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[3414, 6102])).
% 1.37/1.51 tff(6104,plain,
% 1.37/1.51 (op(e1, e0) = e0),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[5651, 6085, 5643, 6103])).
% 1.37/1.51 tff(6105,plain,
% 1.37/1.51 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6086])).
% 1.37/1.51 tff(6106,plain,
% 1.37/1.51 (op(op(e3, e2), e3) = e0),
% 1.37/1.51 inference(transitivity,[status(thm)],[6105, 6076])).
% 1.37/1.51 tff(6107,plain,
% 1.37/1.51 ((op(op(e3, e2), e3) = e2) <=> (e0 = e2)),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6106])).
% 1.37/1.51 tff(6108,plain,
% 1.37/1.51 ((e0 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.37/1.51 inference(symmetry,[status(thm)],[6107])).
% 1.37/1.51 tff(6109,plain,
% 1.37/1.51 ((~(e0 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.51 inference(monotonicity,[status(thm)],[6108])).
% 1.37/1.51 tff(6110,plain,
% 1.37/1.51 (~(op(op(e3, e2), e3) = e2)),
% 1.37/1.51 inference(modus_ponens,[status(thm)],[14, 6109])).
% 1.37/1.51 tff(6111,plain,
% 1.37/1.51 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[2408, 6110])).
% 1.37/1.51 tff(6112,plain,
% 1.37/1.51 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.37/1.51 inference(unit_resolution,[status(thm)],[5372, 183, 121, 80])).
% 1.37/1.52 tff(6113,plain,
% 1.37/1.52 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6090])).
% 1.37/1.52 tff(6114,plain,
% 1.37/1.52 (op(e1, op(e1, e2)) = e2),
% 1.37/1.52 inference(transitivity,[status(thm)],[6113, 6090])).
% 1.37/1.52 tff(6115,plain,
% 1.37/1.52 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2377, 6114])).
% 1.37/1.52 tff(6116,plain,
% 1.37/1.52 ((op(e2, e2) = op(e2, e0)) <=> (op(e2, e0) = op(e2, e2))),
% 1.37/1.52 inference(commutativity,[status(thm)],[])).
% 1.37/1.52 tff(6117,plain,
% 1.37/1.52 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e2, e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[768])).
% 1.37/1.52 tff(6118,plain,
% 1.37/1.52 ((op(e2, e2) = e1) <=> (op(e2, e0) = op(e2, e2))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6117, 6116])).
% 1.37/1.52 tff(6119,plain,
% 1.37/1.52 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6118])).
% 1.37/1.52 tff(6120,plain,
% 1.37/1.52 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6119])).
% 1.37/1.52 tff(6121,plain,
% 1.37/1.52 (~(op(e2, e2) = e1)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[2228, 6120])).
% 1.37/1.52 tff(6122,plain,
% 1.37/1.52 (op(e2, e2) = e3),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[524, 6121, 5552, 5548])).
% 1.37/1.52 tff(6123,plain,
% 1.37/1.52 ((op(e2, e0) = e2) <=> (op(e1, e3) = e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[3832])).
% 1.37/1.52 tff(6124,plain,
% 1.37/1.52 ((op(e1, e3) = e2) <=> (op(e2, e0) = e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6123])).
% 1.37/1.52 tff(6125,plain,
% 1.37/1.52 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6124])).
% 1.37/1.52 tff(6126,plain,
% 1.37/1.52 (~(op(e2, e0) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[72, 6125])).
% 1.37/1.52 tff(6127,plain,
% 1.37/1.52 (op(e2, e3) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2088, 6126, 5548, 5515])).
% 1.37/1.52 tff(6128,plain,
% 1.37/1.52 (op(e2, op(e2, e3)) = op(e2, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6127])).
% 1.37/1.52 tff(6129,plain,
% 1.37/1.52 (op(e2, op(e2, e3)) = e3),
% 1.37/1.52 inference(transitivity,[status(thm)],[6128, 6122])).
% 1.37/1.52 tff(6130,plain,
% 1.37/1.52 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2344, 6129])).
% 1.37/1.52 tff(6131,plain,
% 1.37/1.52 ((op(e3, e0) = op(e2, e0)) <=> (op(e2, e0) = op(e3, e0))),
% 1.37/1.52 inference(commutativity,[status(thm)],[])).
% 1.37/1.52 tff(6132,plain,
% 1.37/1.52 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e2, e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[768])).
% 1.37/1.52 tff(6133,plain,
% 1.37/1.52 ((op(e3, e0) = e1) <=> (op(e2, e0) = op(e3, e0))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6132, 6131])).
% 1.37/1.52 tff(6134,plain,
% 1.37/1.52 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6133])).
% 1.37/1.52 tff(6135,plain,
% 1.37/1.52 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6134])).
% 1.37/1.52 tff(6136,plain,
% 1.37/1.52 (~(op(e3, e0) = e1)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[747, 6135])).
% 1.37/1.52 tff(6137,plain,
% 1.37/1.52 (op(e3, e1) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[939, 6136, 3811, 930])).
% 1.37/1.52 tff(6138,plain,
% 1.37/1.52 (op(e3, e1) = op(e2, e0)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6137, 768])).
% 1.37/1.52 tff(6139,plain,
% 1.37/1.52 (op(e3, op(e3, e1)) = op(e3, op(e2, e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6138])).
% 1.37/1.52 tff(6140,plain,
% 1.37/1.52 (op(e3, op(e3, e1)) = e1),
% 1.37/1.52 inference(transitivity,[status(thm)],[6139, 3833, 3831, 6137])).
% 1.37/1.52 tff(6141,plain,
% 1.37/1.52 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2594, 6140])).
% 1.37/1.52 tff(6142,assumption,(op(e1, e0) = e0), introduced(assumption)).
% 1.37/1.52 tff(6143,plain,
% 1.37/1.52 (op(op(e2, e0), e0) = op(e1, e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[767])).
% 1.37/1.52 tff(6144,plain,
% 1.37/1.52 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[3710])).
% 1.37/1.52 tff(6145,plain,
% 1.37/1.52 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6144])).
% 1.37/1.52 tff(6146,plain,
% 1.37/1.52 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6145])).
% 1.37/1.52 tff(6147,plain,
% 1.37/1.52 (~(op(e1, e2) = e1)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[1850, 6146])).
% 1.37/1.52 tff(6148,plain,
% 1.37/1.52 (op(e0, e2) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1613, 6121, 6147, 930])).
% 1.37/1.52 tff(6149,plain,
% 1.37/1.52 (op(e0, e2) = op(e2, e0)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6148, 768])).
% 1.37/1.52 tff(6150,plain,
% 1.37/1.52 (op(op(e0, e2), e0) = op(op(e2, e0), e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6149])).
% 1.37/1.52 tff(6151,plain,
% 1.37/1.52 (op(op(e0, e2), e0) = e0),
% 1.37/1.52 inference(transitivity,[status(thm)],[6150, 6143, 6142])).
% 1.37/1.52 tff(6152,plain,
% 1.37/1.52 ((op(op(e0, e2), e0) = e2) <=> (e0 = e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6151])).
% 1.37/1.52 tff(6153,plain,
% 1.37/1.52 ((e0 = e2) <=> (op(op(e0, e2), e0) = e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6152])).
% 1.37/1.52 tff(6154,plain,
% 1.37/1.52 ((~(e0 = e2)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6153])).
% 1.37/1.52 tff(6155,plain,
% 1.37/1.52 (~(op(op(e0, e2), e0) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[14, 6154])).
% 1.37/1.52 tff(6156,plain,
% 1.37/1.52 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2446, 6155])).
% 1.37/1.52 tff(6157,plain,
% 1.37/1.52 (op(e2, op(e2, e1)) = op(e2, e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.52 tff(6158,plain,
% 1.37/1.52 ((op(e2, op(e2, e1)) = e1) <=> (op(e2, e0) = e1)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6157])).
% 1.37/1.52 tff(6159,plain,
% 1.37/1.52 ((op(e2, e0) = e1) <=> (op(e2, op(e2, e1)) = e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6158])).
% 1.37/1.52 tff(6160,plain,
% 1.37/1.52 (op(e2, op(e2, e1)) = e1),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[767, 6159])).
% 1.37/1.52 tff(6161,plain,
% 1.37/1.52 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1355, 6160])).
% 1.37/1.52 tff(6162,plain,
% 1.37/1.52 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[3832])).
% 1.37/1.52 tff(6163,plain,
% 1.37/1.52 (op(e2, op(e2, e0)) = e0),
% 1.37/1.52 inference(transitivity,[status(thm)],[6162, 3796, 3508])).
% 1.37/1.52 tff(6164,plain,
% 1.37/1.52 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2653, 6163])).
% 1.37/1.52 tff(6165,plain,
% 1.37/1.52 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6142])).
% 1.37/1.52 tff(6166,plain,
% 1.37/1.52 (op(e1, op(e1, e0)) = e0),
% 1.37/1.52 inference(transitivity,[status(thm)],[6165, 6142])).
% 1.37/1.52 tff(6167,plain,
% 1.37/1.52 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1836, 6166])).
% 1.37/1.52 tff(6168,plain,
% 1.37/1.52 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6148])).
% 1.37/1.52 tff(6169,plain,
% 1.37/1.52 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e1))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6168])).
% 1.37/1.52 tff(6170,plain,
% 1.37/1.52 (~(op(e0, e1) = e1)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[2102, 6169])).
% 1.37/1.52 tff(6171,plain,
% 1.37/1.52 (op(e0, e1) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[829, 6170, 3849, 2527])).
% 1.37/1.52 tff(6172,plain,
% 1.37/1.52 (op(e0, op(e0, e1)) = op(e0, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6171])).
% 1.37/1.52 tff(6173,plain,
% 1.37/1.52 (op(e0, op(e0, e1)) = e1),
% 1.37/1.52 inference(transitivity,[status(thm)],[6172, 6148])).
% 1.37/1.52 tff(6174,plain,
% 1.37/1.52 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2449, 6173])).
% 1.37/1.52 tff(6175,plain,
% 1.37/1.52 ((op(e2, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6127])).
% 1.37/1.52 tff(6176,plain,
% 1.37/1.52 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6175, 565])).
% 1.37/1.52 tff(6177,plain,
% 1.37/1.52 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6176])).
% 1.37/1.52 tff(6178,plain,
% 1.37/1.52 (~(op(e3, e3) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[368, 6177])).
% 1.37/1.52 tff(6179,plain,
% 1.37/1.52 ((op(e3, e1) = e2) <=> (op(e2, e0) = e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6138])).
% 1.37/1.52 tff(6180,plain,
% 1.37/1.52 ((op(e2, e0) = e2) <=> (op(e3, e1) = e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6179])).
% 1.37/1.52 tff(6181,plain,
% 1.37/1.52 ((~(op(e2, e0) = e2)) <=> (~(op(e3, e1) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6180])).
% 1.37/1.52 tff(6182,plain,
% 1.37/1.52 (~(op(e3, e1) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6126, 6181])).
% 1.37/1.52 tff(6183,plain,
% 1.37/1.52 (op(e3, e0) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2015, 6182, 6178, 5823])).
% 1.37/1.52 tff(6184,plain,
% 1.37/1.52 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6183])).
% 1.37/1.52 tff(6185,plain,
% 1.37/1.52 (op(e3, op(e3, e0)) = e0),
% 1.37/1.52 inference(transitivity,[status(thm)],[6184, 5819])).
% 1.37/1.52 tff(6186,plain,
% 1.37/1.52 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1345, 6185])).
% 1.37/1.52 tff(6187,plain,
% 1.37/1.52 ($false),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1459, 6186, 6174, 3342, 6167, 1358, 1304, 6164, 6161, 6156, 6141, 3341, 6130])).
% 1.37/1.52 tff(6188,plain,((~(op(e2, e0) = e1)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e3, e2) = e0)) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (~(op(e1, e0) = e0)) | (~(op(e1, e3) = e1)) | (op(e3, e2) = e1) | (op(e2, e2) = e2) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.52 tff(6189,plain,
% 1.37/1.52 (~(op(e2, e0) = e1)),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[6188, 5469, 6115, 6112, 6111, 6086, 3849, 2527, 6104, 5426, 6100, 6094, 3508, 72])).
% 1.37/1.52 tff(6190,plain,
% 1.37/1.52 (op(e2, e2) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[345, 6189, 6071, 5582])).
% 1.37/1.52 tff(6191,plain,
% 1.37/1.52 (e1 = op(e2, e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6190, 317])).
% 1.37/1.52 tff(6192,plain,
% 1.37/1.52 (op(e2, e2) = op(e1, e3)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6190, 6066])).
% 1.37/1.52 tff(6193,plain,
% 1.37/1.52 (op(e2, op(e2, e2)) = op(e2, op(e1, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6192])).
% 1.37/1.52 tff(6194,plain,
% 1.37/1.52 (op(e2, op(e1, e3)) = op(e2, op(e2, e2))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6193])).
% 1.37/1.52 tff(6195,plain,
% 1.37/1.52 (op(e2, op(e1, e3)) = op(e2, e1)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[5426])).
% 1.37/1.52 tff(6196,plain,
% 1.37/1.52 (op(e2, e1) = op(e2, op(e1, e3))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6195])).
% 1.37/1.52 tff(6197,plain,
% 1.37/1.52 (e0 = op(e2, op(e2, e2))),
% 1.37/1.52 inference(transitivity,[status(thm)],[5560, 6196, 6194])).
% 1.37/1.52 tff(6198,plain,
% 1.37/1.52 (op(e2, op(e2, e2)) = e0),
% 1.37/1.52 inference(transitivity,[status(thm)],[6193, 6195, 3508])).
% 1.37/1.52 tff(6199,plain,
% 1.37/1.52 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6198])).
% 1.37/1.52 tff(6200,plain,
% 1.37/1.52 (op(e2, e0) = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6199])).
% 1.37/1.52 tff(6201,plain,
% 1.37/1.52 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6090])).
% 1.37/1.52 tff(6202,plain,
% 1.37/1.52 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6201])).
% 1.37/1.52 tff(6203,plain,
% 1.37/1.52 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = op(e1, e2)))),
% 1.37/1.52 inference(rewrite,[status(thm)],[])).
% 1.37/1.52 tff(6204,plain,
% 1.37/1.52 (~(op(e0, e2) = op(e1, e2))),
% 1.37/1.52 inference(and_elim,[status(thm)],[220])).
% 1.37/1.52 tff(6205,plain,
% 1.37/1.52 (~(op(e0, e2) = op(e1, e2))),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6204, 6203])).
% 1.37/1.52 tff(6206,plain,
% 1.37/1.52 (~(op(e0, e2) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6205, 6202])).
% 1.37/1.52 tff(6207,plain,
% 1.37/1.52 (op(e2, e0) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[765, 1349, 3272, 983])).
% 1.37/1.52 tff(6208,plain,
% 1.37/1.52 (e2 = op(e2, e0)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6207])).
% 1.37/1.52 tff(6209,plain,
% 1.37/1.52 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e2, e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6208])).
% 1.37/1.52 tff(6210,plain,
% 1.37/1.52 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6209])).
% 1.37/1.52 tff(6211,plain,
% 1.37/1.52 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6210])).
% 1.37/1.52 tff(6212,plain,
% 1.37/1.52 (~(op(e0, e0) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[359, 6211])).
% 1.37/1.52 tff(6213,assumption,(~(op(e0, e0) = e0)), introduced(assumption)).
% 1.37/1.52 tff(6214,plain,
% 1.37/1.52 (op(e2, e2) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[345, 1349, 3715, 4530])).
% 1.37/1.52 tff(6215,plain,
% 1.37/1.52 (op(e2, e2) = op(e1, e3)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6214, 3710])).
% 1.37/1.52 tff(6216,plain,
% 1.37/1.52 ((op(e2, e2) = e3) <=> (op(e1, e3) = e3)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6215])).
% 1.37/1.52 tff(6217,plain,
% 1.37/1.52 ((op(e1, e3) = e3) <=> (op(e2, e2) = e3)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6216])).
% 1.37/1.52 tff(6218,plain,
% 1.37/1.52 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e2) = e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6217])).
% 1.37/1.52 tff(6219,plain,
% 1.37/1.52 (~(op(e2, e2) = e3)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[1080, 6218])).
% 1.37/1.52 tff(6220,plain,
% 1.37/1.52 (op(e0, e2) = e3),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[2111, 6219, 75, 1890])).
% 1.37/1.52 tff(6221,plain,
% 1.37/1.52 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6220])).
% 1.37/1.52 tff(6222,plain,
% 1.37/1.52 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6221])).
% 1.37/1.52 tff(6223,plain,
% 1.37/1.52 (~(op(e0, e0) = e3)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[3603, 6222])).
% 1.37/1.52 tff(6224,plain,
% 1.37/1.52 (op(e0, e0) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[3612, 6223, 6213, 6212])).
% 1.37/1.52 tff(6225,plain,
% 1.37/1.52 (e1 = op(e0, e0)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6224, 74])).
% 1.37/1.52 tff(6226,plain,
% 1.37/1.52 (op(e0, e0) = op(e1, e3)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6224, 3710])).
% 1.37/1.52 tff(6227,plain,
% 1.37/1.52 (op(e0, op(e0, e0)) = op(e0, op(e1, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6226])).
% 1.37/1.52 tff(6228,plain,
% 1.37/1.52 (op(e0, op(e1, e3)) = op(e0, op(e0, e0))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6227])).
% 1.37/1.52 tff(6229,assumption,(~(op(e0, e2) = e2)), introduced(assumption)).
% 1.37/1.52 tff(6230,plain,
% 1.37/1.52 (op(e0, e1) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[3652, 6212, 79, 6229])).
% 1.37/1.52 tff(6231,plain,
% 1.37/1.52 (e2 = op(e0, e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6230])).
% 1.37/1.52 tff(6232,plain,
% 1.37/1.52 (e2 = op(e0, op(e0, e0))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6231, 3789, 6228])).
% 1.37/1.52 tff(6233,plain,
% 1.37/1.52 (op(e0, op(e0, e0)) = op(e2, e0)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6227, 3788, 6230, 6208])).
% 1.37/1.52 tff(6234,plain,
% 1.37/1.52 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e2, e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6233])).
% 1.37/1.52 tff(6235,plain,
% 1.37/1.52 (op(e0, op(e2, e0)) = op(e0, op(e0, op(e0, e0)))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6234])).
% 1.37/1.52 tff(6236,plain,
% 1.37/1.52 (op(e0, op(e2, e0)) = op(e0, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6207])).
% 1.37/1.52 tff(6237,plain,
% 1.37/1.52 (op(e0, e2) = op(e0, op(e2, e0))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6236])).
% 1.37/1.52 tff(6238,plain,
% 1.37/1.52 (e3 = op(e0, e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6220])).
% 1.37/1.52 tff(6239,plain,
% 1.37/1.52 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6238, 6237, 6235])).
% 1.37/1.52 tff(6240,plain,
% 1.37/1.52 ($false),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[3582, 6239, 6232, 6225])).
% 1.37/1.52 tff(6241,plain,((op(e2, e0) = e1) | (~(op(e1, e3) = e1)) | (op(e0, e0) = e0) | (op(e0, e3) = e2) | (op(e0, e2) = e2) | (op(e1, e2) = e3) | (op(e3, e2) = e3) | (op(e1, e3) = e3) | (op(e2, e0) = e3) | (op(e2, e0) = e0) | (op(e2, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.52 tff(6242,plain,
% 1.37/1.52 (op(e2, e0) = e3),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[6241, 6189, 6103, 79, 6206, 75, 1890, 1080, 5426, 5643, 5582])).
% 1.37/1.52 tff(6243,plain,
% 1.37/1.52 (e3 = op(e2, e0)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6242])).
% 1.37/1.52 tff(6244,plain,
% 1.37/1.52 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6243, 6200])).
% 1.37/1.52 tff(6245,plain,
% 1.37/1.52 ($false),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1648, 6244, 6197, 6191])).
% 1.37/1.52 tff(6246,plain,((op(e0, e3) = e2) | (~(op(e2, e1) = e0)) | (op(e1, e2) = e3) | (op(e3, e2) = e3) | (op(e1, e3) = e3) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e3, e1) = e0) | (op(e3, e0) = op(e0, e3)) | (op(e0, e3) = e1) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.52 tff(6247,plain,
% 1.37/1.52 (op(e0, e3) = e2),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[6246, 1890, 6065, 3508, 6061, 3849, 2527, 72, 80, 183, 5528, 121, 6056])).
% 1.37/1.52 tff(6248,plain,
% 1.37/1.52 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6247])).
% 1.37/1.52 tff(6249,plain,
% 1.37/1.52 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6248, 1])).
% 1.37/1.52 tff(6250,plain,
% 1.37/1.52 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6249])).
% 1.37/1.52 tff(6251,plain,
% 1.37/1.52 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6250])).
% 1.37/1.52 tff(6252,plain,
% 1.37/1.52 (~(op(e0, e3) = e0)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[14, 6251])).
% 1.37/1.52 tff(6253,plain,
% 1.37/1.52 (op(e3, e3) = e0),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[1098, 6252, 5446, 80])).
% 1.37/1.52 tff(6254,plain,
% 1.37/1.52 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6253])).
% 1.37/1.52 tff(6255,plain,
% 1.37/1.52 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6254])).
% 1.37/1.52 tff(6256,plain,
% 1.37/1.52 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6255])).
% 1.37/1.52 tff(6257,plain,
% 1.37/1.52 (op(e1, e3) = e1),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[104, 6061, 80, 72])).
% 1.37/1.52 tff(6258,plain,
% 1.37/1.52 (e1 = op(e1, e3)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6257])).
% 1.37/1.52 tff(6259,plain,
% 1.37/1.52 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6258])).
% 1.37/1.52 tff(6260,plain,
% 1.37/1.52 ((op(e2, e3) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6259, 1687])).
% 1.37/1.52 tff(6261,plain,
% 1.37/1.52 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6260])).
% 1.37/1.52 tff(6262,plain,
% 1.37/1.52 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6261])).
% 1.37/1.52 tff(6263,plain,
% 1.37/1.52 (~(op(e2, e3) = e1)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[118, 6262])).
% 1.37/1.52 tff(6264,plain,
% 1.37/1.52 (e2 = op(e0, e3)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6247])).
% 1.37/1.52 tff(6265,plain,
% 1.37/1.52 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6264])).
% 1.37/1.52 tff(6266,plain,
% 1.37/1.52 ((op(e2, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 1.37/1.52 inference(transitivity,[status(thm)],[6265, 925])).
% 1.37/1.52 tff(6267,plain,
% 1.37/1.52 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.37/1.52 inference(symmetry,[status(thm)],[6266])).
% 1.37/1.52 tff(6268,plain,
% 1.37/1.52 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6267])).
% 1.37/1.52 tff(6269,plain,
% 1.37/1.52 (~(op(e2, e3) = e2)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[964, 6268])).
% 1.37/1.52 tff(6270,plain,
% 1.37/1.52 (op(e2, e3) = e3),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[206, 6269, 5446, 6263])).
% 1.37/1.52 tff(6271,plain,
% 1.37/1.52 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6270])).
% 1.37/1.52 tff(6272,plain,
% 1.37/1.52 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.37/1.52 inference(transitivity,[status(thm)],[6271, 666])).
% 1.37/1.52 tff(6273,plain,
% 1.37/1.52 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6272])).
% 1.37/1.52 tff(6274,plain,
% 1.37/1.52 (~(op(e3, e3) = e3)),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[368, 6273])).
% 1.37/1.52 tff(6275,plain,
% 1.37/1.52 (op(e3, e0) = e3),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[422, 6274, 1890, 2839])).
% 1.37/1.52 tff(6276,plain,
% 1.37/1.52 (op(e3, op(e3, e3)) = e3),
% 1.37/1.52 inference(modus_ponens,[status(thm)],[6275, 6256])).
% 1.37/1.52 tff(6277,plain,
% 1.37/1.52 (((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)) | (~(op(e3, op(e3, e3)) = e3))),
% 1.37/1.52 inference(tautology,[status(thm)],[])).
% 1.37/1.52 tff(6278,plain,
% 1.37/1.52 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.37/1.52 inference(unit_resolution,[status(thm)],[6277, 6276])).
% 1.37/1.52 tff(6279,plain,
% 1.37/1.52 (op(e3, op(e0, e3)) = op(e3, e2)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6247])).
% 1.37/1.52 tff(6280,plain,
% 1.37/1.52 (op(e3, e2) = op(e3, op(e0, e3))),
% 1.37/1.52 inference(symmetry,[status(thm)],[6279])).
% 1.37/1.52 tff(6281,plain,
% 1.37/1.52 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 1.37/1.52 inference(monotonicity,[status(thm)],[6280, 6270])).
% 1.37/1.53 tff(6282,plain,
% 1.37/1.53 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 1.37/1.53 inference(symmetry,[status(thm)],[6281])).
% 1.37/1.53 tff(6283,plain,
% 1.37/1.53 ((op(e3, op(e0, e3)) = e3) <=> (op(e2, e3) = op(e3, e2))),
% 1.37/1.53 inference(transitivity,[status(thm)],[6282, 395])).
% 1.37/1.53 tff(6284,plain,
% 1.37/1.53 ((~(op(e3, op(e0, e3)) = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6283])).
% 1.37/1.53 tff(6285,plain,
% 1.37/1.53 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6280])).
% 1.37/1.53 tff(6286,plain,
% 1.37/1.53 ((~(op(e3, e2) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6285])).
% 1.37/1.53 tff(6287,plain,
% 1.37/1.53 (~(op(e3, op(e0, e3)) = e3)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[1890, 6286])).
% 1.37/1.53 tff(6288,plain,
% 1.37/1.53 (~(op(e2, e3) = op(e3, e2))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6287, 6284])).
% 1.37/1.53 tff(6289,plain,
% 1.37/1.53 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[430, 6288])).
% 1.37/1.53 tff(6290,plain,
% 1.37/1.53 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = op(e3, e1))),
% 1.37/1.53 inference(symmetry,[status(thm)],[1674])).
% 1.37/1.53 tff(6291,plain,
% 1.37/1.53 (e3 = op(e1, e1)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6057])).
% 1.37/1.53 tff(6292,plain,
% 1.37/1.53 ((e2 = e3) <=> (e2 = op(e1, e1))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6291])).
% 1.37/1.53 tff(6293,plain,
% 1.37/1.53 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 1.37/1.53 inference(transitivity,[status(thm)],[6292, 2166])).
% 1.37/1.53 tff(6294,plain,
% 1.37/1.53 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6293])).
% 1.37/1.53 tff(6295,plain,
% 1.37/1.53 (~(op(e1, e1) = e2)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[1321, 6294])).
% 1.37/1.53 tff(6296,plain,
% 1.37/1.53 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6264])).
% 1.37/1.53 tff(6297,plain,
% 1.37/1.53 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6296])).
% 1.37/1.53 tff(6298,plain,
% 1.37/1.53 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6297])).
% 1.37/1.53 tff(6299,plain,
% 1.37/1.53 (~(op(e0, e1) = e2)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[818, 6298])).
% 1.37/1.53 tff(6300,plain,
% 1.37/1.53 (op(e3, e1) = e2),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1993, 6299, 6295, 5515])).
% 1.37/1.53 tff(6301,plain,
% 1.37/1.53 (op(e3, e1) = op(e0, e3)),
% 1.37/1.53 inference(transitivity,[status(thm)],[6300, 6264])).
% 1.37/1.53 tff(6302,plain,
% 1.37/1.53 ((op(e3, e1) = op(e1, e3)) <=> (op(e0, e3) = op(e1, e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6301])).
% 1.37/1.53 tff(6303,plain,
% 1.37/1.53 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e1) = op(e1, e3))),
% 1.37/1.53 inference(symmetry,[status(thm)],[6302])).
% 1.37/1.53 tff(6304,plain,
% 1.37/1.53 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = op(e3, e1))),
% 1.37/1.53 inference(transitivity,[status(thm)],[6303, 6290])).
% 1.37/1.53 tff(6305,plain,
% 1.37/1.53 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6304])).
% 1.37/1.53 tff(6306,plain,
% 1.37/1.53 (~(op(e1, e3) = op(e3, e1))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[64, 6305])).
% 1.37/1.53 tff(6307,plain,
% 1.37/1.53 (((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)) | (op(e1, e3) = op(e3, e1))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6308,plain,
% 1.37/1.53 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6307, 6306])).
% 1.37/1.53 tff(6309,plain,
% 1.37/1.53 ((~(op(e3, op(e0, e3)) = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6282])).
% 1.37/1.53 tff(6310,plain,
% 1.37/1.53 (~(op(e3, e2) = op(e2, e3))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6287, 6309])).
% 1.37/1.53 tff(6311,plain,
% 1.37/1.53 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[500, 6310])).
% 1.37/1.53 tff(6312,plain,
% 1.37/1.53 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6270])).
% 1.37/1.53 tff(6313,plain,
% 1.37/1.53 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6312])).
% 1.37/1.53 tff(6314,plain,
% 1.37/1.53 (~(op(e2, e2) = e3)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[515, 6313])).
% 1.37/1.53 tff(6315,plain,
% 1.37/1.53 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6300])).
% 1.37/1.53 tff(6316,plain,
% 1.37/1.53 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.37/1.53 inference(transitivity,[status(thm)],[6315, 2234])).
% 1.37/1.53 tff(6317,plain,
% 1.37/1.53 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6316])).
% 1.37/1.53 tff(6318,plain,
% 1.37/1.53 (~(op(e3, e2) = e2)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3429, 6317])).
% 1.37/1.53 tff(6319,plain,
% 1.37/1.53 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6253])).
% 1.37/1.53 tff(6320,plain,
% 1.37/1.53 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6319])).
% 1.37/1.53 tff(6321,plain,
% 1.37/1.53 (~(op(e3, e2) = e0)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[1888, 6320])).
% 1.37/1.53 tff(6322,plain,
% 1.37/1.53 (op(e3, e2) = e1),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1898, 6321, 1890, 6318])).
% 1.37/1.53 tff(6323,plain,
% 1.37/1.53 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6322])).
% 1.37/1.53 tff(6324,plain,
% 1.37/1.53 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6323])).
% 1.37/1.53 tff(6325,plain,
% 1.37/1.53 (~(op(e2, e2) = e1)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[1546, 6324])).
% 1.37/1.53 tff(6326,plain,
% 1.37/1.53 (op(e2, e2) = e2),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[524, 6325, 5552, 6314])).
% 1.37/1.53 tff(6327,plain,
% 1.37/1.53 (op(e2, op(e2, e2)) = op(e2, e2)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6326])).
% 1.37/1.53 tff(6328,plain,
% 1.37/1.53 (op(e2, op(e2, e2)) = e2),
% 1.37/1.53 inference(transitivity,[status(thm)],[6327, 6326])).
% 1.37/1.53 tff(6329,plain,
% 1.37/1.53 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[528, 6328])).
% 1.37/1.53 tff(6330,plain,
% 1.37/1.53 (op(e3, op(e2, e1)) = op(e3, e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3508])).
% 1.37/1.53 tff(6331,plain,
% 1.37/1.53 ((op(e3, op(e2, e1)) = e3) <=> (op(e3, e0) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6330])).
% 1.37/1.53 tff(6332,plain,
% 1.37/1.53 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e1)) = e3)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6331])).
% 1.37/1.53 tff(6333,plain,
% 1.37/1.53 (op(e3, op(e2, e1)) = e3),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6275, 6332])).
% 1.37/1.53 tff(6334,plain,
% 1.37/1.53 (((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)) | (~(op(e3, op(e2, e1)) = e3))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6335,plain,
% 1.37/1.53 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6334, 6333])).
% 1.37/1.53 tff(6336,plain,
% 1.37/1.53 ((op(e0, e2) = op(e2, e0)) <=> (op(e2, e0) = op(e0, e2))),
% 1.37/1.53 inference(commutativity,[status(thm)],[])).
% 1.37/1.53 tff(6337,plain,
% 1.37/1.53 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e2, e0))),
% 1.37/1.53 inference(symmetry,[status(thm)],[6336])).
% 1.37/1.53 tff(6338,plain,
% 1.37/1.53 (op(e0, e2) = e3),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2111, 6314, 6065, 1890])).
% 1.37/1.53 tff(6339,plain,
% 1.37/1.53 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6338])).
% 1.37/1.53 tff(6340,plain,
% 1.37/1.53 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 1.37/1.53 inference(symmetry,[status(thm)],[6339])).
% 1.37/1.53 tff(6341,plain,
% 1.37/1.53 ((op(e2, e0) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 1.37/1.53 inference(transitivity,[status(thm)],[6340, 6337])).
% 1.37/1.53 tff(6342,plain,
% 1.37/1.53 ((~(op(e2, e0) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6341])).
% 1.37/1.53 tff(6343,plain,
% 1.37/1.53 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6270])).
% 1.37/1.53 tff(6344,plain,
% 1.37/1.53 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6343])).
% 1.37/1.53 tff(6345,plain,
% 1.37/1.53 (~(op(e2, e0) = e3)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[989, 6344])).
% 1.37/1.53 tff(6346,plain,
% 1.37/1.53 (~(op(e0, e2) = op(e2, e0))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6345, 6342])).
% 1.37/1.53 tff(6347,plain,
% 1.37/1.53 (((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)) | (op(e0, e2) = op(e2, e0))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6348,plain,
% 1.37/1.53 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6347, 6346])).
% 1.37/1.53 tff(6349,plain,
% 1.37/1.53 (op(e0, e1) = e1),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[829, 6299, 3849, 2527])).
% 1.37/1.53 tff(6350,plain,
% 1.37/1.53 (op(e0, e1) = op(e1, e3)),
% 1.37/1.53 inference(transitivity,[status(thm)],[6349, 6258])).
% 1.37/1.53 tff(6351,plain,
% 1.37/1.53 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = op(e1, e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6350])).
% 1.37/1.53 tff(6352,plain,
% 1.37/1.53 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 1.37/1.53 inference(symmetry,[status(thm)],[6351])).
% 1.37/1.53 tff(6353,plain,
% 1.37/1.53 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6352])).
% 1.37/1.53 tff(6354,plain,
% 1.37/1.53 (~(op(e1, e0) = op(e0, e1))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[110, 6353])).
% 1.37/1.53 tff(6355,plain,
% 1.37/1.53 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[613, 6354])).
% 1.37/1.53 tff(6356,plain,
% 1.37/1.53 ((~(op(e2, e0) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6340])).
% 1.37/1.53 tff(6357,plain,
% 1.37/1.53 (~(op(e2, e0) = op(e0, e2))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6345, 6356])).
% 1.37/1.53 tff(6358,plain,
% 1.37/1.53 (((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)) | (op(e2, e0) = op(e0, e2))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6359,plain,
% 1.37/1.53 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6358, 6357])).
% 1.37/1.53 tff(6360,plain,
% 1.37/1.53 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6303])).
% 1.37/1.53 tff(6361,plain,
% 1.37/1.53 (~(op(e3, e1) = op(e1, e3))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[64, 6360])).
% 1.37/1.53 tff(6362,plain,
% 1.37/1.53 (((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)) | (op(e3, e1) = op(e1, e3))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6363,plain,
% 1.37/1.53 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6362, 6361])).
% 1.37/1.53 tff(6364,plain,
% 1.37/1.53 ((op(e1, e0) = op(e1, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 1.37/1.53 inference(transitivity,[status(thm)],[6352, 596])).
% 1.37/1.53 tff(6365,plain,
% 1.37/1.53 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6364])).
% 1.37/1.53 tff(6366,plain,
% 1.37/1.53 (~(op(e0, e1) = op(e1, e0))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[110, 6365])).
% 1.37/1.53 tff(6367,plain,
% 1.37/1.53 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[609, 6366])).
% 1.37/1.53 tff(6368,plain,
% 1.37/1.53 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6057])).
% 1.37/1.53 tff(6369,plain,
% 1.37/1.53 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e3) = e1)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6368])).
% 1.37/1.53 tff(6370,plain,
% 1.37/1.53 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6369])).
% 1.37/1.53 tff(6371,plain,
% 1.37/1.53 (op(e1, op(e1, e1)) = e1),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6257, 6370])).
% 1.37/1.53 tff(6372,plain,
% 1.37/1.53 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[5678, 6371])).
% 1.37/1.53 tff(6373,plain,
% 1.37/1.53 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e1)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6349])).
% 1.37/1.53 tff(6374,plain,
% 1.37/1.53 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e1))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6373])).
% 1.37/1.53 tff(6375,plain,
% 1.37/1.53 (~(op(e0, e0) = e1)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[811, 6374])).
% 1.37/1.53 tff(6376,plain,
% 1.37/1.53 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e0, e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6264])).
% 1.37/1.53 tff(6377,plain,
% 1.37/1.53 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6376])).
% 1.37/1.53 tff(6378,plain,
% 1.37/1.53 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6377])).
% 1.37/1.53 tff(6379,plain,
% 1.37/1.53 (~(op(e0, e0) = e2)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3414, 6378])).
% 1.37/1.53 tff(6380,plain,
% 1.37/1.53 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6275])).
% 1.37/1.53 tff(6381,plain,
% 1.37/1.53 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6380])).
% 1.37/1.53 tff(6382,plain,
% 1.37/1.53 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = op(e3, e0)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(6383,plain,
% 1.37/1.53 (~(op(e0, e0) = op(e3, e0))),
% 1.37/1.53 inference(and_elim,[status(thm)],[356])).
% 1.37/1.53 tff(6384,plain,
% 1.37/1.53 (~(op(e0, e0) = op(e3, e0))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6383, 6382])).
% 1.37/1.53 tff(6385,plain,
% 1.37/1.53 (~(op(e0, e0) = e3)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[6384, 6381])).
% 1.37/1.53 tff(6386,plain,
% 1.37/1.53 (op(e0, e0) = e0),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3612, 6385, 6379, 6375])).
% 1.37/1.53 tff(6387,plain,
% 1.37/1.53 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6386])).
% 1.37/1.53 tff(6388,plain,
% 1.37/1.53 (op(e0, op(e0, e0)) = e0),
% 1.37/1.53 inference(transitivity,[status(thm)],[6387, 6386])).
% 1.37/1.53 tff(6389,plain,
% 1.37/1.53 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[5598, 6388])).
% 1.37/1.53 tff(6390,plain,
% 1.37/1.53 ((op(e0, e2) = e0) <=> (e3 = e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6338])).
% 1.37/1.53 tff(6391,plain,
% 1.37/1.53 ((op(e0, e2) = e0) <=> (e0 = e3)),
% 1.37/1.53 inference(transitivity,[status(thm)],[6390, 159])).
% 1.37/1.53 tff(6392,plain,
% 1.37/1.53 ((e0 = e3) <=> (op(e0, e2) = e0)),
% 1.37/1.53 inference(symmetry,[status(thm)],[6391])).
% 1.37/1.53 tff(6393,plain,
% 1.37/1.53 ((~(e0 = e3)) <=> (~(op(e0, e2) = e0))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6392])).
% 1.37/1.53 tff(6394,plain,
% 1.37/1.53 (~(op(e0, e2) = e0)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[181, 6393])).
% 1.37/1.53 tff(6395,plain,
% 1.37/1.53 (op(e1, e2) = e0),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[973, 6394, 5552, 6321])).
% 1.37/1.53 tff(6396,plain,
% 1.37/1.53 (op(e0, op(e1, e2)) = op(e0, e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6395])).
% 1.37/1.53 tff(6397,plain,
% 1.37/1.53 (op(e0, op(e1, e2)) = e0),
% 1.37/1.53 inference(transitivity,[status(thm)],[6396, 6386])).
% 1.37/1.53 tff(6398,plain,
% 1.37/1.53 (((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)) | (~(op(e0, op(e1, e2)) = e0))),
% 1.37/1.53 inference(tautology,[status(thm)],[])).
% 1.37/1.53 tff(6399,plain,
% 1.37/1.53 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6398, 6397])).
% 1.37/1.53 tff(6400,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[5367, 6399, 6389, 6372, 6367, 6363, 6359, 6355, 6348, 6335, 6329, 6311, 5613, 6308, 6289, 6278])).
% 1.37/1.53 tff(6401,plain,((op(e3, e2) = e3) | (~(op(e2, e1) = e0)) | (op(e3, e1) = e3) | (op(e1, e3) = e0) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (op(e1, e3) = e2) | (op(e3, e1) = e0) | (op(e3, e0) = op(e0, e3)) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(6402,plain,
% 1.37/1.53 (op(e3, e2) = e3),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[6401, 2839, 3508, 80, 3849, 2527, 72, 183, 5528, 121])).
% 1.37/1.53 tff(6403,plain,
% 1.37/1.53 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 1.37/1.53 inference(monotonicity,[status(thm)],[6402])).
% 1.44/1.54 tff(6404,plain,
% 1.44/1.54 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6403, 159])).
% 1.44/1.54 tff(6405,plain,
% 1.44/1.54 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6404])).
% 1.44/1.54 tff(6406,plain,
% 1.44/1.54 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6405])).
% 1.44/1.54 tff(6407,plain,
% 1.44/1.54 (~(op(e3, e2) = e0)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[181, 6406])).
% 1.44/1.54 tff(6408,plain,
% 1.44/1.54 (~(op(e0, e3) = e0)),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[5538, 6407, 183, 5528])).
% 1.44/1.54 tff(6409,plain,
% 1.44/1.54 (op(e3, e3) = e0),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1098, 6408, 5446, 80])).
% 1.44/1.54 tff(6410,plain,
% 1.44/1.54 (e0 = op(e3, e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[6409, 3078])).
% 1.44/1.54 tff(6411,plain,
% 1.44/1.54 ((e1 = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 1.44/1.54 inference(commutativity,[status(thm)],[])).
% 1.44/1.54 tff(6412,plain,
% 1.44/1.54 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6409])).
% 1.44/1.54 tff(6413,plain,
% 1.44/1.54 ((e1 = op(e3, op(e3, e3))) <=> (e1 = op(e3, e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6412])).
% 1.44/1.54 tff(6414,plain,
% 1.44/1.54 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e1)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6413, 6411])).
% 1.44/1.54 tff(6415,plain,
% 1.44/1.54 ((op(e3, e0) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6414])).
% 1.44/1.54 tff(6416,plain,
% 1.44/1.54 (e0 = op(e3, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6409])).
% 1.44/1.54 tff(6417,plain,
% 1.44/1.54 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6416])).
% 1.44/1.54 tff(6418,plain,
% 1.44/1.54 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6417])).
% 1.44/1.54 tff(6419,plain,
% 1.44/1.54 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6418])).
% 1.44/1.54 tff(6420,plain,
% 1.44/1.54 (~(op(e3, e0) = e0)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[157, 6419])).
% 1.44/1.54 tff(6421,plain,
% 1.44/1.54 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6402])).
% 1.44/1.54 tff(6422,plain,
% 1.44/1.54 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6421])).
% 1.44/1.54 tff(6423,plain,
% 1.44/1.54 (~(op(e3, e0) = e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[1133, 6422])).
% 1.44/1.54 tff(6424,plain,
% 1.44/1.54 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6402])).
% 1.44/1.54 tff(6425,plain,
% 1.44/1.54 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6424])).
% 1.44/1.54 tff(6426,plain,
% 1.44/1.54 (~(op(e2, e2) = e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[1546, 6425])).
% 1.44/1.54 tff(6427,plain,
% 1.44/1.54 ((op(e0, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[1088])).
% 1.44/1.54 tff(6428,plain,
% 1.44/1.54 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6427, 112])).
% 1.44/1.54 tff(6429,plain,
% 1.44/1.54 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6428])).
% 1.44/1.54 tff(6430,plain,
% 1.44/1.54 (~(op(e2, e3) = e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[964, 6429])).
% 1.44/1.54 tff(6431,plain,
% 1.44/1.54 (op(e2, e3) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[206, 6430, 5446, 3715])).
% 1.44/1.54 tff(6432,plain,
% 1.44/1.54 (e2 = op(e2, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6431])).
% 1.44/1.54 tff(6433,plain,
% 1.44/1.54 ((op(e2, e2) = e2) <=> (op(e2, e2) = op(e2, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6432])).
% 1.44/1.54 tff(6434,plain,
% 1.44/1.54 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6433])).
% 1.44/1.54 tff(6435,plain,
% 1.44/1.54 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6434])).
% 1.44/1.54 tff(6436,plain,
% 1.44/1.54 (~(op(e2, e2) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[515, 6435])).
% 1.44/1.54 tff(6437,plain,
% 1.44/1.54 (op(e2, e2) = e1),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[524, 6436, 5552, 2431])).
% 1.44/1.54 tff(6438,plain,
% 1.44/1.54 (e1 = op(e2, e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[6437, 317])).
% 1.44/1.54 tff(6439,plain,
% 1.44/1.54 (op(e2, e2) = op(e1, e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6437, 3710])).
% 1.44/1.54 tff(6440,plain,
% 1.44/1.54 (op(e2, op(e2, e2)) = op(e2, op(e1, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6439])).
% 1.44/1.54 tff(6441,plain,
% 1.44/1.54 (op(e2, op(e1, e3)) = op(e2, op(e2, e2))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6440])).
% 1.44/1.54 tff(6442,plain,
% 1.44/1.54 (e0 = op(e2, op(e2, e2))),
% 1.44/1.54 inference(transitivity,[status(thm)],[5560, 3884, 6441])).
% 1.44/1.54 tff(6443,plain,
% 1.44/1.54 (op(e3, e3) = e0),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1098, 1087, 5446, 80])).
% 1.44/1.54 tff(6444,plain,
% 1.44/1.54 (e0 = op(e3, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6443])).
% 1.44/1.54 tff(6445,plain,
% 1.44/1.54 (op(e2, op(e2, e2)) = op(e3, e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6440, 3796, 3508, 6444])).
% 1.44/1.54 tff(6446,plain,
% 1.44/1.54 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6445])).
% 1.44/1.54 tff(6447,plain,
% 1.44/1.54 (op(e2, op(e3, e3)) = op(e2, op(e2, op(e2, e2)))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6446])).
% 1.44/1.54 tff(6448,plain,
% 1.44/1.54 (op(e2, op(e3, e3)) = op(e2, e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6443])).
% 1.44/1.54 tff(6449,plain,
% 1.44/1.54 (op(e2, e0) = op(e2, op(e3, e3))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6448])).
% 1.44/1.54 tff(6450,plain,
% 1.44/1.54 (op(e2, e0) = e3),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1559, 6430, 5487, 2431])).
% 1.44/1.54 tff(6451,plain,
% 1.44/1.54 (e3 = op(e2, e0)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6450])).
% 1.44/1.54 tff(6452,plain,
% 1.44/1.54 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.44/1.54 inference(transitivity,[status(thm)],[6451, 6449, 6447])).
% 1.44/1.54 tff(6453,plain,
% 1.44/1.54 ($false),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1648, 6452, 6442, 6438])).
% 1.44/1.54 tff(6454,plain,((op(e0, e3) = e0) | (~(op(e2, e1) = e0)) | (~(op(e1, e3) = e1)) | (op(e2, e2) = e3) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.54 tff(6455,plain,
% 1.44/1.54 (op(e0, e3) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6454, 6408, 6257, 6426, 80, 121, 3508])).
% 1.44/1.54 tff(6456,plain,
% 1.44/1.54 (e2 = op(e0, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6455])).
% 1.44/1.54 tff(6457,plain,
% 1.44/1.54 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6456])).
% 1.44/1.54 tff(6458,plain,
% 1.44/1.54 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6457])).
% 1.44/1.54 tff(6459,plain,
% 1.44/1.54 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6458])).
% 1.44/1.54 tff(6460,plain,
% 1.44/1.54 (~(op(e3, e0) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[5528, 6459])).
% 1.44/1.54 tff(6461,plain,
% 1.44/1.54 (op(e3, e0) = e1),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[5422, 6460, 6423, 6420])).
% 1.44/1.54 tff(6462,plain,
% 1.44/1.54 (e1 = op(e3, op(e3, e3))),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[6461, 6415])).
% 1.44/1.54 tff(6463,plain,
% 1.44/1.54 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6412])).
% 1.44/1.54 tff(6464,plain,
% 1.44/1.54 (op(e3, op(e3, e0)) = op(e3, op(e3, op(e3, e3)))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6463])).
% 1.44/1.54 tff(6465,plain,
% 1.44/1.54 (op(e3, e0) = op(e1, e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6461, 6258])).
% 1.44/1.54 tff(6466,plain,
% 1.44/1.54 (op(e3, op(e3, e0)) = op(e3, op(e1, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6465])).
% 1.44/1.54 tff(6467,plain,
% 1.44/1.54 (op(e3, op(e1, e3)) = op(e3, op(e3, e0))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6466])).
% 1.44/1.54 tff(6468,plain,
% 1.44/1.54 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6257])).
% 1.44/1.54 tff(6469,plain,
% 1.44/1.54 (op(e3, e1) = op(e3, op(e1, e3))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6468])).
% 1.44/1.54 tff(6470,plain,
% 1.44/1.54 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6456])).
% 1.44/1.54 tff(6471,plain,
% 1.44/1.54 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6470])).
% 1.44/1.54 tff(6472,plain,
% 1.44/1.54 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6471])).
% 1.44/1.54 tff(6473,plain,
% 1.44/1.54 (~(op(e0, e1) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[818, 6472])).
% 1.44/1.54 tff(6474,plain,
% 1.44/1.54 (op(e3, e1) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1993, 6473, 6295, 5515])).
% 1.44/1.54 tff(6475,plain,
% 1.44/1.54 (e2 = op(e3, e1)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6474])).
% 1.44/1.54 tff(6476,plain,
% 1.44/1.54 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.44/1.54 inference(transitivity,[status(thm)],[6475, 6469, 6467, 6464])).
% 1.44/1.54 tff(6477,plain,
% 1.44/1.54 ($false),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[5193, 6476, 6462, 6410])).
% 1.44/1.54 tff(6478,plain,((op(e3, e1) = e3) | (op(e3, e0) = op(e0, e3)) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e3, e1) = e0) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.54 tff(6479,plain,
% 1.44/1.54 (op(e3, e0) = op(e0, e3)),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6478, 6046, 80, 121, 3508, 5474, 5478, 2527, 72])).
% 1.44/1.54 tff(6480,plain,
% 1.44/1.54 ($false),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[4654, 6479, 6043, 121, 652, 5724, 6036])).
% 1.44/1.54 tff(6481,plain,((op(e2, e3) = e3) | (op(e0, e3) = e1) | (op(e1, op(e0, e3)) = e1) | (op(e1, e3) = e0) | (~(op(e2, e1) = e0)) | (op(e0, e1) = e3) | (op(e1, e3) = e2) | (~(op(e0, e3) = e0)) | (op(e2, e3) = e1) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.54 tff(6482,plain,
% 1.44/1.54 (op(e2, e3) = e3),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6481, 6031, 121, 80, 3508, 2527, 72, 5447, 6024, 6020])).
% 1.44/1.54 tff(6483,plain,
% 1.44/1.54 ((op(e2, e3) = e2) <=> (e3 = e2)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6482])).
% 1.44/1.54 tff(6484,plain,
% 1.44/1.54 ((op(e2, e3) = e2) <=> (e2 = e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6483, 1314])).
% 1.44/1.54 tff(6485,plain,
% 1.44/1.54 ((e2 = e3) <=> (op(e2, e3) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6484])).
% 1.44/1.54 tff(6486,plain,
% 1.44/1.54 ((~(e2 = e3)) <=> (~(op(e2, e3) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6485])).
% 1.44/1.54 tff(6487,plain,
% 1.44/1.54 (~(op(e2, e3) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[1321, 6486])).
% 1.44/1.54 tff(6488,plain,
% 1.44/1.54 (op(e3, e3) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[2786, 6487, 72, 79])).
% 1.44/1.54 tff(6489,plain,
% 1.44/1.54 (op(e3, op(e3, e2)) = op(e3, e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[5539])).
% 1.44/1.54 tff(6490,plain,
% 1.44/1.54 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[2814])).
% 1.44/1.54 tff(6491,plain,
% 1.44/1.54 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6490, 6489])).
% 1.44/1.54 tff(6492,plain,
% 1.44/1.54 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6491])).
% 1.44/1.54 tff(6493,plain,
% 1.44/1.54 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6492, 6411])).
% 1.44/1.54 tff(6494,plain,
% 1.44/1.54 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6493])).
% 1.44/1.54 tff(6495,plain,
% 1.44/1.54 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[2814])).
% 1.44/1.54 tff(6496,plain,
% 1.44/1.54 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e0)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6495, 4959])).
% 1.44/1.54 tff(6497,plain,
% 1.44/1.54 ((op(e3, e2) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 1.44/1.54 inference(symmetry,[status(thm)],[6496])).
% 1.44/1.54 tff(6498,plain,
% 1.44/1.54 (e0 = op(e3, op(e3, e3))),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[5539, 6497])).
% 1.44/1.54 tff(6499,plain,
% 1.44/1.54 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[5879, 6498, 2813])).
% 1.44/1.54 tff(6500,plain,
% 1.44/1.54 (~(op(e3, e0) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[6499, 6494])).
% 1.44/1.54 tff(6501,plain,
% 1.44/1.54 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[2834])).
% 1.44/1.54 tff(6502,plain,
% 1.44/1.54 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6501])).
% 1.44/1.54 tff(6503,plain,
% 1.44/1.54 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6502])).
% 1.44/1.54 tff(6504,plain,
% 1.44/1.54 (~(op(e3, e0) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[157, 6503])).
% 1.44/1.54 tff(6505,plain,
% 1.44/1.54 (op(e3, e1) = e3),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6478, 5528, 80, 121, 3508, 5474, 5478, 2527, 72])).
% 1.44/1.54 tff(6506,plain,
% 1.44/1.54 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6505])).
% 1.44/1.54 tff(6507,plain,
% 1.44/1.54 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6506])).
% 1.44/1.54 tff(6508,plain,
% 1.44/1.54 (~(op(e3, e0) = e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[580, 6507])).
% 1.44/1.54 tff(6509,plain,
% 1.44/1.54 (op(e3, e0) = e1),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[5422, 6508, 6504, 5536])).
% 1.44/1.54 tff(6510,plain,
% 1.44/1.54 ($false),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6509, 6500])).
% 1.44/1.54 tff(6511,plain,((op(e3, e0) = op(e0, e3)) | (~(op(e3, e3) = e2)) | (~(op(e0, e3) = e0)) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e0, e1) = e3) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.54 tff(6512,plain,
% 1.44/1.54 (op(e3, e0) = op(e0, e3)),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6511, 6488, 5447, 80, 121, 3508, 2527, 72])).
% 1.44/1.54 tff(6513,plain,
% 1.44/1.54 (op(e3, e0) = e0),
% 1.44/1.54 inference(transitivity,[status(thm)],[6512, 5447])).
% 1.44/1.54 tff(6514,plain,
% 1.44/1.54 ((op(e3, e0) = e1) <=> (e0 = e1)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6513])).
% 1.44/1.54 tff(6515,plain,
% 1.44/1.54 ((e0 = e1) <=> (op(e3, e0) = e1)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6514])).
% 1.44/1.54 tff(6516,plain,
% 1.44/1.54 ((~(e0 = e1)) <=> (~(op(e3, e0) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6515])).
% 1.44/1.54 tff(6517,plain,
% 1.44/1.54 (~(op(e3, e0) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[26, 6516])).
% 1.44/1.54 tff(6518,plain,
% 1.44/1.54 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6028])).
% 1.44/1.54 tff(6519,plain,
% 1.44/1.54 (~(op(e1, e0) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[110, 6518])).
% 1.44/1.54 tff(6520,plain,
% 1.44/1.54 (e2 = op(e3, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6488])).
% 1.44/1.54 tff(6521,plain,
% 1.44/1.54 (op(e0, op(e0, e3)) = op(e0, e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[5447])).
% 1.44/1.54 tff(6522,plain,
% 1.44/1.54 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e0) = e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6521])).
% 1.44/1.54 tff(6523,plain,
% 1.44/1.54 ((op(e0, e0) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6522])).
% 1.44/1.54 tff(6524,plain,
% 1.44/1.54 ((~(op(e0, e0) = e0)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6523])).
% 1.44/1.54 tff(6525,plain,
% 1.44/1.54 (~(op(e0, op(e0, e3)) = e0)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[5450, 6524])).
% 1.44/1.54 tff(6526,plain,
% 1.44/1.54 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[5447])).
% 1.44/1.54 tff(6527,plain,
% 1.44/1.54 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6526])).
% 1.44/1.54 tff(6528,plain,
% 1.44/1.54 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6527])).
% 1.44/1.54 tff(6529,plain,
% 1.44/1.54 ((op(e3, e0) = e3) <=> (e0 = e3)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6513])).
% 1.44/1.54 tff(6530,plain,
% 1.44/1.54 ((e0 = e3) <=> (op(e3, e0) = e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6529])).
% 1.44/1.54 tff(6531,plain,
% 1.44/1.54 ((e0 = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6530, 6528])).
% 1.44/1.54 tff(6532,plain,
% 1.44/1.54 ((~(e0 = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6531])).
% 1.44/1.54 tff(6533,plain,
% 1.44/1.54 (~(op(e3, op(e0, e3)) = e3)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[181, 6532])).
% 1.44/1.54 tff(6534,plain,
% 1.44/1.54 (op(e2, op(e0, e3)) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[4654, 6533, 121, 6031, 6525, 6512])).
% 1.44/1.54 tff(6535,plain,
% 1.44/1.54 (e0 = op(e0, e3)),
% 1.44/1.54 inference(symmetry,[status(thm)],[5447])).
% 1.44/1.54 tff(6536,plain,
% 1.44/1.54 (op(e2, e0) = op(e2, op(e0, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6535])).
% 1.44/1.54 tff(6537,plain,
% 1.44/1.54 (op(e2, e0) = op(e3, e3)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6536, 6534, 6520])).
% 1.44/1.54 tff(6538,plain,
% 1.44/1.54 ((op(e2, e0) = e1) <=> (op(e3, e3) = e1)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6537])).
% 1.44/1.54 tff(6539,plain,
% 1.44/1.54 ((op(e3, e3) = e1) <=> (op(e2, e0) = e1)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6538])).
% 1.44/1.54 tff(6540,plain,
% 1.44/1.54 ((~(op(e3, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6539])).
% 1.44/1.54 tff(6541,plain,
% 1.44/1.54 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6016])).
% 1.44/1.54 tff(6542,plain,
% 1.44/1.54 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6541, 657])).
% 1.44/1.54 tff(6543,plain,
% 1.44/1.54 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6542])).
% 1.44/1.54 tff(6544,plain,
% 1.44/1.54 (~(op(e3, e3) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[571, 6543])).
% 1.44/1.54 tff(6545,plain,
% 1.44/1.54 (~(op(e2, e0) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[6544, 6540])).
% 1.44/1.54 tff(6546,plain,
% 1.44/1.54 (op(e0, e0) = e1),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1480, 6545, 6519, 6517])).
% 1.44/1.54 tff(6547,plain,
% 1.44/1.54 (e1 = op(e0, e0)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6546])).
% 1.44/1.54 tff(6548,plain,
% 1.44/1.54 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e0, e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6547])).
% 1.44/1.54 tff(6549,plain,
% 1.44/1.54 ((op(e0, e1) = e1) <=> (op(e0, e0) = op(e0, e1))),
% 1.44/1.54 inference(transitivity,[status(thm)],[6548, 804])).
% 1.44/1.54 tff(6550,plain,
% 1.44/1.54 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6549])).
% 1.44/1.54 tff(6551,plain,
% 1.44/1.54 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e1))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6550])).
% 1.44/1.54 tff(6552,plain,
% 1.44/1.54 (~(op(e0, e1) = e1)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[811, 6551])).
% 1.44/1.54 tff(6553,plain,
% 1.44/1.54 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6520])).
% 1.44/1.54 tff(6554,plain,
% 1.44/1.54 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6553])).
% 1.44/1.54 tff(6555,plain,
% 1.44/1.54 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6554])).
% 1.44/1.54 tff(6556,plain,
% 1.44/1.54 (~(op(e3, e2) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[1888, 6555])).
% 1.44/1.54 tff(6557,plain,
% 1.44/1.54 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6513])).
% 1.44/1.54 tff(6558,plain,
% 1.44/1.54 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6557])).
% 1.44/1.54 tff(6559,plain,
% 1.44/1.54 (~(op(e1, e0) = e0)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[410, 6558])).
% 1.44/1.54 tff(6560,plain,
% 1.44/1.54 (op(e1, e2) = e0),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1830, 6559, 80, 5456])).
% 1.44/1.54 tff(6561,plain,
% 1.44/1.54 ((op(e1, e2) = e2) <=> (e0 = op(e3, e3))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6560, 6520])).
% 1.44/1.54 tff(6562,plain,
% 1.44/1.54 ((op(e1, e2) = e2) <=> (op(e3, e3) = e0)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6561, 3077])).
% 1.44/1.54 tff(6563,plain,
% 1.44/1.54 ((op(e3, e3) = e0) <=> (op(e1, e2) = e2)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6562])).
% 1.44/1.54 tff(6564,plain,
% 1.44/1.54 ((~(op(e3, e3) = e0)) <=> (~(op(e1, e2) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6563])).
% 1.44/1.54 tff(6565,plain,
% 1.44/1.54 (~(op(e1, e2) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[656, 6564])).
% 1.44/1.54 tff(6566,plain,
% 1.44/1.54 (op(e2, e0) = e2),
% 1.44/1.54 inference(transitivity,[status(thm)],[6536, 6534])).
% 1.44/1.54 tff(6567,plain,
% 1.44/1.54 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6566])).
% 1.44/1.54 tff(6568,plain,
% 1.44/1.54 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.44/1.54 inference(transitivity,[status(thm)],[6567, 81])).
% 1.44/1.54 tff(6569,plain,
% 1.44/1.54 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6568])).
% 1.44/1.54 tff(6570,plain,
% 1.44/1.54 (~(op(e2, e2) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[2228, 6569])).
% 1.44/1.54 tff(6571,plain,
% 1.44/1.54 (op(e0, e2) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[1151, 6570, 6565, 6556])).
% 1.44/1.54 tff(6572,plain,
% 1.44/1.54 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6571])).
% 1.44/1.54 tff(6573,plain,
% 1.44/1.54 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e2))),
% 1.44/1.54 inference(monotonicity,[status(thm)],[6572])).
% 1.44/1.54 tff(6574,plain,
% 1.44/1.54 (~(op(e0, e1) = e2)),
% 1.44/1.54 inference(modus_ponens,[status(thm)],[2102, 6573])).
% 1.44/1.54 tff(6575,plain,
% 1.44/1.54 ($false),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[829, 6574, 6552, 5478, 2527])).
% 1.44/1.54 tff(6576,plain,((op(e1, e3) = e2) | (op(e0, e1) = e3) | (op(e3, e3) = e0) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.54 tff(6577,plain,
% 1.44/1.54 (op(e1, e3) = e2),
% 1.44/1.54 inference(unit_resolution,[status(thm)],[6576, 2527, 656, 80, 121, 3508, 79])).
% 1.44/1.54 tff(6578,plain,
% 1.44/1.54 ((op(e1, e0) = e1) <=> (e0 = e1)),
% 1.44/1.54 inference(monotonicity,[status(thm)],[5788])).
% 1.44/1.54 tff(6579,plain,
% 1.44/1.54 ((e0 = e1) <=> (op(e1, e0) = e1)),
% 1.44/1.54 inference(symmetry,[status(thm)],[6578])).
% 1.44/1.54 tff(6580,plain,
% 1.44/1.54 ((~(e0 = e1)) <=> (~(op(e1, e0) = e1))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6579])).
% 1.44/1.55 tff(6581,plain,
% 1.44/1.55 (~(op(e1, e0) = e1)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[26, 6580])).
% 1.44/1.55 tff(6582,plain,
% 1.44/1.55 ((op(e1, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5788])).
% 1.44/1.55 tff(6583,plain,
% 1.44/1.55 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6582, 5637])).
% 1.44/1.55 tff(6584,plain,
% 1.44/1.55 ((op(e0, e1) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 1.44/1.55 inference(symmetry,[status(thm)],[6583])).
% 1.44/1.55 tff(6585,plain,
% 1.44/1.55 ((~(op(e0, e1) = e0)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6584])).
% 1.44/1.55 tff(6586,plain,
% 1.44/1.55 (~(op(e1, e0) = op(e0, e1))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[5478, 6585])).
% 1.44/1.55 tff(6587,plain,
% 1.44/1.55 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[613, 6586])).
% 1.44/1.55 tff(6588,plain,
% 1.44/1.55 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e1, e0))),
% 1.44/1.55 inference(transitivity,[status(thm)],[6584, 596])).
% 1.44/1.55 tff(6589,plain,
% 1.44/1.55 ((~(op(e0, e1) = e0)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6588])).
% 1.44/1.55 tff(6590,plain,
% 1.44/1.55 (~(op(e0, e1) = op(e1, e0))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[5478, 6589])).
% 1.44/1.55 tff(6591,plain,
% 1.44/1.55 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[609, 6590])).
% 1.44/1.55 tff(6592,plain,
% 1.44/1.55 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5788])).
% 1.44/1.55 tff(6593,plain,
% 1.44/1.55 (op(e1, op(e1, e0)) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6592, 5788])).
% 1.44/1.55 tff(6594,plain,
% 1.44/1.55 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[1836, 6593])).
% 1.44/1.55 tff(6595,plain,
% 1.44/1.55 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[264])).
% 1.44/1.55 tff(6596,plain,
% 1.44/1.55 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6595, 120])).
% 1.44/1.55 tff(6597,plain,
% 1.44/1.55 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6596])).
% 1.44/1.55 tff(6598,plain,
% 1.44/1.55 (~(op(e2, e3) = e2)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[118, 6597])).
% 1.44/1.55 tff(6599,plain,
% 1.44/1.55 (op(e2, e3) = e1),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[206, 124, 5446, 6598])).
% 1.44/1.55 tff(6600,plain,
% 1.44/1.55 (op(op(e2, e3), e3) = op(e1, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6599])).
% 1.44/1.55 tff(6601,plain,
% 1.44/1.55 (op(op(e2, e3), e3) = e2),
% 1.44/1.55 inference(transitivity,[status(thm)],[6600, 264])).
% 1.44/1.55 tff(6602,plain,
% 1.44/1.55 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[1288, 6601])).
% 1.44/1.55 tff(6603,plain,
% 1.44/1.55 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5819])).
% 1.44/1.55 tff(6604,plain,
% 1.44/1.55 (op(op(e3, e2), e3) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6603, 771])).
% 1.44/1.55 tff(6605,plain,
% 1.44/1.55 ((op(op(e3, e2), e3) = e2) <=> (e0 = e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6604])).
% 1.44/1.55 tff(6606,plain,
% 1.44/1.55 ((e0 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6605])).
% 1.44/1.55 tff(6607,plain,
% 1.44/1.55 ((~(e0 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6606])).
% 1.44/1.55 tff(6608,plain,
% 1.44/1.55 (~(op(op(e3, e2), e3) = e2)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[14, 6607])).
% 1.44/1.55 tff(6609,plain,
% 1.44/1.55 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[2408, 6608])).
% 1.44/1.55 tff(6610,plain,
% 1.44/1.55 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[264])).
% 1.44/1.55 tff(6611,plain,
% 1.44/1.55 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6610])).
% 1.44/1.55 tff(6612,plain,
% 1.44/1.55 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6611])).
% 1.44/1.55 tff(6613,plain,
% 1.44/1.55 (~(op(e1, e3) = e3)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[1321, 6612])).
% 1.44/1.55 tff(6614,plain,
% 1.44/1.55 (op(e3, e3) = e3),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[480, 124, 5591, 6613])).
% 1.44/1.55 tff(6615,plain,
% 1.44/1.55 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6614])).
% 1.44/1.55 tff(6616,plain,
% 1.44/1.55 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6615])).
% 1.44/1.55 tff(6617,plain,
% 1.44/1.55 (~(op(e3, e1) = e3)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[437, 6616])).
% 1.44/1.55 tff(6618,plain,
% 1.44/1.55 (op(e1, e1) = e3),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[1730, 6617, 5487, 2527])).
% 1.44/1.55 tff(6619,plain,
% 1.44/1.55 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6618])).
% 1.44/1.55 tff(6620,plain,
% 1.44/1.55 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6619, 532])).
% 1.44/1.55 tff(6621,plain,
% 1.44/1.55 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6620])).
% 1.44/1.55 tff(6622,plain,
% 1.44/1.55 (~(op(e1, e2) = e3)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[1604, 6621])).
% 1.44/1.55 tff(6623,plain,
% 1.44/1.55 ((op(e3, e2) = e3) <=> (e0 = e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5819])).
% 1.44/1.55 tff(6624,plain,
% 1.44/1.55 ((e0 = e3) <=> (op(e3, e2) = e3)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6623])).
% 1.44/1.55 tff(6625,plain,
% 1.44/1.55 ((~(e0 = e3)) <=> (~(op(e3, e2) = e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6624])).
% 1.44/1.55 tff(6626,plain,
% 1.44/1.55 (~(op(e3, e2) = e3)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[181, 6625])).
% 1.44/1.55 tff(6627,assumption,(op(e2, e2) = e3), introduced(assumption)).
% 1.44/1.55 tff(6628,plain,
% 1.44/1.55 (e3 = op(e2, e2)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[6627, 1796])).
% 1.44/1.55 tff(6629,plain,
% 1.44/1.55 (op(e2, op(e2, e2)) = op(e2, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6627])).
% 1.44/1.55 tff(6630,plain,
% 1.44/1.55 (op(e2, e3) = op(e2, op(e2, e2))),
% 1.44/1.55 inference(symmetry,[status(thm)],[6629])).
% 1.44/1.55 tff(6631,plain,
% 1.44/1.55 (e1 = op(e2, op(e2, e2))),
% 1.44/1.55 inference(transitivity,[status(thm)],[2685, 6630])).
% 1.44/1.55 tff(6632,plain,
% 1.44/1.55 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6629])).
% 1.44/1.55 tff(6633,plain,
% 1.44/1.55 (op(e2, op(e2, e3)) = op(e2, op(e2, op(e2, e2)))),
% 1.44/1.55 inference(symmetry,[status(thm)],[6632])).
% 1.44/1.55 tff(6634,plain,
% 1.44/1.55 (op(e2, op(e2, e3)) = op(e2, e1)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[2684])).
% 1.44/1.55 tff(6635,plain,
% 1.44/1.55 (op(e2, e1) = op(e2, op(e2, e3))),
% 1.44/1.55 inference(symmetry,[status(thm)],[6634])).
% 1.44/1.55 tff(6636,plain,
% 1.44/1.55 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.44/1.55 inference(transitivity,[status(thm)],[5560, 6635, 6633])).
% 1.44/1.55 tff(6637,plain,
% 1.44/1.55 ($false),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[2952, 6636, 6631, 6628])).
% 1.44/1.55 tff(6638,plain,((~(op(e2, e2) = e3)) | (~(op(e2, e1) = e0)) | (~(op(e2, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.55 tff(6639,plain,
% 1.44/1.55 (~(op(e2, e2) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[6638, 6599, 3508])).
% 1.44/1.55 tff(6640,plain,
% 1.44/1.55 ((op(e3, e2) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5819])).
% 1.44/1.55 tff(6641,plain,
% 1.44/1.55 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6640, 86])).
% 1.44/1.55 tff(6642,plain,
% 1.44/1.55 ((op(e2, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.44/1.55 inference(symmetry,[status(thm)],[6641])).
% 1.44/1.55 tff(6643,plain,
% 1.44/1.55 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.44/1.55 inference(transitivity,[status(thm)],[6642, 395])).
% 1.44/1.55 tff(6644,plain,
% 1.44/1.55 ((~(op(e2, e3) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6643])).
% 1.44/1.55 tff(6645,plain,
% 1.44/1.55 (~(op(e2, e3) = op(e3, e2))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[5446, 6644])).
% 1.44/1.55 tff(6646,plain,
% 1.44/1.55 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[430, 6645])).
% 1.44/1.55 tff(6647,plain,
% 1.44/1.55 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[264])).
% 1.44/1.55 tff(6648,plain,
% 1.44/1.55 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6647, 69])).
% 1.44/1.55 tff(6649,plain,
% 1.44/1.55 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6648])).
% 1.44/1.55 tff(6650,plain,
% 1.44/1.55 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6649])).
% 1.44/1.55 tff(6651,plain,
% 1.44/1.55 (~(op(e1, e3) = e1)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[708, 6650])).
% 1.44/1.55 tff(6652,plain,
% 1.44/1.55 (e1 = op(e2, e3)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6599])).
% 1.44/1.55 tff(6653,plain,
% 1.44/1.55 ((op(e1, e1) = e1) <=> (e3 = op(e2, e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6618, 6652])).
% 1.44/1.55 tff(6654,plain,
% 1.44/1.55 ((op(e1, e1) = e1) <=> (op(e2, e3) = e3)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6653, 112])).
% 1.44/1.55 tff(6655,plain,
% 1.44/1.55 ((op(e2, e3) = e3) <=> (op(e1, e1) = e1)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6654])).
% 1.44/1.55 tff(6656,plain,
% 1.44/1.55 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e1) = e1))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6655])).
% 1.44/1.55 tff(6657,plain,
% 1.44/1.55 (~(op(e1, e1) = e1)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[124, 6656])).
% 1.44/1.55 tff(6658,plain,
% 1.44/1.55 (op(e1, e2) = e1),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[954, 6657, 6651, 929])).
% 1.44/1.55 tff(6659,plain,
% 1.44/1.55 ((~(op(e2, e3) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6642])).
% 1.44/1.55 tff(6660,plain,
% 1.44/1.55 (~(op(e3, e2) = op(e2, e3))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[5446, 6659])).
% 1.44/1.55 tff(6661,plain,
% 1.44/1.55 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[500, 6660])).
% 1.44/1.55 tff(6662,plain,
% 1.44/1.55 (op(e0, op(e3, e3)) = op(e0, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6614])).
% 1.44/1.55 tff(6663,plain,
% 1.44/1.55 (op(e0, op(e3, e3)) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6662, 771])).
% 1.44/1.55 tff(6664,plain,
% 1.44/1.55 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[392, 6663])).
% 1.44/1.55 tff(6665,plain,
% 1.44/1.55 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5819])).
% 1.44/1.55 tff(6666,plain,
% 1.44/1.55 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 1.44/1.55 inference(transitivity,[status(thm)],[6665, 5623, 531])).
% 1.44/1.55 tff(6667,plain,
% 1.44/1.55 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6666])).
% 1.44/1.55 tff(6668,plain,
% 1.44/1.55 (~(op(e1, e2) = op(e2, e1))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[2292, 6667])).
% 1.44/1.55 tff(6669,plain,
% 1.44/1.55 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[539, 6668])).
% 1.44/1.55 tff(6670,plain,
% 1.44/1.55 (op(e1, op(e1, e3)) = op(e1, e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[264])).
% 1.44/1.55 tff(6671,plain,
% 1.44/1.55 ((op(e1, op(e1, e3)) = e1) <=> (op(e1, e2) = e1)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6670])).
% 1.44/1.55 tff(6672,plain,
% 1.44/1.55 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6671])).
% 1.44/1.55 tff(6673,plain,
% 1.44/1.55 (op(e1, op(e1, e3)) = e1),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[6658, 6672])).
% 1.44/1.55 tff(6674,plain,
% 1.44/1.55 (((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)) | (~(op(e1, op(e1, e3)) = e1))),
% 1.44/1.55 inference(tautology,[status(thm)],[])).
% 1.44/1.55 tff(6675,plain,
% 1.44/1.55 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[6674, 6673])).
% 1.44/1.55 tff(6676,plain,
% 1.44/1.55 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e1) = op(e1, e2))),
% 1.44/1.55 inference(transitivity,[status(thm)],[6665, 5623])).
% 1.44/1.55 tff(6677,plain,
% 1.44/1.55 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6676])).
% 1.44/1.55 tff(6678,plain,
% 1.44/1.55 (~(op(e2, e1) = op(e1, e2))),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[2292, 6677])).
% 1.44/1.55 tff(6679,plain,
% 1.44/1.55 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[557, 6678])).
% 1.44/1.55 tff(6680,plain,
% 1.44/1.55 (op(e0, op(e1, e1)) = op(e0, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6618])).
% 1.44/1.55 tff(6681,plain,
% 1.44/1.55 (op(e0, op(e1, e1)) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6680, 771])).
% 1.44/1.55 tff(6682,plain,
% 1.44/1.55 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[635, 6681])).
% 1.44/1.55 tff(6683,assumption,(op(e1, e2) = e1), introduced(assumption)).
% 1.44/1.55 tff(6684,assumption,(op(e3, e1) = e2), introduced(assumption)).
% 1.44/1.55 tff(6685,plain,
% 1.44/1.55 (op(e1, op(e3, e1)) = op(op(e2, e3), e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[2685, 6684])).
% 1.44/1.55 tff(6686,plain,
% 1.44/1.55 (op(e1, op(e3, e1)) = e1),
% 1.44/1.55 inference(transitivity,[status(thm)],[6685, 2897, 6683])).
% 1.44/1.55 tff(6687,assumption,(~(op(e1, e0) = e2)), introduced(assumption)).
% 1.44/1.55 tff(6688,assumption,((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)), introduced(assumption)).
% 1.44/1.55 tff(6689,assumption,((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)), introduced(assumption)).
% 1.44/1.55 tff(6690,plain,
% 1.44/1.55 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6684])).
% 1.44/1.55 tff(6691,plain,
% 1.44/1.55 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6690])).
% 1.44/1.55 tff(6692,plain,
% 1.44/1.55 (~(op(e3, e0) = e2)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[580, 6691])).
% 1.44/1.55 tff(6693,plain,
% 1.44/1.55 ((op(e2, e0) = e2) <=> (e3 = e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5979])).
% 1.44/1.55 tff(6694,plain,
% 1.44/1.55 ((op(e2, e0) = e2) <=> (e2 = e3)),
% 1.44/1.55 inference(transitivity,[status(thm)],[6693, 1314])).
% 1.44/1.55 tff(6695,plain,
% 1.44/1.55 ((e2 = e3) <=> (op(e2, e0) = e2)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6694])).
% 1.44/1.55 tff(6696,plain,
% 1.44/1.55 ((~(e2 = e3)) <=> (~(op(e2, e0) = e2))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6695])).
% 1.44/1.55 tff(6697,plain,
% 1.44/1.55 (~(op(e2, e0) = e2)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[1321, 6696])).
% 1.44/1.55 tff(6698,plain,
% 1.44/1.55 (op(e0, e0) = e2),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[589, 6697, 6687, 3786])).
% 1.44/1.55 tff(6699,plain,
% 1.44/1.55 (op(e1, op(e0, e0)) = op(op(e2, e3), e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[2685, 6698])).
% 1.44/1.55 tff(6700,plain,
% 1.44/1.55 (op(e1, op(e0, e0)) = e1),
% 1.44/1.55 inference(transitivity,[status(thm)],[6699, 2897, 6683])).
% 1.44/1.55 tff(6701,plain,
% 1.44/1.55 (op(e0, op(e2, e0)) = op(e0, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5979])).
% 1.44/1.55 tff(6702,plain,
% 1.44/1.55 (op(e0, op(e2, e0)) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6701, 771])).
% 1.44/1.55 tff(6703,plain,
% 1.44/1.55 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[547, 6702])).
% 1.44/1.55 tff(6704,plain,
% 1.44/1.55 (op(e0, op(e0, e2)) = op(e0, e3)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[5990])).
% 1.44/1.55 tff(6705,plain,
% 1.44/1.55 (op(e0, op(e0, e2)) = e0),
% 1.44/1.55 inference(transitivity,[status(thm)],[6704, 771])).
% 1.44/1.55 tff(6706,plain,
% 1.44/1.55 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[5369, 6705])).
% 1.44/1.55 tff(6707,plain,
% 1.44/1.55 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e2, e3))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[2685])).
% 1.44/1.55 tff(6708,plain,
% 1.44/1.55 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 1.44/1.55 inference(symmetry,[status(thm)],[6707])).
% 1.44/1.55 tff(6709,plain,
% 1.44/1.55 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 1.44/1.55 inference(monotonicity,[status(thm)],[6708])).
% 1.44/1.55 tff(6710,plain,
% 1.44/1.55 (~(op(e2, e2) = e1)),
% 1.44/1.55 inference(modus_ponens,[status(thm)],[515, 6709])).
% 1.44/1.55 tff(6711,plain,
% 1.44/1.55 (op(e2, e2) = e2),
% 1.44/1.55 inference(unit_resolution,[status(thm)],[524, 2431, 17, 6710])).
% 1.44/1.55 tff(6712,plain,
% 1.44/1.55 (op(e1, op(e2, e2)) = op(op(e2, e3), e2)),
% 1.44/1.55 inference(monotonicity,[status(thm)],[2685, 6711])).
% 1.44/1.55 tff(6713,plain,
% 1.44/1.55 (op(e1, op(e2, e2)) = e1),
% 1.44/1.55 inference(transitivity,[status(thm)],[6712, 2897, 6683])).
% 1.44/1.55 tff(6714,plain,
% 1.44/1.56 (((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)) | (~(op(e1, op(e2, e2)) = e1))),
% 1.44/1.56 inference(tautology,[status(thm)],[])).
% 1.44/1.56 tff(6715,plain,
% 1.44/1.56 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[6714, 6713])).
% 1.44/1.56 tff(6716,plain,
% 1.44/1.56 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[5367, 6715, 6689, 5681, 5680, 5511, 5675, 6706, 5673, 6688, 5671, 5670, 5669, 5668, 6703])).
% 1.44/1.56 tff(6717,plain,
% 1.44/1.56 (((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)) | (~(op(e1, op(e0, e0)) = e1))),
% 1.44/1.56 inference(tautology,[status(thm)],[])).
% 1.44/1.56 tff(6718,plain,
% 1.44/1.56 (~(op(e1, op(e0, e0)) = e1)),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[6717, 6716])).
% 1.44/1.56 tff(6719,plain,
% 1.44/1.56 ($false),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[6718, 6700])).
% 1.44/1.56 tff(6720,plain,((op(e2, e2) = e3) | (~(op(e1, e2) = e1)) | (~(op(e2, e3) = e1)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (op(e1, e0) = e2) | (op(e3, e0) = e2) | (~(op(e0, e3) = e0)) | (op(e2, e2) = e0) | (op(e3, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.56 tff(6721,plain,
% 1.44/1.56 (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[6720, 6692, 2684, 6689, 5681, 5680, 5511, 5675, 5673, 6688, 5671, 5670, 6683, 5668, 6687, 2431, 771, 17, 1890, 75, 3271, 124])).
% 1.44/1.56 tff(6722,plain,
% 1.44/1.56 (((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)) | (~(op(e1, op(e3, e1)) = e1))),
% 1.44/1.56 inference(tautology,[status(thm)],[])).
% 1.44/1.56 tff(6723,plain,
% 1.44/1.56 ($false),
% 1.44/1.56 inference(unit_resolution,[status(thm)],[6722, 6721, 6686])).
% 1.44/1.56 tff(6724,plain,((~(op(e3, e1) = e2)) | (~(op(e2, e3) = e1)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~(op(e1, e2) = e1)) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (op(e1, e0) = e2) | (op(e2, e2) = e3) | (~(op(e0, e3) = e0)) | (op(e2, e2) = e0) | (op(e3, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.56 tff(6725,plain,
% 1.46/1.56 (~(op(e3, e1) = e2)),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[6724, 6599, 6682, 5681, 6679, 6675, 5675, 6669, 6664, 6661, 5670, 6658, 6646, 675, 6639, 771, 5552, 6626, 6622, 5487, 124])).
% 1.46/1.56 tff(6726,plain,
% 1.46/1.56 (op(e3, e1) = e1),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[446, 6725, 5474, 6617])).
% 1.46/1.56 tff(6727,plain,
% 1.46/1.56 (op(e3, op(e2, e3)) = op(e3, e1)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6599])).
% 1.46/1.56 tff(6728,plain,
% 1.46/1.56 (op(e3, e1) = op(e2, e3)),
% 1.46/1.56 inference(transitivity,[status(thm)],[6726, 6652])).
% 1.46/1.56 tff(6729,plain,
% 1.46/1.56 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6728])).
% 1.46/1.56 tff(6730,plain,
% 1.46/1.56 (op(e3, op(e3, e1)) = e1),
% 1.46/1.56 inference(transitivity,[status(thm)],[6729, 6727, 6726])).
% 1.46/1.56 tff(6731,plain,
% 1.46/1.56 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2594, 6730])).
% 1.46/1.56 tff(6732,plain,
% 1.46/1.56 (op(op(e2, e3), e2) = op(e1, e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6599])).
% 1.46/1.56 tff(6733,plain,
% 1.46/1.56 (op(e1, e2) = op(e2, e3)),
% 1.46/1.56 inference(transitivity,[status(thm)],[6658, 6652])).
% 1.46/1.56 tff(6734,plain,
% 1.46/1.56 (op(op(e1, e2), e2) = op(op(e2, e3), e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6733])).
% 1.46/1.56 tff(6735,plain,
% 1.46/1.56 (op(op(e1, e2), e2) = e1),
% 1.46/1.56 inference(transitivity,[status(thm)],[6734, 6732, 6658])).
% 1.46/1.56 tff(6736,plain,
% 1.46/1.56 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1335, 6735])).
% 1.46/1.56 tff(6737,plain,
% 1.46/1.56 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6658])).
% 1.46/1.56 tff(6738,plain,
% 1.46/1.56 ((op(e0, e2) = op(e1, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 1.46/1.56 inference(transitivity,[status(thm)],[6737, 5799])).
% 1.46/1.56 tff(6739,plain,
% 1.46/1.56 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6738])).
% 1.46/1.56 tff(6740,plain,
% 1.46/1.56 (~(op(op(e2, e1), e2) = e1)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[6205, 6739])).
% 1.46/1.56 tff(6741,plain,
% 1.46/1.56 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[5808, 6740])).
% 1.46/1.56 tff(6742,plain,
% 1.46/1.56 (op(e3, e0) = e2),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2015, 6725, 4442, 5823])).
% 1.46/1.56 tff(6743,plain,
% 1.46/1.56 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6742])).
% 1.46/1.56 tff(6744,plain,
% 1.46/1.56 (op(e3, op(e3, e0)) = e0),
% 1.46/1.56 inference(transitivity,[status(thm)],[6743, 5819])).
% 1.46/1.56 tff(6745,plain,
% 1.46/1.56 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1345, 6744])).
% 1.46/1.56 tff(6746,plain,
% 1.46/1.56 (op(e0, e2) = e3),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2111, 6639, 6626, 6622])).
% 1.46/1.56 tff(6747,plain,
% 1.46/1.56 (op(op(e0, e2), e2) = op(e3, e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6746])).
% 1.46/1.56 tff(6748,plain,
% 1.46/1.56 (op(op(e0, e2), e2) = e0),
% 1.46/1.56 inference(transitivity,[status(thm)],[6747, 5819])).
% 1.46/1.56 tff(6749,plain,
% 1.46/1.56 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1956, 6748])).
% 1.46/1.56 tff(6750,plain,
% 1.46/1.56 (op(e2, e0) = e3),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1559, 6639, 5487, 124])).
% 1.46/1.56 tff(6751,plain,
% 1.46/1.56 (op(op(e2, e0), e0) = op(e3, e0)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6750])).
% 1.46/1.56 tff(6752,plain,
% 1.46/1.56 ((op(op(e2, e0), e0) = e2) <=> (op(e3, e0) = e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6751])).
% 1.46/1.56 tff(6753,plain,
% 1.46/1.56 ((op(e3, e0) = e2) <=> (op(op(e2, e0), e0) = e2)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6752])).
% 1.46/1.56 tff(6754,plain,
% 1.46/1.56 (op(op(e2, e0), e0) = e2),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[6742, 6753])).
% 1.46/1.56 tff(6755,plain,
% 1.46/1.56 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1945, 6754])).
% 1.46/1.56 tff(6756,plain,
% 1.46/1.56 (op(e2, op(e2, e3)) = op(e2, e1)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6599])).
% 1.46/1.56 tff(6757,plain,
% 1.46/1.56 (op(e0, e1) = e2),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1993, 6725, 741, 5515])).
% 1.46/1.56 tff(6758,plain,
% 1.46/1.56 (op(op(e0, e1), e1) = op(e2, op(e2, e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6757, 6652])).
% 1.46/1.56 tff(6759,plain,
% 1.46/1.56 (op(op(e0, e1), e1) = e0),
% 1.46/1.56 inference(transitivity,[status(thm)],[6758, 6756, 3508])).
% 1.46/1.56 tff(6760,plain,
% 1.46/1.56 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2650, 6759])).
% 1.46/1.56 tff(6761,plain,
% 1.46/1.56 ($false),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1459, 6760, 6755, 6749, 6745, 3342, 1304, 1357, 6741, 6736, 6731, 6609, 6602])).
% 1.46/1.56 tff(6762,plain,((op(e2, e3) = e3) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~(op(e2, e1) = e0)) | (~(op(e3, e2) = e0)) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~(op(e0, e3) = e0)) | (~(op(e1, e3) = e2)) | (op(e1, e0) = e1) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.56 tff(6763,plain,
% 1.46/1.56 (op(e2, e3) = e3),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[6762, 6594, 1304, 3342, 3508, 5539, 6591, 6587, 5613, 771, 264, 6581, 2527])).
% 1.46/1.56 tff(6764,plain,
% 1.46/1.56 (e3 = op(e2, e3)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6763])).
% 1.46/1.56 tff(6765,plain,
% 1.46/1.56 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e2, e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6764])).
% 1.46/1.56 tff(6766,plain,
% 1.46/1.56 ((op(e3, e3) = e3) <=> (op(e2, e3) = op(e3, e3))),
% 1.46/1.56 inference(transitivity,[status(thm)],[6765, 2820])).
% 1.46/1.56 tff(6767,plain,
% 1.46/1.56 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6766])).
% 1.46/1.56 tff(6768,plain,
% 1.46/1.56 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6767])).
% 1.46/1.56 tff(6769,plain,
% 1.46/1.56 (~(op(e3, e3) = e3)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[368, 6768])).
% 1.46/1.56 tff(6770,plain,
% 1.46/1.56 (op(e3, e3) = e1),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1071, 6769, 656, 4442])).
% 1.46/1.56 tff(6771,plain,
% 1.46/1.56 (e1 = op(e3, e3)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[305, 658])).
% 1.46/1.56 tff(6772,plain,
% 1.46/1.56 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[305])).
% 1.46/1.56 tff(6773,plain,
% 1.46/1.56 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e1))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6772])).
% 1.46/1.56 tff(6774,plain,
% 1.46/1.56 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e2)),
% 1.46/1.56 inference(transitivity,[status(thm)],[6773, 637])).
% 1.46/1.56 tff(6775,plain,
% 1.46/1.56 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.46/1.56 inference(symmetry,[status(thm)],[6774])).
% 1.46/1.56 tff(6776,plain,
% 1.46/1.56 (e2 = op(e3, op(e3, e3))),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[6684, 6775])).
% 1.46/1.56 tff(6777,plain,
% 1.46/1.56 (op(e3, op(e3, e3)) = e2),
% 1.46/1.56 inference(transitivity,[status(thm)],[6772, 6684])).
% 1.46/1.56 tff(6778,assumption,(op(e2, e3) = e3), introduced(assumption)).
% 1.46/1.56 tff(6779,plain,
% 1.46/1.56 (e3 = op(e2, e3)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6778])).
% 1.46/1.56 tff(6780,plain,
% 1.46/1.56 (op(e3, op(e3, op(e3, e3))) = op(op(e2, e3), e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6779, 6777])).
% 1.46/1.56 tff(6781,plain,
% 1.46/1.56 (op(op(e2, e3), e2) = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.56 inference(symmetry,[status(thm)],[6780])).
% 1.46/1.56 tff(6782,plain,
% 1.46/1.56 (op(op(e2, e3), e2) = op(e3, e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6778])).
% 1.46/1.56 tff(6783,plain,
% 1.46/1.56 (op(e3, e2) = op(op(e2, e3), e2)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6782])).
% 1.46/1.56 tff(6784,plain,
% 1.46/1.56 (e0 = op(e3, e2)),
% 1.46/1.56 inference(symmetry,[status(thm)],[5819])).
% 1.46/1.56 tff(6785,plain,
% 1.46/1.56 (e0 = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.56 inference(transitivity,[status(thm)],[6784, 6783, 6781])).
% 1.46/1.56 tff(6786,plain,
% 1.46/1.56 ($false),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2034, 6785, 6776, 6771])).
% 1.46/1.56 tff(6787,plain,((~(op(e3, e1) = e2)) | (~(op(e3, e2) = e0)) | (~(op(e3, e3) = e1)) | (~(op(e2, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.56 tff(6788,plain,
% 1.46/1.56 (~(op(e3, e1) = e2)),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[6787, 5539, 6770, 6763])).
% 1.46/1.56 tff(6789,plain,
% 1.46/1.56 (op(e0, e1) = e2),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[1993, 6788, 741, 5515])).
% 1.46/1.56 tff(6790,plain,
% 1.46/1.56 (op(e0, op(e3, e3)) = op(e0, e1)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6770])).
% 1.46/1.56 tff(6791,plain,
% 1.46/1.56 (e1 = op(e3, e3)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6770])).
% 1.46/1.56 tff(6792,plain,
% 1.46/1.56 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 1.46/1.56 inference(monotonicity,[status(thm)],[5539])).
% 1.46/1.56 tff(6793,plain,
% 1.46/1.56 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6792])).
% 1.46/1.56 tff(6794,plain,
% 1.46/1.56 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6793])).
% 1.46/1.56 tff(6795,plain,
% 1.46/1.56 (~(op(e3, e2) = e2)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[14, 6794])).
% 1.46/1.56 tff(6796,plain,
% 1.46/1.56 (op(e3, e0) = e2),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[2015, 6788, 4442, 6795])).
% 1.46/1.56 tff(6797,plain,
% 1.46/1.56 (e2 = op(e3, e0)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6796])).
% 1.46/1.56 tff(6798,plain,
% 1.46/1.56 (op(e0, e1) = op(e3, e0)),
% 1.46/1.56 inference(transitivity,[status(thm)],[6789, 6797])).
% 1.46/1.56 tff(6799,plain,
% 1.46/1.56 ((op(e0, e1) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6798, 6791])).
% 1.46/1.56 tff(6800,plain,
% 1.46/1.56 ((op(e3, e0) = op(e3, e3)) <=> (op(e0, e1) = e1)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6799])).
% 1.46/1.56 tff(6801,plain,
% 1.46/1.56 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e0, e1) = e1))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6800])).
% 1.46/1.56 tff(6802,plain,
% 1.46/1.56 (~(op(e0, e1) = e1)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[157, 6801])).
% 1.46/1.56 tff(6803,plain,
% 1.46/1.56 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e2, e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6764])).
% 1.46/1.56 tff(6804,plain,
% 1.46/1.56 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6803])).
% 1.46/1.56 tff(6805,plain,
% 1.46/1.56 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6804])).
% 1.46/1.56 tff(6806,plain,
% 1.46/1.56 (~(op(e2, e0) = e3)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[989, 6805])).
% 1.46/1.56 tff(6807,plain,
% 1.46/1.56 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6797])).
% 1.46/1.56 tff(6808,plain,
% 1.46/1.56 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e2)),
% 1.46/1.56 inference(symmetry,[status(thm)],[6807])).
% 1.46/1.56 tff(6809,plain,
% 1.46/1.56 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e2))),
% 1.46/1.56 inference(monotonicity,[status(thm)],[6808])).
% 1.46/1.56 tff(6810,plain,
% 1.46/1.56 (~(op(e2, e0) = e2)),
% 1.46/1.56 inference(modus_ponens,[status(thm)],[747, 6809])).
% 1.46/1.56 tff(6811,plain,
% 1.46/1.56 (op(e2, e0) = e1),
% 1.46/1.56 inference(unit_resolution,[status(thm)],[765, 6810, 6806, 5643])).
% 1.46/1.56 tff(6812,plain,
% 1.46/1.56 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e1)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6811])).
% 1.46/1.57 tff(6813,plain,
% 1.46/1.57 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e1))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6812])).
% 1.46/1.57 tff(6814,plain,
% 1.46/1.57 (~(op(e0, e0) = e1)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[359, 6813])).
% 1.46/1.57 tff(6815,plain,
% 1.46/1.57 (op(e0, e2) = e1),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[384, 6814, 121, 6802])).
% 1.46/1.57 tff(6816,plain,
% 1.46/1.57 (op(e0, e2) = op(e3, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6815, 6791])).
% 1.46/1.57 tff(6817,plain,
% 1.46/1.57 (op(e0, op(e0, e2)) = op(e0, op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6816])).
% 1.46/1.57 tff(6818,plain,
% 1.46/1.57 (op(e0, op(e0, e2)) = e2),
% 1.46/1.57 inference(transitivity,[status(thm)],[6817, 6790, 6789])).
% 1.46/1.57 tff(6819,plain,
% 1.46/1.57 (op(e2, op(e2, e3)) = op(e2, e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6763])).
% 1.46/1.57 tff(6820,plain,
% 1.46/1.57 (op(e2, op(e2, e3)) = e3),
% 1.46/1.57 inference(transitivity,[status(thm)],[6819, 6763])).
% 1.46/1.57 tff(6821,plain,
% 1.46/1.57 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2344, 6820])).
% 1.46/1.57 tff(6822,plain,
% 1.46/1.57 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6791])).
% 1.46/1.57 tff(6823,plain,
% 1.46/1.57 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6822])).
% 1.46/1.57 tff(6824,plain,
% 1.46/1.57 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6823])).
% 1.46/1.57 tff(6825,plain,
% 1.46/1.57 (~(op(e3, e1) = e1)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[437, 6824])).
% 1.46/1.57 tff(6826,plain,
% 1.46/1.57 (op(e3, e1) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[446, 6788, 5474, 6825])).
% 1.46/1.57 tff(6827,plain,
% 1.46/1.57 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6770])).
% 1.46/1.57 tff(6828,plain,
% 1.46/1.57 (op(op(e3, e1), e1) = op(e3, op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6826, 6791])).
% 1.46/1.57 tff(6829,plain,
% 1.46/1.57 (op(op(e3, e1), e1) = e3),
% 1.46/1.57 inference(transitivity,[status(thm)],[6828, 6827, 6826])).
% 1.46/1.57 tff(6830,plain,
% 1.46/1.57 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2416, 6829])).
% 1.46/1.57 tff(6831,plain,
% 1.46/1.57 (op(e1, op(e2, e3)) = op(e1, e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6763])).
% 1.46/1.57 tff(6832,plain,
% 1.46/1.57 ((op(e1, e0) = e3) <=> (e0 = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[5788])).
% 1.46/1.57 tff(6833,plain,
% 1.46/1.57 ((e0 = e3) <=> (op(e1, e0) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6832])).
% 1.46/1.57 tff(6834,plain,
% 1.46/1.57 ((~(e0 = e3)) <=> (~(op(e1, e0) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6833])).
% 1.46/1.57 tff(6835,plain,
% 1.46/1.57 (~(op(e1, e0) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[181, 6834])).
% 1.46/1.57 tff(6836,plain,
% 1.46/1.57 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6826])).
% 1.46/1.57 tff(6837,plain,
% 1.46/1.57 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6836])).
% 1.46/1.57 tff(6838,plain,
% 1.46/1.57 (~(op(e1, e1) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[945, 6837])).
% 1.46/1.57 tff(6839,plain,
% 1.46/1.57 (op(e1, e2) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[247, 6838, 6613, 6835])).
% 1.46/1.57 tff(6840,plain,
% 1.46/1.57 (op(e1, e2) = op(e2, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6839, 6764])).
% 1.46/1.57 tff(6841,plain,
% 1.46/1.57 (op(e1, op(e1, e2)) = op(e1, op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6840])).
% 1.46/1.57 tff(6842,plain,
% 1.46/1.57 (op(e1, op(e1, e2)) = e2),
% 1.46/1.57 inference(transitivity,[status(thm)],[6841, 6831, 264])).
% 1.46/1.57 tff(6843,plain,
% 1.46/1.57 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2377, 6842])).
% 1.46/1.57 tff(6844,plain,
% 1.46/1.57 ((op(op(e2, e1), e1) = e2) <=> (op(e0, e1) = e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[3517])).
% 1.46/1.57 tff(6845,plain,
% 1.46/1.57 ((op(e0, e1) = e2) <=> (op(op(e2, e1), e1) = e2)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6844])).
% 1.46/1.57 tff(6846,plain,
% 1.46/1.57 (op(op(e2, e1), e1) = e2),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[6789, 6845])).
% 1.46/1.57 tff(6847,plain,
% 1.46/1.57 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2371, 6846])).
% 1.46/1.57 tff(6848,plain,
% 1.46/1.57 (op(op(e2, e3), e2) = op(e3, e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6763])).
% 1.46/1.57 tff(6849,plain,
% 1.46/1.57 (op(e3, op(e3, e0)) = op(op(e2, e3), e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6764, 6796])).
% 1.46/1.57 tff(6850,plain,
% 1.46/1.57 (op(e3, op(e3, e0)) = e0),
% 1.46/1.57 inference(transitivity,[status(thm)],[6849, 6848, 5539])).
% 1.46/1.57 tff(6851,plain,
% 1.46/1.57 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1345, 6850])).
% 1.46/1.57 tff(6852,plain,
% 1.46/1.57 (op(e2, op(e3, e3)) = op(e2, e1)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6770])).
% 1.46/1.57 tff(6853,plain,
% 1.46/1.57 (op(op(e0, e1), e1) = op(e2, op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6789, 6791])).
% 1.46/1.57 tff(6854,plain,
% 1.46/1.57 (op(op(e0, e1), e1) = e0),
% 1.46/1.57 inference(transitivity,[status(thm)],[6853, 6852, 3508])).
% 1.46/1.57 tff(6855,plain,
% 1.46/1.57 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2650, 6854])).
% 1.46/1.57 tff(6856,plain,
% 1.46/1.57 (op(e2, e0) = op(e3, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6811, 6791])).
% 1.46/1.57 tff(6857,plain,
% 1.46/1.57 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6856])).
% 1.46/1.57 tff(6858,plain,
% 1.46/1.57 (op(e2, op(e2, e0)) = e0),
% 1.46/1.57 inference(transitivity,[status(thm)],[6857, 6852, 3508])).
% 1.46/1.57 tff(6859,plain,
% 1.46/1.57 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2653, 6858])).
% 1.46/1.57 tff(6860,plain,
% 1.46/1.57 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1459, 6859, 6855, 6851, 3342, 1304, 6594, 6847, 6843, 6830, 5781, 6821])).
% 1.46/1.57 tff(6861,plain,
% 1.46/1.57 (~(op(e0, op(e0, e2)) = e2)),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1331, 6860])).
% 1.46/1.57 tff(6862,plain,
% 1.46/1.57 ($false),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[6861, 6818])).
% 1.46/1.57 tff(6863,plain,((op(e3, e0) = op(e0, e3)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1) | (~(op(e1, e3) = e2)) | (~(op(e2, e1) = e0)) | (op(e3, e3) = e0) | (~(op(e0, e3) = e0)) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.57 tff(6864,plain,
% 1.46/1.57 (op(e3, e0) = op(e0, e3)),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[6863, 6577, 5475, 121, 5469, 3508, 656, 5447, 2527])).
% 1.46/1.57 tff(6865,plain,
% 1.46/1.57 (op(e3, e0) = e0),
% 1.46/1.57 inference(transitivity,[status(thm)],[6864, 5447])).
% 1.46/1.57 tff(6866,plain,
% 1.46/1.57 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6865])).
% 1.46/1.57 tff(6867,plain,
% 1.46/1.57 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6866])).
% 1.46/1.57 tff(6868,plain,
% 1.46/1.57 (~(op(e1, e0) = e0)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[410, 6867])).
% 1.46/1.57 tff(6869,plain,
% 1.46/1.57 (op(e1, e2) = e0),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1830, 6868, 80, 5456])).
% 1.46/1.57 tff(6870,plain,
% 1.46/1.57 ((op(e1, e2) = e3) <=> (e0 = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6869])).
% 1.46/1.57 tff(6871,plain,
% 1.46/1.57 ((e0 = e3) <=> (op(e1, e2) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6870])).
% 1.46/1.57 tff(6872,plain,
% 1.46/1.57 ((~(e0 = e3)) <=> (~(op(e1, e2) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6871])).
% 1.46/1.57 tff(6873,plain,
% 1.46/1.57 (~(op(e1, e2) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[181, 6872])).
% 1.46/1.57 tff(6874,plain,
% 1.46/1.57 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6577])).
% 1.46/1.57 tff(6875,plain,
% 1.46/1.57 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6874])).
% 1.46/1.57 tff(6876,plain,
% 1.46/1.57 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6875])).
% 1.46/1.57 tff(6877,plain,
% 1.46/1.57 (~(op(e1, e3) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[1321, 6876])).
% 1.46/1.57 tff(6878,plain,
% 1.46/1.57 ((op(e0, e3) = e3) <=> (e0 = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[5447])).
% 1.46/1.57 tff(6879,plain,
% 1.46/1.57 ((e0 = e3) <=> (op(e0, e3) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6878])).
% 1.46/1.57 tff(6880,plain,
% 1.46/1.57 ((~(e0 = e3)) <=> (~(op(e0, e3) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6879])).
% 1.46/1.57 tff(6881,plain,
% 1.46/1.57 (~(op(e0, e3) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[181, 6880])).
% 1.46/1.57 tff(6882,plain,
% 1.46/1.57 (op(e3, e3) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[480, 124, 661, 6613])).
% 1.46/1.57 tff(6883,plain,
% 1.46/1.57 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6882])).
% 1.46/1.57 tff(6884,plain,
% 1.46/1.57 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6883])).
% 1.46/1.57 tff(6885,plain,
% 1.46/1.57 (~(op(e3, e1) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[437, 6884])).
% 1.46/1.57 tff(6886,plain,
% 1.46/1.57 (op(e1, e1) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1730, 6885, 5487, 2527])).
% 1.46/1.57 tff(6887,plain,
% 1.46/1.57 (e3 = op(e1, e1)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[6886, 1740])).
% 1.46/1.57 tff(6888,plain,
% 1.46/1.57 (e3 = op(e2, e0)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6750])).
% 1.46/1.57 tff(6889,plain,
% 1.46/1.57 (op(e1, e1) = op(e2, e0)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6886, 6888])).
% 1.46/1.57 tff(6890,plain,
% 1.46/1.57 (op(e1, op(e1, e1)) = op(e1, op(e2, e0))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6889])).
% 1.46/1.57 tff(6891,plain,
% 1.46/1.57 (op(e1, op(e2, e0)) = op(e1, op(e1, e1))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6890])).
% 1.46/1.57 tff(6892,plain,
% 1.46/1.57 (op(e1, op(e2, e0)) = op(op(e2, e3), e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6652, 6750])).
% 1.46/1.57 tff(6893,plain,
% 1.46/1.57 (op(op(e2, e3), e3) = op(e1, op(e2, e0))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6892])).
% 1.46/1.57 tff(6894,plain,
% 1.46/1.57 (op(e1, e3) = op(op(e2, e3), e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6600])).
% 1.46/1.57 tff(6895,plain,
% 1.46/1.57 (e2 = op(e1, op(e1, e1))),
% 1.46/1.57 inference(transitivity,[status(thm)],[265, 6894, 6893, 6891])).
% 1.46/1.57 tff(6896,plain,
% 1.46/1.57 (op(e1, op(e1, e1)) = e2),
% 1.46/1.57 inference(transitivity,[status(thm)],[6890, 6892, 6600, 264])).
% 1.46/1.57 tff(6897,plain,
% 1.46/1.57 (op(e1, op(e1, op(e1, e1))) = op(op(e2, e3), e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6652, 6896])).
% 1.46/1.57 tff(6898,plain,
% 1.46/1.57 (op(op(e2, e3), e2) = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6897])).
% 1.46/1.57 tff(6899,plain,
% 1.46/1.57 (op(e1, e2) = op(op(e2, e3), e2)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6732])).
% 1.46/1.57 tff(6900,assumption,(op(e1, e2) = e0), introduced(assumption)).
% 1.46/1.57 tff(6901,plain,
% 1.46/1.57 (e0 = op(e1, e2)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6900])).
% 1.46/1.57 tff(6902,plain,
% 1.46/1.57 (e0 = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6901, 6899, 6898])).
% 1.46/1.57 tff(6903,plain,
% 1.46/1.57 ($false),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1753, 6902, 6895, 6887])).
% 1.46/1.57 tff(6904,plain,((op(e2, e3) = e3) | (~(op(e1, e2) = e0)) | (~(op(e1, e3) = e2)) | (op(e0, e1) = e3) | (~(op(e2, e1) = e0)) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.57 tff(6905,plain,
% 1.46/1.57 (op(e2, e3) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[6904, 6869, 6577, 2527, 3508, 6881])).
% 1.46/1.57 tff(6906,plain,
% 1.46/1.57 (e3 = op(e1, e1)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[4960, 1740])).
% 1.46/1.57 tff(6907,plain,
% 1.46/1.57 (op(e1, e1) = op(e2, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[4960, 6779])).
% 1.46/1.57 tff(6908,plain,
% 1.46/1.57 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6907])).
% 1.46/1.57 tff(6909,plain,
% 1.46/1.57 (op(e1, op(e2, e3)) = op(e1, op(e1, e1))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6908])).
% 1.46/1.57 tff(6910,plain,
% 1.46/1.57 (op(e1, op(e2, e3)) = op(e1, e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6778])).
% 1.46/1.57 tff(6911,plain,
% 1.46/1.57 (op(e1, e3) = op(e1, op(e2, e3))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6910])).
% 1.46/1.57 tff(6912,plain,
% 1.46/1.57 (e2 = op(e1, op(e1, e1))),
% 1.46/1.57 inference(transitivity,[status(thm)],[265, 6911, 6909])).
% 1.46/1.57 tff(6913,plain,
% 1.46/1.57 (op(e1, op(e1, e1)) = e2),
% 1.46/1.57 inference(transitivity,[status(thm)],[6908, 6910, 264])).
% 1.46/1.57 tff(6914,plain,
% 1.46/1.57 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6913])).
% 1.46/1.57 tff(6915,plain,
% 1.46/1.57 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6914])).
% 1.46/1.57 tff(6916,plain,
% 1.46/1.57 (e0 = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6901, 6915])).
% 1.46/1.57 tff(6917,plain,
% 1.46/1.57 ($false),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1753, 6916, 6912, 6906])).
% 1.46/1.57 tff(6918,plain,((~(op(e1, e1) = e3)) | (~(op(e1, e2) = e0)) | (~(op(e1, e3) = e2)) | (~(op(e2, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.57 tff(6919,plain,
% 1.46/1.57 (~(op(e1, e1) = e3)),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[6918, 6869, 6577, 6905])).
% 1.46/1.57 tff(6920,plain,
% 1.46/1.57 (op(e1, e0) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[247, 6919, 6877, 6873])).
% 1.46/1.57 tff(6921,plain,
% 1.46/1.57 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6920])).
% 1.46/1.57 tff(6922,plain,
% 1.46/1.57 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6921])).
% 1.46/1.57 tff(6923,plain,
% 1.46/1.57 (~(op(e0, e0) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[2471, 6922])).
% 1.46/1.57 tff(6924,plain,
% 1.46/1.57 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6577])).
% 1.46/1.57 tff(6925,plain,
% 1.46/1.57 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6924])).
% 1.46/1.57 tff(6926,plain,
% 1.46/1.57 (~(op(e1, e1) = e2)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[619, 6925])).
% 1.46/1.57 tff(6927,plain,
% 1.46/1.57 ((op(e1, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6577])).
% 1.46/1.57 tff(6928,plain,
% 1.46/1.57 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6927, 565])).
% 1.46/1.57 tff(6929,plain,
% 1.46/1.57 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6928])).
% 1.46/1.57 tff(6930,plain,
% 1.46/1.57 (~(op(e3, e3) = e2)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[571, 6929])).
% 1.46/1.57 tff(6931,plain,
% 1.46/1.57 (e3 = op(e2, e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6905])).
% 1.46/1.57 tff(6932,plain,
% 1.46/1.57 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6931])).
% 1.46/1.57 tff(6933,plain,
% 1.46/1.57 ((op(e3, e3) = e3) <=> (op(e2, e3) = op(e3, e3))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6932, 2820])).
% 1.46/1.57 tff(6934,plain,
% 1.46/1.57 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6933])).
% 1.46/1.57 tff(6935,plain,
% 1.46/1.57 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6934])).
% 1.46/1.57 tff(6936,plain,
% 1.46/1.57 (~(op(e3, e3) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[368, 6935])).
% 1.46/1.57 tff(6937,plain,
% 1.46/1.57 (op(e3, e3) = e1),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1071, 6936, 656, 6930])).
% 1.46/1.57 tff(6938,plain,
% 1.46/1.57 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6937])).
% 1.46/1.57 tff(6939,plain,
% 1.46/1.57 (op(e3, e1) = op(e3, op(e3, e3))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6938])).
% 1.46/1.57 tff(6940,plain,
% 1.46/1.57 ((op(e3, e1) = e2) <=> (op(e3, op(e3, e3)) = e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6939])).
% 1.46/1.57 tff(6941,plain,
% 1.46/1.57 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6940, 1974])).
% 1.46/1.57 tff(6942,plain,
% 1.46/1.57 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e2)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6941])).
% 1.46/1.57 tff(6943,plain,
% 1.46/1.57 (op(e3, e1) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1730, 6919, 5487, 2527])).
% 1.46/1.57 tff(6944,plain,
% 1.46/1.57 (op(e3, op(e3, e3)) = op(e2, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6938, 6943, 6931])).
% 1.46/1.57 tff(6945,plain,
% 1.46/1.57 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6944])).
% 1.46/1.57 tff(6946,plain,
% 1.46/1.57 ((e2 = op(e3, op(e3, e3))) <=> (op(e2, e3) = e2)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6945, 120])).
% 1.46/1.57 tff(6947,plain,
% 1.46/1.57 ((op(e2, e3) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6946])).
% 1.46/1.57 tff(6948,plain,
% 1.46/1.57 ((op(e2, e3) = e2) <=> (op(e3, e1) = e2)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6947, 6942])).
% 1.46/1.57 tff(6949,plain,
% 1.46/1.57 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e1) = e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6948])).
% 1.46/1.57 tff(6950,plain,
% 1.46/1.57 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6577])).
% 1.46/1.57 tff(6951,plain,
% 1.46/1.57 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6950, 120])).
% 1.46/1.57 tff(6952,plain,
% 1.46/1.57 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6951])).
% 1.46/1.57 tff(6953,plain,
% 1.46/1.57 (~(op(e2, e3) = e2)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[118, 6952])).
% 1.46/1.57 tff(6954,plain,
% 1.46/1.57 (~(op(e3, e1) = e2)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[6953, 6949])).
% 1.46/1.57 tff(6955,plain,
% 1.46/1.57 (op(e0, e1) = e2),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[1993, 6954, 6926, 5515])).
% 1.46/1.57 tff(6956,plain,
% 1.46/1.57 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6955])).
% 1.46/1.57 tff(6957,plain,
% 1.46/1.57 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6956])).
% 1.46/1.57 tff(6958,plain,
% 1.46/1.57 (~(op(e0, e0) = e2)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[811, 6957])).
% 1.46/1.57 tff(6959,plain,
% 1.46/1.57 (op(e0, e0) = e1),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[3612, 6958, 5450, 6923])).
% 1.46/1.57 tff(6960,plain,
% 1.46/1.57 (e1 = op(e0, e0)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[6959, 74])).
% 1.46/1.57 tff(6961,plain,
% 1.46/1.57 (e1 = op(e3, e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6937])).
% 1.46/1.57 tff(6962,plain,
% 1.46/1.57 (op(e0, e0) = op(e3, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6959, 6961])).
% 1.46/1.57 tff(6963,plain,
% 1.46/1.57 (op(e0, op(e0, e0)) = op(e0, op(e3, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6962])).
% 1.46/1.57 tff(6964,plain,
% 1.46/1.57 (op(e0, op(e3, e3)) = op(e0, op(e0, e0))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6963])).
% 1.46/1.57 tff(6965,plain,
% 1.46/1.57 (op(e0, op(e3, e3)) = op(e0, e1)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6937])).
% 1.46/1.57 tff(6966,plain,
% 1.46/1.57 (op(e0, e1) = op(e0, op(e3, e3))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6965])).
% 1.46/1.57 tff(6967,plain,
% 1.46/1.57 (e2 = op(e0, e1)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6955])).
% 1.46/1.57 tff(6968,plain,
% 1.46/1.57 (e2 = op(e0, op(e0, e0))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6967, 6966, 6964])).
% 1.46/1.57 tff(6969,plain,
% 1.46/1.57 (op(e0, op(e0, e0)) = e2),
% 1.46/1.57 inference(transitivity,[status(thm)],[6963, 6965, 6955])).
% 1.46/1.57 tff(6970,plain,
% 1.46/1.57 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6969])).
% 1.46/1.57 tff(6971,plain,
% 1.46/1.57 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.57 inference(symmetry,[status(thm)],[6970])).
% 1.46/1.57 tff(6972,plain,
% 1.46/1.57 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6931])).
% 1.46/1.57 tff(6973,plain,
% 1.46/1.57 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6972])).
% 1.46/1.57 tff(6974,plain,
% 1.46/1.57 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6973])).
% 1.46/1.57 tff(6975,plain,
% 1.46/1.57 (~(op(e2, e2) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[515, 6974])).
% 1.46/1.57 tff(6976,plain,
% 1.46/1.57 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6931])).
% 1.46/1.57 tff(6977,plain,
% 1.46/1.57 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6976])).
% 1.46/1.57 tff(6978,plain,
% 1.46/1.57 (op(e3, e1) = op(e2, e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6943, 6931])).
% 1.46/1.57 tff(6979,plain,
% 1.46/1.57 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6978])).
% 1.46/1.57 tff(6980,plain,
% 1.46/1.57 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6979, 394])).
% 1.46/1.57 tff(6981,plain,
% 1.46/1.57 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.46/1.57 inference(transitivity,[status(thm)],[6980, 6977])).
% 1.46/1.57 tff(6982,plain,
% 1.46/1.57 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.46/1.57 inference(monotonicity,[status(thm)],[6981])).
% 1.46/1.57 tff(6983,plain,
% 1.46/1.57 (~(op(e3, e2) = e3)),
% 1.46/1.57 inference(modus_ponens,[status(thm)],[3429, 6982])).
% 1.46/1.57 tff(6984,plain,
% 1.46/1.57 (op(e0, e2) = e3),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[2111, 6983, 6873, 6975])).
% 1.46/1.57 tff(6985,plain,
% 1.46/1.57 (e3 = op(e0, e2)),
% 1.46/1.57 inference(symmetry,[status(thm)],[6984])).
% 1.46/1.57 tff(6986,plain,
% 1.46/1.57 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.57 inference(transitivity,[status(thm)],[6985, 6971])).
% 1.46/1.57 tff(6987,plain,
% 1.46/1.57 ($false),
% 1.46/1.57 inference(unit_resolution,[status(thm)],[3582, 6986, 6968, 6960])).
% 1.46/1.57 tff(6988,plain,((op(e0, e1) = e3) | (op(e3, e3) = e0) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.58 tff(6989,plain,
% 1.46/1.58 (op(e0, e1) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[6988, 656, 3508, 80, 121, 79])).
% 1.46/1.58 tff(6990,plain,
% 1.46/1.58 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4840])).
% 1.46/1.58 tff(6991,plain,
% 1.46/1.58 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[6990])).
% 1.46/1.58 tff(6992,plain,
% 1.46/1.58 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[6991])).
% 1.46/1.58 tff(6993,plain,
% 1.46/1.58 (~(op(e0, e0) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[811, 6992])).
% 1.46/1.58 tff(6994,plain,
% 1.46/1.58 (e2 = op(e2, e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[5793])).
% 1.46/1.58 tff(6995,plain,
% 1.46/1.58 ((op(e2, e2) = e2) <=> (op(e2, e2) = op(e2, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[6994])).
% 1.46/1.58 tff(6996,plain,
% 1.46/1.58 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[6995])).
% 1.46/1.58 tff(6997,plain,
% 1.46/1.58 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[6996])).
% 1.46/1.58 tff(6998,plain,
% 1.46/1.58 (~(op(e2, e2) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[515, 6997])).
% 1.46/1.58 tff(6999,plain,
% 1.46/1.58 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[5553])).
% 1.46/1.58 tff(7000,plain,
% 1.46/1.58 (op(e2, e1) = op(e2, op(e2, e2))),
% 1.46/1.58 inference(symmetry,[status(thm)],[6999])).
% 1.46/1.58 tff(7001,plain,
% 1.46/1.58 (e0 = op(e2, op(e2, e2))),
% 1.46/1.58 inference(transitivity,[status(thm)],[5560, 7000])).
% 1.46/1.58 tff(7002,plain,
% 1.46/1.58 (op(e2, op(e2, e2)) = e0),
% 1.46/1.58 inference(transitivity,[status(thm)],[6999, 3508])).
% 1.46/1.58 tff(7003,plain,
% 1.46/1.58 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7002])).
% 1.46/1.58 tff(7004,plain,
% 1.46/1.58 (op(e2, e0) = op(e2, op(e2, op(e2, e2)))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7003])).
% 1.46/1.58 tff(7005,plain,
% 1.46/1.58 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.46/1.58 inference(transitivity,[status(thm)],[5568, 7004])).
% 1.46/1.58 tff(7006,plain,
% 1.46/1.58 ($false),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1648, 7005, 7001, 5554])).
% 1.46/1.58 tff(7007,plain,((op(e2, e2) = e3) | (~(op(e2, e1) = e0)) | (op(e2, e2) = e2) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.58 tff(7008,plain,
% 1.46/1.58 (op(e2, e2) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[7007, 6998, 3508, 124])).
% 1.46/1.58 tff(7009,plain,
% 1.46/1.58 (op(e2, e2) = op(e0, e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7008, 4840])).
% 1.46/1.58 tff(7010,plain,
% 1.46/1.58 ((op(e2, e2) = e1) <=> (op(e0, e1) = e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7009])).
% 1.46/1.58 tff(7011,plain,
% 1.46/1.58 ((op(e0, e1) = e1) <=> (op(e2, e2) = e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7010])).
% 1.46/1.58 tff(7012,plain,
% 1.46/1.58 ((~(op(e0, e1) = e1)) <=> (~(op(e2, e2) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7011])).
% 1.46/1.58 tff(7013,plain,
% 1.46/1.58 ((e1 = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 1.46/1.58 inference(commutativity,[status(thm)],[])).
% 1.46/1.58 tff(7014,plain,
% 1.46/1.58 ((e1 = e3) <=> (e1 = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4840])).
% 1.46/1.58 tff(7015,plain,
% 1.46/1.58 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7014, 7013])).
% 1.46/1.58 tff(7016,plain,
% 1.46/1.58 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7015])).
% 1.46/1.58 tff(7017,plain,
% 1.46/1.58 (~(op(e0, e1) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[303, 7016])).
% 1.46/1.58 tff(7018,plain,
% 1.46/1.58 (~(op(e2, e2) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7017, 7012])).
% 1.46/1.58 tff(7019,plain,
% 1.46/1.58 (op(e2, e0) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[345, 7018, 76, 5582])).
% 1.46/1.58 tff(7020,plain,
% 1.46/1.58 (e1 = op(e2, e0)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7019])).
% 1.46/1.58 tff(7021,plain,
% 1.46/1.58 ((op(e0, e0) = e1) <=> (op(e0, e0) = op(e2, e0))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7020])).
% 1.46/1.58 tff(7022,plain,
% 1.46/1.58 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7021])).
% 1.46/1.58 tff(7023,plain,
% 1.46/1.58 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7022])).
% 1.46/1.58 tff(7024,plain,
% 1.46/1.58 (~(op(e0, e0) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[359, 7023])).
% 1.46/1.58 tff(7025,plain,
% 1.46/1.58 (op(e0, e0) = e2),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[3612, 7024, 6213, 6993])).
% 1.46/1.58 tff(7026,plain,
% 1.46/1.58 (e2 = op(e0, e0)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7025, 78])).
% 1.46/1.58 tff(7027,plain,
% 1.46/1.58 (op(e0, e0) = op(e2, e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7025, 6994])).
% 1.46/1.58 tff(7028,plain,
% 1.46/1.58 (op(e0, op(e0, e0)) = op(e0, op(e2, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7027])).
% 1.46/1.58 tff(7029,plain,
% 1.46/1.58 (op(e0, op(e2, e3)) = op(e0, op(e0, e0))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7028])).
% 1.46/1.58 tff(7030,plain,
% 1.46/1.58 (op(e0, op(e2, e3)) = op(e0, e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[5793])).
% 1.46/1.58 tff(7031,plain,
% 1.46/1.58 (op(e0, e2) = op(e0, op(e2, e3))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7030])).
% 1.46/1.58 tff(7032,plain,
% 1.46/1.58 (op(e0, e2) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[384, 7024, 121, 7017])).
% 1.46/1.58 tff(7033,plain,
% 1.46/1.58 (e1 = op(e0, e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7032])).
% 1.46/1.58 tff(7034,plain,
% 1.46/1.58 (e1 = op(e0, op(e0, e0))),
% 1.46/1.58 inference(transitivity,[status(thm)],[7033, 7031, 7029])).
% 1.46/1.58 tff(7035,plain,
% 1.46/1.58 (op(e0, op(e0, e0)) = op(e2, e0)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7028, 7030, 7032, 7020])).
% 1.46/1.58 tff(7036,plain,
% 1.46/1.58 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e2, e0))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7035])).
% 1.46/1.58 tff(7037,plain,
% 1.46/1.58 (op(e0, op(e2, e0)) = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7036])).
% 1.46/1.58 tff(7038,plain,
% 1.46/1.58 (op(e0, op(e2, e0)) = op(e0, e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7019])).
% 1.46/1.58 tff(7039,plain,
% 1.46/1.58 (op(e0, e1) = op(e0, op(e2, e0))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7038])).
% 1.46/1.58 tff(7040,plain,
% 1.46/1.58 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.58 inference(transitivity,[status(thm)],[4840, 7039, 7037])).
% 1.46/1.58 tff(7041,plain,
% 1.46/1.58 ($false),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[842, 7040, 7034, 7026])).
% 1.46/1.58 tff(7042,plain,((op(e2, e3) = e1) | (~(op(e0, e1) = e3)) | (op(e0, e0) = e0) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.58 tff(7043,plain,
% 1.46/1.58 (op(e2, e3) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[7042, 124, 6213, 121, 3508, 4839])).
% 1.46/1.58 tff(7044,plain,
% 1.46/1.58 (~(op(e2, e2) = e3)),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[6638, 7043, 3508])).
% 1.46/1.58 tff(7045,plain,
% 1.46/1.58 (op(e2, e2) = e2),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[7007, 7044, 3508, 124])).
% 1.46/1.58 tff(7046,plain,
% 1.46/1.58 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7045])).
% 1.46/1.58 tff(7047,plain,
% 1.46/1.58 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7046])).
% 1.46/1.58 tff(7048,plain,
% 1.46/1.58 (~(op(e0, e2) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[2736, 7047])).
% 1.46/1.58 tff(7049,plain,
% 1.46/1.58 (op(e0, e0) = e2),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[3652, 7048, 79, 4844])).
% 1.46/1.58 tff(7050,plain,
% 1.46/1.58 (e2 = op(e0, e0)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7049, 78])).
% 1.46/1.58 tff(7051,plain,
% 1.46/1.58 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7049])).
% 1.46/1.58 tff(7052,plain,
% 1.46/1.58 (op(e0, e2) = op(e0, op(e0, e0))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7051])).
% 1.46/1.58 tff(7053,assumption,(~(op(e0, e2) = e0)), introduced(assumption)).
% 1.46/1.58 tff(7054,plain,
% 1.46/1.58 (op(e0, e2) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2745, 7048, 7053, 4860])).
% 1.46/1.58 tff(7055,plain,
% 1.46/1.58 (e1 = op(e0, e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7054])).
% 1.46/1.58 tff(7056,plain,
% 1.46/1.58 (e1 = op(e0, op(e0, e0))),
% 1.46/1.58 inference(transitivity,[status(thm)],[7055, 7052])).
% 1.46/1.58 tff(7057,plain,
% 1.46/1.58 (e1 = op(e2, e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7043])).
% 1.46/1.58 tff(7058,plain,
% 1.46/1.58 (op(e0, op(e0, e0)) = op(e2, e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7051, 7054, 7057])).
% 1.46/1.58 tff(7059,plain,
% 1.46/1.58 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e2, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7058])).
% 1.46/1.58 tff(7060,plain,
% 1.46/1.58 (op(e0, op(e2, e3)) = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7059])).
% 1.46/1.58 tff(7061,plain,
% 1.46/1.58 (op(e0, op(e2, e3)) = op(e0, e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7043])).
% 1.46/1.58 tff(7062,plain,
% 1.46/1.58 (op(e0, e1) = op(e0, op(e2, e3))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7061])).
% 1.46/1.58 tff(7063,plain,
% 1.46/1.58 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.58 inference(transitivity,[status(thm)],[4840, 7062, 7060])).
% 1.46/1.58 tff(7064,plain,
% 1.46/1.58 ($false),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[842, 7063, 7056, 7050])).
% 1.46/1.58 tff(7065,plain,((op(e2, e3) = e3) | (~(op(e0, e1) = e3)) | (op(e0, e3) = e2) | (op(e0, e2) = e0) | (~(op(e2, e1) = e0)) | (op(e0, e0) = e0) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.58 tff(7066,plain,
% 1.46/1.58 (op(e2, e3) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[7065, 6989, 79, 5453, 3508, 5450, 121])).
% 1.46/1.58 tff(7067,plain,
% 1.46/1.58 (op(e2, op(e0, e1)) = op(e2, e3)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[6989])).
% 1.46/1.58 tff(7068,plain,
% 1.46/1.58 (e3 = op(e0, e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[6989])).
% 1.46/1.58 tff(7069,plain,
% 1.46/1.58 (op(e2, e3) = op(e0, e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7066, 7068])).
% 1.46/1.58 tff(7070,plain,
% 1.46/1.58 (op(e2, op(e2, e3)) = op(e2, op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7069])).
% 1.46/1.58 tff(7071,plain,
% 1.46/1.58 (op(e2, op(e2, e3)) = e3),
% 1.46/1.58 inference(transitivity,[status(thm)],[7070, 7067, 7066])).
% 1.46/1.58 tff(7072,plain,
% 1.46/1.58 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2344, 7071])).
% 1.46/1.58 tff(7073,plain,
% 1.46/1.58 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7066])).
% 1.46/1.58 tff(7074,plain,
% 1.46/1.58 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7073, 666])).
% 1.46/1.58 tff(7075,plain,
% 1.46/1.58 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7074])).
% 1.46/1.58 tff(7076,plain,
% 1.46/1.58 (~(op(e3, e3) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[368, 7075])).
% 1.46/1.58 tff(7077,plain,
% 1.46/1.58 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7066])).
% 1.46/1.58 tff(7078,plain,
% 1.46/1.58 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7077])).
% 1.46/1.58 tff(7079,plain,
% 1.46/1.58 (~(op(e1, e3) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[118, 7078])).
% 1.46/1.58 tff(7080,plain,
% 1.46/1.58 ((op(e2, e3) = e1) <=> (op(e0, e1) = e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7069])).
% 1.46/1.58 tff(7081,plain,
% 1.46/1.58 ((op(e0, e1) = e1) <=> (op(e2, e3) = e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7080])).
% 1.46/1.58 tff(7082,plain,
% 1.46/1.58 ((~(op(e0, e1) = e1)) <=> (~(op(e2, e3) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7081])).
% 1.46/1.58 tff(7083,plain,
% 1.46/1.58 ((e1 = e3) <=> (e1 = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7068])).
% 1.46/1.58 tff(7084,plain,
% 1.46/1.58 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7083, 7013])).
% 1.46/1.58 tff(7085,plain,
% 1.46/1.58 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7084])).
% 1.46/1.58 tff(7086,plain,
% 1.46/1.58 (~(op(e0, e1) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[303, 7085])).
% 1.46/1.58 tff(7087,plain,
% 1.46/1.58 (~(op(e2, e3) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7086, 7082])).
% 1.46/1.58 tff(7088,plain,
% 1.46/1.58 (op(e2, e3) = op(e2, op(e0, e1))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7067])).
% 1.46/1.58 tff(7089,plain,
% 1.46/1.58 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e1)) = e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7088])).
% 1.46/1.58 tff(7090,plain,
% 1.46/1.58 ((op(e2, op(e0, e1)) = e2) <=> (op(e2, e3) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7089])).
% 1.46/1.58 tff(7091,plain,
% 1.46/1.58 (op(e2, op(e0, e1)) = op(e0, e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7067, 7066, 7068])).
% 1.46/1.58 tff(7092,plain,
% 1.46/1.58 ((op(e2, op(e0, e1)) = e2) <=> (op(e0, e1) = e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7091])).
% 1.46/1.58 tff(7093,plain,
% 1.46/1.58 ((op(e0, e1) = e2) <=> (op(e2, op(e0, e1)) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7092])).
% 1.46/1.58 tff(7094,plain,
% 1.46/1.58 ((op(e0, e1) = e2) <=> (op(e2, e3) = e2)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7093, 7090])).
% 1.46/1.58 tff(7095,plain,
% 1.46/1.58 ((~(op(e0, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7094])).
% 1.46/1.58 tff(7096,plain,
% 1.46/1.58 ((e2 = e3) <=> (e2 = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7068])).
% 1.46/1.58 tff(7097,plain,
% 1.46/1.58 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7096, 4838])).
% 1.46/1.58 tff(7098,plain,
% 1.46/1.58 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7097])).
% 1.46/1.58 tff(7099,plain,
% 1.46/1.58 (~(op(e0, e1) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[1321, 7098])).
% 1.46/1.58 tff(7100,plain,
% 1.46/1.58 (~(op(e2, e3) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7099, 7095])).
% 1.46/1.58 tff(7101,plain,
% 1.46/1.58 (op(e3, e3) = e2),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2786, 72, 4382, 79])).
% 1.46/1.58 tff(7102,plain,
% 1.46/1.58 (e2 = op(e3, e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7101])).
% 1.46/1.58 tff(7103,plain,
% 1.46/1.58 (op(e0, op(e0, e1)) = op(e0, e3)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4839])).
% 1.46/1.58 tff(7104,plain,
% 1.46/1.58 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4840])).
% 1.46/1.58 tff(7105,plain,
% 1.46/1.58 ((op(e1, e1) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 1.46/1.58 inference(transitivity,[status(thm)],[7104, 5033])).
% 1.46/1.58 tff(7106,plain,
% 1.46/1.58 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7105])).
% 1.46/1.58 tff(7107,plain,
% 1.46/1.58 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7106])).
% 1.46/1.58 tff(7108,plain,
% 1.46/1.58 (~(op(e1, e1) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[792, 7107])).
% 1.46/1.58 tff(7109,plain,
% 1.46/1.58 (op(e1, e3) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[104, 72, 80, 1080])).
% 1.46/1.58 tff(7110,plain,
% 1.46/1.58 (e1 = op(e1, e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7109])).
% 1.46/1.58 tff(7111,plain,
% 1.46/1.58 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7110])).
% 1.46/1.58 tff(7112,plain,
% 1.46/1.58 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7111])).
% 1.46/1.58 tff(7113,plain,
% 1.46/1.58 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7112])).
% 1.46/1.58 tff(7114,plain,
% 1.46/1.58 (~(op(e1, e2) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[1850, 7113])).
% 1.46/1.58 tff(7115,plain,
% 1.46/1.58 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e3, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7102])).
% 1.46/1.58 tff(7116,plain,
% 1.46/1.58 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7115])).
% 1.46/1.58 tff(7117,plain,
% 1.46/1.58 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7116])).
% 1.46/1.58 tff(7118,plain,
% 1.46/1.58 (~(op(e3, e1) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[437, 7117])).
% 1.46/1.58 tff(7119,plain,
% 1.46/1.58 (op(e1, e1) = e2),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1993, 7118, 4844, 5515])).
% 1.46/1.58 tff(7120,plain,
% 1.46/1.58 (op(e1, op(e3, e3)) = op(e1, e2)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[2812])).
% 1.46/1.58 tff(7121,plain,
% 1.46/1.58 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.46/1.58 inference(transitivity,[status(thm)],[2893, 7120])).
% 1.46/1.58 tff(7122,plain,
% 1.46/1.58 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7121])).
% 1.46/1.58 tff(7123,plain,
% 1.46/1.58 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7122, 67])).
% 1.46/1.58 tff(7124,plain,
% 1.46/1.58 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7123])).
% 1.46/1.58 tff(7125,plain,
% 1.46/1.58 (op(e1, e2) = e0),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1859, 75, 5766, 4515])).
% 1.46/1.58 tff(7126,plain,
% 1.46/1.58 (e0 = op(e1, op(e1, e1))),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7125, 7124])).
% 1.46/1.58 tff(7127,plain,
% 1.46/1.58 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7121])).
% 1.46/1.58 tff(7128,plain,
% 1.46/1.58 (op(e1, op(e1, e2)) = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7127])).
% 1.46/1.58 tff(7129,plain,
% 1.46/1.58 (op(e1, op(e1, e2)) = op(e1, e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7125])).
% 1.46/1.58 tff(7130,plain,
% 1.46/1.58 (op(e1, e0) = op(e1, op(e1, e2))),
% 1.46/1.58 inference(symmetry,[status(thm)],[7129])).
% 1.46/1.58 tff(7131,plain,
% 1.46/1.58 (op(e1, e0) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[247, 75, 1291, 1080])).
% 1.46/1.58 tff(7132,plain,
% 1.46/1.58 (e3 = op(e1, e0)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7131])).
% 1.46/1.58 tff(7133,plain,
% 1.46/1.58 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.58 inference(transitivity,[status(thm)],[7132, 7130, 7128])).
% 1.46/1.58 tff(7134,plain,
% 1.46/1.58 ($false),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2269, 7133, 7126, 2902])).
% 1.46/1.58 tff(7135,plain,((op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (~(op(e1, e1) = e2)) | (op(e1, e2) = e1) | (op(e1, e1) = e3) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.58 tff(7136,plain,
% 1.46/1.58 (op(e1, e2) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[7135, 7101, 7119, 7114, 7108, 1080])).
% 1.46/1.58 tff(7137,plain,
% 1.46/1.58 (op(e1, e2) = op(e0, e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7136, 4840])).
% 1.46/1.58 tff(7138,plain,
% 1.46/1.58 ((op(e1, e2) = e0) <=> (op(e0, e1) = e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7137])).
% 1.46/1.58 tff(7139,plain,
% 1.46/1.58 ((op(e0, e1) = e0) <=> (op(e1, e2) = e0)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7138])).
% 1.46/1.58 tff(7140,plain,
% 1.46/1.58 ((~(op(e0, e1) = e0)) <=> (~(op(e1, e2) = e0))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7139])).
% 1.46/1.58 tff(7141,plain,
% 1.46/1.58 (~(op(e1, e2) = e0)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[5478, 7140])).
% 1.46/1.58 tff(7142,plain,
% 1.46/1.58 (op(e3, e2) = e0),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[973, 7141, 5552, 5453])).
% 1.46/1.58 tff(7143,plain,
% 1.46/1.58 (op(op(e3, e2), e3) = op(e0, op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7142, 4840])).
% 1.46/1.58 tff(7144,plain,
% 1.46/1.58 (op(op(e3, e2), e3) = e0),
% 1.46/1.58 inference(transitivity,[status(thm)],[7143, 7103, 5447])).
% 1.46/1.58 tff(7145,plain,
% 1.46/1.58 ((op(op(e3, e2), e3) = e2) <=> (e0 = op(e3, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7144, 7102])).
% 1.46/1.58 tff(7146,plain,
% 1.46/1.58 ((op(op(e3, e2), e3) = e2) <=> (op(e3, e3) = e0)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7145, 3077])).
% 1.46/1.58 tff(7147,plain,
% 1.46/1.58 ((op(e3, e3) = e0) <=> (op(op(e3, e2), e3) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7146])).
% 1.46/1.58 tff(7148,plain,
% 1.46/1.58 ((~(op(e3, e3) = e0)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7147])).
% 1.46/1.58 tff(7149,plain,
% 1.46/1.58 (~(op(op(e3, e2), e3) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[656, 7148])).
% 1.46/1.58 tff(7150,plain,
% 1.46/1.58 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2408, 7149])).
% 1.46/1.58 tff(7151,plain,
% 1.46/1.58 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e0, e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4840])).
% 1.46/1.58 tff(7152,plain,
% 1.46/1.58 ((op(e3, e1) = e3) <=> (op(e0, e1) = op(e3, e1))),
% 1.46/1.58 inference(transitivity,[status(thm)],[7151, 5104])).
% 1.46/1.58 tff(7153,plain,
% 1.46/1.58 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7152])).
% 1.46/1.58 tff(7154,plain,
% 1.46/1.58 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7153])).
% 1.46/1.58 tff(7155,plain,
% 1.46/1.58 (~(op(e3, e1) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[3046, 7154])).
% 1.46/1.58 tff(7156,plain,
% 1.46/1.58 (op(e3, e1) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[446, 7118, 5474, 7155])).
% 1.46/1.58 tff(7157,plain,
% 1.46/1.58 (op(op(e0, e1), e1) = op(e3, e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4839])).
% 1.46/1.58 tff(7158,plain,
% 1.46/1.58 (op(e3, op(e1, e3)) = op(op(e0, e1), e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4840, 7109])).
% 1.46/1.58 tff(7159,plain,
% 1.46/1.58 (op(e3, e1) = op(e1, e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7156, 7110])).
% 1.46/1.58 tff(7160,plain,
% 1.46/1.58 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7159])).
% 1.46/1.58 tff(7161,plain,
% 1.46/1.58 (op(e3, op(e3, e1)) = e1),
% 1.46/1.58 inference(transitivity,[status(thm)],[7160, 7158, 7157, 7156])).
% 1.46/1.58 tff(7162,plain,
% 1.46/1.58 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2594, 7161])).
% 1.46/1.58 tff(7163,plain,
% 1.46/1.58 (op(op(e0, e1), e0) = op(e3, e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[4839])).
% 1.46/1.58 tff(7164,plain,
% 1.46/1.58 ((op(op(e0, e1), e0) = e1) <=> (op(e3, e0) = e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7163])).
% 1.46/1.58 tff(7165,plain,
% 1.46/1.58 ((op(e3, e0) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7164])).
% 1.46/1.58 tff(7166,plain,
% 1.46/1.58 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7156])).
% 1.46/1.58 tff(7167,plain,
% 1.46/1.58 ((op(e3, e0) = op(e3, e1)) <=> (op(op(e0, e1), e0) = e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7166, 7165])).
% 1.46/1.58 tff(7168,plain,
% 1.46/1.58 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7167])).
% 1.46/1.58 tff(7169,plain,
% 1.46/1.58 (~(op(op(e0, e1), e0) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[580, 7168])).
% 1.46/1.58 tff(7170,plain,
% 1.46/1.58 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1461, 7169])).
% 1.46/1.58 tff(7171,plain,
% 1.46/1.58 ((e1 = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.46/1.58 inference(commutativity,[status(thm)],[])).
% 1.46/1.58 tff(7172,plain,
% 1.46/1.58 ((op(e3, e1) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7156])).
% 1.46/1.58 tff(7173,plain,
% 1.46/1.58 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7172, 7171])).
% 1.46/1.58 tff(7174,plain,
% 1.46/1.58 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7173])).
% 1.46/1.58 tff(7175,plain,
% 1.46/1.58 (~(op(e3, e2) = e1)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[3429, 7174])).
% 1.46/1.58 tff(7176,plain,
% 1.46/1.58 (op(e1, e0) = e0),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1830, 7141, 80, 5456])).
% 1.46/1.58 tff(7177,plain,
% 1.46/1.58 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7136])).
% 1.46/1.58 tff(7178,plain,
% 1.46/1.58 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7177, 3423])).
% 1.46/1.58 tff(7179,plain,
% 1.46/1.58 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7178])).
% 1.46/1.58 tff(7180,plain,
% 1.46/1.58 (~(op(e3, e2) = e3)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[2292, 7179])).
% 1.46/1.58 tff(7181,plain,
% 1.46/1.58 (op(e3, e0) = e3),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[422, 7180, 7155, 468])).
% 1.46/1.58 tff(7182,plain,
% 1.46/1.58 (op(e3, e0) = op(e0, e1)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7181, 4840])).
% 1.46/1.58 tff(7183,plain,
% 1.46/1.58 (op(op(e3, e0), e0) = op(op(e0, e1), e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7182])).
% 1.46/1.58 tff(7184,plain,
% 1.46/1.58 (op(op(e3, e0), e0) = e3),
% 1.46/1.58 inference(transitivity,[status(thm)],[7183, 7163, 7181])).
% 1.46/1.58 tff(7185,plain,
% 1.46/1.58 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[4026, 7184])).
% 1.46/1.58 tff(7186,plain,
% 1.46/1.58 (op(op(e1, e2), e1) = op(e3, op(e1, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7136, 7110])).
% 1.46/1.58 tff(7187,plain,
% 1.46/1.58 (op(op(e1, e2), e1) = op(e1, e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7186, 7158, 7157, 7156, 7110])).
% 1.46/1.58 tff(7188,plain,
% 1.46/1.58 ((op(op(e1, e2), e1) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7187, 7102])).
% 1.46/1.58 tff(7189,plain,
% 1.46/1.58 ((op(e1, e3) = op(e3, e3)) <=> (op(op(e1, e2), e1) = e2)),
% 1.46/1.58 inference(symmetry,[status(thm)],[7188])).
% 1.46/1.58 tff(7190,plain,
% 1.46/1.58 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7189])).
% 1.46/1.58 tff(7191,plain,
% 1.46/1.58 (~(op(op(e1, e2), e1) = e2)),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[571, 7190])).
% 1.46/1.58 tff(7192,plain,
% 1.46/1.58 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[5959, 7191])).
% 1.46/1.58 tff(7193,plain,
% 1.46/1.58 (op(e2, e0) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[345, 1348, 76, 5582])).
% 1.46/1.58 tff(7194,plain,
% 1.46/1.58 (op(e2, op(e2, e1)) = e1),
% 1.46/1.58 inference(modus_ponens,[status(thm)],[7193, 6159])).
% 1.46/1.58 tff(7195,plain,
% 1.46/1.58 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1355, 7194])).
% 1.46/1.58 tff(7196,plain,
% 1.46/1.58 (op(e2, e0) = op(e1, e3)),
% 1.46/1.58 inference(transitivity,[status(thm)],[7193, 3710])).
% 1.46/1.58 tff(7197,plain,
% 1.46/1.58 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7196])).
% 1.46/1.58 tff(7198,plain,
% 1.46/1.58 (op(e2, op(e2, e0)) = e0),
% 1.46/1.58 inference(transitivity,[status(thm)],[7197, 3796, 3508])).
% 1.46/1.58 tff(7199,plain,
% 1.46/1.58 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[2653, 7198])).
% 1.46/1.58 tff(7200,plain,
% 1.46/1.58 (op(e0, e2) = e1),
% 1.46/1.58 inference(unit_resolution,[status(thm)],[1613, 1348, 6147, 930])).
% 1.46/1.58 tff(7201,plain,
% 1.46/1.58 (op(op(e0, e2), e0) = op(e1, e0)),
% 1.46/1.58 inference(monotonicity,[status(thm)],[7200])).
% 1.46/1.59 tff(7202,plain,
% 1.46/1.59 (op(op(e0, e2), e0) = e0),
% 1.46/1.59 inference(transitivity,[status(thm)],[7201, 6142])).
% 1.46/1.59 tff(7203,plain,
% 1.46/1.59 ((op(op(e0, e2), e0) = e2) <=> (e0 = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7202, 2834])).
% 1.46/1.59 tff(7204,plain,
% 1.46/1.59 ((op(op(e0, e2), e0) = e2) <=> (op(e3, e3) = e0)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7203, 3077])).
% 1.46/1.59 tff(7205,plain,
% 1.46/1.59 ((op(e3, e3) = e0) <=> (op(op(e0, e2), e0) = e2)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7204])).
% 1.46/1.59 tff(7206,plain,
% 1.46/1.59 ((~(op(e3, e3) = e0)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7205])).
% 1.46/1.59 tff(7207,plain,
% 1.46/1.59 (~(op(op(e0, e2), e0) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[656, 7206])).
% 1.46/1.59 tff(7208,plain,
% 1.46/1.59 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[2446, 7207])).
% 1.46/1.59 tff(7209,plain,
% 1.46/1.59 ($false),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1459, 7208, 7199, 1358, 1926, 3342, 1304, 6167, 7195, 4549, 1275, 3341, 1347])).
% 1.46/1.59 tff(7210,plain,((op(e2, e2) = e1) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e3, e3) = e0) | (~(op(e3, e3) = e2)) | (~(op(e1, e0) = e0)) | (~(op(e2, e1) = e0)) | (~(op(e1, e3) = e1)) | (op(e3, e2) = e1) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.59 tff(7211,plain,
% 1.46/1.59 (op(e2, e2) = e1),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[7210, 7192, 7185, 3342, 1304, 7170, 7162, 7150, 1347, 656, 7101, 7176, 3508, 7109, 7175, 76])).
% 1.46/1.59 tff(7212,plain,
% 1.46/1.59 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7211])).
% 1.46/1.59 tff(7213,plain,
% 1.46/1.59 ((op(e0, e2) = op(e2, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7212, 5799])).
% 1.46/1.59 tff(7214,plain,
% 1.46/1.59 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7213])).
% 1.46/1.59 tff(7215,plain,
% 1.46/1.59 (~(op(op(e2, e1), e2) = e1)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[2736, 7214])).
% 1.46/1.59 tff(7216,plain,
% 1.46/1.59 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[5808, 7215])).
% 1.46/1.59 tff(7217,plain,
% 1.46/1.59 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7176])).
% 1.46/1.59 tff(7218,plain,
% 1.46/1.59 (op(e1, op(e1, e0)) = e0),
% 1.46/1.59 inference(transitivity,[status(thm)],[7217, 7176])).
% 1.46/1.59 tff(7219,plain,
% 1.46/1.59 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1836, 7218])).
% 1.46/1.59 tff(7220,plain,
% 1.46/1.59 (op(e2, e2) = op(e1, e3)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7211, 7110])).
% 1.46/1.59 tff(7221,plain,
% 1.46/1.59 ((op(e2, e2) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7220, 7102])).
% 1.46/1.59 tff(7222,plain,
% 1.46/1.59 ((op(e1, e3) = op(e3, e3)) <=> (op(e2, e2) = e2)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7221])).
% 1.46/1.59 tff(7223,plain,
% 1.46/1.59 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7222])).
% 1.46/1.59 tff(7224,plain,
% 1.46/1.59 (~(op(e2, e2) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[571, 7223])).
% 1.46/1.59 tff(7225,plain,
% 1.46/1.59 (op(e2, e0) = e2),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[2088, 7224, 4382, 5515])).
% 1.46/1.59 tff(7226,plain,
% 1.46/1.59 (op(op(e2, e0), e0) = op(e2, e0)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7225])).
% 1.46/1.59 tff(7227,plain,
% 1.46/1.59 (op(op(e2, e0), e0) = e2),
% 1.46/1.59 inference(transitivity,[status(thm)],[7226, 7225])).
% 1.46/1.59 tff(7228,plain,
% 1.46/1.59 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1945, 7227])).
% 1.46/1.59 tff(7229,plain,
% 1.46/1.59 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7119])).
% 1.46/1.59 tff(7230,plain,
% 1.46/1.59 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7229, 5762])).
% 1.46/1.59 tff(7231,plain,
% 1.46/1.59 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7230])).
% 1.46/1.59 tff(7232,plain,
% 1.46/1.59 (~(op(e1, e2) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[1604, 7231])).
% 1.46/1.59 tff(7233,plain,
% 1.46/1.59 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7102])).
% 1.46/1.59 tff(7234,plain,
% 1.46/1.59 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e2)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7233])).
% 1.46/1.59 tff(7235,plain,
% 1.46/1.59 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7234])).
% 1.46/1.59 tff(7236,plain,
% 1.46/1.59 (~(op(e3, e2) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[1888, 7235])).
% 1.46/1.59 tff(7237,plain,
% 1.46/1.59 (op(e0, e2) = e2),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1151, 7224, 7236, 7232])).
% 1.46/1.59 tff(7238,plain,
% 1.46/1.59 (op(e0, op(e3, e3)) = op(e0, e2)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7101])).
% 1.46/1.59 tff(7239,plain,
% 1.46/1.59 (op(e0, e2) = op(e3, e3)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7237, 7102])).
% 1.46/1.59 tff(7240,plain,
% 1.46/1.59 (op(e0, op(e0, e2)) = op(e0, op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7239])).
% 1.46/1.59 tff(7241,plain,
% 1.46/1.59 (op(e0, op(e0, e2)) = e2),
% 1.46/1.59 inference(transitivity,[status(thm)],[7240, 7238, 7237])).
% 1.46/1.59 tff(7242,plain,
% 1.46/1.59 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1331, 7241])).
% 1.46/1.59 tff(7243,plain,
% 1.46/1.59 ($false),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1459, 7242, 7228, 7192, 7185, 3342, 1304, 7219, 7216, 7170, 7162, 7150, 1347])).
% 1.46/1.59 tff(7244,plain,((op(e1, e3) = e2) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e3) = e2) | (~(op(e2, e1) = e0)) | (op(e3, e3) = e0) | (op(e2, e3) = e1) | (~(op(e0, e1) = e3)) | (op(e3, e3) = e3) | (op(e1, e3) = e0) | (op(e1, e3) = e3) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.59 tff(7245,plain,
% 1.46/1.59 (op(e1, e3) = e2),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[7244, 7072, 5475, 5469, 7100, 3508, 656, 7087, 6989, 7076, 80, 7079, 79])).
% 1.46/1.59 tff(7246,plain,
% 1.46/1.59 (e2 = op(e1, e3)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7245])).
% 1.46/1.59 tff(7247,plain,
% 1.46/1.59 ((op(e3, e3) = e2) <=> (op(e3, e3) = op(e1, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7246])).
% 1.46/1.59 tff(7248,plain,
% 1.46/1.59 ((op(e3, e3) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 1.46/1.59 inference(transitivity,[status(thm)],[7247, 1659])).
% 1.46/1.59 tff(7249,plain,
% 1.46/1.59 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7248])).
% 1.46/1.59 tff(7250,plain,
% 1.46/1.59 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7249])).
% 1.46/1.59 tff(7251,plain,
% 1.46/1.59 (~(op(e3, e3) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[571, 7250])).
% 1.46/1.59 tff(7252,plain,
% 1.46/1.59 (op(e3, e3) = e1),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1071, 7251, 656, 7076])).
% 1.46/1.59 tff(7253,plain,
% 1.46/1.59 (e1 = op(e3, e3)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7252])).
% 1.46/1.59 tff(7254,plain,
% 1.46/1.59 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7253])).
% 1.46/1.59 tff(7255,plain,
% 1.46/1.59 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7254])).
% 1.46/1.59 tff(7256,plain,
% 1.46/1.59 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7255])).
% 1.46/1.59 tff(7257,plain,
% 1.46/1.59 (~(op(e3, e2) = e1)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[1888, 7256])).
% 1.46/1.59 tff(7258,plain,
% 1.46/1.59 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7246])).
% 1.46/1.59 tff(7259,plain,
% 1.46/1.59 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7258])).
% 1.46/1.59 tff(7260,plain,
% 1.46/1.59 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7259])).
% 1.46/1.59 tff(7261,plain,
% 1.46/1.59 (~(op(e1, e1) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[619, 7260])).
% 1.46/1.59 tff(7262,plain,
% 1.46/1.59 (op(e3, e1) = e2),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1993, 7261, 7099, 5515])).
% 1.46/1.59 tff(7263,plain,
% 1.46/1.59 (~(op(e3, e2) = e0)),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[6787, 7262, 7066, 7252])).
% 1.46/1.59 tff(7264,plain,
% 1.46/1.59 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7262])).
% 1.46/1.59 tff(7265,plain,
% 1.46/1.59 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7264, 2234])).
% 1.46/1.59 tff(7266,plain,
% 1.46/1.59 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7265])).
% 1.46/1.59 tff(7267,plain,
% 1.46/1.59 (~(op(e3, e2) = e2)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[3429, 7266])).
% 1.46/1.59 tff(7268,plain,
% 1.46/1.59 (op(e3, e2) = e3),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1898, 7267, 7263, 7257])).
% 1.46/1.59 tff(7269,plain,
% 1.46/1.59 (op(e3, op(e1, e3)) = op(e3, e2)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7245])).
% 1.46/1.59 tff(7270,plain,
% 1.46/1.59 (op(op(e3, e2), e2) = op(e3, op(e1, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7268, 7246])).
% 1.46/1.59 tff(7271,plain,
% 1.46/1.59 (op(op(e3, e2), e2) = e3),
% 1.46/1.59 inference(transitivity,[status(thm)],[7270, 7269, 7268])).
% 1.46/1.59 tff(7272,plain,
% 1.46/1.59 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1339, 7271])).
% 1.46/1.59 tff(7273,plain,
% 1.46/1.59 (op(op(e1, e3), e3) = op(e2, op(e0, e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7245, 7068])).
% 1.46/1.59 tff(7274,plain,
% 1.46/1.59 (op(e3, e1) = op(e1, e3)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7262, 7246])).
% 1.46/1.59 tff(7275,plain,
% 1.46/1.59 (op(op(e3, e1), e3) = op(op(e1, e3), e3)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7274])).
% 1.46/1.59 tff(7276,plain,
% 1.46/1.59 (op(op(e3, e1), e3) = e3),
% 1.46/1.59 inference(transitivity,[status(thm)],[7275, 7273, 7067, 7066])).
% 1.46/1.59 tff(7277,plain,
% 1.46/1.59 ((op(op(e3, e1), e3) = e1) <=> (e3 = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7276, 7253])).
% 1.46/1.59 tff(7278,plain,
% 1.46/1.59 ((op(op(e3, e1), e3) = e1) <=> (op(e3, e3) = e3)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7277, 666])).
% 1.46/1.59 tff(7279,plain,
% 1.46/1.59 ((op(e3, e3) = e3) <=> (op(op(e3, e1), e3) = e1)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7278])).
% 1.46/1.59 tff(7280,plain,
% 1.46/1.59 ((~(op(e3, e3) = e3)) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7279])).
% 1.46/1.59 tff(7281,plain,
% 1.46/1.59 (~(op(op(e3, e1), e3) = e1)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[7076, 7280])).
% 1.46/1.59 tff(7282,plain,
% 1.46/1.59 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1050, 7281])).
% 1.46/1.59 tff(7283,plain,
% 1.46/1.59 (op(op(e0, e1), e0) = op(e3, e0)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[6989])).
% 1.46/1.59 tff(7284,plain,
% 1.46/1.59 ((op(op(e0, e1), e0) = e1) <=> (op(e3, e0) = e1)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7283])).
% 1.46/1.59 tff(7285,plain,
% 1.46/1.59 ((op(e3, e0) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7284])).
% 1.46/1.59 tff(7286,plain,
% 1.46/1.59 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7253])).
% 1.46/1.59 tff(7287,plain,
% 1.46/1.59 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7286])).
% 1.46/1.59 tff(7288,plain,
% 1.46/1.59 ((op(e3, e0) = op(e3, e3)) <=> (op(op(e0, e1), e0) = e1)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7287, 7285])).
% 1.46/1.59 tff(7289,plain,
% 1.46/1.59 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7288])).
% 1.46/1.59 tff(7290,plain,
% 1.46/1.59 (~(op(op(e0, e1), e0) = e1)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[157, 7289])).
% 1.46/1.59 tff(7291,plain,
% 1.46/1.59 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1461, 7290])).
% 1.46/1.59 tff(7292,plain,
% 1.46/1.59 (op(e3, e0) = op(e0, e3)),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[5538, 7263, 5474, 5447])).
% 1.46/1.59 tff(7293,plain,
% 1.46/1.59 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e0, e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.46/1.59 tff(7294,plain,
% 1.46/1.59 ((op(e1, e1) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 1.46/1.59 inference(transitivity,[status(thm)],[7293, 5033])).
% 1.46/1.59 tff(7295,plain,
% 1.46/1.59 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7294])).
% 1.46/1.59 tff(7296,plain,
% 1.46/1.59 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7295])).
% 1.46/1.59 tff(7297,plain,
% 1.46/1.59 (~(op(e1, e1) = e3)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[792, 7296])).
% 1.46/1.59 tff(7298,plain,
% 1.46/1.59 (op(e1, e1) = e1),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[630, 7261, 5456, 7297])).
% 1.46/1.59 tff(7299,plain,
% 1.46/1.59 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7298])).
% 1.46/1.59 tff(7300,plain,
% 1.46/1.59 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, op(e0, e3)) = e1)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7299, 6027])).
% 1.46/1.59 tff(7301,plain,
% 1.46/1.59 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7300])).
% 1.46/1.59 tff(7302,plain,
% 1.46/1.59 (~(op(e1, op(e0, e3)) = e1)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[737, 7301])).
% 1.46/1.59 tff(7303,plain,
% 1.46/1.59 (op(e2, op(e0, e3)) = e2),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[844, 7302, 121, 7245, 7292, 6881])).
% 1.46/1.59 tff(7304,plain,
% 1.46/1.59 (op(e2, e0) = e2),
% 1.46/1.59 inference(transitivity,[status(thm)],[6536, 7303])).
% 1.46/1.59 tff(7305,plain,
% 1.46/1.59 (op(op(e2, e0), e0) = op(e2, e0)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7304])).
% 1.46/1.59 tff(7306,plain,
% 1.46/1.59 (op(op(e2, e0), e0) = e2),
% 1.46/1.59 inference(transitivity,[status(thm)],[7305, 6536, 7303])).
% 1.46/1.59 tff(7307,plain,
% 1.46/1.59 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[1945, 7306])).
% 1.46/1.59 tff(7308,plain,
% 1.46/1.59 (op(op(e0, e1), e1) = op(e3, e1)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[6989])).
% 1.46/1.59 tff(7309,plain,
% 1.46/1.59 (op(e3, op(e3, e3)) = op(op(e0, e1), e1)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7068, 7252])).
% 1.46/1.59 tff(7310,plain,
% 1.46/1.59 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7066])).
% 1.46/1.59 tff(7311,plain,
% 1.46/1.59 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7310])).
% 1.46/1.59 tff(7312,plain,
% 1.46/1.59 (~(op(e2, e0) = e3)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[989, 7311])).
% 1.46/1.59 tff(7313,plain,
% 1.46/1.59 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7068])).
% 1.46/1.59 tff(7314,plain,
% 1.46/1.59 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7313])).
% 1.46/1.59 tff(7315,plain,
% 1.46/1.59 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7314])).
% 1.46/1.59 tff(7316,plain,
% 1.46/1.59 (~(op(e0, e0) = e3)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[811, 7315])).
% 1.46/1.59 tff(7317,plain,
% 1.46/1.59 (op(e3, e0) = e0),
% 1.46/1.59 inference(transitivity,[status(thm)],[7292, 5447])).
% 1.46/1.59 tff(7318,plain,
% 1.46/1.59 ((op(e3, e0) = e3) <=> (e0 = op(e0, e1))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7317, 7068])).
% 1.46/1.59 tff(7319,plain,
% 1.46/1.59 ((op(e3, e0) = e3) <=> (op(e0, e1) = e0)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7318, 5637])).
% 1.46/1.59 tff(7320,plain,
% 1.46/1.59 ((op(e0, e1) = e0) <=> (op(e3, e0) = e3)),
% 1.46/1.59 inference(symmetry,[status(thm)],[7319])).
% 1.46/1.59 tff(7321,plain,
% 1.46/1.59 ((~(op(e0, e1) = e0)) <=> (~(op(e3, e0) = e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7320])).
% 1.46/1.59 tff(7322,plain,
% 1.46/1.59 (~(op(e3, e0) = e3)),
% 1.46/1.59 inference(modus_ponens,[status(thm)],[5478, 7321])).
% 1.46/1.59 tff(7323,plain,
% 1.46/1.59 (op(e1, e0) = e3),
% 1.46/1.59 inference(unit_resolution,[status(thm)],[2713, 7322, 7316, 7312])).
% 1.46/1.59 tff(7324,plain,
% 1.46/1.59 (op(op(e1, e0), e1) = op(e3, op(e3, e3))),
% 1.46/1.59 inference(monotonicity,[status(thm)],[7323, 7253])).
% 1.46/1.59 tff(7325,plain,
% 1.46/1.59 (op(op(e1, e0), e1) = op(e1, e3)),
% 1.46/1.59 inference(transitivity,[status(thm)],[7324, 7309, 7308, 7262, 7246])).
% 1.46/1.59 tff(7326,plain,
% 1.46/1.59 ((op(op(e1, e0), e1) = e0) <=> (op(e1, e3) = e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7325])).
% 1.46/1.60 tff(7327,plain,
% 1.46/1.60 ((op(e1, e3) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7326])).
% 1.46/1.60 tff(7328,plain,
% 1.46/1.60 ((~(op(e1, e3) = e0)) <=> (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7327])).
% 1.46/1.60 tff(7329,plain,
% 1.46/1.60 (~(op(op(e1, e0), e1) = e0)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[80, 7328])).
% 1.46/1.60 tff(7330,plain,
% 1.46/1.60 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1302, 7329])).
% 1.46/1.60 tff(7331,plain,
% 1.46/1.60 (op(e3, op(e3, e0)) = op(op(e0, e1), e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7068, 7317])).
% 1.46/1.60 tff(7332,plain,
% 1.46/1.60 (op(e3, op(e3, e0)) = e0),
% 1.46/1.60 inference(transitivity,[status(thm)],[7331, 7283, 7292, 5447])).
% 1.46/1.60 tff(7333,plain,
% 1.46/1.60 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1345, 7332])).
% 1.46/1.60 tff(7334,plain,
% 1.46/1.60 (op(e0, op(e3, e3)) = op(e0, e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7252])).
% 1.46/1.60 tff(7335,plain,
% 1.46/1.60 (op(e1, e2) = e0),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[973, 7263, 5552, 5453])).
% 1.46/1.60 tff(7336,plain,
% 1.46/1.60 (op(op(e1, e2), e1) = op(e0, op(e3, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7335, 7253])).
% 1.46/1.60 tff(7337,plain,
% 1.46/1.60 (op(op(e1, e2), e1) = e3),
% 1.46/1.60 inference(transitivity,[status(thm)],[7336, 7334, 6989])).
% 1.46/1.60 tff(7338,plain,
% 1.46/1.60 ((op(op(e1, e2), e1) = e2) <=> (e3 = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7337, 7246])).
% 1.46/1.60 tff(7339,plain,
% 1.46/1.60 ((op(op(e1, e2), e1) = e2) <=> (op(e1, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7338, 3230])).
% 1.46/1.60 tff(7340,plain,
% 1.46/1.60 ((op(e1, e3) = e3) <=> (op(op(e1, e2), e1) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7339])).
% 1.46/1.60 tff(7341,plain,
% 1.46/1.60 ((~(op(e1, e3) = e3)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7340])).
% 1.46/1.60 tff(7342,plain,
% 1.46/1.60 (~(op(op(e1, e2), e1) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7079, 7341])).
% 1.46/1.60 tff(7343,plain,
% 1.46/1.60 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[5959, 7342])).
% 1.46/1.60 tff(7344,plain,
% 1.46/1.60 (op(e2, e0) = op(e1, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[6536, 7303, 7246])).
% 1.46/1.60 tff(7345,plain,
% 1.46/1.60 ((op(e2, e0) = e1) <=> (op(e1, e3) = op(e3, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7344, 7253])).
% 1.46/1.60 tff(7346,plain,
% 1.46/1.60 ((op(e1, e3) = op(e3, e3)) <=> (op(e2, e0) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7345])).
% 1.46/1.60 tff(7347,plain,
% 1.46/1.60 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e2, e0) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7346])).
% 1.46/1.60 tff(7348,plain,
% 1.46/1.60 (~(op(e2, e0) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[571, 7347])).
% 1.46/1.60 tff(7349,plain,
% 1.46/1.60 (op(e2, e2) = e1),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[345, 7348, 7087, 5582])).
% 1.46/1.60 tff(7350,plain,
% 1.46/1.60 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7349])).
% 1.46/1.60 tff(7351,plain,
% 1.46/1.60 ((op(e0, e2) = op(e2, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7350, 5799])).
% 1.46/1.60 tff(7352,plain,
% 1.46/1.60 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7351])).
% 1.46/1.60 tff(7353,plain,
% 1.46/1.60 (~(op(op(e2, e1), e2) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[2736, 7352])).
% 1.46/1.60 tff(7354,plain,
% 1.46/1.60 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[5808, 7353])).
% 1.46/1.60 tff(7355,plain,
% 1.46/1.60 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7304])).
% 1.46/1.60 tff(7356,plain,
% 1.46/1.60 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7355])).
% 1.46/1.60 tff(7357,plain,
% 1.46/1.60 (~(op(e0, e0) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[359, 7356])).
% 1.46/1.60 tff(7358,plain,
% 1.46/1.60 (op(e0, e2) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[3652, 7357, 79, 7099])).
% 1.46/1.60 tff(7359,plain,
% 1.46/1.60 (op(e0, op(e1, e3)) = op(e0, e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7245])).
% 1.46/1.60 tff(7360,plain,
% 1.46/1.60 (op(e0, e2) = op(e1, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7358, 7246])).
% 1.46/1.60 tff(7361,plain,
% 1.46/1.60 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7360])).
% 1.46/1.60 tff(7362,plain,
% 1.46/1.60 (op(e0, op(e0, e2)) = e2),
% 1.46/1.60 inference(transitivity,[status(thm)],[7361, 7359, 7358])).
% 1.46/1.60 tff(7363,plain,
% 1.46/1.60 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1331, 7362])).
% 1.46/1.60 tff(7364,plain,
% 1.46/1.60 ($false),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1459, 7363, 7354, 7343, 7333, 5469, 5475, 7330, 7307, 7291, 7282, 7272, 7072])).
% 1.46/1.60 tff(7365,plain,((op(e3, e3) = e0) | (~(op(e2, e1) = e0)) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.60 tff(7366,plain,
% 1.46/1.60 (op(e3, e3) = e0),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[7365, 3508, 79, 80, 121])).
% 1.46/1.60 tff(7367,plain,
% 1.46/1.60 (e0 = op(e3, e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7366, 3078])).
% 1.46/1.60 tff(7368,plain,
% 1.46/1.60 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.60 tff(7369,plain,
% 1.46/1.60 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7368])).
% 1.46/1.60 tff(7370,plain,
% 1.46/1.60 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7369, 5377])).
% 1.46/1.60 tff(7371,plain,
% 1.46/1.60 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7370])).
% 1.46/1.60 tff(7372,plain,
% 1.46/1.60 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.60 tff(7373,plain,
% 1.46/1.60 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7372])).
% 1.46/1.60 tff(7374,plain,
% 1.46/1.60 (~(op(e0, e3) = e0)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1077, 7373])).
% 1.46/1.60 tff(7375,plain,
% 1.46/1.60 (op(e0, e3) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[687, 7374, 121, 79])).
% 1.46/1.60 tff(7376,plain,
% 1.46/1.60 ((op(e0, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7375])).
% 1.46/1.60 tff(7377,plain,
% 1.46/1.60 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7376, 112])).
% 1.46/1.60 tff(7378,plain,
% 1.46/1.60 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7377])).
% 1.46/1.60 tff(7379,plain,
% 1.46/1.60 (~(op(e2, e3) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[964, 7378])).
% 1.46/1.60 tff(7380,plain,
% 1.46/1.60 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.60 tff(7381,plain,
% 1.46/1.60 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7380])).
% 1.46/1.60 tff(7382,plain,
% 1.46/1.60 (~(op(e3, e2) = e0)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1888, 7381])).
% 1.46/1.60 tff(7383,plain,
% 1.46/1.60 ((op(e3, e3) = e1) <=> (e0 = e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.60 tff(7384,plain,
% 1.46/1.60 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7383])).
% 1.46/1.60 tff(7385,plain,
% 1.46/1.60 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7384])).
% 1.46/1.60 tff(7386,plain,
% 1.46/1.60 (~(op(e3, e3) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[26, 7385])).
% 1.46/1.60 tff(7387,plain,
% 1.46/1.60 (op(e1, e3) = e1),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[151, 76, 121, 7386])).
% 1.46/1.60 tff(7388,plain,
% 1.46/1.60 (e1 = op(e1, e3)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7387])).
% 1.46/1.60 tff(7389,plain,
% 1.46/1.60 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7388])).
% 1.46/1.60 tff(7390,plain,
% 1.46/1.60 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7389])).
% 1.46/1.60 tff(7391,plain,
% 1.46/1.60 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7390])).
% 1.46/1.60 tff(7392,plain,
% 1.46/1.60 (~(op(e1, e2) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1850, 7391])).
% 1.46/1.60 tff(7393,plain,
% 1.46/1.60 (op(e2, e2) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[6454, 7387, 79, 7374, 80, 121, 3508])).
% 1.46/1.60 tff(7394,plain,
% 1.46/1.60 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7393])).
% 1.46/1.60 tff(7395,plain,
% 1.46/1.60 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7394])).
% 1.46/1.60 tff(7396,plain,
% 1.46/1.60 (~(op(e1, e2) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1273, 7395])).
% 1.46/1.60 tff(7397,plain,
% 1.46/1.60 (op(e2, e3) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[206, 76, 5446, 7379])).
% 1.46/1.60 tff(7398,plain,
% 1.46/1.60 (e2 = op(e2, e3)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7397])).
% 1.46/1.60 tff(7399,plain,
% 1.46/1.60 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7393])).
% 1.46/1.60 tff(7400,plain,
% 1.46/1.60 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7399, 3423])).
% 1.46/1.60 tff(7401,plain,
% 1.46/1.60 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7400])).
% 1.46/1.60 tff(7402,plain,
% 1.46/1.60 (~(op(e3, e2) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1546, 7401])).
% 1.46/1.60 tff(7403,plain,
% 1.46/1.60 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7387])).
% 1.46/1.60 tff(7404,plain,
% 1.46/1.60 (op(e3, e1) = op(e3, op(e1, e3))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7403])).
% 1.46/1.60 tff(7405,plain,
% 1.46/1.60 ((op(e3, e1) = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7404])).
% 1.46/1.60 tff(7406,plain,
% 1.46/1.60 ((op(e3, op(e1, e3)) = e3) <=> (op(e3, e1) = e3)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7405])).
% 1.46/1.60 tff(7407,plain,
% 1.46/1.60 ((e3 = op(e3, op(e1, e3))) <=> (op(e3, op(e1, e3)) = e3)),
% 1.46/1.60 inference(commutativity,[status(thm)],[])).
% 1.46/1.60 tff(7408,plain,
% 1.46/1.60 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7398])).
% 1.46/1.60 tff(7409,plain,
% 1.46/1.60 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7408])).
% 1.46/1.60 tff(7410,plain,
% 1.46/1.60 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7409])).
% 1.46/1.60 tff(7411,plain,
% 1.46/1.60 (~(op(e1, e3) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[118, 7410])).
% 1.46/1.60 tff(7412,plain,
% 1.46/1.60 (op(e0, e3) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[687, 79, 121, 1087])).
% 1.46/1.60 tff(7413,plain,
% 1.46/1.60 ((op(e0, e3) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7412])).
% 1.46/1.60 tff(7414,plain,
% 1.46/1.60 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7413, 3230])).
% 1.46/1.60 tff(7415,plain,
% 1.46/1.60 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7414])).
% 1.46/1.60 tff(7416,plain,
% 1.46/1.60 (~(op(e1, e3) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[64, 7415])).
% 1.46/1.60 tff(7417,plain,
% 1.46/1.60 (op(e1, e3) = e1),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[104, 7416, 80, 72])).
% 1.46/1.60 tff(7418,plain,
% 1.46/1.60 (e1 = op(e1, e3)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7417])).
% 1.46/1.60 tff(7419,plain,
% 1.46/1.60 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7418])).
% 1.46/1.60 tff(7420,plain,
% 1.46/1.60 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7419])).
% 1.46/1.60 tff(7421,plain,
% 1.46/1.60 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7420])).
% 1.46/1.60 tff(7422,plain,
% 1.46/1.60 (~(op(e1, e1) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[619, 7421])).
% 1.46/1.60 tff(7423,plain,
% 1.46/1.60 (op(e1, e1) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[630, 7422, 84, 1291])).
% 1.46/1.60 tff(7424,plain,
% 1.46/1.60 (e2 = op(e1, e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7423, 2254])).
% 1.46/1.60 tff(7425,plain,
% 1.46/1.60 ((e0 = e2) <=> (op(e3, e3) = e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[6444])).
% 1.46/1.60 tff(7426,plain,
% 1.46/1.60 ((~(e0 = e2)) <=> (~(op(e3, e3) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7425])).
% 1.46/1.60 tff(7427,plain,
% 1.46/1.60 (~(op(e3, e3) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[14, 7426])).
% 1.46/1.60 tff(7428,plain,
% 1.46/1.60 (op(e2, e3) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2786, 79, 72, 7427])).
% 1.46/1.60 tff(7429,plain,
% 1.46/1.60 (op(e1, op(e2, e3)) = op(e1, e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7428])).
% 1.46/1.60 tff(7430,plain,
% 1.46/1.60 (e2 = op(e2, e3)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7428])).
% 1.46/1.60 tff(7431,plain,
% 1.46/1.60 (op(e1, e1) = op(e2, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7423, 7430])).
% 1.46/1.60 tff(7432,plain,
% 1.46/1.60 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7431])).
% 1.46/1.60 tff(7433,plain,
% 1.46/1.60 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7432, 7429])).
% 1.46/1.60 tff(7434,plain,
% 1.46/1.60 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7433])).
% 1.46/1.60 tff(7435,plain,
% 1.46/1.60 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7434, 67])).
% 1.46/1.60 tff(7436,plain,
% 1.46/1.60 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7435])).
% 1.46/1.60 tff(7437,plain,
% 1.46/1.60 (op(e2, e2) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[6454, 7417, 1087, 79, 80, 121, 3508])).
% 1.46/1.60 tff(7438,plain,
% 1.46/1.60 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e3)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7437])).
% 1.46/1.60 tff(7439,plain,
% 1.46/1.60 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7438])).
% 1.46/1.60 tff(7440,plain,
% 1.46/1.60 (~(op(e1, e2) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1273, 7439])).
% 1.46/1.60 tff(7441,plain,
% 1.46/1.60 (op(e1, e2) = op(e1, op(e2, e3))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7429])).
% 1.46/1.60 tff(7442,plain,
% 1.46/1.60 ((op(e1, e2) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7441])).
% 1.46/1.60 tff(7443,plain,
% 1.46/1.60 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e2) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7442])).
% 1.46/1.60 tff(7444,plain,
% 1.46/1.60 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7429, 7418])).
% 1.46/1.60 tff(7445,plain,
% 1.46/1.60 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, op(e2, e3)) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7444])).
% 1.46/1.60 tff(7446,plain,
% 1.46/1.60 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7445, 7443])).
% 1.46/1.60 tff(7447,plain,
% 1.46/1.60 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7446])).
% 1.46/1.60 tff(7448,plain,
% 1.46/1.60 (~(op(e1, e2) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1850, 7447])).
% 1.46/1.60 tff(7449,plain,
% 1.46/1.60 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7423])).
% 1.46/1.60 tff(7450,plain,
% 1.46/1.60 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7449, 5762])).
% 1.46/1.60 tff(7451,plain,
% 1.46/1.60 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7450])).
% 1.46/1.60 tff(7452,plain,
% 1.46/1.60 (~(op(e1, e2) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[1604, 7451])).
% 1.46/1.60 tff(7453,plain,
% 1.46/1.60 (op(e1, e2) = e0),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1859, 7452, 7448, 7440])).
% 1.46/1.60 tff(7454,plain,
% 1.46/1.60 (e0 = op(e1, op(e1, e1))),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7453, 7436])).
% 1.46/1.60 tff(7455,plain,
% 1.46/1.60 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7433])).
% 1.46/1.60 tff(7456,plain,
% 1.46/1.60 (op(e1, op(e1, e2)) = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7455])).
% 1.46/1.60 tff(7457,plain,
% 1.46/1.60 (op(e1, e2) = op(e3, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7453, 6444])).
% 1.46/1.60 tff(7458,plain,
% 1.46/1.60 (op(e1, op(e1, e2)) = op(e1, op(e3, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7457])).
% 1.46/1.60 tff(7459,plain,
% 1.46/1.60 (op(e1, op(e3, e3)) = op(e1, op(e1, e2))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7458])).
% 1.46/1.60 tff(7460,plain,
% 1.46/1.60 (op(e1, op(e3, e3)) = op(e1, e0)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[6443])).
% 1.46/1.60 tff(7461,plain,
% 1.46/1.60 (op(e1, e0) = op(e1, op(e3, e3))),
% 1.46/1.60 inference(symmetry,[status(thm)],[7460])).
% 1.46/1.60 tff(7462,plain,
% 1.46/1.60 (op(e1, e0) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[247, 7440, 1291, 7416])).
% 1.46/1.60 tff(7463,plain,
% 1.46/1.60 (e3 = op(e1, e0)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7462])).
% 1.46/1.60 tff(7464,plain,
% 1.46/1.60 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.60 inference(transitivity,[status(thm)],[7463, 7461, 7459, 7456])).
% 1.46/1.60 tff(7465,plain,
% 1.46/1.60 ($false),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2269, 7464, 7454, 7424])).
% 1.46/1.60 tff(7466,plain,((op(e0, e3) = e2) | (op(e1, e1) = e3) | (op(e1, e1) = e0) | (op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.60 tff(7467,plain,
% 1.46/1.60 (op(e1, e1) = e3),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[7466, 7411, 79, 5456, 80, 121, 3508, 7374])).
% 1.46/1.60 tff(7468,plain,
% 1.46/1.60 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, op(e1, e3)))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7467, 7404])).
% 1.46/1.60 tff(7469,plain,
% 1.46/1.60 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, op(e1, e3)) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7468, 7407])).
% 1.46/1.60 tff(7470,plain,
% 1.46/1.60 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7469, 7406])).
% 1.46/1.60 tff(7471,plain,
% 1.46/1.60 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7470])).
% 1.46/1.60 tff(7472,plain,
% 1.46/1.60 (~(op(e3, e1) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[945, 7471])).
% 1.46/1.60 tff(7473,plain,
% 1.46/1.60 (op(e3, e0) = op(e0, e3)),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[6055, 7472, 7375, 7402])).
% 1.46/1.60 tff(7474,plain,
% 1.46/1.60 (op(e3, e0) = e3),
% 1.46/1.60 inference(transitivity,[status(thm)],[7473, 7375])).
% 1.46/1.60 tff(7475,plain,
% 1.46/1.60 ((op(e3, e0) = e2) <=> (e3 = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7474, 7398])).
% 1.46/1.60 tff(7476,plain,
% 1.46/1.60 ((op(e3, e0) = e2) <=> (op(e2, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7475, 112])).
% 1.46/1.60 tff(7477,plain,
% 1.46/1.60 ((op(e2, e3) = e3) <=> (op(e3, e0) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7476])).
% 1.46/1.60 tff(7478,plain,
% 1.46/1.60 ((~(op(e2, e3) = e3)) <=> (~(op(e3, e0) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7477])).
% 1.46/1.60 tff(7479,plain,
% 1.46/1.60 (~(op(e3, e0) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7379, 7478])).
% 1.46/1.60 tff(7480,plain,
% 1.46/1.60 ((op(e3, e3) = e2) <=> (e0 = e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.60 tff(7481,plain,
% 1.46/1.60 ((e0 = e2) <=> (op(e3, e3) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7480])).
% 1.46/1.60 tff(7482,plain,
% 1.46/1.60 ((~(e0 = e2)) <=> (~(op(e3, e3) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7481])).
% 1.46/1.60 tff(7483,plain,
% 1.46/1.60 (~(op(e3, e3) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[14, 7482])).
% 1.46/1.60 tff(7484,plain,
% 1.46/1.60 ((op(e2, e2) = e1) <=> (e3 = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7393, 7388])).
% 1.46/1.60 tff(7485,plain,
% 1.46/1.60 ((op(e2, e2) = e1) <=> (op(e1, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7484, 3230])).
% 1.46/1.60 tff(7486,plain,
% 1.46/1.60 ((op(e1, e3) = e3) <=> (op(e2, e2) = e1)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7485])).
% 1.46/1.60 tff(7487,plain,
% 1.46/1.60 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e2) = e1))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7486])).
% 1.46/1.60 tff(7488,plain,
% 1.46/1.60 ((op(e0, e3) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7375])).
% 1.46/1.60 tff(7489,plain,
% 1.46/1.60 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7488, 3230])).
% 1.46/1.60 tff(7490,plain,
% 1.46/1.60 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7489])).
% 1.46/1.60 tff(7491,plain,
% 1.46/1.60 (~(op(e1, e3) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[64, 7490])).
% 1.46/1.60 tff(7492,plain,
% 1.46/1.60 (~(op(e2, e2) = e1)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7491, 7487])).
% 1.46/1.60 tff(7493,plain,
% 1.46/1.60 ((op(e1, e1) = e2) <=> (e3 = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7467, 7398])).
% 1.46/1.60 tff(7494,plain,
% 1.46/1.60 ((op(e1, e1) = e2) <=> (op(e2, e3) = e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7493, 112])).
% 1.46/1.60 tff(7495,plain,
% 1.46/1.60 ((op(e2, e3) = e3) <=> (op(e1, e1) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7494])).
% 1.46/1.60 tff(7496,plain,
% 1.46/1.60 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e1) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7495])).
% 1.46/1.60 tff(7497,plain,
% 1.46/1.60 (~(op(e1, e1) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7379, 7496])).
% 1.46/1.60 tff(7498,plain,
% 1.46/1.60 (op(e2, op(e1, e3)) = op(e2, e1)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7387])).
% 1.46/1.60 tff(7499,plain,
% 1.46/1.60 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7393])).
% 1.46/1.60 tff(7500,plain,
% 1.46/1.60 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7499])).
% 1.46/1.60 tff(7501,plain,
% 1.46/1.60 (~(op(e2, e0) = e3)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[2228, 7500])).
% 1.46/1.60 tff(7502,plain,
% 1.46/1.60 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7398])).
% 1.46/1.60 tff(7503,plain,
% 1.46/1.60 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.46/1.60 inference(symmetry,[status(thm)],[7502])).
% 1.46/1.60 tff(7504,plain,
% 1.46/1.60 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7503])).
% 1.46/1.60 tff(7505,plain,
% 1.46/1.60 (~(op(e2, e0) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[989, 7504])).
% 1.46/1.60 tff(7506,plain,
% 1.46/1.60 (op(e2, e0) = e1),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[765, 7505, 7501, 5643])).
% 1.46/1.60 tff(7507,plain,
% 1.46/1.60 (op(e2, e0) = op(e1, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7506, 7388])).
% 1.46/1.60 tff(7508,plain,
% 1.46/1.60 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7507])).
% 1.46/1.60 tff(7509,plain,
% 1.46/1.60 (op(e2, op(e2, e0)) = e0),
% 1.46/1.60 inference(transitivity,[status(thm)],[7508, 7498, 3508])).
% 1.46/1.60 tff(7510,plain,
% 1.46/1.60 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2653, 7509])).
% 1.46/1.60 tff(7511,plain,
% 1.46/1.60 (op(e3, op(e3, e0)) = op(e3, e3)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7474])).
% 1.46/1.60 tff(7512,plain,
% 1.46/1.60 (op(e3, op(e3, e0)) = e0),
% 1.46/1.60 inference(transitivity,[status(thm)],[7511, 7366])).
% 1.46/1.60 tff(7513,plain,
% 1.46/1.60 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1345, 7512])).
% 1.46/1.60 tff(7514,plain,
% 1.46/1.60 (op(e2, op(e2, e1)) = e1),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[7506, 6159])).
% 1.46/1.60 tff(7515,plain,
% 1.46/1.60 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1355, 7514])).
% 1.46/1.60 tff(7516,plain,
% 1.46/1.60 (op(e3, e2) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2015, 82, 126, 3786])).
% 1.46/1.60 tff(7517,plain,
% 1.46/1.60 (op(e3, e2) = op(e2, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7516, 3797])).
% 1.46/1.60 tff(7518,plain,
% 1.46/1.60 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7517])).
% 1.46/1.60 tff(7519,plain,
% 1.46/1.60 (op(e3, op(e3, e2)) = e2),
% 1.46/1.60 inference(transitivity,[status(thm)],[7518, 3817, 7516])).
% 1.46/1.60 tff(7520,plain,
% 1.46/1.60 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1904, 7519])).
% 1.46/1.60 tff(7521,plain,
% 1.46/1.60 (op(e3, e1) = e1),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[446, 82, 5474, 2839])).
% 1.46/1.60 tff(7522,plain,
% 1.46/1.60 (op(e3, e1) = op(e1, e3)),
% 1.46/1.60 inference(transitivity,[status(thm)],[7521, 3710])).
% 1.46/1.60 tff(7523,plain,
% 1.46/1.60 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7522])).
% 1.46/1.60 tff(7524,plain,
% 1.46/1.60 (op(e3, op(e3, e1)) = e1),
% 1.46/1.60 inference(transitivity,[status(thm)],[7523, 3831, 7521])).
% 1.46/1.60 tff(7525,plain,
% 1.46/1.60 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2594, 7524])).
% 1.46/1.60 tff(7526,plain,
% 1.46/1.60 (op(e0, e1) = e2),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1993, 82, 68, 5515])).
% 1.46/1.60 tff(7527,plain,
% 1.46/1.60 (op(op(e0, e1), e1) = op(e2, op(e1, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7526, 3710])).
% 1.46/1.60 tff(7528,plain,
% 1.46/1.60 (op(op(e0, e1), e1) = e0),
% 1.46/1.60 inference(transitivity,[status(thm)],[7527, 3796, 3508])).
% 1.46/1.60 tff(7529,plain,
% 1.46/1.60 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[2650, 7528])).
% 1.46/1.60 tff(7530,plain,
% 1.46/1.60 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7516])).
% 1.46/1.60 tff(7531,plain,
% 1.46/1.60 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[7530])).
% 1.46/1.60 tff(7532,plain,
% 1.46/1.60 (~(op(e1, e2) = e2)),
% 1.46/1.60 inference(modus_ponens,[status(thm)],[2292, 7531])).
% 1.46/1.60 tff(7533,plain,
% 1.46/1.60 (op(e1, e2) = e0),
% 1.46/1.60 inference(unit_resolution,[status(thm)],[1859, 7532, 75, 6147])).
% 1.46/1.60 tff(7534,plain,
% 1.46/1.60 (op(e1, op(e2, e3)) = op(e1, e2)),
% 1.46/1.60 inference(monotonicity,[status(thm)],[3787])).
% 1.46/1.60 tff(7535,plain,
% 1.46/1.60 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e2, e3))),
% 1.46/1.60 inference(monotonicity,[status(thm)],[3797])).
% 1.46/1.61 tff(7536,plain,
% 1.46/1.61 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e2)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7535])).
% 1.46/1.61 tff(7537,plain,
% 1.46/1.61 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7536])).
% 1.46/1.61 tff(7538,plain,
% 1.46/1.61 (~(op(e1, e3) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[118, 7537])).
% 1.46/1.61 tff(7539,plain,
% 1.46/1.61 (op(e1, e0) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2285, 7532, 7538, 68])).
% 1.46/1.61 tff(7540,plain,
% 1.46/1.61 (op(e1, e0) = op(e2, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7539, 3797])).
% 1.46/1.61 tff(7541,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7540])).
% 1.46/1.61 tff(7542,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = e0),
% 1.46/1.61 inference(transitivity,[status(thm)],[7541, 7534, 7533])).
% 1.46/1.61 tff(7543,plain,
% 1.46/1.61 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1836, 7542])).
% 1.46/1.61 tff(7544,plain,
% 1.46/1.61 ((op(e3, e2) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7517, 3710])).
% 1.46/1.61 tff(7545,plain,
% 1.46/1.61 ((op(e3, e2) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.46/1.61 inference(transitivity,[status(thm)],[7544, 1687])).
% 1.46/1.61 tff(7546,plain,
% 1.46/1.61 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7545])).
% 1.46/1.61 tff(7547,plain,
% 1.46/1.61 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e2) = e1))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7546])).
% 1.46/1.61 tff(7548,plain,
% 1.46/1.61 (~(op(e3, e2) = e1)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[118, 7547])).
% 1.46/1.61 tff(7549,plain,
% 1.46/1.61 (op(e0, e2) = e1),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1613, 7548, 6147, 1348])).
% 1.46/1.61 tff(7550,plain,
% 1.46/1.61 (op(e0, e2) = op(e1, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7549, 3710])).
% 1.46/1.61 tff(7551,plain,
% 1.46/1.61 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7550])).
% 1.46/1.61 tff(7552,plain,
% 1.46/1.61 (op(e0, op(e0, e2)) = e2),
% 1.46/1.61 inference(transitivity,[status(thm)],[7551, 3788, 7526])).
% 1.46/1.61 tff(7553,plain,
% 1.46/1.61 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1331, 7552])).
% 1.46/1.61 tff(7554,plain,
% 1.46/1.61 (op(e1, op(e1, e2)) = op(e1, e0)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7533])).
% 1.46/1.61 tff(7555,plain,
% 1.46/1.61 (op(e1, op(e1, e2)) = e2),
% 1.46/1.61 inference(transitivity,[status(thm)],[7554, 7539])).
% 1.46/1.61 tff(7556,plain,
% 1.46/1.61 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2377, 7555])).
% 1.46/1.61 tff(7557,plain,
% 1.46/1.61 ($false),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1459, 7556, 7553, 1936, 1926, 3342, 1304, 7543, 2421, 7529, 7525, 7520, 3869])).
% 1.46/1.61 tff(7558,plain,((op(e3, e1) = e2) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~(op(e2, e3) = e2)) | (~(op(e1, e3) = e1)) | (op(e1, e2) = e3) | (op(e1, e1) = e2) | (op(e2, e2) = e1) | (~(op(e2, e1) = e0)) | (op(e3, e1) = e3) | (op(e3, e3) = e2) | (op(e3, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.61 tff(7559,plain,
% 1.46/1.61 (op(e3, e1) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[7558, 7515, 7513, 5469, 5475, 7510, 7397, 7387, 7396, 7497, 7492, 3508, 7472, 7483, 7479])).
% 1.46/1.61 tff(7560,plain,
% 1.46/1.61 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7398])).
% 1.46/1.61 tff(7561,plain,
% 1.46/1.61 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7560])).
% 1.46/1.61 tff(7562,plain,
% 1.46/1.61 (op(e3, e1) = op(e2, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7559, 7398])).
% 1.46/1.61 tff(7563,plain,
% 1.46/1.61 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7562])).
% 1.46/1.61 tff(7564,plain,
% 1.46/1.61 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 1.46/1.61 inference(transitivity,[status(thm)],[7563, 394])).
% 1.46/1.61 tff(7565,plain,
% 1.46/1.61 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7564, 7561])).
% 1.46/1.61 tff(7566,plain,
% 1.46/1.61 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7565])).
% 1.46/1.61 tff(7567,plain,
% 1.46/1.61 (~(op(e3, e2) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[3429, 7566])).
% 1.46/1.61 tff(7568,plain,
% 1.46/1.61 (op(e3, e2) = e1),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1898, 7567, 7382, 7402])).
% 1.46/1.61 tff(7569,plain,
% 1.46/1.61 (op(e3, e2) = op(e1, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7568, 7388])).
% 1.46/1.61 tff(7570,plain,
% 1.46/1.61 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7569])).
% 1.46/1.61 tff(7571,plain,
% 1.46/1.61 (op(e3, op(e3, e2)) = e2),
% 1.46/1.61 inference(transitivity,[status(thm)],[7570, 7403, 7559])).
% 1.46/1.61 tff(7572,plain,
% 1.46/1.61 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1904, 7571])).
% 1.46/1.61 tff(7573,plain,
% 1.46/1.61 (op(op(e2, e3), e3) = op(e2, e3)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7397])).
% 1.46/1.61 tff(7574,plain,
% 1.46/1.61 (op(op(e3, e1), e3) = op(op(e2, e3), e3)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7562])).
% 1.46/1.61 tff(7575,plain,
% 1.46/1.61 (op(op(e3, e1), e3) = op(e2, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7574, 7573])).
% 1.46/1.61 tff(7576,plain,
% 1.46/1.61 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7575, 7388])).
% 1.46/1.61 tff(7577,plain,
% 1.46/1.61 ((op(op(e3, e1), e3) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.46/1.61 inference(transitivity,[status(thm)],[7576, 1687])).
% 1.46/1.61 tff(7578,plain,
% 1.46/1.61 ((op(e1, e3) = op(e2, e3)) <=> (op(op(e3, e1), e3) = e1)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7577])).
% 1.46/1.61 tff(7579,plain,
% 1.46/1.61 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7578])).
% 1.46/1.61 tff(7580,plain,
% 1.46/1.61 (~(op(op(e3, e1), e3) = e1)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[118, 7579])).
% 1.46/1.61 tff(7581,plain,
% 1.46/1.61 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1050, 7580])).
% 1.46/1.61 tff(7582,plain,
% 1.46/1.61 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7375])).
% 1.46/1.61 tff(7583,plain,
% 1.46/1.61 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7582])).
% 1.46/1.61 tff(7584,plain,
% 1.46/1.61 (~(op(e0, e1) = e3)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[818, 7583])).
% 1.46/1.61 tff(7585,plain,
% 1.46/1.61 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7559])).
% 1.46/1.61 tff(7586,plain,
% 1.46/1.61 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7585])).
% 1.46/1.61 tff(7587,plain,
% 1.46/1.61 (~(op(e0, e1) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[3046, 7586])).
% 1.46/1.61 tff(7588,plain,
% 1.46/1.61 (op(e0, e1) = e1),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[829, 7587, 5478, 7584])).
% 1.46/1.61 tff(7589,plain,
% 1.46/1.61 (op(e0, op(e1, e3)) = op(e0, e1)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7387])).
% 1.46/1.61 tff(7590,plain,
% 1.46/1.61 (op(e0, e1) = op(e1, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7588, 7388])).
% 1.46/1.61 tff(7591,plain,
% 1.46/1.61 (op(e0, op(e0, e1)) = op(e0, op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7590])).
% 1.46/1.61 tff(7592,plain,
% 1.46/1.61 (op(e0, op(e0, e1)) = e1),
% 1.46/1.61 inference(transitivity,[status(thm)],[7591, 7589, 7588])).
% 1.46/1.61 tff(7593,plain,
% 1.46/1.61 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2449, 7592])).
% 1.46/1.61 tff(7594,plain,
% 1.46/1.61 (op(e1, e0) = e0),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1830, 1947, 80, 84])).
% 1.46/1.61 tff(7595,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7594])).
% 1.46/1.61 tff(7596,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = e0),
% 1.46/1.61 inference(transitivity,[status(thm)],[7595, 7594])).
% 1.46/1.61 tff(7597,plain,
% 1.46/1.61 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1836, 7596])).
% 1.46/1.61 tff(7598,plain,
% 1.46/1.61 (op(e0, e2) = e0),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[973, 1947, 17, 85])).
% 1.46/1.61 tff(7599,plain,
% 1.46/1.61 (op(op(e0, e2), e2) = op(e0, op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7598, 3797])).
% 1.46/1.61 tff(7600,plain,
% 1.46/1.61 (op(op(e0, e2), e2) = e0),
% 1.46/1.61 inference(transitivity,[status(thm)],[7599, 3870, 7598])).
% 1.46/1.61 tff(7601,plain,
% 1.46/1.61 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1956, 7600])).
% 1.46/1.61 tff(7602,plain,
% 1.46/1.61 (op(e1, e2) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1859, 1947, 75, 4515])).
% 1.46/1.61 tff(7603,plain,
% 1.46/1.61 (op(e1, e2) = op(e2, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7602, 3797])).
% 1.46/1.61 tff(7604,plain,
% 1.46/1.61 (op(e1, op(e1, e2)) = op(e1, op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7603])).
% 1.46/1.61 tff(7605,plain,
% 1.46/1.61 (op(e1, op(e1, e2)) = e2),
% 1.46/1.61 inference(transitivity,[status(thm)],[7604, 7534, 7602])).
% 1.46/1.61 tff(7606,plain,
% 1.46/1.61 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2377, 7605])).
% 1.46/1.61 tff(7607,plain,
% 1.46/1.61 ($false),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1459, 7606, 7601, 1936, 1926, 3342, 1304, 7597, 2421, 4549, 1275, 3341, 3869])).
% 1.46/1.61 tff(7608,plain,((op(e1, e2) = e0) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e2, e3) = e2)) | (op(e1, e2) = e3) | (op(e1, e2) = e1) | (op(e2, e2) = e0) | (op(e3, e2) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.61 tff(7609,plain,
% 1.46/1.61 (op(e1, e2) = e0),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[7608, 7515, 7513, 5469, 5475, 7510, 7593, 7581, 7572, 7397, 7396, 7392, 5552, 7382, 80, 5456])).
% 1.46/1.61 tff(7610,plain,
% 1.46/1.61 (op(e1, op(e2, e3)) = op(e1, e2)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7397])).
% 1.46/1.61 tff(7611,plain,
% 1.46/1.61 ((op(e1, e2) = e2) <=> (e0 = op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7609, 7398])).
% 1.46/1.61 tff(7612,plain,
% 1.46/1.61 ((op(e1, e2) = e2) <=> (op(e2, e3) = e0)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7611, 86])).
% 1.46/1.61 tff(7613,plain,
% 1.46/1.61 ((op(e2, e3) = e0) <=> (op(e1, e2) = e2)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7612])).
% 1.46/1.61 tff(7614,plain,
% 1.46/1.61 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e2) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7613])).
% 1.46/1.61 tff(7615,plain,
% 1.46/1.61 (~(op(e1, e2) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[5446, 7614])).
% 1.46/1.61 tff(7616,plain,
% 1.46/1.61 (op(e1, e0) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2285, 7615, 7411, 7497])).
% 1.46/1.61 tff(7617,plain,
% 1.46/1.61 (op(e1, e0) = op(e2, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7616, 7398])).
% 1.46/1.61 tff(7618,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7617])).
% 1.46/1.61 tff(7619,plain,
% 1.46/1.61 (op(e1, op(e1, e0)) = e0),
% 1.46/1.61 inference(transitivity,[status(thm)],[7618, 7610, 7609])).
% 1.46/1.61 tff(7620,plain,
% 1.46/1.61 (op(op(e1, e2), e1) = op(e0, op(e1, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7609, 7388])).
% 1.46/1.61 tff(7621,plain,
% 1.46/1.61 (op(op(e1, e2), e1) = op(e1, e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7620, 7589, 7588, 7388])).
% 1.46/1.61 tff(7622,plain,
% 1.46/1.61 ((op(op(e1, e2), e1) = e2) <=> (op(e1, e3) = op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7621, 7398])).
% 1.46/1.61 tff(7623,plain,
% 1.46/1.61 ((op(e1, e3) = op(e2, e3)) <=> (op(op(e1, e2), e1) = e2)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7622])).
% 1.46/1.61 tff(7624,plain,
% 1.46/1.61 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7623])).
% 1.46/1.61 tff(7625,plain,
% 1.46/1.61 (~(op(op(e1, e2), e1) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[118, 7624])).
% 1.46/1.61 tff(7626,plain,
% 1.46/1.61 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[5959, 7625])).
% 1.46/1.61 tff(7627,plain,
% 1.46/1.61 (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[3878, 7626, 7387, 7397, 7479, 5475, 5469, 7506, 7515, 7513, 7510, 7584, 5478, 7567, 7483, 7581, 7382, 7402, 7615])).
% 1.46/1.61 tff(7628,plain,
% 1.46/1.61 (~(op(e1, op(e1, e0)) = e0)),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1836, 7627])).
% 1.46/1.61 tff(7629,plain,
% 1.46/1.61 ($false),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[7628, 7619])).
% 1.46/1.61 tff(7630,plain,((op(e2, e3) = e1) | (op(e1, e3) = e0) | (~(op(e2, e1) = e0)) | (op(e0, e3) = e2) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.61 tff(7631,plain,
% 1.46/1.61 (op(e2, e3) = e1),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[7630, 3508, 80, 79, 121])).
% 1.46/1.61 tff(7632,plain,
% 1.46/1.61 (~(op(e2, e2) = e3)),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[6638, 7631, 3508])).
% 1.46/1.61 tff(7633,plain,
% 1.46/1.61 (op(e2, e2) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[7007, 7632, 3508, 7379])).
% 1.46/1.61 tff(7634,plain,
% 1.46/1.61 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7633])).
% 1.46/1.61 tff(7635,plain,
% 1.46/1.61 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7634, 2234])).
% 1.46/1.61 tff(7636,plain,
% 1.46/1.61 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7635])).
% 1.46/1.61 tff(7637,plain,
% 1.46/1.61 (~(op(e3, e2) = e2)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[1546, 7636])).
% 1.46/1.61 tff(7638,plain,
% 1.46/1.61 ((op(e3, e3) = e3) <=> (e0 = e3)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7366])).
% 1.46/1.61 tff(7639,plain,
% 1.46/1.61 ((e0 = e3) <=> (op(e3, e3) = e3)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7638])).
% 1.46/1.61 tff(7640,plain,
% 1.46/1.61 ((~(e0 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7639])).
% 1.46/1.61 tff(7641,plain,
% 1.46/1.61 (~(op(e3, e3) = e3)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[181, 7640])).
% 1.46/1.61 tff(7642,plain,
% 1.46/1.61 (op(e2, e0) = e3),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[1559, 7632, 5487, 7379])).
% 1.46/1.61 tff(7643,plain,
% 1.46/1.61 ((op(e2, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7642])).
% 1.46/1.61 tff(7644,plain,
% 1.46/1.61 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7643, 404])).
% 1.46/1.61 tff(7645,plain,
% 1.46/1.61 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7644])).
% 1.46/1.61 tff(7646,plain,
% 1.46/1.61 (~(op(e3, e0) = e3)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[747, 7645])).
% 1.46/1.61 tff(7647,plain,
% 1.46/1.61 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7375])).
% 1.46/1.61 tff(7648,plain,
% 1.46/1.61 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7647])).
% 1.46/1.61 tff(7649,plain,
% 1.46/1.61 (~(op(e0, e2) = e3)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[918, 7648])).
% 1.46/1.61 tff(7650,plain,
% 1.46/1.61 (~(op(e1, e3) = e1)),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[6454, 7632, 79, 7374, 80, 121, 3508])).
% 1.46/1.61 tff(7651,plain,
% 1.46/1.61 (op(e1, e3) = e2),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[104, 7650, 80, 7491])).
% 1.46/1.61 tff(7652,plain,
% 1.46/1.61 ((e1 = op(e3, op(e3, e3))) <=> (e1 = op(e3, e0))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[3067])).
% 1.46/1.61 tff(7653,plain,
% 1.46/1.61 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e1)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7652, 6411])).
% 1.46/1.61 tff(7654,plain,
% 1.46/1.61 ((op(e3, e0) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 1.46/1.61 inference(symmetry,[status(thm)],[7653])).
% 1.46/1.61 tff(7655,plain,
% 1.46/1.61 (~(op(e2, e2) = e3)),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[6638, 2684, 3508])).
% 1.46/1.61 tff(7656,plain,
% 1.46/1.61 (op(e3, e2) = e3),
% 1.46/1.61 inference(unit_resolution,[status(thm)],[2111, 75, 4412, 7655])).
% 1.46/1.61 tff(7657,plain,
% 1.46/1.61 ((op(e3, e2) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7656])).
% 1.46/1.61 tff(7658,plain,
% 1.46/1.61 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.46/1.61 inference(transitivity,[status(thm)],[7657, 112])).
% 1.46/1.61 tff(7659,plain,
% 1.46/1.61 ((op(e2, e3) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 1.46/1.61 inference(symmetry,[status(thm)],[7658])).
% 1.46/1.61 tff(7660,plain,
% 1.46/1.61 ((~(op(e2, e3) = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7659])).
% 1.46/1.61 tff(7661,plain,
% 1.46/1.61 (~(op(e3, e2) = op(e2, e3))),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[124, 7660])).
% 1.46/1.61 tff(7662,plain,
% 1.46/1.61 ((op(e3, e3) = e1) <=> (e0 = e1)),
% 1.46/1.61 inference(monotonicity,[status(thm)],[3066])).
% 1.46/1.61 tff(7663,plain,
% 1.46/1.61 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 1.46/1.61 inference(symmetry,[status(thm)],[7662])).
% 1.46/1.61 tff(7664,plain,
% 1.46/1.61 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 1.46/1.61 inference(monotonicity,[status(thm)],[7663])).
% 1.46/1.61 tff(7665,plain,
% 1.46/1.61 (~(op(e3, e3) = e1)),
% 1.46/1.61 inference(modus_ponens,[status(thm)],[26, 7664])).
% 1.46/1.61 tff(7666,plain,
% 1.46/1.61 ((op(e3, e1) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 1.46/1.61 inference(transitivity,[status(thm)],[1972, 6290])).
% 1.46/1.62 tff(7667,plain,
% 1.46/1.62 (op(e2, e2) = e2),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[7007, 7655, 3508, 124])).
% 1.46/1.62 tff(7668,plain,
% 1.46/1.62 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7667])).
% 1.46/1.62 tff(7669,plain,
% 1.46/1.62 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7668, 2234])).
% 1.46/1.62 tff(7670,plain,
% 1.46/1.62 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7669])).
% 1.46/1.62 tff(7671,plain,
% 1.46/1.62 (~(op(e3, e2) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[1546, 7670])).
% 1.46/1.62 tff(7672,plain,
% 1.46/1.62 ((op(e3, e3) = e2) <=> (e0 = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[3066])).
% 1.46/1.62 tff(7673,plain,
% 1.46/1.62 ((e0 = e2) <=> (op(e3, e3) = e2)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7672])).
% 1.46/1.62 tff(7674,plain,
% 1.46/1.62 ((~(e0 = e2)) <=> (~(op(e3, e3) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7673])).
% 1.46/1.62 tff(7675,plain,
% 1.46/1.62 (~(op(e3, e3) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[14, 7674])).
% 1.46/1.62 tff(7676,plain,
% 1.46/1.62 ((op(e3, e1) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[2833])).
% 1.46/1.62 tff(7677,plain,
% 1.46/1.62 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e1) = e3)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7676])).
% 1.46/1.62 tff(7678,plain,
% 1.46/1.62 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, op(e2, e3)) = e3)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[2833, 7656])).
% 1.46/1.62 tff(7679,plain,
% 1.46/1.62 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7678, 7677])).
% 1.46/1.62 tff(7680,plain,
% 1.46/1.62 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7679])).
% 1.46/1.62 tff(7681,plain,
% 1.46/1.62 (~(op(e3, e1) = e3)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[3429, 7680])).
% 1.46/1.62 tff(7682,plain,
% 1.46/1.62 (op(e2, e0) = e3),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1559, 7655, 5487, 124])).
% 1.46/1.62 tff(7683,plain,
% 1.46/1.62 (op(op(e3, e2), e2) = op(e3, e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7656])).
% 1.46/1.62 tff(7684,plain,
% 1.46/1.62 (op(op(e3, e2), e2) = e3),
% 1.46/1.62 inference(transitivity,[status(thm)],[7683, 7656])).
% 1.46/1.62 tff(7685,plain,
% 1.46/1.62 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1339, 7684])).
% 1.46/1.62 tff(7686,plain,
% 1.46/1.62 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e3)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7682])).
% 1.46/1.62 tff(7687,plain,
% 1.46/1.62 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7686])).
% 1.46/1.62 tff(7688,plain,
% 1.46/1.62 (~(op(e1, e0) = e3)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[756, 7687])).
% 1.46/1.62 tff(7689,plain,
% 1.46/1.62 (op(e1, e1) = e3),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[247, 75, 7688, 1080])).
% 1.46/1.62 tff(7690,plain,
% 1.46/1.62 (op(e1, op(e1, e1)) = op(op(e2, e3), e3)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[2685, 7689])).
% 1.46/1.62 tff(7691,plain,
% 1.46/1.62 (op(e1, op(e1, e1)) = e2),
% 1.46/1.62 inference(transitivity,[status(thm)],[7690, 4481, 264])).
% 1.46/1.62 tff(7692,plain,
% 1.46/1.62 (op(e1, op(e1, op(e1, e1))) = op(op(e2, e3), e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[2685, 7691])).
% 1.46/1.62 tff(7693,plain,
% 1.46/1.62 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7692, 2897])).
% 1.46/1.62 tff(7694,plain,
% 1.46/1.62 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7693])).
% 1.46/1.62 tff(7695,plain,
% 1.46/1.62 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7694, 67])).
% 1.46/1.62 tff(7696,plain,
% 1.46/1.62 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7695])).
% 1.46/1.62 tff(7697,plain,
% 1.46/1.62 (e3 = op(e1, e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7689, 1740])).
% 1.46/1.62 tff(7698,plain,
% 1.46/1.62 (op(op(e2, e3), e3) = op(e1, op(e1, e1))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7690])).
% 1.46/1.62 tff(7699,plain,
% 1.46/1.62 (op(e1, e3) = op(op(e2, e3), e3)),
% 1.46/1.62 inference(symmetry,[status(thm)],[4481])).
% 1.46/1.62 tff(7700,plain,
% 1.46/1.62 (e2 = op(e1, op(e1, e1))),
% 1.46/1.62 inference(transitivity,[status(thm)],[265, 7699, 7698])).
% 1.46/1.62 tff(7701,plain,
% 1.46/1.62 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1753, 7700, 7697])).
% 1.46/1.62 tff(7702,plain,
% 1.46/1.62 (~(op(e1, e2) = e0)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7701, 7696])).
% 1.46/1.62 tff(7703,plain,
% 1.46/1.62 (op(e0, e2) = e0),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[973, 7702, 5552, 3099])).
% 1.46/1.62 tff(7704,plain,
% 1.46/1.62 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7703])).
% 1.46/1.62 tff(7705,plain,
% 1.46/1.62 (op(op(e0, e2), e2) = e0),
% 1.46/1.62 inference(transitivity,[status(thm)],[7704, 7703])).
% 1.46/1.62 tff(7706,plain,
% 1.46/1.62 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1956, 7705])).
% 1.46/1.62 tff(7707,plain,
% 1.46/1.62 (op(op(e2, e0), e2) = op(e3, e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7682])).
% 1.46/1.62 tff(7708,plain,
% 1.46/1.62 ((op(op(e2, e0), e2) = e0) <=> (op(e3, e2) = e0)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7707])).
% 1.46/1.62 tff(7709,plain,
% 1.46/1.62 ((op(e3, e2) = e0) <=> (op(op(e2, e0), e2) = e0)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7708])).
% 1.46/1.62 tff(7710,plain,
% 1.46/1.62 ((~(op(e3, e2) = e0)) <=> (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7709])).
% 1.46/1.62 tff(7711,plain,
% 1.46/1.62 (~(op(op(e2, e0), e2) = e0)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[3099, 7710])).
% 1.46/1.62 tff(7712,plain,
% 1.46/1.62 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1379, 7711])).
% 1.46/1.62 tff(7713,plain,
% 1.46/1.62 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7667])).
% 1.46/1.62 tff(7714,plain,
% 1.46/1.62 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7713])).
% 1.46/1.62 tff(7715,plain,
% 1.46/1.62 (~(op(e1, e2) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[1273, 7714])).
% 1.46/1.62 tff(7716,plain,
% 1.46/1.62 (op(e1, e2) = e1),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1859, 7702, 7715, 75])).
% 1.46/1.62 tff(7717,plain,
% 1.46/1.62 (op(e1, e2) = op(e2, e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7716, 2685])).
% 1.46/1.62 tff(7718,plain,
% 1.46/1.62 (op(op(e1, e2), e2) = op(op(e2, e3), e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7717])).
% 1.46/1.62 tff(7719,plain,
% 1.46/1.62 (op(op(e1, e2), e2) = e1),
% 1.46/1.62 inference(transitivity,[status(thm)],[7718, 2897, 7716])).
% 1.46/1.62 tff(7720,plain,
% 1.46/1.62 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1335, 7719])).
% 1.46/1.62 tff(7721,plain,
% 1.46/1.62 (op(e1, e0) = e0),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1830, 7702, 80, 5456])).
% 1.46/1.62 tff(7722,plain,
% 1.46/1.62 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7721])).
% 1.46/1.62 tff(7723,plain,
% 1.46/1.62 (op(e1, op(e1, e0)) = e0),
% 1.46/1.62 inference(transitivity,[status(thm)],[7722, 7721])).
% 1.46/1.62 tff(7724,plain,
% 1.46/1.62 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1836, 7723])).
% 1.46/1.62 tff(7725,plain,
% 1.46/1.62 ((op(e0, e2) = e1) <=> (e0 = op(e2, e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7703, 2685])).
% 1.46/1.62 tff(7726,plain,
% 1.46/1.62 ((op(e0, e2) = e1) <=> (op(e2, e3) = e0)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7725, 86])).
% 1.46/1.62 tff(7727,plain,
% 1.46/1.62 ((op(e2, e3) = e0) <=> (op(e0, e2) = e1)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7726])).
% 1.46/1.62 tff(7728,plain,
% 1.46/1.62 ((op(e2, e3) = e0) <=> (op(op(e2, e1), e2) = e1)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7727, 5799])).
% 1.46/1.62 tff(7729,plain,
% 1.46/1.62 ((~(op(e2, e3) = e0)) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7728])).
% 1.46/1.62 tff(7730,plain,
% 1.46/1.62 (~(op(op(e2, e1), e2) = e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[5446, 7729])).
% 1.46/1.62 tff(7731,plain,
% 1.46/1.62 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[5808, 7730])).
% 1.46/1.62 tff(7732,plain,
% 1.46/1.62 (op(e3, e1) = op(e2, e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7521, 2685])).
% 1.46/1.62 tff(7733,plain,
% 1.46/1.62 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7732])).
% 1.46/1.62 tff(7734,plain,
% 1.46/1.62 (op(e3, op(e3, e1)) = e1),
% 1.46/1.62 inference(transitivity,[status(thm)],[7733, 2832, 7521])).
% 1.46/1.62 tff(7735,plain,
% 1.46/1.62 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2594, 7734])).
% 1.46/1.62 tff(7736,assumption,(op(e2, e0) = e3), introduced(assumption)).
% 1.46/1.62 tff(7737,plain,
% 1.46/1.62 (op(e3, e0) = e2),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2015, 82, 126, 2386])).
% 1.46/1.62 tff(7738,plain,
% 1.46/1.62 (op(op(e3, e0), e0) = op(e2, e0)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7737])).
% 1.46/1.62 tff(7739,plain,
% 1.46/1.62 (op(op(e3, e0), e0) = e3),
% 1.46/1.62 inference(transitivity,[status(thm)],[7738, 7736])).
% 1.46/1.62 tff(7740,plain,
% 1.46/1.62 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[4026, 7739])).
% 1.46/1.62 tff(7741,plain,
% 1.46/1.62 (op(op(e0, e1), e1) = op(e2, op(e2, e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7526, 2685])).
% 1.46/1.62 tff(7742,plain,
% 1.46/1.62 (op(op(e0, e1), e1) = e0),
% 1.46/1.62 inference(transitivity,[status(thm)],[7741, 6634, 3508])).
% 1.46/1.62 tff(7743,plain,
% 1.46/1.62 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2650, 7742])).
% 1.46/1.62 tff(7744,plain,
% 1.46/1.62 ($false),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1459, 7743, 7740, 1936, 1357, 3342, 1304, 1358, 2421, 1363, 7735, 3341, 1347])).
% 1.46/1.62 tff(7745,plain,((op(e3, e1) = e2) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e2, e3) = e1)) | (~(op(e2, e1) = e0)) | (~(op(e2, e0) = e3)) | (op(e3, e1) = e3) | (op(e1, e1) = e2) | (op(e3, e3) = e2) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.62 tff(7746,plain,
% 1.46/1.62 (op(e3, e1) = e2),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[7745, 7731, 7724, 3342, 1304, 7720, 7712, 7706, 7685, 4483, 2684, 3508, 7682, 7681, 741, 7675, 7671])).
% 1.46/1.62 tff(7747,plain,
% 1.46/1.62 (op(e1, e3) = op(e3, e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7746, 7666])).
% 1.46/1.62 tff(7748,assumption,(op(e1, e3) = op(e3, e1)), introduced(assumption)).
% 1.46/1.62 tff(7749,plain,
% 1.46/1.62 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e1) = e1)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7748, 2684])).
% 1.46/1.62 tff(7750,plain,
% 1.46/1.62 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e1))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7749])).
% 1.46/1.62 tff(7751,plain,
% 1.46/1.62 (~(op(e3, e1) = e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[118, 7750])).
% 1.46/1.62 tff(7752,plain,
% 1.46/1.62 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[2684])).
% 1.46/1.62 tff(7753,plain,
% 1.46/1.62 ((~(op(e3, e2) = op(e2, e3))) <=> (~(op(e3, e2) = e1))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7752])).
% 1.46/1.62 tff(7754,assumption,(~(op(e3, e2) = op(e2, e3))), introduced(assumption)).
% 1.46/1.62 tff(7755,plain,
% 1.46/1.62 (~(op(e3, e2) = e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 1.46/1.62 tff(7756,plain,
% 1.46/1.62 ($false),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[939, 7755, 7751, 931, 926])).
% 1.46/1.62 tff(7757,plain,((~(op(e2, e3) = e1)) | (op(e3, e0) = e1) | (op(e3, e3) = e1) | (op(e3, e2) = op(e2, e3)) | (~(op(e1, e3) = op(e3, e1)))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.62 tff(7758,plain,
% 1.46/1.62 (op(e3, e0) = e1),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[7757, 7747, 7665, 2684, 7661])).
% 1.46/1.62 tff(7759,plain,
% 1.46/1.62 (e1 = op(e3, op(e3, e3))),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7758, 7654])).
% 1.46/1.62 tff(7760,plain,
% 1.46/1.62 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[3067])).
% 1.46/1.62 tff(7761,plain,
% 1.46/1.62 (op(e3, op(e3, e0)) = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7760])).
% 1.46/1.62 tff(7762,plain,
% 1.46/1.62 (op(e3, e0) = op(e2, e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7758, 2685])).
% 1.46/1.62 tff(7763,plain,
% 1.46/1.62 (op(e3, op(e3, e0)) = op(e3, op(e2, e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7762])).
% 1.46/1.62 tff(7764,plain,
% 1.46/1.62 (op(e3, op(e2, e3)) = op(e3, op(e3, e0))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7763])).
% 1.46/1.62 tff(7765,plain,
% 1.46/1.62 (e2 = op(e3, e1)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7746])).
% 1.46/1.62 tff(7766,plain,
% 1.46/1.62 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.62 inference(transitivity,[status(thm)],[7765, 2833, 7764, 7761])).
% 1.46/1.62 tff(7767,plain,
% 1.46/1.62 ($false),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[5193, 7766, 7759, 3079])).
% 1.46/1.62 tff(7768,plain,((op(e1, e2) = e3) | (~(op(e2, e3) = e1)) | (~(op(e3, e3) = e0)) | (~(op(e1, e3) = e2)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (op(e2, e3) = e3) | (op(e1, e3) = e3) | (op(e0, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.62 tff(7769,plain,
% 1.46/1.62 (op(e1, e2) = e3),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[7768, 7631, 7366, 7651, 5469, 5475, 3508, 80, 7379, 7491, 7649])).
% 1.46/1.62 tff(7770,plain,
% 1.46/1.62 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7769])).
% 1.46/1.62 tff(7771,plain,
% 1.46/1.62 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7770, 3423])).
% 1.46/1.62 tff(7772,plain,
% 1.46/1.62 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7771])).
% 1.46/1.62 tff(7773,plain,
% 1.46/1.62 (~(op(e3, e2) = e3)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[2292, 7772])).
% 1.46/1.62 tff(7774,plain,
% 1.46/1.62 (op(e3, e1) = e3),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[422, 7773, 7646, 7641])).
% 1.46/1.62 tff(7775,plain,
% 1.46/1.62 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7774])).
% 1.46/1.62 tff(7776,plain,
% 1.46/1.62 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7775, 1314])).
% 1.46/1.62 tff(7777,plain,
% 1.46/1.62 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7776])).
% 1.46/1.62 tff(7778,plain,
% 1.46/1.62 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7777])).
% 1.46/1.62 tff(7779,plain,
% 1.46/1.62 (~(op(e3, e1) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[1321, 7778])).
% 1.46/1.62 tff(7780,plain,
% 1.46/1.62 (op(e3, e0) = e2),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2015, 7779, 7483, 7637])).
% 1.46/1.62 tff(7781,plain,
% 1.46/1.62 (e2 = op(e3, op(e3, e3))),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[7780, 7371])).
% 1.46/1.62 tff(7782,plain,
% 1.46/1.62 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7368])).
% 1.46/1.62 tff(7783,plain,
% 1.46/1.62 (op(e3, op(e3, e0)) = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7782])).
% 1.46/1.62 tff(7784,plain,
% 1.46/1.62 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7780])).
% 1.46/1.62 tff(7785,plain,
% 1.46/1.62 (op(e3, e2) = op(e3, op(e3, e0))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7784])).
% 1.46/1.62 tff(7786,plain,
% 1.46/1.62 (op(e3, e2) = e1),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[1898, 7773, 7382, 7637])).
% 1.46/1.62 tff(7787,plain,
% 1.46/1.62 (e1 = op(e3, e2)),
% 1.46/1.62 inference(symmetry,[status(thm)],[7786])).
% 1.46/1.62 tff(7788,plain,
% 1.46/1.62 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.46/1.62 inference(transitivity,[status(thm)],[7787, 7785, 7783])).
% 1.46/1.62 tff(7789,plain,
% 1.46/1.62 ($false),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[3093, 7788, 7781, 7367])).
% 1.46/1.62 tff(7790,plain,((~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (op(e0, e3) = e2) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.62 tff(7791,plain,
% 1.46/1.62 (~(op(e2, e1) = e0)),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[7790, 79, 80, 121])).
% 1.46/1.62 tff(7792,plain,
% 1.46/1.62 ((op(e3, e3) = op(e3, e1)) <=> (op(e3, e1) = op(e3, e3))),
% 1.46/1.62 inference(commutativity,[status(thm)],[])).
% 1.46/1.62 tff(7793,plain,
% 1.46/1.62 ((e1 = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.46/1.62 inference(commutativity,[status(thm)],[])).
% 1.46/1.62 tff(7794,plain,
% 1.46/1.62 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[5431])).
% 1.46/1.62 tff(7795,plain,
% 1.46/1.62 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7794])).
% 1.46/1.62 tff(7796,plain,
% 1.46/1.62 (~(op(e2, e1) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[197, 7795])).
% 1.46/1.62 tff(7797,plain,
% 1.46/1.62 ((op(e0, e3) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.46/1.62 inference(commutativity,[status(thm)],[])).
% 1.46/1.62 tff(7798,plain,
% 1.46/1.62 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[5426])).
% 1.46/1.62 tff(7799,plain,
% 1.46/1.62 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7798])).
% 1.46/1.62 tff(7800,plain,
% 1.46/1.62 (~(op(e1, e2) = e1)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[1850, 7799])).
% 1.46/1.62 tff(7801,plain,
% 1.46/1.62 (op(e3, e0) = e2),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2015, 2386, 126, 82])).
% 1.46/1.62 tff(7802,plain,
% 1.46/1.62 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7801])).
% 1.46/1.62 tff(7803,plain,
% 1.46/1.62 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7802])).
% 1.46/1.62 tff(7804,plain,
% 1.46/1.62 (~(op(e1, e0) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[410, 7803])).
% 1.46/1.62 tff(7805,plain,
% 1.46/1.62 ((op(e3, e3) = op(e3, e2)) <=> (op(e3, e2) = op(e3, e3))),
% 1.46/1.62 inference(commutativity,[status(thm)],[])).
% 1.46/1.62 tff(7806,plain,
% 1.46/1.62 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[5431])).
% 1.46/1.62 tff(7807,plain,
% 1.46/1.62 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7806])).
% 1.46/1.62 tff(7808,plain,
% 1.46/1.62 (~(op(e2, e2) = e2)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[515, 7807])).
% 1.46/1.62 tff(7809,plain,
% 1.46/1.62 (op(e0, e2) = e3),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[2111, 1890, 75, 2431])).
% 1.46/1.62 tff(7810,plain,
% 1.46/1.62 ((op(e3, e0) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7801])).
% 1.46/1.62 tff(7811,plain,
% 1.46/1.62 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7810, 1681])).
% 1.46/1.62 tff(7812,plain,
% 1.46/1.62 ((op(e0, e3) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 1.46/1.62 inference(symmetry,[status(thm)],[7811])).
% 1.46/1.62 tff(7813,plain,
% 1.46/1.62 ((~(op(e0, e3) = e2)) <=> (~(op(e3, e0) = op(e0, e3)))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7812])).
% 1.46/1.62 tff(7814,plain,
% 1.46/1.62 (~(op(e3, e0) = op(e0, e3))),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[79, 7813])).
% 1.46/1.62 tff(7815,plain,
% 1.46/1.62 (~(op(e0, e3) = e3)),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[6055, 1890, 2839, 7814])).
% 1.46/1.62 tff(7816,plain,
% 1.46/1.62 (op(e0, e3) = e0),
% 1.46/1.62 inference(unit_resolution,[status(thm)],[687, 7815, 121, 79])).
% 1.46/1.62 tff(7817,plain,
% 1.46/1.62 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7816])).
% 1.46/1.62 tff(7818,plain,
% 1.46/1.62 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7817])).
% 1.46/1.62 tff(7819,plain,
% 1.46/1.62 (~(op(e0, e0) = e0)),
% 1.46/1.62 inference(modus_ponens,[status(thm)],[3414, 7818])).
% 1.46/1.62 tff(7820,plain,
% 1.46/1.62 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 1.46/1.62 inference(monotonicity,[status(thm)],[7809])).
% 1.46/1.62 tff(7821,plain,
% 1.46/1.62 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 1.46/1.62 inference(transitivity,[status(thm)],[7820, 1314])).
% 1.46/1.63 tff(7822,plain,
% 1.46/1.63 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7821])).
% 1.46/1.63 tff(7823,plain,
% 1.46/1.63 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7822])).
% 1.46/1.63 tff(7824,plain,
% 1.46/1.63 (~(op(e0, e2) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1321, 7823])).
% 1.46/1.63 tff(7825,plain,
% 1.46/1.63 (op(e1, e2) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1151, 7824, 5548, 2386])).
% 1.46/1.63 tff(7826,assumption,(op(e0, e2) = e3), introduced(assumption)).
% 1.46/1.63 tff(7827,plain,
% 1.46/1.63 (e3 = op(e0, e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7826])).
% 1.46/1.63 tff(7828,plain,
% 1.46/1.63 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7827])).
% 1.46/1.63 tff(7829,plain,
% 1.46/1.63 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7828])).
% 1.46/1.63 tff(7830,plain,
% 1.46/1.63 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7829])).
% 1.46/1.63 tff(7831,plain,
% 1.46/1.63 (~(op(e0, e0) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[3603, 7830])).
% 1.46/1.63 tff(7832,assumption,(op(e1, e2) = e2), introduced(assumption)).
% 1.46/1.63 tff(7833,plain,
% 1.46/1.63 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7832])).
% 1.46/1.63 tff(7834,plain,
% 1.46/1.63 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7833, 2234])).
% 1.46/1.63 tff(7835,plain,
% 1.46/1.63 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7834])).
% 1.46/1.63 tff(7836,plain,
% 1.46/1.63 (~(op(e3, e2) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[2292, 7835])).
% 1.46/1.63 tff(7837,plain,
% 1.46/1.63 (op(e3, e0) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2015, 7836, 126, 82])).
% 1.46/1.63 tff(7838,plain,
% 1.46/1.63 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7837])).
% 1.46/1.63 tff(7839,plain,
% 1.46/1.63 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7838])).
% 1.46/1.63 tff(7840,plain,
% 1.46/1.63 (~(op(e0, e0) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[6384, 7839])).
% 1.46/1.63 tff(7841,plain,
% 1.46/1.63 (op(e0, e0) = e1),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[3612, 7840, 6213, 7831])).
% 1.46/1.63 tff(7842,plain,
% 1.46/1.63 (e1 = op(e0, e0)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[7841, 74])).
% 1.46/1.63 tff(7843,plain,
% 1.46/1.63 (op(e0, op(e0, e0)) = op(e0, e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7841])).
% 1.46/1.63 tff(7844,plain,
% 1.46/1.63 (op(e0, e1) = op(e0, op(e0, e0))),
% 1.46/1.63 inference(symmetry,[status(thm)],[7843])).
% 1.46/1.63 tff(7845,plain,
% 1.46/1.63 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7832])).
% 1.46/1.63 tff(7846,plain,
% 1.46/1.63 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7845])).
% 1.46/1.63 tff(7847,plain,
% 1.46/1.63 (~(op(e1, e1) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1604, 7846])).
% 1.46/1.63 tff(7848,plain,
% 1.46/1.63 (op(e0, e1) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1993, 7847, 82, 3540])).
% 1.46/1.63 tff(7849,plain,
% 1.46/1.63 (e2 = op(e0, e1)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7848])).
% 1.46/1.63 tff(7850,plain,
% 1.46/1.63 (e2 = op(e0, op(e0, e0))),
% 1.46/1.63 inference(transitivity,[status(thm)],[7849, 7844])).
% 1.46/1.63 tff(7851,plain,
% 1.46/1.63 (op(e0, op(e0, e0)) = e2),
% 1.46/1.63 inference(transitivity,[status(thm)],[7843, 7848])).
% 1.46/1.63 tff(7852,plain,
% 1.46/1.63 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7851])).
% 1.46/1.63 tff(7853,plain,
% 1.46/1.63 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.63 inference(symmetry,[status(thm)],[7852])).
% 1.46/1.63 tff(7854,plain,
% 1.46/1.63 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.46/1.63 inference(transitivity,[status(thm)],[7827, 7853])).
% 1.46/1.63 tff(7855,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[3582, 7854, 7850, 7842])).
% 1.46/1.63 tff(7856,plain,((~(op(e1, e2) = e2)) | (~(op(e0, e2) = e3)) | (op(e0, e0) = e0) | (op(e3, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7857,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7856, 7825, 7819, 7809, 82, 3540, 126])).
% 1.46/1.63 tff(7858,plain,((op(e3, e2) = e3) | (op(e3, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e3) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e3, e1) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7859,plain,
% 1.46/1.63 (op(e3, e2) = e3),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7858, 2386, 7796, 126, 7808, 82, 121, 79, 2839, 75, 2431])).
% 1.46/1.63 tff(7860,plain,
% 1.46/1.63 (e3 = op(e3, e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7859])).
% 1.46/1.63 tff(7861,plain,
% 1.46/1.63 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e3, e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7860])).
% 1.46/1.63 tff(7862,plain,
% 1.46/1.63 ((op(e3, e3) = e3) <=> (op(e3, e2) = op(e3, e3))),
% 1.46/1.63 inference(transitivity,[status(thm)],[7861, 7805])).
% 1.46/1.63 tff(7863,plain,
% 1.46/1.63 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7862])).
% 1.46/1.63 tff(7864,plain,
% 1.46/1.63 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7863])).
% 1.46/1.63 tff(7865,plain,
% 1.46/1.63 (~(op(e3, e3) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1888, 7864])).
% 1.46/1.63 tff(7866,plain,
% 1.46/1.63 (op(e3, e3) = e0),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1071, 7865, 126, 926])).
% 1.46/1.63 tff(7867,plain,
% 1.46/1.63 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7801])).
% 1.46/1.63 tff(7868,plain,
% 1.46/1.63 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7867, 69])).
% 1.46/1.63 tff(7869,plain,
% 1.46/1.63 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7868])).
% 1.46/1.63 tff(7870,plain,
% 1.46/1.63 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7869])).
% 1.46/1.63 tff(7871,plain,
% 1.46/1.63 (~(op(e3, e0) = e1)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[708, 7870])).
% 1.46/1.63 tff(7872,plain,
% 1.46/1.63 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7859])).
% 1.46/1.63 tff(7873,plain,
% 1.46/1.63 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7872, 128])).
% 1.46/1.63 tff(7874,plain,
% 1.46/1.63 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7873])).
% 1.46/1.63 tff(7875,plain,
% 1.46/1.63 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7874])).
% 1.46/1.63 tff(7876,plain,
% 1.46/1.63 (~(op(e3, e2) = e1)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[303, 7875])).
% 1.46/1.63 tff(7877,plain,
% 1.46/1.63 (op(e3, e1) = e1),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[939, 7876, 926, 7871])).
% 1.46/1.63 tff(7878,plain,
% 1.46/1.63 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7877])).
% 1.46/1.63 tff(7879,plain,
% 1.46/1.63 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e1))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7878])).
% 1.46/1.63 tff(7880,plain,
% 1.46/1.63 (~(op(e2, e1) = e1)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[402, 7879])).
% 1.46/1.63 tff(7881,plain,
% 1.46/1.63 (op(e2, e1) = e3),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2367, 7880, 2559, 7796])).
% 1.46/1.63 tff(7882,plain,
% 1.46/1.63 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7881])).
% 1.46/1.63 tff(7883,plain,
% 1.46/1.63 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7882])).
% 1.46/1.63 tff(7884,plain,
% 1.46/1.63 (~(op(e1, e1) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[225, 7883])).
% 1.46/1.63 tff(7885,plain,
% 1.46/1.63 (op(e1, e0) = e3),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[247, 7884, 75, 1080])).
% 1.46/1.63 tff(7886,plain,
% 1.46/1.63 (op(e1, e1) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2285, 3785, 72, 6687])).
% 1.46/1.63 tff(7887,plain,
% 1.46/1.63 (e2 = op(e1, e1)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[7886, 2254])).
% 1.46/1.63 tff(7888,plain,
% 1.46/1.63 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7886])).
% 1.46/1.63 tff(7889,plain,
% 1.46/1.63 (op(e1, e2) = op(e1, op(e1, e1))),
% 1.46/1.63 inference(symmetry,[status(thm)],[7888])).
% 1.46/1.63 tff(7890,plain,
% 1.46/1.63 (op(e1, e2) = e0),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1859, 3785, 4515, 75])).
% 1.46/1.63 tff(7891,plain,
% 1.46/1.63 (e0 = op(e1, e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7890])).
% 1.46/1.63 tff(7892,plain,
% 1.46/1.63 (e0 = op(e1, op(e1, e1))),
% 1.46/1.63 inference(transitivity,[status(thm)],[7891, 7889])).
% 1.46/1.63 tff(7893,plain,
% 1.46/1.63 (op(e1, op(e1, e1)) = op(e3, e3)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7888, 7890, 4451])).
% 1.46/1.63 tff(7894,plain,
% 1.46/1.63 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e3, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7893])).
% 1.46/1.63 tff(7895,plain,
% 1.46/1.63 (op(e1, op(e3, e3)) = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.63 inference(symmetry,[status(thm)],[7894])).
% 1.46/1.63 tff(7896,plain,
% 1.46/1.63 (op(e1, e0) = op(e1, op(e3, e3))),
% 1.46/1.63 inference(symmetry,[status(thm)],[4468])).
% 1.46/1.63 tff(7897,plain,
% 1.46/1.63 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.46/1.63 inference(transitivity,[status(thm)],[259, 7896, 7895])).
% 1.46/1.63 tff(7898,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2269, 7897, 7892, 7887])).
% 1.46/1.63 tff(7899,plain,((op(e1, e2) = e2) | (~(op(e1, e0) = e3)) | (~(op(e3, e3) = e0)) | (op(e1, e3) = e2) | (op(e1, e0) = e2) | (op(e1, e2) = e1) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7900,plain,
% 1.46/1.63 (op(e1, e2) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7899, 7885, 7866, 72, 7804, 4515, 75])).
% 1.46/1.63 tff(7901,plain,
% 1.46/1.63 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7900])).
% 1.46/1.63 tff(7902,plain,
% 1.46/1.63 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7901])).
% 1.46/1.63 tff(7903,plain,
% 1.46/1.63 (~(op(e0, e2) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[6205, 7902])).
% 1.46/1.63 tff(7904,plain,
% 1.46/1.63 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e3, e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7860])).
% 1.46/1.63 tff(7905,plain,
% 1.46/1.63 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7904])).
% 1.46/1.63 tff(7906,plain,
% 1.46/1.63 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7905])).
% 1.46/1.63 tff(7907,plain,
% 1.46/1.63 (~(op(e0, e2) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1467, 7906])).
% 1.46/1.63 tff(7908,plain,
% 1.46/1.63 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7801])).
% 1.46/1.63 tff(7909,plain,
% 1.46/1.63 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7908])).
% 1.46/1.63 tff(7910,plain,
% 1.46/1.63 (~(op(e0, e0) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[6384, 7909])).
% 1.46/1.63 tff(7911,plain,
% 1.46/1.63 (op(e0, e1) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[3652, 7903, 79, 7910])).
% 1.46/1.63 tff(7912,plain,
% 1.46/1.63 (op(op(e2, e3), e3) = op(e2, e3)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[5431])).
% 1.46/1.63 tff(7913,plain,
% 1.46/1.63 (op(op(e2, e3), e3) = e2),
% 1.46/1.63 inference(transitivity,[status(thm)],[7912, 5431])).
% 1.46/1.63 tff(7914,plain,
% 1.46/1.63 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1288, 7913])).
% 1.46/1.63 tff(7915,assumption,(~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))), introduced(assumption)).
% 1.46/1.63 tff(7916,plain,
% 1.46/1.63 (~(op(op(e3, e2), e2) = e3)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1339, 7915])).
% 1.46/1.63 tff(7917,assumption,(~(op(op(e3, e2), e2) = e3)), introduced(assumption)).
% 1.46/1.63 tff(7918,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7917, 1338])).
% 1.46/1.63 tff(7919,plain,((~(op(e3, e2) = e3)) | (op(op(e3, e2), e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7920,plain,
% 1.46/1.63 (~(op(e3, e2) = e3)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7919, 7916])).
% 1.46/1.63 tff(7921,plain,
% 1.46/1.63 (op(e0, e2) = e3),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2111, 7920, 75, 2431])).
% 1.46/1.63 tff(7922,plain,
% 1.46/1.63 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7921])).
% 1.46/1.63 tff(7923,plain,
% 1.46/1.63 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7922, 1314])).
% 1.46/1.63 tff(7924,plain,
% 1.46/1.63 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7923])).
% 1.46/1.63 tff(7925,plain,
% 1.46/1.63 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7924])).
% 1.46/1.63 tff(7926,plain,
% 1.46/1.63 (~(op(e0, e2) = e2)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1321, 7925])).
% 1.46/1.63 tff(7927,plain,
% 1.46/1.63 (e3 = op(e0, e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7921])).
% 1.46/1.63 tff(7928,plain,
% 1.46/1.63 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e0, e2))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7927])).
% 1.46/1.63 tff(7929,plain,
% 1.46/1.63 ((op(e0, e3) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 1.46/1.63 inference(transitivity,[status(thm)],[7928, 7797])).
% 1.46/1.63 tff(7930,plain,
% 1.46/1.63 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7929])).
% 1.46/1.63 tff(7931,plain,
% 1.46/1.63 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7930])).
% 1.46/1.63 tff(7932,plain,
% 1.46/1.63 (~(op(e0, e3) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[918, 7931])).
% 1.46/1.63 tff(7933,plain,
% 1.46/1.63 (op(e0, e3) = e0),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[687, 7932, 121, 79])).
% 1.46/1.63 tff(7934,plain,
% 1.46/1.63 (e0 = op(e0, e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7933])).
% 1.46/1.63 tff(7935,plain,
% 1.46/1.63 ((op(e0, e0) = e0) <=> (op(e0, e0) = op(e0, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7934])).
% 1.46/1.63 tff(7936,plain,
% 1.46/1.63 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7935])).
% 1.46/1.63 tff(7937,plain,
% 1.46/1.63 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7936])).
% 1.46/1.63 tff(7938,plain,
% 1.46/1.63 (~(op(e0, e0) = e0)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[3414, 7937])).
% 1.46/1.63 tff(7939,plain,
% 1.46/1.63 (~(op(e1, e2) = e2)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7856, 7921, 7938, 82, 3540, 126])).
% 1.46/1.63 tff(7940,plain,
% 1.46/1.63 (op(e3, e2) = e2),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1151, 7939, 5548, 7926])).
% 1.46/1.63 tff(7941,plain,
% 1.46/1.63 (op(op(e0, e2), e2) = op(e3, e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7921])).
% 1.46/1.63 tff(7942,plain,
% 1.46/1.63 (op(e3, op(e3, e2)) = op(op(e0, e2), e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7927, 7940])).
% 1.46/1.63 tff(7943,plain,
% 1.46/1.63 (op(e3, op(e3, e2)) = e2),
% 1.46/1.63 inference(transitivity,[status(thm)],[7942, 7941, 7940])).
% 1.46/1.63 tff(7944,plain,
% 1.46/1.63 (~(op(e3, op(e3, e2)) = e2)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1904, 7915])).
% 1.46/1.63 tff(7945,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7944, 7943])).
% 1.46/1.63 tff(7946,plain,(((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))) | (op(e2, e2) = e2) | (op(e3, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e2) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7947,plain,
% 1.46/1.63 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7946, 2431, 82, 7796, 126, 121, 79, 75, 7808])).
% 1.46/1.63 tff(7948,plain,
% 1.46/1.63 (op(e3, op(e3, e1)) = op(e3, e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7877])).
% 1.46/1.63 tff(7949,plain,
% 1.46/1.63 (op(e3, op(e3, e1)) = e1),
% 1.46/1.63 inference(transitivity,[status(thm)],[7948, 7877])).
% 1.46/1.63 tff(7950,plain,
% 1.46/1.63 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2594, 7949])).
% 1.46/1.63 tff(7951,plain,
% 1.46/1.63 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e3)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7881])).
% 1.46/1.63 tff(7952,plain,
% 1.46/1.63 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7951])).
% 1.46/1.63 tff(7953,plain,
% 1.46/1.63 (~(op(e2, e0) = e3)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[1966, 7952])).
% 1.46/1.63 tff(7954,plain,
% 1.46/1.63 (op(op(e0, e1), e0) = op(e2, op(e3, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[3492, 4451])).
% 1.46/1.63 tff(7955,plain,
% 1.46/1.63 (op(op(e0, e1), e0) = op(e2, e0)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7954, 4551])).
% 1.46/1.63 tff(7956,plain,
% 1.46/1.63 ((op(op(e0, e1), e0) = e1) <=> (op(e2, e0) = e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7955])).
% 1.46/1.63 tff(7957,plain,
% 1.46/1.63 ((~(op(op(e0, e1), e0) = e1)) <=> (~(op(e2, e0) = e1))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7956])).
% 1.46/1.63 tff(7958,assumption,(~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))), introduced(assumption)).
% 1.46/1.63 tff(7959,plain,
% 1.46/1.63 (op(op(e2, e0), e2) = e0),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1379, 7958])).
% 1.46/1.63 tff(7960,assumption,(op(op(e0, e1), e0) = e1), introduced(assumption)).
% 1.46/1.63 tff(7961,plain,
% 1.46/1.63 (op(e2, op(e3, e3)) = op(op(e0, e1), e0)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[5555, 3066])).
% 1.46/1.63 tff(7962,plain,
% 1.46/1.63 (op(e2, e0) = op(e2, op(e3, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[4451])).
% 1.46/1.63 tff(7963,plain,
% 1.46/1.63 (op(e2, e0) = e1),
% 1.46/1.63 inference(transitivity,[status(thm)],[7962, 7961, 7960])).
% 1.46/1.63 tff(7964,plain,
% 1.46/1.63 (op(op(e2, e0), e2) = op(e1, e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7963])).
% 1.46/1.63 tff(7965,assumption,(op(op(e2, e0), e2) = e0), introduced(assumption)).
% 1.46/1.63 tff(7966,plain,
% 1.46/1.63 (e0 = op(op(e2, e0), e2)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7965])).
% 1.46/1.63 tff(7967,plain,
% 1.46/1.63 (op(e3, e3) = e2),
% 1.46/1.63 inference(transitivity,[status(thm)],[3066, 7966, 7964, 7832])).
% 1.46/1.63 tff(7968,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[126, 7967])).
% 1.46/1.63 tff(7969,plain,((~(op(op(e0, e1), e0) = e1)) | (op(e3, e3) = e2) | (~(op(e3, e3) = e0)) | (~(op(op(e2, e0), e2) = e0)) | (~(op(e1, e2) = e2)) | (~(op(e0, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7970,plain,
% 1.46/1.63 (~(op(op(e0, e1), e0) = e1)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7969, 7959, 3066, 126, 7832, 3492])).
% 1.46/1.63 tff(7971,plain,
% 1.46/1.63 (~(op(e2, e0) = e1)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[7970, 7957])).
% 1.46/1.63 tff(7972,plain,
% 1.46/1.63 (op(e2, e0) = e0),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[765, 7971, 982, 3272])).
% 1.46/1.63 tff(7973,plain,
% 1.46/1.63 (op(e2, e0) = op(e3, e3)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7972, 4451])).
% 1.46/1.63 tff(7974,plain,
% 1.46/1.63 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7973])).
% 1.46/1.63 tff(7975,plain,
% 1.46/1.63 (op(e2, op(e2, e0)) = e0),
% 1.46/1.63 inference(transitivity,[status(thm)],[7974, 4551, 7972])).
% 1.46/1.63 tff(7976,plain,
% 1.46/1.63 (~(op(e2, op(e2, e0)) = e0)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2653, 7958])).
% 1.46/1.63 tff(7977,plain,
% 1.46/1.63 ($false),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7976, 7975])).
% 1.46/1.63 tff(7978,plain,(((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))) | (~(op(e3, e3) = e0)) | (op(e2, e0) = e2) | (op(e2, e0) = e3) | (~(op(e0, e1) = e2)) | (op(e3, e3) = e2) | (~(op(e1, e2) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.63 tff(7979,plain,
% 1.46/1.63 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7978, 7866, 5442, 7953, 7911, 126, 7900])).
% 1.46/1.63 tff(7980,plain,
% 1.46/1.63 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7900])).
% 1.46/1.63 tff(7981,plain,
% 1.46/1.63 (op(e1, op(e1, e2)) = e2),
% 1.46/1.63 inference(transitivity,[status(thm)],[7980, 7900])).
% 1.46/1.63 tff(7982,plain,
% 1.46/1.63 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2377, 7981])).
% 1.46/1.63 tff(7983,plain,
% 1.46/1.63 (e0 = op(e3, e3)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7866])).
% 1.46/1.63 tff(7984,plain,
% 1.46/1.63 (op(op(e1, e0), e1) = op(e3, e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7885])).
% 1.46/1.63 tff(7985,plain,
% 1.46/1.63 (op(op(e1, e0), e1) = e1),
% 1.46/1.63 inference(transitivity,[status(thm)],[7984, 7877])).
% 1.46/1.63 tff(7986,plain,
% 1.46/1.63 ((op(op(e1, e0), e1) = e0) <=> (e1 = op(e3, e3))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7985, 7983])).
% 1.46/1.63 tff(7987,plain,
% 1.46/1.63 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e3) = e1)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7986, 657])).
% 1.46/1.63 tff(7988,plain,
% 1.46/1.63 ((op(e3, e3) = e1) <=> (op(op(e1, e0), e1) = e0)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7987])).
% 1.46/1.63 tff(7989,plain,
% 1.46/1.63 ((~(op(e3, e3) = e1)) <=> (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7988])).
% 1.46/1.63 tff(7990,plain,
% 1.46/1.63 (~(op(op(e1, e0), e1) = e0)),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[926, 7989])).
% 1.46/1.63 tff(7991,plain,
% 1.46/1.63 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1302, 7990])).
% 1.46/1.63 tff(7992,plain,
% 1.46/1.63 (op(op(e3, e2), e2) = e3),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[7919, 7859])).
% 1.46/1.63 tff(7993,plain,
% 1.46/1.63 (op(e2, e1) = op(e3, e2)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7881, 7860])).
% 1.46/1.63 tff(7994,plain,
% 1.46/1.63 (op(op(e2, e1), e2) = op(op(e3, e2), e2)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7993])).
% 1.46/1.63 tff(7995,plain,
% 1.46/1.63 (op(op(e2, e1), e2) = op(e3, e2)),
% 1.46/1.63 inference(transitivity,[status(thm)],[7994, 7992, 7860])).
% 1.46/1.63 tff(7996,plain,
% 1.46/1.63 ((op(op(e2, e1), e2) = e1) <=> (op(e3, e2) = e1)),
% 1.46/1.63 inference(monotonicity,[status(thm)],[7995])).
% 1.46/1.63 tff(7997,plain,
% 1.46/1.63 ((op(e3, e2) = e1) <=> (op(op(e2, e1), e2) = e1)),
% 1.46/1.63 inference(symmetry,[status(thm)],[7996])).
% 1.46/1.63 tff(7998,plain,
% 1.46/1.64 ((~(op(e3, e2) = e1)) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[7997])).
% 1.46/1.64 tff(7999,plain,
% 1.46/1.64 (~(op(op(e2, e1), e2) = e1)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[7876, 7998])).
% 1.46/1.64 tff(8000,plain,
% 1.46/1.64 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[5808, 7999])).
% 1.46/1.64 tff(8001,plain,
% 1.46/1.64 (op(op(e3, e0), e3) = op(e2, e3)),
% 1.46/1.64 inference(monotonicity,[status(thm)],[7801])).
% 1.46/1.64 tff(8002,plain,
% 1.46/1.64 (op(op(e3, e0), e3) = e2),
% 1.46/1.64 inference(transitivity,[status(thm)],[8001, 5431])).
% 1.46/1.64 tff(8003,plain,
% 1.46/1.64 ((op(op(e3, e0), e3) = e0) <=> (e2 = e0)),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8002])).
% 1.46/1.64 tff(8004,plain,
% 1.46/1.64 ((op(op(e3, e0), e3) = e0) <=> (e0 = e2)),
% 1.46/1.64 inference(transitivity,[status(thm)],[8003, 1])).
% 1.46/1.64 tff(8005,plain,
% 1.46/1.64 ((e0 = e2) <=> (op(op(e3, e0), e3) = e0)),
% 1.46/1.64 inference(symmetry,[status(thm)],[8004])).
% 1.46/1.64 tff(8006,plain,
% 1.46/1.64 ((~(e0 = e2)) <=> (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8005])).
% 1.46/1.64 tff(8007,plain,
% 1.46/1.64 (~(op(op(e3, e0), e3) = e0)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[14, 8006])).
% 1.46/1.64 tff(8008,plain,
% 1.46/1.64 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1764, 8007])).
% 1.46/1.64 tff(8009,plain,
% 1.46/1.64 (op(e0, op(e0, e1)) = op(e0, e2)),
% 1.46/1.64 inference(monotonicity,[status(thm)],[3492])).
% 1.46/1.64 tff(8010,plain,
% 1.46/1.64 ((op(e0, op(e0, e1)) = e1) <=> (op(e0, e2) = e1)),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8009])).
% 1.46/1.64 tff(8011,plain,
% 1.46/1.64 ((~(op(e0, op(e0, e1)) = e1)) <=> (~(op(e0, e2) = e1))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8010])).
% 1.46/1.64 tff(8012,assumption,(~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))), introduced(assumption)).
% 1.46/1.64 tff(8013,plain,
% 1.46/1.64 (~(op(e0, op(e0, e1)) = e1)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2449, 8012])).
% 1.46/1.64 tff(8014,plain,
% 1.46/1.64 (~(op(e0, e2) = e1)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[8013, 8011])).
% 1.46/1.64 tff(8015,plain,
% 1.46/1.64 (op(op(e0, e1), e0) = e1),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1461, 8012])).
% 1.46/1.64 tff(8016,plain,
% 1.46/1.64 (op(e2, e0) = e1),
% 1.46/1.64 inference(transitivity,[status(thm)],[7962, 7961, 8015])).
% 1.46/1.64 tff(8017,plain,
% 1.46/1.64 ((op(e2, e0) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8016])).
% 1.46/1.64 tff(8018,plain,
% 1.46/1.64 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.46/1.64 inference(transitivity,[status(thm)],[8017, 316])).
% 1.46/1.64 tff(8019,plain,
% 1.46/1.64 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8018])).
% 1.46/1.64 tff(8020,plain,
% 1.46/1.64 (~(op(e2, e2) = e1)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2228, 8019])).
% 1.46/1.64 tff(8021,plain,
% 1.46/1.64 ($false),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1613, 8020, 8014, 4515, 930])).
% 1.46/1.64 tff(8022,plain,(((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))) | (op(e1, e2) = e1) | (op(e3, e2) = e1) | (~(op(e0, e1) = e2)) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.64 tff(8023,plain,
% 1.46/1.64 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[8022, 7876, 4515, 7911, 7866])).
% 1.46/1.64 tff(8024,plain,
% 1.46/1.64 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1459, 8023, 8008, 8000, 5469, 1304, 7991, 7982, 7979, 7950, 7947, 7914])).
% 1.46/1.64 tff(8025,plain,
% 1.46/1.64 (~(op(e0, op(e0, e2)) = e2)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1331, 8024])).
% 1.46/1.64 tff(8026,assumption,(op(e0, e2) = e1), introduced(assumption)).
% 1.46/1.64 tff(8027,plain,
% 1.46/1.64 (op(e0, op(e0, e2)) = op(e0, e1)),
% 1.46/1.64 inference(monotonicity,[status(thm)],[8026])).
% 1.46/1.64 tff(8028,plain,
% 1.46/1.64 (op(e0, op(e0, e2)) = e2),
% 1.46/1.64 inference(transitivity,[status(thm)],[8027, 3492])).
% 1.46/1.64 tff(8029,assumption,(~(op(e0, op(e0, e2)) = e2)), introduced(assumption)).
% 1.46/1.64 tff(8030,plain,
% 1.46/1.64 ($false),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[8029, 8028])).
% 1.46/1.64 tff(8031,plain,((~(op(e0, e2) = e1)) | (op(e0, op(e0, e2)) = e2) | (~(op(e0, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.64 tff(8032,plain,
% 1.54/1.64 (~(op(e0, e2) = e1)),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[8031, 8025, 7911])).
% 1.54/1.64 tff(8033,plain,
% 1.54/1.64 (op(e0, e2) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2745, 8032, 7907, 7903])).
% 1.54/1.64 tff(8034,plain,
% 1.54/1.64 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8033])).
% 1.54/1.64 tff(8035,plain,
% 1.54/1.64 (op(op(e0, e2), e2) = e0),
% 1.54/1.64 inference(transitivity,[status(thm)],[8034, 8033])).
% 1.54/1.64 tff(8036,plain,
% 1.54/1.64 (~(op(op(e0, e2), e2) = e0)),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[1956, 8024])).
% 1.54/1.64 tff(8037,plain,
% 1.54/1.64 ($false),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[8036, 8035])).
% 1.54/1.64 tff(8038,plain,((op(e3, e2) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e2) = e1) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e3, e3) = e1) | (op(e1, e3) = e3) | (op(e2, e1) = e0) | (op(e3, e1) = e2) | (op(e0, e3) = e1) | (op(e3, e1) = e3) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.64 tff(8039,plain,
% 1.54/1.64 (op(e3, e2) = e2),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[8038, 2431, 7800, 126, 79, 72, 75, 5430, 1080, 7791, 82, 121, 2839, 1304])).
% 1.54/1.64 tff(8040,plain,
% 1.54/1.64 ((op(e3, e2) = e3) <=> (e2 = e3)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8039])).
% 1.54/1.64 tff(8041,plain,
% 1.54/1.64 ((e2 = e3) <=> (op(e3, e2) = e3)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8040])).
% 1.54/1.64 tff(8042,plain,
% 1.54/1.64 ((~(e2 = e3)) <=> (~(op(e3, e2) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8041])).
% 1.54/1.64 tff(8043,plain,
% 1.54/1.64 (~(op(e3, e2) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1321, 8042])).
% 1.54/1.64 tff(8044,plain,
% 1.54/1.64 (op(e0, e2) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2111, 8043, 75, 2431])).
% 1.54/1.64 tff(8045,plain,
% 1.54/1.64 (e3 = op(e0, e2)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8044])).
% 1.54/1.64 tff(8046,plain,
% 1.54/1.64 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e0, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8045])).
% 1.54/1.64 tff(8047,plain,
% 1.54/1.64 ((op(e0, e3) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 1.54/1.64 inference(transitivity,[status(thm)],[8046, 7797])).
% 1.54/1.64 tff(8048,plain,
% 1.54/1.64 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8047])).
% 1.54/1.64 tff(8049,plain,
% 1.54/1.64 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8048])).
% 1.54/1.64 tff(8050,plain,
% 1.54/1.64 (~(op(e0, e3) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[918, 8049])).
% 1.54/1.64 tff(8051,plain,
% 1.54/1.64 (op(e3, e3) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[480, 8050, 124, 1080])).
% 1.54/1.64 tff(8052,plain,
% 1.54/1.64 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8051])).
% 1.54/1.64 tff(8053,plain,
% 1.54/1.64 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8052])).
% 1.54/1.64 tff(8054,plain,
% 1.54/1.64 (~(op(e3, e0) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[157, 8053])).
% 1.54/1.64 tff(8055,plain,
% 1.54/1.64 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8044])).
% 1.54/1.64 tff(8056,plain,
% 1.54/1.64 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8055])).
% 1.54/1.64 tff(8057,plain,
% 1.54/1.64 (~(op(e0, e0) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[3603, 8056])).
% 1.54/1.64 tff(8058,plain,
% 1.54/1.64 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8045])).
% 1.54/1.64 tff(8059,plain,
% 1.54/1.64 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8058])).
% 1.54/1.64 tff(8060,plain,
% 1.54/1.64 ((op(e1, e2) = op(e0, e2)) <=> (op(e0, e2) = op(e1, e2))),
% 1.54/1.64 inference(commutativity,[status(thm)],[])).
% 1.54/1.64 tff(8061,plain,
% 1.54/1.64 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8039])).
% 1.54/1.64 tff(8062,plain,
% 1.54/1.64 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8061])).
% 1.54/1.64 tff(8063,plain,
% 1.54/1.64 (~(op(e1, e2) = e2)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[2292, 8062])).
% 1.54/1.64 tff(8064,plain,
% 1.54/1.64 (op(e1, e2) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[1859, 8063, 7800, 75])).
% 1.54/1.64 tff(8065,plain,
% 1.54/1.64 (e0 = op(e1, e2)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8064])).
% 1.54/1.64 tff(8066,plain,
% 1.54/1.64 ((op(e2, e2) = op(e1, e2)) <=> (op(e1, e2) = op(e2, e2))),
% 1.54/1.64 inference(commutativity,[status(thm)],[])).
% 1.54/1.64 tff(8067,plain,
% 1.54/1.64 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e1, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8065])).
% 1.54/1.64 tff(8068,plain,
% 1.54/1.64 ((op(e2, e2) = e0) <=> (op(e1, e2) = op(e2, e2))),
% 1.54/1.64 inference(transitivity,[status(thm)],[8067, 8066])).
% 1.54/1.64 tff(8069,plain,
% 1.54/1.64 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8068])).
% 1.54/1.64 tff(8070,plain,
% 1.54/1.64 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8069])).
% 1.54/1.64 tff(8071,plain,
% 1.54/1.64 (~(op(e2, e2) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1273, 8070])).
% 1.54/1.64 tff(8072,plain,
% 1.54/1.64 (op(e2, e0) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2311, 8071, 7791, 5436])).
% 1.54/1.64 tff(8073,plain,
% 1.54/1.64 (op(e2, e0) = op(e1, e2)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8072, 8065])).
% 1.54/1.64 tff(8074,plain,
% 1.54/1.64 ((op(e2, e0) = op(e0, e2)) <=> (op(e1, e2) = op(e0, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8073])).
% 1.54/1.64 tff(8075,plain,
% 1.54/1.64 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e1, e2))),
% 1.54/1.64 inference(transitivity,[status(thm)],[8074, 8060])).
% 1.54/1.64 tff(8076,plain,
% 1.54/1.64 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 1.54/1.64 inference(symmetry,[status(thm)],[8075])).
% 1.54/1.64 tff(8077,plain,
% 1.54/1.64 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = e3)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8076, 8059])).
% 1.54/1.64 tff(8078,plain,
% 1.54/1.64 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e2, e0) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8077])).
% 1.54/1.64 tff(8079,plain,
% 1.54/1.64 (~(op(e2, e0) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[6205, 8078])).
% 1.54/1.64 tff(8080,plain,
% 1.54/1.64 (op(e1, e0) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2713, 8079, 8057, 8054])).
% 1.54/1.64 tff(8081,plain,
% 1.54/1.64 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e0)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8064])).
% 1.54/1.64 tff(8082,plain,
% 1.54/1.64 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8081])).
% 1.54/1.64 tff(8083,plain,
% 1.54/1.64 (~(op(e1, e1) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1604, 8082])).
% 1.54/1.64 tff(8084,plain,
% 1.54/1.64 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e1, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8065])).
% 1.54/1.64 tff(8085,plain,
% 1.54/1.64 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e0)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8084])).
% 1.54/1.64 tff(8086,plain,
% 1.54/1.64 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8085])).
% 1.54/1.64 tff(8087,plain,
% 1.54/1.64 (~(op(e1, e0) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1312, 8086])).
% 1.54/1.64 tff(8088,plain,
% 1.54/1.64 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[5426])).
% 1.54/1.64 tff(8089,plain,
% 1.54/1.64 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8088])).
% 1.54/1.64 tff(8090,plain,
% 1.54/1.64 (~(op(e1, e1) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[619, 8089])).
% 1.54/1.64 tff(8091,plain,
% 1.54/1.64 (op(e0, e3) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[687, 8050, 121, 79])).
% 1.54/1.64 tff(8092,plain,
% 1.54/1.64 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8039])).
% 1.54/1.64 tff(8093,plain,
% 1.54/1.64 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8092, 69])).
% 1.54/1.64 tff(8094,plain,
% 1.54/1.64 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8093])).
% 1.54/1.64 tff(8095,plain,
% 1.54/1.64 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8094])).
% 1.54/1.64 tff(8096,plain,
% 1.54/1.64 (~(op(e3, e2) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[708, 8095])).
% 1.54/1.64 tff(8097,plain,
% 1.54/1.64 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8044])).
% 1.54/1.64 tff(8098,plain,
% 1.54/1.64 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8097, 128])).
% 1.54/1.64 tff(8099,plain,
% 1.54/1.64 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8098])).
% 1.54/1.64 tff(8100,plain,
% 1.54/1.64 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8099])).
% 1.54/1.64 tff(8101,plain,
% 1.54/1.64 (~(op(e0, e2) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[303, 8100])).
% 1.54/1.64 tff(8102,plain,
% 1.54/1.64 (op(e2, e2) = e1),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[1613, 8101, 7800, 8096])).
% 1.54/1.64 tff(8103,plain,
% 1.54/1.64 (e1 = op(e2, e2)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8102])).
% 1.54/1.64 tff(8104,plain,
% 1.54/1.64 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8103])).
% 1.54/1.64 tff(8105,plain,
% 1.54/1.64 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8104])).
% 1.54/1.64 tff(8106,plain,
% 1.54/1.64 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8105])).
% 1.54/1.64 tff(8107,plain,
% 1.54/1.64 (~(op(e2, e1) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[508, 8106])).
% 1.54/1.64 tff(8108,plain,
% 1.54/1.64 (op(e2, e1) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2367, 8107, 7791, 7796])).
% 1.54/1.64 tff(8109,plain,
% 1.54/1.64 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8108])).
% 1.54/1.64 tff(8110,plain,
% 1.54/1.64 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8109])).
% 1.54/1.64 tff(8111,plain,
% 1.54/1.64 (~(op(e1, e1) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[225, 8110])).
% 1.54/1.64 tff(8112,plain,
% 1.54/1.64 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8091])).
% 1.54/1.64 tff(8113,plain,
% 1.54/1.64 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8112])).
% 1.54/1.64 tff(8114,plain,
% 1.54/1.64 (~(op(e0, e0) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[3414, 8113])).
% 1.54/1.64 tff(8115,plain,
% 1.54/1.64 ((e0 = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.54/1.64 inference(commutativity,[status(thm)],[])).
% 1.54/1.64 tff(8116,plain,
% 1.54/1.64 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8072])).
% 1.54/1.64 tff(8117,plain,
% 1.54/1.64 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8116, 8115])).
% 1.54/1.64 tff(8118,plain,
% 1.54/1.64 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8117])).
% 1.54/1.64 tff(8119,plain,
% 1.54/1.64 (~(op(e3, e0) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[747, 8118])).
% 1.54/1.64 tff(8120,plain,
% 1.54/1.64 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e2)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8039])).
% 1.54/1.64 tff(8121,plain,
% 1.54/1.64 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8120])).
% 1.54/1.64 tff(8122,plain,
% 1.54/1.64 (~(op(e3, e0) = e2)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1133, 8121])).
% 1.54/1.64 tff(8123,plain,
% 1.54/1.64 (op(e3, e0) = e1),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[5422, 8054, 8122, 8119])).
% 1.54/1.64 tff(8124,plain,
% 1.54/1.64 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8123])).
% 1.54/1.64 tff(8125,plain,
% 1.54/1.64 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8124])).
% 1.54/1.64 tff(8126,plain,
% 1.54/1.64 (~(op(e0, e0) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[6384, 8125])).
% 1.54/1.64 tff(8127,plain,
% 1.54/1.64 (op(e0, e0) = e2),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[3612, 8126, 8114, 8057])).
% 1.54/1.64 tff(8128,plain,
% 1.54/1.64 ($false),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2271, 8127, 8111, 8091, 8090, 8087, 80, 8083, 8080])).
% 1.54/1.64 tff(8129,plain,((op(e2, e2) = e3) | (op(e1, e3) = e0) | (op(e2, e3) = e3) | (op(e1, e3) = e3) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e2) = e3) | (op(e3, e3) = e2) | (op(e1, e3) = e2) | (op(e3, e1) = e2) | (op(e3, e1) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.64 tff(8130,plain,
% 1.54/1.64 (op(e2, e2) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[8129, 2839, 124, 1080, 121, 79, 75, 126, 72, 82, 80, 1304])).
% 1.54/1.64 tff(8131,plain,
% 1.54/1.64 (e3 = op(e2, e2)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8130])).
% 1.54/1.64 tff(8132,plain,
% 1.54/1.64 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8131])).
% 1.54/1.64 tff(8133,plain,
% 1.54/1.64 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e3)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8132])).
% 1.54/1.64 tff(8134,plain,
% 1.54/1.64 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8133])).
% 1.54/1.64 tff(8135,plain,
% 1.54/1.64 (~(op(e2, e1) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[508, 8134])).
% 1.54/1.64 tff(8136,plain,
% 1.54/1.64 (op(e2, e1) = e1),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2367, 8135, 7791, 7796])).
% 1.54/1.64 tff(8137,plain,
% 1.54/1.64 ((op(e2, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8136])).
% 1.54/1.64 tff(8138,plain,
% 1.54/1.64 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8137, 7793])).
% 1.54/1.64 tff(8139,plain,
% 1.54/1.64 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8138])).
% 1.54/1.64 tff(8140,plain,
% 1.54/1.64 (~(op(e3, e1) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[402, 8139])).
% 1.54/1.64 tff(8141,plain,
% 1.54/1.64 (op(e3, e1) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[446, 8140, 82, 2839])).
% 1.54/1.64 tff(8142,plain,
% 1.54/1.64 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8136])).
% 1.54/1.64 tff(8143,plain,
% 1.54/1.64 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8142])).
% 1.54/1.64 tff(8144,plain,
% 1.54/1.64 (~(op(e2, e0) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1966, 8143])).
% 1.54/1.64 tff(8145,plain,
% 1.54/1.64 ((op(e3, e1) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8141])).
% 1.54/1.64 tff(8146,plain,
% 1.54/1.64 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8145, 3077])).
% 1.54/1.64 tff(8147,plain,
% 1.54/1.64 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8146])).
% 1.54/1.64 tff(8148,plain,
% 1.54/1.64 (~(op(e3, e3) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[437, 8147])).
% 1.54/1.64 tff(8149,plain,
% 1.54/1.64 (op(e3, e3) = e3),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[1071, 8148, 126, 5430])).
% 1.54/1.64 tff(8150,plain,
% 1.54/1.64 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8149])).
% 1.54/1.64 tff(8151,plain,
% 1.54/1.64 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8150])).
% 1.54/1.64 tff(8152,plain,
% 1.54/1.64 (~(op(e0, e3) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[1077, 8151])).
% 1.54/1.64 tff(8153,plain,
% 1.54/1.64 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8131])).
% 1.54/1.64 tff(8154,plain,
% 1.54/1.64 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.54/1.64 inference(symmetry,[status(thm)],[8153])).
% 1.54/1.64 tff(8155,plain,
% 1.54/1.64 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8154])).
% 1.54/1.64 tff(8156,plain,
% 1.54/1.64 (~(op(e0, e2) = e3)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[2736, 8155])).
% 1.54/1.64 tff(8157,plain,
% 1.54/1.64 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8141])).
% 1.54/1.64 tff(8158,plain,
% 1.54/1.64 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8157])).
% 1.54/1.64 tff(8159,plain,
% 1.54/1.64 (~(op(e0, e1) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[3046, 8158])).
% 1.54/1.64 tff(8160,plain,
% 1.54/1.64 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e1)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8136])).
% 1.54/1.64 tff(8161,plain,
% 1.54/1.64 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e1))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8160])).
% 1.54/1.64 tff(8162,plain,
% 1.54/1.64 (~(op(e0, e1) = e1)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[606, 8161])).
% 1.54/1.64 tff(8163,plain,
% 1.54/1.64 ((e0 = e3) <=> (e0 = op(e2, e2))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8131])).
% 1.54/1.64 tff(8164,plain,
% 1.54/1.64 ((e0 = e3) <=> (op(e2, e2) = e0)),
% 1.54/1.64 inference(transitivity,[status(thm)],[8163, 994])).
% 1.54/1.64 tff(8165,plain,
% 1.54/1.64 ((~(e0 = e3)) <=> (~(op(e2, e2) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8164])).
% 1.54/1.64 tff(8166,plain,
% 1.54/1.64 (~(op(e2, e2) = e0)),
% 1.54/1.64 inference(modus_ponens,[status(thm)],[181, 8165])).
% 1.54/1.64 tff(8167,plain,
% 1.54/1.64 (op(e2, e0) = e0),
% 1.54/1.64 inference(unit_resolution,[status(thm)],[2311, 8166, 7791, 5436])).
% 1.54/1.64 tff(8168,plain,
% 1.54/1.64 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8167])).
% 1.54/1.64 tff(8169,plain,
% 1.54/1.64 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 1.54/1.64 inference(monotonicity,[status(thm)],[8168])).
% 1.54/1.65 tff(8170,plain,
% 1.54/1.65 (~(op(e1, e0) = e0)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[756, 8169])).
% 1.54/1.65 tff(8171,plain,
% 1.54/1.65 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8141])).
% 1.54/1.65 tff(8172,plain,
% 1.54/1.65 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8171])).
% 1.54/1.65 tff(8173,plain,
% 1.54/1.65 (~(op(e1, e1) = e0)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[945, 8172])).
% 1.54/1.65 tff(8174,plain,
% 1.54/1.65 (op(e1, e2) = e0),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1830, 8173, 80, 8170])).
% 1.54/1.65 tff(8175,plain,
% 1.54/1.65 (op(e1, e1) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1993, 5828, 82, 3540])).
% 1.54/1.65 tff(8176,plain,
% 1.54/1.65 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8175])).
% 1.54/1.65 tff(8177,plain,
% 1.54/1.65 (op(e1, op(e1, e1)) = e0),
% 1.54/1.65 inference(transitivity,[status(thm)],[8176, 6900])).
% 1.54/1.65 tff(8178,plain,
% 1.54/1.65 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8177])).
% 1.54/1.65 tff(8179,plain,
% 1.54/1.65 ((e3 = op(e1, op(e1, op(e1, e1)))) <=> (e3 = op(e1, e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8178])).
% 1.54/1.65 tff(8180,plain,
% 1.54/1.65 ((e3 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e3)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8179, 3497])).
% 1.54/1.65 tff(8181,plain,
% 1.54/1.65 ((op(e1, e0) = e3) <=> (e3 = op(e1, op(e1, op(e1, e1))))),
% 1.54/1.65 inference(symmetry,[status(thm)],[8180])).
% 1.54/1.65 tff(8182,plain,
% 1.54/1.65 (op(e0, e1) = e3),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[829, 5828, 3528, 3849])).
% 1.54/1.65 tff(8183,plain,
% 1.54/1.65 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8182])).
% 1.54/1.65 tff(8184,plain,
% 1.54/1.65 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8183, 1112])).
% 1.54/1.65 tff(8185,plain,
% 1.54/1.65 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8184])).
% 1.54/1.65 tff(8186,plain,
% 1.54/1.65 (~(op(e1, e1) = e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[792, 8185])).
% 1.54/1.65 tff(8187,plain,
% 1.54/1.65 (op(e1, e0) = e3),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[247, 8186, 75, 1080])).
% 1.54/1.65 tff(8188,plain,
% 1.54/1.65 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8187, 8181])).
% 1.54/1.65 tff(8189,plain,
% 1.54/1.65 (e2 = op(e1, e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8175, 2254])).
% 1.54/1.65 tff(8190,plain,
% 1.54/1.65 (op(e1, e2) = op(e1, op(e1, e1))),
% 1.54/1.65 inference(symmetry,[status(thm)],[8176])).
% 1.54/1.65 tff(8191,plain,
% 1.54/1.65 (e0 = op(e1, op(e1, e1))),
% 1.54/1.65 inference(transitivity,[status(thm)],[6901, 8190])).
% 1.54/1.65 tff(8192,plain,
% 1.54/1.65 (~(e3 = op(e1, op(e1, op(e1, e1))))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2269, 8191, 8189])).
% 1.54/1.65 tff(8193,plain,
% 1.54/1.65 ($false),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8192, 8188])).
% 1.54/1.65 tff(8194,plain,((op(e0, e1) = e2) | (~(op(e1, e2) = e0)) | (op(e1, e2) = e3) | (op(e1, e3) = e3) | (op(e3, e1) = e2) | (op(e2, e1) = e2) | (op(e0, e1) = e1) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.65 tff(8195,plain,
% 1.54/1.65 (op(e0, e1) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8194, 8174, 75, 1080, 82, 7796, 8162, 8159])).
% 1.54/1.65 tff(8196,plain,
% 1.54/1.65 ((op(e0, e1) = e3) <=> (e2 = op(e2, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8195, 8131])).
% 1.54/1.65 tff(8197,plain,
% 1.54/1.65 ((op(e0, e1) = e3) <=> (op(e2, e2) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8196, 81])).
% 1.54/1.65 tff(8198,plain,
% 1.54/1.65 ((op(e2, e2) = e2) <=> (op(e0, e1) = e3)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8197])).
% 1.54/1.65 tff(8199,plain,
% 1.54/1.65 ((~(op(e2, e2) = e2)) <=> (~(op(e0, e1) = e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8198])).
% 1.54/1.65 tff(8200,plain,
% 1.54/1.65 (~(op(e0, e1) = e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[7808, 8199])).
% 1.54/1.65 tff(8201,plain,
% 1.54/1.65 (op(e0, e0) = e3),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1495, 8200, 8156, 8152])).
% 1.54/1.65 tff(8202,plain,
% 1.54/1.65 (op(e0, e0) = op(e2, e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8201, 8131])).
% 1.54/1.65 tff(8203,plain,
% 1.54/1.65 ((op(e0, e0) = e1) <=> (op(e2, e2) = e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8202])).
% 1.54/1.65 tff(8204,plain,
% 1.54/1.65 ((op(e2, e2) = e1) <=> (op(e0, e0) = e1)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8203])).
% 1.54/1.65 tff(8205,plain,
% 1.54/1.65 ((~(op(e2, e2) = e1)) <=> (~(op(e0, e0) = e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8204])).
% 1.54/1.65 tff(8206,plain,
% 1.54/1.65 ((e1 = e3) <=> (e1 = op(e2, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8131])).
% 1.54/1.65 tff(8207,plain,
% 1.54/1.65 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8206, 316])).
% 1.54/1.65 tff(8208,plain,
% 1.54/1.65 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8207])).
% 1.54/1.65 tff(8209,plain,
% 1.54/1.65 (~(op(e2, e2) = e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[303, 8208])).
% 1.54/1.65 tff(8210,plain,
% 1.54/1.65 (~(op(e0, e0) = e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8209, 8205])).
% 1.54/1.65 tff(8211,plain,
% 1.54/1.65 (op(e3, e0) = e1),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1480, 8210, 8144, 5439])).
% 1.54/1.65 tff(8212,plain,
% 1.54/1.65 (op(e3, op(e3, e0)) = op(e3, e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8211])).
% 1.54/1.65 tff(8213,plain,
% 1.54/1.65 (op(e3, op(e3, e0)) = e0),
% 1.54/1.65 inference(transitivity,[status(thm)],[8212, 8141])).
% 1.54/1.65 tff(8214,plain,
% 1.54/1.65 ((op(e1, e2) = e2) <=> (e0 = e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8174])).
% 1.54/1.65 tff(8215,plain,
% 1.54/1.65 ((e0 = e2) <=> (op(e1, e2) = e2)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8214])).
% 1.54/1.65 tff(8216,plain,
% 1.54/1.65 ((~(e0 = e2)) <=> (~(op(e1, e2) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8215])).
% 1.54/1.65 tff(8217,plain,
% 1.54/1.65 (~(op(e1, e2) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[14, 8216])).
% 1.54/1.65 tff(8218,plain,
% 1.54/1.65 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8195])).
% 1.54/1.65 tff(8219,plain,
% 1.54/1.65 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8218, 3491])).
% 1.54/1.65 tff(8220,plain,
% 1.54/1.65 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8219])).
% 1.54/1.65 tff(8221,plain,
% 1.54/1.65 (~(op(e0, e2) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[2102, 8220])).
% 1.54/1.65 tff(8222,plain,
% 1.54/1.65 (op(e3, e2) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1151, 8221, 7808, 8217])).
% 1.54/1.65 tff(8223,plain,
% 1.54/1.65 (op(e3, op(e3, e2)) = op(e3, e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8222])).
% 1.54/1.65 tff(8224,plain,
% 1.54/1.65 (op(e3, op(e3, e2)) = e2),
% 1.54/1.65 inference(transitivity,[status(thm)],[8223, 8222])).
% 1.54/1.65 tff(8225,plain,
% 1.54/1.65 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1904, 8224])).
% 1.54/1.65 tff(8226,plain,
% 1.54/1.65 (op(e0, op(e2, e2)) = op(e0, e3)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8130])).
% 1.54/1.65 tff(8227,plain,
% 1.54/1.65 (op(op(e3, e1), e3) = op(e0, op(e2, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8141, 8131])).
% 1.54/1.65 tff(8228,plain,
% 1.54/1.65 (op(op(e3, e1), e3) = op(e0, e3)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8227, 8226])).
% 1.54/1.65 tff(8229,plain,
% 1.54/1.65 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8228])).
% 1.54/1.65 tff(8230,plain,
% 1.54/1.65 ((op(e0, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8229])).
% 1.54/1.65 tff(8231,plain,
% 1.54/1.65 ((~(op(e0, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8230])).
% 1.54/1.65 tff(8232,plain,
% 1.54/1.65 (~(op(op(e3, e1), e3) = e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[121, 8231])).
% 1.54/1.65 tff(8233,plain,
% 1.54/1.65 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1050, 8232])).
% 1.54/1.65 tff(8234,plain,
% 1.54/1.65 (op(e2, op(e2, e0)) = op(e2, e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8167])).
% 1.54/1.65 tff(8235,plain,
% 1.54/1.65 (op(e2, op(e2, e0)) = e0),
% 1.54/1.65 inference(transitivity,[status(thm)],[8234, 8167])).
% 1.54/1.65 tff(8236,plain,
% 1.54/1.65 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2653, 8235])).
% 1.54/1.65 tff(8237,plain,
% 1.54/1.65 (op(e1, op(e1, e2)) = op(e1, e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8174])).
% 1.54/1.65 tff(8238,plain,
% 1.54/1.65 ((op(e1, op(e1, e2)) = e2) <=> (op(e1, e0) = e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8237])).
% 1.54/1.65 tff(8239,plain,
% 1.54/1.65 ((op(e1, e0) = e2) <=> (op(e1, op(e1, e2)) = e2)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8238])).
% 1.54/1.65 tff(8240,plain,
% 1.54/1.65 ((op(e0, e1) = op(e1, e1)) <=> (e2 = op(e1, e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8195])).
% 1.54/1.65 tff(8241,plain,
% 1.54/1.65 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8240, 2166])).
% 1.54/1.65 tff(8242,plain,
% 1.54/1.65 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8241])).
% 1.54/1.65 tff(8243,plain,
% 1.54/1.65 (~(op(e1, e1) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[792, 8242])).
% 1.54/1.65 tff(8244,plain,
% 1.54/1.65 (op(e1, e0) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2285, 8243, 72, 8217])).
% 1.54/1.65 tff(8245,plain,
% 1.54/1.65 (op(e1, op(e1, e2)) = e2),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8244, 8239])).
% 1.54/1.65 tff(8246,plain,
% 1.54/1.65 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2377, 8245])).
% 1.54/1.65 tff(8247,plain,
% 1.54/1.65 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8174])).
% 1.54/1.65 tff(8248,plain,
% 1.54/1.65 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8247])).
% 1.54/1.65 tff(8249,plain,
% 1.54/1.65 (~(op(e0, e2) = e0)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[6205, 8248])).
% 1.54/1.65 tff(8250,plain,
% 1.54/1.65 (op(e0, e2) = e1),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2745, 8221, 8156, 8249])).
% 1.54/1.65 tff(8251,plain,
% 1.54/1.65 (op(e0, op(e0, e2)) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8031, 8250, 8195])).
% 1.54/1.65 tff(8252,plain,
% 1.54/1.65 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1331, 8251])).
% 1.54/1.65 tff(8253,plain,
% 1.54/1.65 (op(e2, op(e2, e1)) = op(e2, e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8136])).
% 1.54/1.65 tff(8254,plain,
% 1.54/1.65 (op(e2, op(e2, e1)) = e1),
% 1.54/1.65 inference(transitivity,[status(thm)],[8253, 8136])).
% 1.54/1.65 tff(8255,plain,
% 1.54/1.65 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1355, 8254])).
% 1.54/1.65 tff(8256,plain,
% 1.54/1.65 (op(op(e0, e1), e0) = op(e2, e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8195])).
% 1.54/1.65 tff(8257,plain,
% 1.54/1.65 (op(op(e0, e1), e0) = e0),
% 1.54/1.65 inference(transitivity,[status(thm)],[8256, 8167])).
% 1.54/1.65 tff(8258,plain,
% 1.54/1.65 ((op(op(e0, e1), e0) = e1) <=> (e0 = e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8257])).
% 1.54/1.65 tff(8259,plain,
% 1.54/1.65 ((e0 = e1) <=> (op(op(e0, e1), e0) = e1)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8258])).
% 1.54/1.65 tff(8260,plain,
% 1.54/1.65 ((~(e0 = e1)) <=> (~(op(op(e0, e1), e0) = e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8259])).
% 1.54/1.65 tff(8261,plain,
% 1.54/1.65 (~(op(op(e0, e1), e0) = e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[26, 8260])).
% 1.54/1.65 tff(8262,plain,
% 1.54/1.65 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1461, 8261])).
% 1.54/1.65 tff(8263,plain,
% 1.54/1.65 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8244])).
% 1.54/1.65 tff(8264,plain,
% 1.54/1.65 (op(e1, op(e1, e0)) = e0),
% 1.54/1.65 inference(transitivity,[status(thm)],[8263, 8174])).
% 1.54/1.65 tff(8265,plain,
% 1.54/1.65 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1836, 8264])).
% 1.54/1.65 tff(8266,plain,
% 1.54/1.65 (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1459, 8265, 8262, 8255, 5469, 1304, 8252, 8246, 8236, 8233, 8225, 7914])).
% 1.54/1.65 tff(8267,plain,
% 1.54/1.65 (~(op(e3, op(e3, e0)) = e0)),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1345, 8266])).
% 1.54/1.65 tff(8268,plain,
% 1.54/1.65 ($false),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8267, 8213])).
% 1.54/1.65 tff(8269,plain,((op(e3, e1) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e3) = e3) | (op(e3, e1) = e2) | (op(e3, e3) = e2) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.65 tff(8270,plain,
% 1.54/1.65 (op(e3, e1) = e3),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8269, 82, 72, 75, 1080, 1304, 126, 80, 121, 124, 79])).
% 1.54/1.65 tff(8271,plain,
% 1.54/1.65 (e3 = op(e3, e1)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8270])).
% 1.54/1.65 tff(8272,plain,
% 1.54/1.65 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e3, e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8271])).
% 1.54/1.65 tff(8273,plain,
% 1.54/1.65 ((op(e3, e3) = e3) <=> (op(e3, e1) = op(e3, e3))),
% 1.54/1.65 inference(transitivity,[status(thm)],[8272, 7792])).
% 1.54/1.65 tff(8274,plain,
% 1.54/1.65 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8273])).
% 1.54/1.65 tff(8275,plain,
% 1.54/1.65 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8274])).
% 1.54/1.65 tff(8276,plain,
% 1.54/1.65 (~(op(e3, e3) = e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[437, 8275])).
% 1.54/1.65 tff(8277,plain,
% 1.54/1.65 (op(e3, e3) = e0),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1071, 8276, 126, 5430])).
% 1.54/1.65 tff(8278,plain,
% 1.54/1.65 (e0 = op(e3, e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8277, 3078])).
% 1.54/1.65 tff(8279,plain,
% 1.54/1.65 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8277])).
% 1.54/1.65 tff(8280,plain,
% 1.54/1.65 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8279])).
% 1.54/1.65 tff(8281,plain,
% 1.54/1.65 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8280, 5377])).
% 1.54/1.65 tff(8282,plain,
% 1.54/1.65 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.54/1.65 inference(symmetry,[status(thm)],[8281])).
% 1.54/1.65 tff(8283,plain,
% 1.54/1.65 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e3, e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8271])).
% 1.54/1.65 tff(8284,plain,
% 1.54/1.65 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8283])).
% 1.54/1.65 tff(8285,plain,
% 1.54/1.65 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8284])).
% 1.54/1.65 tff(8286,plain,
% 1.54/1.65 (~(op(e1, e1) = e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[945, 8285])).
% 1.54/1.65 tff(8287,plain,
% 1.54/1.65 (op(e1, e0) = e3),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[247, 8286, 75, 1080])).
% 1.54/1.65 tff(8288,plain,
% 1.54/1.65 (op(e1, e0) = op(e3, e1)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8287, 8271])).
% 1.54/1.65 tff(8289,plain,
% 1.54/1.65 ((op(e1, e0) = e2) <=> (op(e3, e1) = e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8288])).
% 1.54/1.65 tff(8290,plain,
% 1.54/1.65 ((op(e3, e1) = e2) <=> (op(e1, e0) = e2)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8289])).
% 1.54/1.65 tff(8291,plain,
% 1.54/1.65 ((~(op(e3, e1) = e2)) <=> (~(op(e1, e0) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8290])).
% 1.54/1.65 tff(8292,plain,
% 1.54/1.65 (~(op(e1, e0) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[82, 8291])).
% 1.54/1.65 tff(8293,plain,
% 1.54/1.65 (op(e1, e2) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[7899, 8292, 8287, 72, 8277, 7800, 75])).
% 1.54/1.65 tff(8294,plain,
% 1.54/1.65 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8293])).
% 1.54/1.65 tff(8295,plain,
% 1.54/1.65 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8294, 2234])).
% 1.54/1.65 tff(8296,plain,
% 1.54/1.65 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8295])).
% 1.54/1.65 tff(8297,plain,
% 1.54/1.65 (~(op(e3, e2) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[2292, 8296])).
% 1.54/1.65 tff(8298,plain,
% 1.54/1.65 (op(e3, e0) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[2015, 8297, 126, 82])).
% 1.54/1.65 tff(8299,plain,
% 1.54/1.65 (e2 = op(e3, op(e3, e3))),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[8298, 8282])).
% 1.54/1.65 tff(8300,plain,
% 1.54/1.65 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8279])).
% 1.54/1.65 tff(8301,plain,
% 1.54/1.65 (op(e3, op(e3, e0)) = op(e3, op(e3, op(e3, e3)))),
% 1.54/1.65 inference(symmetry,[status(thm)],[8300])).
% 1.54/1.65 tff(8302,plain,
% 1.54/1.65 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8298])).
% 1.54/1.65 tff(8303,plain,
% 1.54/1.65 (op(e3, e2) = op(e3, op(e3, e0))),
% 1.54/1.65 inference(symmetry,[status(thm)],[8302])).
% 1.54/1.65 tff(8304,plain,
% 1.54/1.65 (e0 = op(e3, e3)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8277])).
% 1.54/1.65 tff(8305,plain,
% 1.54/1.65 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8304])).
% 1.54/1.65 tff(8306,plain,
% 1.54/1.65 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8305])).
% 1.54/1.65 tff(8307,plain,
% 1.54/1.65 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8306])).
% 1.54/1.65 tff(8308,plain,
% 1.54/1.65 (~(op(e3, e2) = e0)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[1888, 8307])).
% 1.54/1.65 tff(8309,plain,
% 1.54/1.65 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8271])).
% 1.54/1.65 tff(8310,plain,
% 1.54/1.65 ((op(e3, e2) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 1.54/1.65 inference(transitivity,[status(thm)],[8309, 4845])).
% 1.54/1.65 tff(8311,plain,
% 1.54/1.65 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8310])).
% 1.54/1.65 tff(8312,plain,
% 1.54/1.65 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8311])).
% 1.54/1.65 tff(8313,plain,
% 1.54/1.65 (~(op(e3, e2) = e3)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[3429, 8312])).
% 1.54/1.65 tff(8314,plain,
% 1.54/1.65 (op(e3, e2) = e1),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1898, 8297, 8313, 8308])).
% 1.54/1.65 tff(8315,plain,
% 1.54/1.65 (e1 = op(e3, e2)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8314])).
% 1.54/1.65 tff(8316,plain,
% 1.54/1.65 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.54/1.65 inference(transitivity,[status(thm)],[8315, 8303, 8301])).
% 1.54/1.65 tff(8317,plain,
% 1.54/1.65 ($false),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[3093, 8316, 8299, 8278])).
% 1.54/1.65 tff(8318,plain,((op(e3, e1) = e2) | (op(e3, e3) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.65 tff(8319,plain,
% 1.54/1.65 (op(e3, e1) = e2),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[8318, 1080, 72, 75, 126, 1304, 80, 121, 124, 79])).
% 1.54/1.65 tff(8320,plain,
% 1.54/1.65 (op(op(e3, e1), e3) = op(e2, e3)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.65 tff(8321,plain,
% 1.54/1.65 (op(op(e3, e1), e3) = e2),
% 1.54/1.65 inference(transitivity,[status(thm)],[8320, 5431])).
% 1.54/1.65 tff(8322,plain,
% 1.54/1.65 ((op(op(e3, e1), e3) = e1) <=> (e2 = e1)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8321])).
% 1.54/1.65 tff(8323,plain,
% 1.54/1.65 ((op(op(e3, e1), e3) = e1) <=> (e1 = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8322, 69])).
% 1.54/1.65 tff(8324,plain,
% 1.54/1.65 ((e1 = e2) <=> (op(op(e3, e1), e3) = e1)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8323])).
% 1.54/1.65 tff(8325,plain,
% 1.54/1.65 ((~(e1 = e2)) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8324])).
% 1.54/1.65 tff(8326,plain,
% 1.54/1.65 (~(op(op(e3, e1), e3) = e1)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[708, 8325])).
% 1.54/1.65 tff(8327,plain,
% 1.54/1.65 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.54/1.65 inference(unit_resolution,[status(thm)],[1050, 8326])).
% 1.54/1.65 tff(8328,plain,
% 1.54/1.65 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.65 tff(8329,plain,
% 1.54/1.65 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8328, 2234])).
% 1.54/1.65 tff(8330,plain,
% 1.54/1.65 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8329])).
% 1.54/1.65 tff(8331,plain,
% 1.54/1.65 (~(op(e3, e2) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[3429, 8330])).
% 1.54/1.65 tff(8332,plain,
% 1.54/1.65 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.65 tff(8333,plain,
% 1.54/1.65 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8332])).
% 1.54/1.65 tff(8334,plain,
% 1.54/1.65 (~(op(e0, e1) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[3046, 8333])).
% 1.54/1.65 tff(8335,plain,
% 1.54/1.65 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e2)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.65 tff(8336,plain,
% 1.54/1.65 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e2))),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8335])).
% 1.54/1.65 tff(8337,plain,
% 1.54/1.65 (~(op(e1, e1) = e2)),
% 1.54/1.65 inference(modus_ponens,[status(thm)],[945, 8336])).
% 1.54/1.65 tff(8338,plain,
% 1.54/1.65 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 1.54/1.65 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.65 tff(8339,plain,
% 1.54/1.65 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 1.54/1.65 inference(transitivity,[status(thm)],[8338, 1])).
% 1.54/1.65 tff(8340,plain,
% 1.54/1.65 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 1.54/1.65 inference(symmetry,[status(thm)],[8339])).
% 1.54/1.65 tff(8341,plain,
% 1.54/1.65 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8340])).
% 1.54/1.66 tff(8342,plain,
% 1.54/1.66 (~(op(e3, e1) = e0)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[14, 8341])).
% 1.54/1.66 tff(8343,plain,
% 1.54/1.66 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[5431])).
% 1.54/1.66 tff(8344,plain,
% 1.54/1.66 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 1.54/1.66 inference(symmetry,[status(thm)],[8343])).
% 1.54/1.66 tff(8345,plain,
% 1.54/1.66 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8329, 8344, 395])).
% 1.54/1.66 tff(8346,plain,
% 1.54/1.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8345])).
% 1.54/1.66 tff(8347,plain,
% 1.54/1.66 (~(op(e2, e3) = op(e3, e2))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[3429, 8346])).
% 1.54/1.66 tff(8348,plain,
% 1.54/1.66 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[430, 8347])).
% 1.54/1.66 tff(8349,plain,
% 1.54/1.66 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8329, 8344])).
% 1.54/1.66 tff(8350,plain,
% 1.54/1.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8349])).
% 1.54/1.66 tff(8351,plain,
% 1.54/1.66 (~(op(e3, e2) = op(e2, e3))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[3429, 8350])).
% 1.54/1.66 tff(8352,plain,
% 1.54/1.66 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[500, 8351])).
% 1.54/1.66 tff(8353,plain,
% 1.54/1.66 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[5426])).
% 1.54/1.66 tff(8354,plain,
% 1.54/1.66 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.54/1.66 inference(symmetry,[status(thm)],[8353])).
% 1.54/1.66 tff(8355,plain,
% 1.54/1.66 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8319])).
% 1.54/1.66 tff(8356,plain,
% 1.54/1.66 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8355, 69])).
% 1.54/1.66 tff(8357,plain,
% 1.54/1.66 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8356])).
% 1.54/1.66 tff(8358,plain,
% 1.54/1.66 ((e1 = e2) <=> (op(e3, e1) = op(e1, e3))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8357, 8354])).
% 1.54/1.66 tff(8359,plain,
% 1.54/1.66 ((~(e1 = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8358])).
% 1.54/1.66 tff(8360,plain,
% 1.54/1.66 (~(op(e3, e1) = op(e1, e3))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[708, 8359])).
% 1.54/1.66 tff(8361,plain,
% 1.54/1.66 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6362, 8360])).
% 1.54/1.66 tff(8362,plain,
% 1.54/1.66 ((e1 = e2) <=> (op(e1, e3) = op(e3, e1))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8357, 8354, 6290])).
% 1.54/1.66 tff(8363,plain,
% 1.54/1.66 ((~(e1 = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8362])).
% 1.54/1.66 tff(8364,plain,
% 1.54/1.66 (~(op(e1, e3) = op(e3, e1))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[708, 8363])).
% 1.54/1.66 tff(8365,plain,
% 1.54/1.66 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6307, 8364])).
% 1.54/1.66 tff(8366,plain,
% 1.54/1.66 (op(e0, e2) = e2),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[1151, 3785, 5548, 2386])).
% 1.54/1.66 tff(8367,plain,
% 1.54/1.66 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e2)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8366])).
% 1.54/1.66 tff(8368,plain,
% 1.54/1.66 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 1.54/1.66 inference(symmetry,[status(thm)],[8367])).
% 1.54/1.66 tff(8369,plain,
% 1.54/1.66 ((op(e2, e0) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8368, 6337])).
% 1.54/1.66 tff(8370,plain,
% 1.54/1.66 ((~(op(e2, e0) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8369])).
% 1.54/1.66 tff(8371,plain,
% 1.54/1.66 (~(op(e0, e2) = op(e2, e0))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[982, 8370])).
% 1.54/1.66 tff(8372,plain,
% 1.54/1.66 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6347, 8371])).
% 1.54/1.66 tff(8373,plain,
% 1.54/1.66 ((~(op(e2, e0) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8368])).
% 1.54/1.66 tff(8374,plain,
% 1.54/1.66 (~(op(e2, e0) = op(e0, e2))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[982, 8373])).
% 1.54/1.66 tff(8375,plain,
% 1.54/1.66 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6358, 8374])).
% 1.54/1.66 tff(8376,plain,
% 1.54/1.66 (op(e1, e2) = e0),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[1859, 3785, 2232, 75])).
% 1.54/1.66 tff(8377,plain,
% 1.54/1.66 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e0)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8376])).
% 1.54/1.66 tff(8378,plain,
% 1.54/1.66 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e0))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8377])).
% 1.54/1.66 tff(8379,plain,
% 1.54/1.66 (~(op(e1, e1) = e0)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[1604, 8378])).
% 1.54/1.66 tff(8380,plain,
% 1.54/1.66 (op(e0, e1) = e0),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[292, 8379, 2559, 183])).
% 1.54/1.66 tff(8381,plain,
% 1.54/1.66 (op(op(e1, e2), e1) = op(e0, e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8376])).
% 1.54/1.66 tff(8382,plain,
% 1.54/1.66 ((op(e0, e2) = e1) <=> (e2 = e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8366])).
% 1.54/1.66 tff(8383,plain,
% 1.54/1.66 ((op(e0, e2) = e1) <=> (e1 = e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8382, 69])).
% 1.54/1.66 tff(8384,plain,
% 1.54/1.66 ((e1 = e2) <=> (op(e0, e2) = e1)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8383])).
% 1.54/1.66 tff(8385,plain,
% 1.54/1.66 ((~(e1 = e2)) <=> (~(op(e0, e2) = e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8384])).
% 1.54/1.66 tff(8386,plain,
% 1.54/1.66 (~(op(e0, e2) = e1)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[708, 8385])).
% 1.54/1.66 tff(8387,plain,
% 1.54/1.66 (e0 = op(e1, e2)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8376])).
% 1.54/1.66 tff(8388,plain,
% 1.54/1.66 (op(e0, e1) = op(e1, e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8380, 8387])).
% 1.54/1.66 tff(8389,plain,
% 1.54/1.66 ((op(e0, e1) = e1) <=> (op(e1, e2) = e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8388])).
% 1.54/1.66 tff(8390,plain,
% 1.54/1.66 ((op(e1, e2) = e1) <=> (op(e0, e1) = e1)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8389])).
% 1.54/1.66 tff(8391,plain,
% 1.54/1.66 ((~(op(e1, e2) = e1)) <=> (~(op(e0, e1) = e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8390])).
% 1.54/1.66 tff(8392,plain,
% 1.54/1.66 (~(op(e0, e1) = e1)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[2232, 8391])).
% 1.54/1.66 tff(8393,plain,
% 1.54/1.66 (op(e0, e0) = e1),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[384, 8392, 121, 8386])).
% 1.54/1.66 tff(8394,plain,
% 1.54/1.66 (op(e0, op(e0, e0)) = op(op(e1, e2), e1)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8387, 8393])).
% 1.54/1.66 tff(8395,plain,
% 1.54/1.66 (op(e0, op(e0, e0)) = e0),
% 1.54/1.66 inference(transitivity,[status(thm)],[8394, 8381, 8380])).
% 1.54/1.66 tff(8396,plain,
% 1.54/1.66 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[5598, 8395])).
% 1.54/1.66 tff(8397,plain,
% 1.54/1.66 (op(e1, e1) = e3),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[630, 8379, 2165, 68])).
% 1.54/1.66 tff(8398,plain,
% 1.54/1.66 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8397])).
% 1.54/1.66 tff(8399,plain,
% 1.54/1.66 (op(e1, op(e1, e1)) = e1),
% 1.54/1.66 inference(transitivity,[status(thm)],[8398, 132])).
% 1.54/1.66 tff(8400,plain,
% 1.54/1.66 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[5678, 8399])).
% 1.54/1.66 tff(8401,plain,
% 1.54/1.66 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8387])).
% 1.54/1.66 tff(8402,plain,
% 1.54/1.66 ((op(e2, e1) = e0) <=> (op(e1, e2) = op(e2, e1))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8401, 531])).
% 1.54/1.66 tff(8403,plain,
% 1.54/1.66 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8402])).
% 1.54/1.66 tff(8404,plain,
% 1.54/1.66 (~(op(e1, e2) = op(e2, e1))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[2559, 8403])).
% 1.54/1.66 tff(8405,plain,
% 1.54/1.66 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[539, 8404])).
% 1.54/1.66 tff(8406,plain,
% 1.54/1.66 (op(e1, e0) = e2),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[2285, 3785, 72, 68])).
% 1.54/1.66 tff(8407,plain,
% 1.54/1.66 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8406])).
% 1.54/1.66 tff(8408,plain,
% 1.54/1.66 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8407, 4838])).
% 1.54/1.66 tff(8409,plain,
% 1.54/1.66 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.54/1.66 inference(symmetry,[status(thm)],[8408])).
% 1.54/1.66 tff(8410,plain,
% 1.54/1.66 ((~(op(e0, e1) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8409])).
% 1.54/1.66 tff(8411,plain,
% 1.54/1.66 (~(op(e1, e0) = op(e0, e1))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[5828, 8410])).
% 1.54/1.66 tff(8412,plain,
% 1.54/1.66 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[613, 8411])).
% 1.54/1.66 tff(8413,plain,
% 1.54/1.66 (e3 = op(e1, e1)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8397])).
% 1.54/1.66 tff(8414,plain,
% 1.54/1.66 ((op(e2, e1) = op(e1, e1)) <=> (op(e1, e1) = op(e2, e1))),
% 1.54/1.66 inference(commutativity,[status(thm)],[])).
% 1.54/1.66 tff(8415,plain,
% 1.54/1.66 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8413])).
% 1.54/1.66 tff(8416,plain,
% 1.54/1.66 ((op(e2, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8415, 8414])).
% 1.54/1.66 tff(8417,plain,
% 1.54/1.66 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8416])).
% 1.54/1.66 tff(8418,plain,
% 1.54/1.66 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8417])).
% 1.54/1.66 tff(8419,plain,
% 1.54/1.66 (~(op(e2, e1) = e3)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[225, 8418])).
% 1.54/1.66 tff(8420,plain,
% 1.54/1.66 ((op(e1, e2) = op(e1, e1)) <=> (op(e1, e1) = op(e1, e2))),
% 1.54/1.66 inference(commutativity,[status(thm)],[])).
% 1.54/1.66 tff(8421,plain,
% 1.54/1.66 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e1, e2))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8387])).
% 1.54/1.66 tff(8422,plain,
% 1.54/1.66 ((op(e2, e2) = e0) <=> (op(e1, e2) = op(e2, e2))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8421, 8066])).
% 1.54/1.66 tff(8423,plain,
% 1.54/1.66 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8422])).
% 1.54/1.66 tff(8424,plain,
% 1.54/1.66 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8423])).
% 1.54/1.66 tff(8425,plain,
% 1.54/1.66 (~(op(e2, e2) = e0)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[1273, 8424])).
% 1.54/1.66 tff(8426,plain,
% 1.54/1.66 (op(e2, e0) = e0),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[2311, 8425, 2559, 1063])).
% 1.54/1.66 tff(8427,plain,
% 1.54/1.66 (op(e2, e0) = op(e1, e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8426, 8387])).
% 1.54/1.66 tff(8428,plain,
% 1.54/1.66 ((op(e2, e0) = e3) <=> (op(e1, e2) = op(e1, e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8427, 8413])).
% 1.54/1.66 tff(8429,plain,
% 1.54/1.66 ((op(e2, e0) = e3) <=> (op(e1, e1) = op(e1, e2))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8428, 8420])).
% 1.54/1.66 tff(8430,plain,
% 1.54/1.66 ((op(e1, e1) = op(e1, e2)) <=> (op(e2, e0) = e3)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8429])).
% 1.54/1.66 tff(8431,plain,
% 1.54/1.66 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e2, e0) = e3))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8430])).
% 1.54/1.66 tff(8432,plain,
% 1.54/1.66 (~(op(e2, e0) = e3)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[1604, 8431])).
% 1.54/1.66 tff(8433,plain,
% 1.54/1.66 (op(e2, e2) = e3),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[1559, 8432, 8419, 124])).
% 1.54/1.66 tff(8434,plain,
% 1.54/1.66 (op(e2, e2) = op(e1, e1)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8433, 8413])).
% 1.54/1.66 tff(8435,plain,
% 1.54/1.66 (op(e1, op(e2, e2)) = op(e1, op(e1, e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8434])).
% 1.54/1.66 tff(8436,plain,
% 1.54/1.66 (op(e1, op(e2, e2)) = e1),
% 1.54/1.66 inference(transitivity,[status(thm)],[8435, 8398, 132])).
% 1.54/1.66 tff(8437,plain,
% 1.54/1.66 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6714, 8436])).
% 1.54/1.66 tff(8438,plain,
% 1.54/1.66 ((~(op(e2, e1) = e0)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8401])).
% 1.54/1.66 tff(8439,plain,
% 1.54/1.66 (~(op(e2, e1) = op(e1, e2))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[2559, 8438])).
% 1.54/1.66 tff(8440,plain,
% 1.54/1.66 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[557, 8439])).
% 1.54/1.66 tff(8441,plain,
% 1.54/1.66 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 1.54/1.66 inference(transitivity,[status(thm)],[8409, 596])).
% 1.54/1.66 tff(8442,plain,
% 1.54/1.66 ((~(op(e0, e1) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8441])).
% 1.54/1.66 tff(8443,plain,
% 1.54/1.66 (~(op(e0, e1) = op(e1, e0))),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[5828, 8442])).
% 1.54/1.66 tff(8444,plain,
% 1.54/1.66 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[609, 8443])).
% 1.54/1.66 tff(8445,plain,
% 1.54/1.66 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8380])).
% 1.54/1.66 tff(8446,plain,
% 1.54/1.66 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8445, 1079])).
% 1.54/1.66 tff(8447,plain,
% 1.54/1.66 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8446])).
% 1.54/1.66 tff(8448,plain,
% 1.54/1.66 (~(op(e0, e3) = e0)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[818, 8447])).
% 1.54/1.66 tff(8449,plain,
% 1.54/1.66 (op(e3, e3) = e0),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[1098, 8448, 1063, 80])).
% 1.54/1.66 tff(8450,plain,
% 1.54/1.66 (op(e3, e3) = op(e1, e2)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8449, 8387])).
% 1.54/1.66 tff(8451,plain,
% 1.54/1.66 (op(e3, op(e3, e3)) = op(e3, op(e1, e2))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8450])).
% 1.54/1.66 tff(8452,plain,
% 1.54/1.66 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, op(e1, e2)) = e3)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8451])).
% 1.54/1.66 tff(8453,plain,
% 1.54/1.66 ((op(e3, op(e1, e2)) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8452])).
% 1.54/1.66 tff(8454,plain,
% 1.54/1.66 (op(e3, op(e1, e2)) = op(e3, e0)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8376])).
% 1.54/1.66 tff(8455,plain,
% 1.54/1.66 (op(e3, e0) = op(e3, op(e1, e2))),
% 1.54/1.66 inference(symmetry,[status(thm)],[8454])).
% 1.54/1.66 tff(8456,plain,
% 1.54/1.66 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e2)) = e3)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8455])).
% 1.54/1.66 tff(8457,plain,
% 1.54/1.66 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8456, 8453])).
% 1.54/1.66 tff(8458,plain,
% 1.54/1.66 ((op(e1, e0) = e3) <=> (e2 = e3)),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8406])).
% 1.54/1.66 tff(8459,plain,
% 1.54/1.66 ((e2 = e3) <=> (op(e1, e0) = e3)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8458])).
% 1.54/1.66 tff(8460,plain,
% 1.54/1.66 ((~(e2 = e3)) <=> (~(op(e1, e0) = e3))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8459])).
% 1.54/1.66 tff(8461,plain,
% 1.54/1.66 (~(op(e1, e0) = e3)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[1321, 8460])).
% 1.54/1.66 tff(8462,plain,
% 1.54/1.66 ((e1 = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 1.54/1.66 inference(commutativity,[status(thm)],[])).
% 1.54/1.66 tff(8463,plain,
% 1.54/1.66 ((op(e0, e0) = e3) <=> (e1 = op(e1, e1))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8393, 8413])).
% 1.54/1.66 tff(8464,plain,
% 1.54/1.66 ((op(e0, e0) = e3) <=> (op(e1, e1) = e1)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8463, 8462])).
% 1.54/1.66 tff(8465,plain,
% 1.54/1.66 ((op(e1, e1) = e1) <=> (op(e0, e0) = e3)),
% 1.54/1.66 inference(symmetry,[status(thm)],[8464])).
% 1.54/1.66 tff(8466,plain,
% 1.54/1.66 ((~(op(e1, e1) = e1)) <=> (~(op(e0, e0) = e3))),
% 1.54/1.66 inference(monotonicity,[status(thm)],[8465])).
% 1.54/1.66 tff(8467,plain,
% 1.54/1.66 (~(op(e0, e0) = e3)),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[2165, 8466])).
% 1.54/1.66 tff(8468,plain,
% 1.54/1.66 (op(e3, e0) = e3),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[2713, 8467, 8461, 8432])).
% 1.54/1.66 tff(8469,plain,
% 1.54/1.66 (op(e3, op(e3, e3)) = e3),
% 1.54/1.66 inference(modus_ponens,[status(thm)],[8468, 8457])).
% 1.54/1.66 tff(8470,plain,
% 1.54/1.66 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.54/1.66 inference(unit_resolution,[status(thm)],[6277, 8469])).
% 1.54/1.66 tff(8471,plain,
% 1.54/1.66 (op(e3, e0) = op(e1, e1)),
% 1.54/1.66 inference(transitivity,[status(thm)],[8468, 8413])).
% 1.54/1.66 tff(8472,plain,
% 1.54/1.67 (op(e1, op(e3, e0)) = op(e1, op(e1, e1))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8471])).
% 1.54/1.67 tff(8473,plain,
% 1.54/1.67 (op(e1, op(e3, e0)) = e1),
% 1.54/1.67 inference(transitivity,[status(thm)],[8472, 8398, 132])).
% 1.54/1.67 tff(8474,plain,
% 1.54/1.67 (((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)) | (~(op(e1, op(e3, e0)) = e1))),
% 1.54/1.67 inference(tautology,[status(thm)],[])).
% 1.54/1.67 tff(8475,plain,
% 1.54/1.67 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[8474, 8473])).
% 1.54/1.67 tff(8476,plain,
% 1.54/1.67 ($false),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[5367, 8475, 8470, 8444, 8440, 5669, 5511, 8437, 8412, 8405, 8400, 5671, 8396, 8375, 5668, 8372])).
% 1.54/1.67 tff(8477,plain,((op(e1, e2) = e2) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~(op(e1, e3) = e1)) | (op(e2, e3) = e3) | (op(e2, e3) = e0) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e2, e1) = e0) | (op(e3, e1) = e0) | (op(e1, e1) = e2) | (op(e2, e0) = e2) | (op(e0, e1) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.67 tff(8478,plain,
% 1.54/1.67 (op(e1, e2) = e2),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[8477, 8365, 8361, 8352, 8348, 5426, 124, 5436, 80, 121, 7791, 8342, 8337, 5442, 8334, 7808, 8331, 72, 75])).
% 1.54/1.67 tff(8479,plain,
% 1.54/1.67 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8478])).
% 1.54/1.67 tff(8480,plain,
% 1.54/1.67 (op(e1, op(e1, e2)) = e2),
% 1.54/1.67 inference(transitivity,[status(thm)],[8479, 8478])).
% 1.54/1.67 tff(8481,plain,
% 1.54/1.67 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2377, 8480])).
% 1.54/1.67 tff(8482,plain,
% 1.54/1.67 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8478])).
% 1.54/1.67 tff(8483,plain,
% 1.54/1.67 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8482])).
% 1.54/1.67 tff(8484,plain,
% 1.54/1.67 (~(op(e0, e2) = e2)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[6205, 8483])).
% 1.54/1.67 tff(8485,plain,
% 1.54/1.67 (op(e0, e0) = e2),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[3652, 8484, 79, 8334])).
% 1.54/1.67 tff(8486,plain,
% 1.54/1.67 (e2 = op(e0, e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[2244, 78])).
% 1.54/1.67 tff(8487,plain,
% 1.54/1.67 ((e1 = op(e0, op(e0, e0))) <=> (e1 = op(e0, e2))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[2381])).
% 1.54/1.67 tff(8488,plain,
% 1.54/1.67 ((e1 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e1)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8487, 697])).
% 1.54/1.67 tff(8489,plain,
% 1.54/1.67 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 1.54/1.67 inference(symmetry,[status(thm)],[8488])).
% 1.54/1.67 tff(8490,plain,
% 1.54/1.67 (op(e0, e3) = e0),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[1098, 656, 1063, 80])).
% 1.54/1.67 tff(8491,plain,
% 1.54/1.67 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[6684])).
% 1.54/1.67 tff(8492,plain,
% 1.54/1.67 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8491, 1])).
% 1.54/1.67 tff(8493,plain,
% 1.54/1.67 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8492])).
% 1.54/1.67 tff(8494,plain,
% 1.54/1.67 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8493])).
% 1.54/1.67 tff(8495,plain,
% 1.54/1.67 (~(op(e3, e1) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[14, 8494])).
% 1.54/1.67 tff(8496,plain,
% 1.54/1.67 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8497,plain,
% 1.54/1.67 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8496])).
% 1.54/1.67 tff(8498,plain,
% 1.54/1.67 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8497])).
% 1.54/1.67 tff(8499,plain,
% 1.54/1.67 ((~(op(e3, e0) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8498])).
% 1.54/1.67 tff(8500,plain,
% 1.54/1.67 (op(e3, e3) = e3),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[1071, 656, 126, 926])).
% 1.54/1.67 tff(8501,plain,
% 1.54/1.67 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8500])).
% 1.54/1.67 tff(8502,plain,
% 1.54/1.67 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8501])).
% 1.54/1.67 tff(8503,plain,
% 1.54/1.67 (~(op(e3, e0) = e3)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[157, 8502])).
% 1.54/1.67 tff(8504,plain,
% 1.54/1.67 (~(op(e3, op(e0, e3)) = e3)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[8503, 8499])).
% 1.54/1.67 tff(8505,plain,
% 1.54/1.67 (op(e0, op(e0, e3)) = op(e0, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8506,plain,
% 1.54/1.67 (op(e0, op(e0, e3)) = e2),
% 1.54/1.67 inference(transitivity,[status(thm)],[8505, 2244])).
% 1.54/1.67 tff(8507,plain,
% 1.54/1.67 ((op(e0, op(e0, e3)) = e0) <=> (e2 = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8506])).
% 1.54/1.67 tff(8508,plain,
% 1.54/1.67 ((op(e0, op(e0, e3)) = e0) <=> (e0 = e2)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8507, 1])).
% 1.54/1.67 tff(8509,plain,
% 1.54/1.67 ((e0 = e2) <=> (op(e0, op(e0, e3)) = e0)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8508])).
% 1.54/1.67 tff(8510,plain,
% 1.54/1.67 ((~(e0 = e2)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8509])).
% 1.54/1.67 tff(8511,plain,
% 1.54/1.67 (~(op(e0, op(e0, e3)) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[14, 8510])).
% 1.54/1.67 tff(8512,plain,
% 1.54/1.67 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8513,plain,
% 1.54/1.67 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8512])).
% 1.54/1.67 tff(8514,plain,
% 1.54/1.67 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8513])).
% 1.54/1.67 tff(8515,plain,
% 1.54/1.67 ((~(op(e1, e0) = e1)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8514])).
% 1.54/1.67 tff(8516,plain,
% 1.54/1.67 (~(op(e1, op(e0, e3)) = e1)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[929, 8515])).
% 1.54/1.67 tff(8517,plain,
% 1.54/1.67 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8518,plain,
% 1.54/1.67 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8517])).
% 1.54/1.67 tff(8519,plain,
% 1.54/1.67 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8518])).
% 1.54/1.67 tff(8520,plain,
% 1.54/1.67 ((~(op(e2, e0) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8519])).
% 1.54/1.67 tff(8521,plain,
% 1.54/1.67 (~(op(e2, op(e0, e3)) = e2)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[982, 8520])).
% 1.54/1.67 tff(8522,plain,
% 1.54/1.67 (~(op(e3, e0) = op(e0, e3))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[4654, 8521, 121, 8516, 8511, 8504])).
% 1.54/1.67 tff(8523,plain,
% 1.54/1.67 (op(e3, e2) = e0),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[5538, 8522, 8495, 8490])).
% 1.54/1.67 tff(8524,plain,
% 1.54/1.67 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8523])).
% 1.54/1.67 tff(8525,plain,
% 1.54/1.67 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8524])).
% 1.54/1.67 tff(8526,plain,
% 1.54/1.67 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8525])).
% 1.54/1.67 tff(8527,plain,
% 1.54/1.67 (~(op(e3, e2) = e1)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[26, 8526])).
% 1.54/1.67 tff(8528,plain,
% 1.54/1.67 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8500])).
% 1.54/1.67 tff(8529,plain,
% 1.54/1.67 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8528])).
% 1.54/1.67 tff(8530,plain,
% 1.54/1.67 (~(op(e3, e2) = e3)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[1888, 8529])).
% 1.54/1.67 tff(8531,plain,
% 1.54/1.67 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8532,plain,
% 1.54/1.67 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8531])).
% 1.54/1.67 tff(8533,plain,
% 1.54/1.67 (~(op(e0, e1) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[818, 8532])).
% 1.54/1.67 tff(8534,plain,
% 1.54/1.67 (op(e1, e1) = e0),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[292, 8533, 2559, 8495])).
% 1.54/1.67 tff(8535,plain,
% 1.54/1.67 ((op(e1, e1) = e3) <=> (e0 = e3)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8534])).
% 1.54/1.67 tff(8536,plain,
% 1.54/1.67 ((e0 = e3) <=> (op(e1, e1) = e3)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8535])).
% 1.54/1.67 tff(8537,plain,
% 1.54/1.67 ((~(e0 = e3)) <=> (~(op(e1, e1) = e3))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8536])).
% 1.54/1.67 tff(8538,plain,
% 1.54/1.67 (~(op(e1, e1) = e3)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[181, 8537])).
% 1.54/1.67 tff(8539,plain,
% 1.54/1.67 (op(e1, e0) = e3),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[247, 8538, 75, 1080])).
% 1.54/1.67 tff(8540,plain,
% 1.54/1.67 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8539])).
% 1.54/1.67 tff(8541,plain,
% 1.54/1.67 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8540, 660])).
% 1.54/1.67 tff(8542,plain,
% 1.54/1.67 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8541])).
% 1.54/1.67 tff(8543,plain,
% 1.54/1.67 (~(op(e2, e0) = e3)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[756, 8542])).
% 1.54/1.67 tff(8544,plain,
% 1.54/1.67 ((op(e0, e0) = e1) <=> (e2 = e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[2244])).
% 1.54/1.67 tff(8545,plain,
% 1.54/1.67 ((op(e0, e0) = e1) <=> (e1 = e2)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8544, 69])).
% 1.54/1.67 tff(8546,plain,
% 1.54/1.67 ((e1 = e2) <=> (op(e0, e0) = e1)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8545])).
% 1.54/1.67 tff(8547,plain,
% 1.54/1.67 ((~(e1 = e2)) <=> (~(op(e0, e0) = e1))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8546])).
% 1.54/1.67 tff(8548,plain,
% 1.54/1.67 (~(op(e0, e0) = e1)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[708, 8547])).
% 1.54/1.67 tff(8549,plain,
% 1.54/1.67 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8490])).
% 1.54/1.67 tff(8550,plain,
% 1.54/1.67 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8549])).
% 1.54/1.67 tff(8551,plain,
% 1.54/1.67 (~(op(e3, e0) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[8522, 8550])).
% 1.54/1.67 tff(8552,plain,
% 1.54/1.67 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[2244])).
% 1.54/1.67 tff(8553,plain,
% 1.54/1.67 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8552, 1])).
% 1.54/1.67 tff(8554,plain,
% 1.54/1.67 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8553])).
% 1.54/1.67 tff(8555,plain,
% 1.54/1.67 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8554])).
% 1.54/1.67 tff(8556,plain,
% 1.54/1.67 (~(op(e0, e0) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[14, 8555])).
% 1.54/1.67 tff(8557,plain,
% 1.54/1.67 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8534])).
% 1.54/1.67 tff(8558,plain,
% 1.54/1.67 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8557])).
% 1.54/1.67 tff(8559,plain,
% 1.54/1.67 (~(op(e1, e0) = e0)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[737, 8558])).
% 1.54/1.67 tff(8560,plain,
% 1.54/1.67 (op(e2, e0) = e0),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[5651, 8559, 8556, 8551])).
% 1.54/1.67 tff(8561,plain,
% 1.54/1.67 (op(e2, op(e2, e0)) = op(e2, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8560])).
% 1.54/1.67 tff(8562,plain,
% 1.54/1.67 (op(e2, op(e2, e0)) = e0),
% 1.54/1.67 inference(transitivity,[status(thm)],[8561, 8560])).
% 1.54/1.67 tff(8563,plain,
% 1.54/1.67 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2653, 8562])).
% 1.54/1.67 tff(8564,plain,
% 1.54/1.67 (op(e3, e0) = e1),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[5422, 8551, 6692, 8503])).
% 1.54/1.67 tff(8565,plain,
% 1.54/1.67 (op(op(e1, e0), e0) = op(e3, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8539])).
% 1.54/1.67 tff(8566,plain,
% 1.54/1.67 (op(op(e1, e0), e0) = e1),
% 1.54/1.67 inference(transitivity,[status(thm)],[8565, 8564])).
% 1.54/1.67 tff(8567,plain,
% 1.54/1.67 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[3015, 8566])).
% 1.54/1.67 tff(8568,plain,
% 1.54/1.67 (op(op(e3, e0), e0) = op(e1, e0)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8564])).
% 1.54/1.67 tff(8569,plain,
% 1.54/1.67 (op(op(e3, e0), e0) = e3),
% 1.54/1.67 inference(transitivity,[status(thm)],[8568, 8539])).
% 1.54/1.67 tff(8570,plain,
% 1.54/1.67 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[4026, 8569])).
% 1.54/1.67 tff(8571,plain,
% 1.54/1.67 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8523])).
% 1.54/1.67 tff(8572,plain,
% 1.54/1.67 (op(op(e3, e2), e3) = e0),
% 1.54/1.67 inference(transitivity,[status(thm)],[8571, 8490])).
% 1.54/1.67 tff(8573,plain,
% 1.54/1.67 ((op(op(e3, e2), e3) = e2) <=> (e0 = e2)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8572])).
% 1.54/1.67 tff(8574,plain,
% 1.54/1.67 ((e0 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8573])).
% 1.54/1.67 tff(8575,plain,
% 1.54/1.67 ((~(e0 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8574])).
% 1.54/1.67 tff(8576,plain,
% 1.54/1.67 (~(op(op(e3, e2), e3) = e2)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[14, 8575])).
% 1.54/1.67 tff(8577,plain,
% 1.54/1.67 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2408, 8576])).
% 1.54/1.67 tff(8578,plain,
% 1.54/1.67 (op(e0, e2) = e3),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2111, 2431, 75, 1890])).
% 1.54/1.67 tff(8579,plain,
% 1.54/1.67 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8578])).
% 1.54/1.67 tff(8580,plain,
% 1.54/1.67 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 1.54/1.67 inference(transitivity,[status(thm)],[8579, 128])).
% 1.54/1.67 tff(8581,plain,
% 1.54/1.67 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 1.54/1.67 inference(symmetry,[status(thm)],[8580])).
% 1.54/1.67 tff(8582,plain,
% 1.54/1.67 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8581])).
% 1.54/1.67 tff(8583,plain,
% 1.54/1.67 (~(op(e0, e2) = e1)),
% 1.54/1.67 inference(modus_ponens,[status(thm)],[303, 8582])).
% 1.54/1.67 tff(8584,plain,
% 1.54/1.67 (op(e0, e1) = e1),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[384, 8583, 121, 2379])).
% 1.54/1.67 tff(8585,plain,
% 1.54/1.67 (op(e0, op(e0, e1)) = op(e0, e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8584])).
% 1.54/1.67 tff(8586,plain,
% 1.54/1.67 (op(e0, op(e0, e1)) = e1),
% 1.54/1.67 inference(transitivity,[status(thm)],[8585, 8584])).
% 1.54/1.67 tff(8587,plain,
% 1.54/1.67 (op(e2, e1) = e3),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[1559, 2431, 3272, 124])).
% 1.54/1.67 tff(8588,plain,
% 1.54/1.67 (op(op(e2, e1), e1) = op(e3, e1)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8587])).
% 1.54/1.67 tff(8589,plain,
% 1.54/1.67 (op(op(e2, e1), e1) = e2),
% 1.54/1.67 inference(transitivity,[status(thm)],[8588, 6684])).
% 1.54/1.67 tff(8590,plain,
% 1.54/1.67 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2371, 8589])).
% 1.54/1.67 tff(8591,plain,
% 1.54/1.67 (op(op(e0, e2), e2) = op(e3, e2)),
% 1.54/1.67 inference(monotonicity,[status(thm)],[8578])).
% 1.54/1.67 tff(8592,plain,
% 1.54/1.67 (op(op(e0, e2), e2) = e0),
% 1.54/1.67 inference(transitivity,[status(thm)],[8591, 5819])).
% 1.54/1.67 tff(8593,plain,
% 1.54/1.67 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[1956, 8592])).
% 1.54/1.67 tff(8594,plain,
% 1.54/1.67 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[1459, 8593, 3341, 1926, 3342, 1304, 1357, 1358, 2421, 1275, 8590, 1347])).
% 1.54/1.67 tff(8595,plain,
% 1.54/1.67 (~(op(e0, op(e0, e1)) = e1)),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[2449, 8594])).
% 1.54/1.67 tff(8596,plain,
% 1.54/1.67 ($false),
% 1.54/1.67 inference(unit_resolution,[status(thm)],[8595, 8586])).
% 1.54/1.67 tff(8597,plain,((op(e2, e2) = e3) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e0, e3) = e1) | (op(e0, e0) = e1) | (~(op(e3, e1) = e2)) | (~(op(e3, e2) = e0)) | (op(e2, e0) = e3) | (op(e2, e3) = e3) | (op(e1, e2) = e3) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.68 tff(8598,plain,
% 1.58/1.68 (op(e2, e2) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[8597, 8577, 8570, 3342, 1304, 8567, 1358, 8563, 1275, 1347, 121, 8548, 6684, 8523, 8543, 124, 75, 8530])).
% 1.58/1.68 tff(8599,plain,
% 1.58/1.68 ((op(e2, e2) = e1) <=> (e3 = e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8598])).
% 1.58/1.68 tff(8600,plain,
% 1.58/1.68 ((op(e2, e2) = e1) <=> (e1 = e3)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8599, 128])).
% 1.58/1.68 tff(8601,plain,
% 1.58/1.68 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8600])).
% 1.58/1.68 tff(8602,plain,
% 1.58/1.68 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8601])).
% 1.58/1.68 tff(8603,plain,
% 1.58/1.68 (~(op(e2, e2) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[303, 8602])).
% 1.58/1.68 tff(8604,plain,
% 1.58/1.68 (op(e0, e2) = e1),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[1613, 8603, 4515, 8527])).
% 1.58/1.68 tff(8605,plain,
% 1.58/1.68 (e1 = op(e0, op(e0, e0))),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8604, 8489])).
% 1.58/1.68 tff(8606,plain,
% 1.58/1.68 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e2))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[2381])).
% 1.58/1.68 tff(8607,plain,
% 1.58/1.68 (op(e0, op(e0, e2)) = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.68 inference(symmetry,[status(thm)],[8606])).
% 1.58/1.68 tff(8608,plain,
% 1.58/1.68 (op(e0, op(e0, e2)) = op(e0, e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8604])).
% 1.58/1.68 tff(8609,plain,
% 1.58/1.68 (op(e0, e1) = op(e0, op(e0, e2))),
% 1.58/1.68 inference(symmetry,[status(thm)],[8608])).
% 1.58/1.68 tff(8610,plain,
% 1.58/1.68 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8500])).
% 1.58/1.68 tff(8611,plain,
% 1.58/1.68 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8610])).
% 1.58/1.68 tff(8612,plain,
% 1.58/1.68 (~(op(e0, e3) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[1077, 8611])).
% 1.58/1.68 tff(8613,plain,
% 1.58/1.68 ((op(e0, e0) = e3) <=> (e2 = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[2244])).
% 1.58/1.68 tff(8614,plain,
% 1.58/1.68 ((e2 = e3) <=> (op(e0, e0) = e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8613])).
% 1.58/1.68 tff(8615,plain,
% 1.58/1.68 ((~(e2 = e3)) <=> (~(op(e0, e0) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8614])).
% 1.58/1.68 tff(8616,plain,
% 1.58/1.68 (~(op(e0, e0) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[1321, 8615])).
% 1.58/1.68 tff(8617,plain,
% 1.58/1.68 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8598])).
% 1.58/1.68 tff(8618,plain,
% 1.58/1.68 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8617])).
% 1.58/1.68 tff(8619,plain,
% 1.58/1.68 (~(op(e0, e2) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[2736, 8618])).
% 1.58/1.68 tff(8620,plain,
% 1.58/1.68 (op(e0, e1) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[1495, 8619, 8616, 8612])).
% 1.58/1.68 tff(8621,plain,
% 1.58/1.68 (e3 = op(e0, e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8620])).
% 1.58/1.68 tff(8622,plain,
% 1.58/1.68 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.68 inference(transitivity,[status(thm)],[8621, 8609, 8607])).
% 1.58/1.68 tff(8623,plain,
% 1.58/1.68 ($false),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[842, 8622, 8605, 8486])).
% 1.58/1.68 tff(8624,plain,((op(e3, e3) = e0) | (~(op(e0, e0) = e2)) | (op(e1, e2) = e1) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e0, e3) = e1) | (~(op(e3, e1) = e2)) | (op(e2, e3) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3) | (op(e2, e1) = e0) | (op(e2, e0) = e2) | (op(e1, e0) = e1) | (op(e2, e3) = e0) | (op(e1, e3) = e0) | (op(e3, e3) = e2) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.68 tff(8625,plain,
% 1.58/1.68 (op(e3, e3) = e0),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[8624, 8485, 7800, 5469, 1304, 8481, 8327, 7914, 121, 8319, 124, 75, 1080, 7791, 5442, 5439, 5436, 80, 126, 5430])).
% 1.58/1.68 tff(8626,plain,
% 1.58/1.68 ((op(e3, e3) = e3) <=> (e0 = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8625])).
% 1.58/1.68 tff(8627,plain,
% 1.58/1.68 ((e0 = e3) <=> (op(e3, e3) = e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8626])).
% 1.58/1.68 tff(8628,plain,
% 1.58/1.68 ((~(e0 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8627])).
% 1.58/1.68 tff(8629,plain,
% 1.58/1.68 (~(op(e3, e3) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[181, 8628])).
% 1.58/1.68 tff(8630,plain,
% 1.58/1.68 (op(e0, e3) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[480, 8629, 124, 1080])).
% 1.58/1.68 tff(8631,plain,
% 1.58/1.68 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8630])).
% 1.58/1.68 tff(8632,plain,
% 1.58/1.68 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8631])).
% 1.58/1.68 tff(8633,plain,
% 1.58/1.68 (~(op(e0, e2) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[918, 8632])).
% 1.58/1.68 tff(8634,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8625])).
% 1.58/1.68 tff(8635,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8634])).
% 1.58/1.68 tff(8636,plain,
% 1.58/1.68 (~(op(e3, e0) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[157, 8635])).
% 1.58/1.68 tff(8637,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8319])).
% 1.58/1.68 tff(8638,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8637])).
% 1.58/1.68 tff(8639,plain,
% 1.58/1.68 (~(op(e3, e0) = e2)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[580, 8638])).
% 1.58/1.68 tff(8640,assumption,(op(e3, e0) = e1), introduced(assumption)).
% 1.58/1.68 tff(8641,plain,
% 1.58/1.68 (e1 = op(e3, op(e3, e3))),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8640, 7654])).
% 1.58/1.68 tff(8642,plain,
% 1.58/1.68 (op(e3, op(e3, e0)) = op(e3, e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8640])).
% 1.58/1.68 tff(8643,plain,
% 1.58/1.68 (op(e3, e1) = op(e3, op(e3, e0))),
% 1.58/1.68 inference(symmetry,[status(thm)],[8642])).
% 1.58/1.68 tff(8644,plain,
% 1.58/1.68 (e2 = op(e3, e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[6684])).
% 1.58/1.68 tff(8645,plain,
% 1.58/1.68 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.58/1.68 inference(transitivity,[status(thm)],[8644, 8643, 7761])).
% 1.58/1.68 tff(8646,plain,
% 1.58/1.68 ($false),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[5193, 8645, 8641, 3079])).
% 1.58/1.68 tff(8647,plain,((~(op(e3, e0) = e1)) | (~(op(e3, e1) = e2)) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.58/1.68 tff(8648,plain,
% 1.58/1.68 (~(op(e3, e0) = e1)),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[8647, 8319, 8625])).
% 1.58/1.68 tff(8649,plain,
% 1.58/1.68 (op(e3, e0) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[5422, 8648, 8639, 8636])).
% 1.58/1.68 tff(8650,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8649])).
% 1.58/1.68 tff(8651,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8650, 3423])).
% 1.58/1.68 tff(8652,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8651])).
% 1.58/1.68 tff(8653,plain,
% 1.58/1.68 (~(op(e3, e2) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[1133, 8652])).
% 1.58/1.68 tff(8654,plain,
% 1.58/1.68 (op(e2, e2) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[2111, 8653, 75, 8633])).
% 1.58/1.68 tff(8655,plain,
% 1.58/1.68 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8357])).
% 1.58/1.68 tff(8656,plain,
% 1.58/1.68 (~(op(e3, e1) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[708, 8655])).
% 1.58/1.68 tff(8657,plain,
% 1.58/1.68 (op(e3, e2) = e1),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[939, 8648, 5430, 8656])).
% 1.58/1.68 tff(8658,plain,
% 1.58/1.68 (e1 = op(e3, e2)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8657])).
% 1.58/1.68 tff(8659,plain,
% 1.58/1.68 ((op(e0, e0) = e1) <=> (e2 = e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8485])).
% 1.58/1.68 tff(8660,plain,
% 1.58/1.68 ((op(e0, e0) = e1) <=> (e1 = e2)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8659, 69])).
% 1.58/1.68 tff(8661,plain,
% 1.58/1.68 ((e1 = e2) <=> (op(e0, e0) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8660])).
% 1.58/1.68 tff(8662,plain,
% 1.58/1.68 ((~(e1 = e2)) <=> (~(op(e0, e0) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8661])).
% 1.58/1.68 tff(8663,plain,
% 1.58/1.68 (~(op(e0, e0) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[708, 8662])).
% 1.58/1.68 tff(8664,plain,
% 1.58/1.68 (op(e2, e0) = e1),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[1480, 8648, 8663, 5439])).
% 1.58/1.68 tff(8665,plain,
% 1.58/1.68 (op(e2, e0) = op(e3, e2)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8664, 8658])).
% 1.58/1.68 tff(8666,plain,
% 1.58/1.68 ((op(e2, e0) = e0) <=> (op(e3, e2) = e0)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8665])).
% 1.58/1.68 tff(8667,plain,
% 1.58/1.68 ((op(e3, e2) = e0) <=> (op(e2, e0) = e0)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8666])).
% 1.58/1.68 tff(8668,plain,
% 1.58/1.68 ((~(op(e3, e2) = e0)) <=> (~(op(e2, e0) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8667])).
% 1.58/1.68 tff(8669,plain,
% 1.58/1.68 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8625])).
% 1.58/1.68 tff(8670,plain,
% 1.58/1.68 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8669])).
% 1.58/1.68 tff(8671,plain,
% 1.58/1.68 (~(op(e3, e2) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[1888, 8670])).
% 1.58/1.68 tff(8672,plain,
% 1.58/1.68 (~(op(e2, e0) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8671, 8668])).
% 1.58/1.68 tff(8673,plain,
% 1.58/1.68 (op(e2, e2) = e0),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[2311, 8672, 7791, 5436])).
% 1.58/1.68 tff(8674,plain,
% 1.58/1.68 (e0 = op(e2, e2)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8673])).
% 1.58/1.68 tff(8675,plain,
% 1.58/1.68 (e0 = e3),
% 1.58/1.68 inference(transitivity,[status(thm)],[8674, 8654])).
% 1.58/1.68 tff(8676,plain,
% 1.58/1.68 ($false),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[181, 8675])).
% 1.58/1.68 tff(8677,plain,((op(e1, e3) = e3) | (op(e1, e2) = e3) | (op(e2, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.68 tff(8678,plain,
% 1.58/1.68 (op(e1, e3) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[8677, 75, 124, 5425, 121, 80, 126, 79, 72])).
% 1.58/1.68 tff(8679,plain,
% 1.58/1.68 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.68 tff(8680,plain,
% 1.58/1.68 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8679, 128])).
% 1.58/1.68 tff(8681,plain,
% 1.58/1.68 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8680])).
% 1.58/1.68 tff(8682,plain,
% 1.58/1.68 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8681])).
% 1.58/1.68 tff(8683,plain,
% 1.58/1.68 (~(op(e1, e3) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[303, 8682])).
% 1.58/1.68 tff(8684,plain,
% 1.58/1.68 (op(e3, e3) = e1),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[151, 8683, 121, 76])).
% 1.58/1.68 tff(8685,plain,
% 1.58/1.68 (e1 = op(e3, e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8684])).
% 1.58/1.68 tff(8686,plain,
% 1.58/1.68 (op(e0, e1) = op(e0, op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8685])).
% 1.58/1.68 tff(8687,plain,
% 1.58/1.68 (op(e0, op(e3, e3)) = op(e0, e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8686])).
% 1.58/1.68 tff(8688,plain,
% 1.58/1.68 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.68 tff(8689,plain,
% 1.58/1.68 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8688])).
% 1.58/1.68 tff(8690,plain,
% 1.58/1.68 (~(op(e0, e3) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[64, 8689])).
% 1.58/1.68 tff(8691,plain,
% 1.58/1.68 (op(e0, e3) = e0),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[687, 8690, 121, 79])).
% 1.58/1.68 tff(8692,plain,
% 1.58/1.68 (e0 = op(e0, e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8691])).
% 1.58/1.68 tff(8693,plain,
% 1.58/1.68 (op(e3, e3) = e1),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[151, 87, 121, 76])).
% 1.58/1.68 tff(8694,plain,
% 1.58/1.68 (e1 = op(e3, e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8693, 658])).
% 1.58/1.68 tff(8695,plain,
% 1.58/1.68 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8693])).
% 1.58/1.68 tff(8696,plain,
% 1.58/1.68 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8695])).
% 1.58/1.68 tff(8697,plain,
% 1.58/1.68 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8696, 5470])).
% 1.58/1.68 tff(8698,plain,
% 1.58/1.68 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 1.58/1.68 inference(symmetry,[status(thm)],[8697])).
% 1.58/1.68 tff(8699,plain,
% 1.58/1.68 (e1 = op(e3, e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8693])).
% 1.58/1.68 tff(8700,plain,
% 1.58/1.68 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8699])).
% 1.58/1.68 tff(8701,plain,
% 1.58/1.68 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8700])).
% 1.58/1.68 tff(8702,plain,
% 1.58/1.68 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8701])).
% 1.58/1.68 tff(8703,plain,
% 1.58/1.68 (~(op(e3, e1) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[437, 8702])).
% 1.58/1.68 tff(8704,plain,
% 1.58/1.68 ((op(e0, e0) = e0) <=> (op(e0, e0) = op(e0, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[772])).
% 1.58/1.68 tff(8705,plain,
% 1.58/1.68 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8704])).
% 1.58/1.68 tff(8706,plain,
% 1.58/1.68 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8705])).
% 1.58/1.68 tff(8707,plain,
% 1.58/1.68 (~(op(e0, e0) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[3414, 8706])).
% 1.58/1.68 tff(8708,plain,
% 1.58/1.68 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[7946, 2431, 82, 3540, 126, 121, 79, 75, 5548])).
% 1.58/1.68 tff(8709,plain,
% 1.58/1.68 ((op(e1, e1) = e0) <=> (e2 = op(e0, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[2891, 772])).
% 1.58/1.68 tff(8710,plain,
% 1.58/1.68 ((op(e1, e1) = e0) <=> (op(e0, e3) = e2)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8709, 1681])).
% 1.58/1.68 tff(8711,plain,
% 1.58/1.68 ((op(e0, e3) = e2) <=> (op(e1, e1) = e0)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8710])).
% 1.58/1.68 tff(8712,plain,
% 1.58/1.68 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e1) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8711])).
% 1.58/1.68 tff(8713,plain,
% 1.58/1.68 (~(op(e1, e1) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[79, 8712])).
% 1.58/1.68 tff(8714,plain,
% 1.58/1.68 (op(e3, e1) = e0),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[292, 8713, 2559, 3457])).
% 1.58/1.68 tff(8715,plain,
% 1.58/1.68 ((op(e3, e1) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8714])).
% 1.58/1.68 tff(8716,plain,
% 1.58/1.68 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8715, 4959])).
% 1.58/1.68 tff(8717,plain,
% 1.58/1.68 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8716])).
% 1.58/1.68 tff(8718,plain,
% 1.58/1.68 (~(op(e3, e2) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[3429, 8717])).
% 1.58/1.68 tff(8719,plain,
% 1.58/1.68 (op(e3, e1) = op(e0, e3)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8714, 772])).
% 1.58/1.68 tff(8720,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = op(e0, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8719])).
% 1.58/1.68 tff(8721,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8720, 5534])).
% 1.58/1.68 tff(8722,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8721])).
% 1.58/1.68 tff(8723,plain,
% 1.58/1.68 (~(op(e3, e0) = e0)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[580, 8722])).
% 1.58/1.68 tff(8724,plain,
% 1.58/1.68 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[306])).
% 1.58/1.68 tff(8725,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8724])).
% 1.58/1.68 tff(8726,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8725])).
% 1.58/1.68 tff(8727,plain,
% 1.58/1.68 (~(op(e3, e0) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[157, 8726])).
% 1.58/1.68 tff(8728,plain,
% 1.58/1.68 (op(e3, op(e3, e1)) = op(e3, op(e0, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8719])).
% 1.58/1.68 tff(8729,plain,
% 1.58/1.68 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[6772])).
% 1.58/1.68 tff(8730,plain,
% 1.58/1.68 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8729, 8728, 1342])).
% 1.58/1.68 tff(8731,plain,
% 1.58/1.68 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8730])).
% 1.58/1.68 tff(8732,plain,
% 1.58/1.68 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8731, 5377])).
% 1.58/1.68 tff(8733,plain,
% 1.58/1.68 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8732])).
% 1.58/1.68 tff(8734,plain,
% 1.58/1.68 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[6772])).
% 1.58/1.68 tff(8735,plain,
% 1.58/1.68 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8734, 5470])).
% 1.58/1.68 tff(8736,plain,
% 1.58/1.68 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 1.58/1.68 inference(symmetry,[status(thm)],[8735])).
% 1.58/1.68 tff(8737,plain,
% 1.58/1.68 (e0 = op(e3, op(e3, e3))),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8714, 8736])).
% 1.58/1.68 tff(8738,plain,
% 1.58/1.68 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[5397, 8737, 6771])).
% 1.58/1.68 tff(8739,plain,
% 1.58/1.68 (~(op(e3, e0) = e2)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[8738, 8733])).
% 1.58/1.68 tff(8740,plain,
% 1.58/1.68 (op(e3, e0) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[5422, 8739, 8727, 8723])).
% 1.58/1.68 tff(8741,plain,
% 1.58/1.68 (e3 = op(e3, e0)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8740])).
% 1.58/1.68 tff(8742,plain,
% 1.58/1.68 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8741])).
% 1.58/1.68 tff(8743,plain,
% 1.58/1.68 ((op(e3, e2) = e3) <=> (op(e3, e0) = op(e3, e2))),
% 1.58/1.68 inference(transitivity,[status(thm)],[8742, 1123])).
% 1.58/1.68 tff(8744,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8743])).
% 1.58/1.68 tff(8745,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8744])).
% 1.58/1.68 tff(8746,plain,
% 1.58/1.68 (~(op(e3, e2) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[1133, 8745])).
% 1.58/1.68 tff(8747,plain,
% 1.58/1.68 (op(e0, e2) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[2111, 8746, 75, 2431])).
% 1.58/1.68 tff(8748,plain,
% 1.58/1.68 (op(e0, e2) = op(e3, e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8747, 8741])).
% 1.58/1.68 tff(8749,plain,
% 1.58/1.68 ((op(e0, e2) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8748, 306])).
% 1.58/1.68 tff(8750,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e3)) <=> (op(e0, e2) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8749])).
% 1.58/1.68 tff(8751,plain,
% 1.58/1.68 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e0, e2) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8750])).
% 1.58/1.68 tff(8752,plain,
% 1.58/1.68 (~(op(e0, e2) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[157, 8751])).
% 1.58/1.68 tff(8753,plain,
% 1.58/1.68 ((op(e1, e1) = e1) <=> (e2 = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[2891, 306])).
% 1.58/1.68 tff(8754,plain,
% 1.58/1.68 ((op(e1, e1) = e1) <=> (op(e3, e3) = e2)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8753, 565])).
% 1.58/1.68 tff(8755,plain,
% 1.58/1.68 ((op(e3, e3) = e2) <=> (op(e1, e1) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8754])).
% 1.58/1.68 tff(8756,plain,
% 1.58/1.68 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e1) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8755])).
% 1.58/1.68 tff(8757,plain,
% 1.58/1.68 (~(op(e1, e1) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[126, 8756])).
% 1.58/1.68 tff(8758,plain,
% 1.58/1.68 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[306])).
% 1.58/1.68 tff(8759,plain,
% 1.58/1.68 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8758])).
% 1.58/1.68 tff(8760,plain,
% 1.58/1.68 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8759])).
% 1.58/1.68 tff(8761,plain,
% 1.58/1.68 (~(op(e3, e1) = e1)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[437, 8760])).
% 1.58/1.68 tff(8762,plain,
% 1.58/1.68 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8741])).
% 1.58/1.68 tff(8763,plain,
% 1.58/1.68 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 1.58/1.68 inference(symmetry,[status(thm)],[8762])).
% 1.58/1.68 tff(8764,plain,
% 1.58/1.68 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8763])).
% 1.58/1.68 tff(8765,plain,
% 1.58/1.68 (~(op(e2, e0) = e3)),
% 1.58/1.68 inference(modus_ponens,[status(thm)],[747, 8764])).
% 1.58/1.68 tff(8766,plain,
% 1.58/1.68 (op(e2, e1) = e3),
% 1.58/1.68 inference(unit_resolution,[status(thm)],[1559, 8765, 2431, 124])).
% 1.58/1.68 tff(8767,plain,
% 1.58/1.68 (op(e2, e1) = op(e3, e0)),
% 1.58/1.68 inference(transitivity,[status(thm)],[8766, 8741])).
% 1.58/1.68 tff(8768,plain,
% 1.58/1.68 ((op(e2, e1) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 1.58/1.68 inference(monotonicity,[status(thm)],[8767, 306])).
% 1.58/1.68 tff(8769,plain,
% 1.58/1.68 ((op(e3, e0) = op(e3, e3)) <=> (op(e2, e1) = e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8768])).
% 1.58/1.69 tff(8770,plain,
% 1.58/1.69 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e2, e1) = e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8769])).
% 1.58/1.69 tff(8771,plain,
% 1.58/1.69 (~(op(e2, e1) = e1)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[157, 8770])).
% 1.58/1.69 tff(8772,plain,
% 1.58/1.69 (op(e0, e1) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1252, 8771, 8757, 8761])).
% 1.58/1.69 tff(8773,plain,
% 1.58/1.69 (op(e3, e2) = e2),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2015, 8739, 126, 82])).
% 1.58/1.69 tff(8774,plain,
% 1.58/1.69 (op(op(e2, e1), e2) = op(e3, e2)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8766])).
% 1.58/1.69 tff(8775,plain,
% 1.58/1.69 (op(op(e2, e1), e2) = e2),
% 1.58/1.69 inference(transitivity,[status(thm)],[8774, 8773])).
% 1.58/1.69 tff(8776,plain,
% 1.58/1.69 ((op(op(e2, e1), e2) = e1) <=> (e2 = op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8775, 306])).
% 1.58/1.69 tff(8777,plain,
% 1.58/1.69 ((op(op(e2, e1), e2) = e1) <=> (op(e3, e3) = e2)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8776, 565])).
% 1.58/1.69 tff(8778,plain,
% 1.58/1.69 ((op(e3, e3) = e2) <=> (op(op(e2, e1), e2) = e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8777])).
% 1.58/1.69 tff(8779,plain,
% 1.58/1.69 ((~(op(e3, e3) = e2)) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8778])).
% 1.58/1.69 tff(8780,plain,
% 1.58/1.69 (~(op(op(e2, e1), e2) = e1)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[126, 8779])).
% 1.58/1.69 tff(8781,plain,
% 1.58/1.69 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[5808, 8780])).
% 1.58/1.69 tff(8782,plain,
% 1.58/1.69 (op(op(e0, e3), e3) = e0),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[5461, 771])).
% 1.58/1.69 tff(8783,plain,
% 1.58/1.69 (op(op(e3, e1), e3) = op(op(e0, e3), e3)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8719])).
% 1.58/1.69 tff(8784,plain,
% 1.58/1.69 (op(op(e3, e1), e3) = op(e0, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8783, 8782, 772])).
% 1.58/1.69 tff(8785,plain,
% 1.58/1.69 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8784, 306])).
% 1.58/1.69 tff(8786,plain,
% 1.58/1.69 ((op(e0, e3) = op(e3, e3)) <=> (op(op(e3, e1), e3) = e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8785])).
% 1.58/1.69 tff(8787,plain,
% 1.58/1.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8786])).
% 1.58/1.69 tff(8788,plain,
% 1.58/1.69 (~(op(op(e3, e1), e3) = e1)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1077, 8787])).
% 1.58/1.69 tff(8789,plain,
% 1.58/1.69 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1050, 8788])).
% 1.58/1.69 tff(8790,plain,
% 1.58/1.69 (op(op(e3, e0), e0) = op(e3, op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8740, 772])).
% 1.58/1.69 tff(8791,plain,
% 1.58/1.69 (op(op(e0, e2), e0) = op(op(e3, e0), e0)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8748])).
% 1.58/1.69 tff(8792,plain,
% 1.58/1.69 (op(op(e0, e2), e0) = op(e3, e0)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8791, 8790, 1342])).
% 1.58/1.69 tff(8793,plain,
% 1.58/1.69 ((op(op(e0, e2), e0) = e2) <=> (op(e3, e0) = e2)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8792])).
% 1.58/1.69 tff(8794,plain,
% 1.58/1.69 ((op(e3, e0) = e2) <=> (op(op(e0, e2), e0) = e2)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8793])).
% 1.58/1.69 tff(8795,plain,
% 1.58/1.69 ((~(op(e3, e0) = e2)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8794])).
% 1.58/1.69 tff(8796,plain,
% 1.58/1.69 (~(op(op(e0, e2), e0) = e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[8739, 8795])).
% 1.58/1.69 tff(8797,plain,
% 1.58/1.69 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2446, 8796])).
% 1.58/1.69 tff(8798,plain,
% 1.58/1.69 (op(op(e3, e0), e0) = e3),
% 1.58/1.69 inference(transitivity,[status(thm)],[8790, 1342, 8740])).
% 1.58/1.69 tff(8799,plain,
% 1.58/1.69 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[4026, 8798])).
% 1.58/1.69 tff(8800,plain,
% 1.58/1.69 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[306])).
% 1.58/1.69 tff(8801,plain,
% 1.58/1.69 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8800])).
% 1.58/1.69 tff(8802,plain,
% 1.58/1.69 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8801])).
% 1.58/1.69 tff(8803,plain,
% 1.58/1.69 (~(op(e3, e2) = e1)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1888, 8802])).
% 1.58/1.69 tff(8804,plain,
% 1.58/1.69 (op(e2, e2) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1613, 4515, 8803, 4484])).
% 1.58/1.69 tff(8805,plain,
% 1.58/1.69 (op(e2, e2) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8804, 306])).
% 1.58/1.69 tff(8806,plain,
% 1.58/1.69 ((op(e2, e2) = e0) <=> (op(e3, e3) = op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8805, 772])).
% 1.58/1.69 tff(8807,plain,
% 1.58/1.69 ((op(e2, e2) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8806, 659])).
% 1.58/1.69 tff(8808,plain,
% 1.58/1.69 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e2) = e0)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8807])).
% 1.58/1.69 tff(8809,plain,
% 1.58/1.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e0))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8808])).
% 1.58/1.69 tff(8810,plain,
% 1.58/1.69 (~(op(e2, e2) = e0)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1077, 8809])).
% 1.58/1.69 tff(8811,plain,
% 1.58/1.69 (op(e2, e0) = e0),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2311, 8810, 2559, 1063])).
% 1.58/1.69 tff(8812,plain,
% 1.58/1.69 (op(e2, e0) = op(e0, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8811, 772])).
% 1.58/1.69 tff(8813,plain,
% 1.58/1.69 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8812])).
% 1.58/1.69 tff(8814,plain,
% 1.58/1.69 (op(e2, op(e2, e0)) = e0),
% 1.58/1.69 inference(transitivity,[status(thm)],[8813, 980, 8811])).
% 1.58/1.69 tff(8815,plain,
% 1.58/1.69 (op(e1, e0) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[954, 4515, 87, 1266])).
% 1.58/1.69 tff(8816,plain,
% 1.58/1.69 (op(op(e1, e0), e0) = op(e1, op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8815, 772])).
% 1.58/1.69 tff(8817,plain,
% 1.58/1.69 (op(op(e1, e0), e0) = e1),
% 1.58/1.69 inference(transitivity,[status(thm)],[8816, 2179, 8815])).
% 1.58/1.69 tff(8818,plain,
% 1.58/1.69 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[3015, 8817])).
% 1.58/1.69 tff(8819,plain,
% 1.58/1.69 (op(e0, e1) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[5800, 306])).
% 1.58/1.69 tff(8820,plain,
% 1.58/1.69 (op(e0, op(e0, e1)) = op(e0, op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8819])).
% 1.58/1.69 tff(8821,plain,
% 1.58/1.69 (op(e0, op(e0, e1)) = e1),
% 1.58/1.69 inference(transitivity,[status(thm)],[8820, 3348, 5800])).
% 1.58/1.69 tff(8822,plain,
% 1.58/1.69 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2449, 8821])).
% 1.58/1.69 tff(8823,plain,
% 1.58/1.69 (op(e1, e2) = e0),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1859, 4515, 3785, 75])).
% 1.58/1.69 tff(8824,plain,
% 1.58/1.69 (op(op(e1, e2), e1) = op(e0, op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8823, 306])).
% 1.58/1.69 tff(8825,plain,
% 1.58/1.69 (op(op(e1, e2), e1) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8824, 3348, 5800, 306])).
% 1.58/1.69 tff(8826,plain,
% 1.58/1.69 ((op(op(e1, e2), e1) = e2) <=> (op(e3, e3) = e2)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8825])).
% 1.58/1.69 tff(8827,plain,
% 1.58/1.69 ((op(e3, e3) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8826])).
% 1.58/1.69 tff(8828,plain,
% 1.58/1.69 ((~(op(e3, e3) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8827])).
% 1.58/1.69 tff(8829,plain,
% 1.58/1.69 (~(op(op(e1, e2), e1) = e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[126, 8828])).
% 1.58/1.69 tff(8830,plain,
% 1.58/1.69 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[5959, 8829])).
% 1.58/1.69 tff(8831,plain,
% 1.58/1.69 (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1459, 8830, 3341, 1926, 3342, 1304, 1363, 8822, 8818, 1275, 1936, 1347])).
% 1.58/1.69 tff(8832,plain,
% 1.58/1.69 (~(op(e2, op(e2, e0)) = e0)),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2653, 8831])).
% 1.58/1.69 tff(8833,plain,
% 1.58/1.69 ($false),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[8832, 8814])).
% 1.58/1.69 tff(8834,plain,((op(e1, e2) = e1) | (~(op(e0, e3) = e0)) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e1) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e2) | (~(op(e0, e1) = e1)) | (~(op(e3, e3) = e1)) | (op(e1, e3) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3) | (op(e0, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.69 tff(8835,plain,
% 1.58/1.69 (op(e1, e2) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[8834, 8799, 3341, 771, 3342, 1304, 8797, 8789, 8781, 1347, 2559, 1063, 126, 8772, 305, 87, 8757, 3785, 75, 8752])).
% 1.58/1.69 tff(8836,plain,
% 1.58/1.69 (op(e1, e2) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8835, 306])).
% 1.58/1.69 tff(8837,plain,
% 1.58/1.69 ((op(e1, e2) = e0) <=> (op(e3, e3) = op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8836, 772])).
% 1.58/1.69 tff(8838,plain,
% 1.58/1.69 ((op(e1, e2) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8837, 659])).
% 1.58/1.69 tff(8839,plain,
% 1.58/1.69 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e2) = e0)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8838])).
% 1.58/1.69 tff(8840,plain,
% 1.58/1.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e2) = e0))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8839])).
% 1.58/1.69 tff(8841,plain,
% 1.58/1.69 (~(op(e1, e2) = e0)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1077, 8840])).
% 1.58/1.69 tff(8842,plain,
% 1.58/1.69 (op(e2, e2) = e0),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[973, 8841, 919, 8718])).
% 1.58/1.69 tff(8843,plain,
% 1.58/1.69 (e0 = op(e2, e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[8842, 995])).
% 1.58/1.69 tff(8844,plain,
% 1.58/1.69 (op(e2, e2) = op(e0, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8842, 772])).
% 1.58/1.69 tff(8845,plain,
% 1.58/1.69 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8844])).
% 1.58/1.69 tff(8846,plain,
% 1.58/1.69 (op(e2, op(e0, e3)) = op(e2, op(e2, e2))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8845])).
% 1.58/1.69 tff(8847,plain,
% 1.58/1.69 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8835])).
% 1.58/1.69 tff(8848,plain,
% 1.58/1.69 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8847, 316])).
% 1.58/1.69 tff(8849,plain,
% 1.58/1.69 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8848])).
% 1.58/1.69 tff(8850,plain,
% 1.58/1.69 (~(op(e2, e2) = e1)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1273, 8849])).
% 1.58/1.69 tff(8851,plain,
% 1.58/1.69 (op(e2, e0) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[345, 8850, 76, 8771])).
% 1.58/1.69 tff(8852,plain,
% 1.58/1.69 (e1 = op(e2, e0)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8851])).
% 1.58/1.69 tff(8853,plain,
% 1.58/1.69 (e1 = op(e2, op(e2, e2))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8852, 981, 8846])).
% 1.58/1.69 tff(8854,plain,
% 1.58/1.69 (op(e2, op(e2, e2)) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8845, 980, 8851, 306])).
% 1.58/1.69 tff(8855,plain,
% 1.58/1.69 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8854])).
% 1.58/1.69 tff(8856,plain,
% 1.58/1.69 (op(e2, op(e3, e3)) = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8855])).
% 1.58/1.69 tff(8857,plain,
% 1.58/1.69 (op(e2, op(e3, e3)) = op(e2, e1)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[305])).
% 1.58/1.69 tff(8858,plain,
% 1.58/1.69 (op(e2, e1) = op(e2, op(e3, e3))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8857])).
% 1.58/1.69 tff(8859,plain,
% 1.58/1.69 (e3 = op(e2, e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8766])).
% 1.58/1.69 tff(8860,plain,
% 1.58/1.69 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8859, 8858, 8856])).
% 1.58/1.69 tff(8861,plain,
% 1.58/1.69 ($false),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1539, 8860, 8853, 8843])).
% 1.58/1.69 tff(8862,plain,((~(op(e1, e1) = e2)) | (~(op(e3, e3) = e1)) | (~(op(e0, e3) = e0)) | (op(e2, e3) = e1) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e1) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e2) | (op(e1, e3) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3) | (op(e3, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.69 tff(8863,plain,
% 1.58/1.69 (~(op(e1, e1) = e2)),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[8862, 3785, 771, 76, 3341, 3342, 1304, 1347, 2559, 1063, 126, 87, 305, 75, 2431, 124, 82, 79])).
% 1.58/1.69 tff(8864,plain,
% 1.58/1.69 (op(e0, e1) = e2),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1993, 8863, 82, 3540])).
% 1.58/1.69 tff(8865,plain,
% 1.58/1.69 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8864])).
% 1.58/1.69 tff(8866,plain,
% 1.58/1.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8865])).
% 1.58/1.69 tff(8867,plain,
% 1.58/1.69 (~(op(e0, e0) = e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[811, 8866])).
% 1.58/1.69 tff(8868,plain,
% 1.58/1.69 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8864])).
% 1.58/1.69 tff(8869,plain,
% 1.58/1.69 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8868, 3491])).
% 1.58/1.69 tff(8870,plain,
% 1.58/1.69 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8869])).
% 1.58/1.69 tff(8871,plain,
% 1.58/1.69 (~(op(e0, e2) = e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[2102, 8870])).
% 1.58/1.69 tff(8872,plain,
% 1.58/1.69 (op(e3, e2) = e2),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[1151, 8871, 5548, 3785])).
% 1.58/1.69 tff(8873,plain,
% 1.58/1.69 ((op(e3, e2) = e3) <=> (e2 = e3)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8872])).
% 1.58/1.69 tff(8874,plain,
% 1.58/1.69 ((e2 = e3) <=> (op(e3, e2) = e3)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8873])).
% 1.58/1.69 tff(8875,plain,
% 1.58/1.69 ((~(e2 = e3)) <=> (~(op(e3, e2) = e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8874])).
% 1.58/1.69 tff(8876,plain,
% 1.58/1.69 (~(op(e3, e2) = e3)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[1321, 8875])).
% 1.58/1.69 tff(8877,plain,
% 1.58/1.69 (op(e0, e2) = e3),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2111, 8876, 75, 2431])).
% 1.58/1.69 tff(8878,plain,
% 1.58/1.69 (e3 = op(e0, e2)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8877])).
% 1.58/1.69 tff(8879,plain,
% 1.58/1.69 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8878])).
% 1.58/1.69 tff(8880,plain,
% 1.58/1.69 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8879])).
% 1.58/1.69 tff(8881,plain,
% 1.58/1.69 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8880])).
% 1.58/1.69 tff(8882,plain,
% 1.58/1.69 (~(op(e0, e0) = e3)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[3603, 8881])).
% 1.58/1.69 tff(8883,plain,
% 1.58/1.69 (op(e0, e0) = e1),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[3612, 8882, 8867, 8707])).
% 1.58/1.69 tff(8884,plain,
% 1.58/1.69 (e1 = op(e0, e0)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[8883, 74])).
% 1.58/1.69 tff(8885,plain,
% 1.58/1.69 (op(e0, e0) = op(e3, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8883, 306])).
% 1.58/1.69 tff(8886,plain,
% 1.58/1.69 (op(e0, op(e0, e0)) = op(e0, op(e3, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8885])).
% 1.58/1.69 tff(8887,plain,
% 1.58/1.69 (op(e0, op(e3, e3)) = op(e0, op(e0, e0))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8886])).
% 1.58/1.69 tff(8888,plain,
% 1.58/1.69 (op(e0, e1) = op(e0, op(e3, e3))),
% 1.58/1.69 inference(symmetry,[status(thm)],[3348])).
% 1.58/1.69 tff(8889,plain,
% 1.58/1.69 (e2 = op(e0, e1)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8864])).
% 1.58/1.69 tff(8890,plain,
% 1.58/1.69 (e2 = op(e0, op(e0, e0))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8889, 8888, 8887])).
% 1.58/1.69 tff(8891,plain,
% 1.58/1.69 (op(e0, op(e0, e0)) = e2),
% 1.58/1.69 inference(transitivity,[status(thm)],[8886, 3348, 8864])).
% 1.58/1.69 tff(8892,plain,
% 1.58/1.69 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8891])).
% 1.58/1.69 tff(8893,plain,
% 1.58/1.69 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8892])).
% 1.58/1.69 tff(8894,plain,
% 1.58/1.69 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8878, 8893])).
% 1.58/1.69 tff(8895,plain,
% 1.58/1.69 ($false),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[3582, 8894, 8890, 8884])).
% 1.58/1.69 tff(8896,plain,((op(e1, e2) = e2) | (~(op(e3, e3) = e1)) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e2, e2) = e2) | (op(e3, e1) = e2) | (op(e2, e1) = e2) | (~(op(e0, e3) = e0)) | (op(e2, e3) = e1) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e1) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e2) | (op(e1, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.69 tff(8897,plain,
% 1.58/1.69 (op(e1, e2) = e2),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[8896, 2431, 75, 8693, 5548, 82, 3540, 771, 76, 8708, 5469, 1304, 1347, 2559, 1063, 126, 87, 124, 79])).
% 1.58/1.69 tff(8898,plain,
% 1.58/1.69 (~(op(e0, e2) = e3)),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[7856, 8897, 82, 8707, 3540, 126])).
% 1.58/1.69 tff(8899,plain,
% 1.58/1.69 (op(e3, e2) = e3),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2111, 8898, 75, 2431])).
% 1.58/1.69 tff(8900,plain,
% 1.58/1.69 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8899])).
% 1.58/1.69 tff(8901,plain,
% 1.58/1.69 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8900])).
% 1.58/1.69 tff(8902,plain,
% 1.58/1.69 (~(op(e3, e1) = e3)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[3429, 8901])).
% 1.58/1.69 tff(8903,plain,
% 1.58/1.69 (op(e3, e1) = e0),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[446, 8902, 8703, 82])).
% 1.58/1.69 tff(8904,plain,
% 1.58/1.69 (e0 = op(e3, op(e3, e3))),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[8903, 8698])).
% 1.58/1.69 tff(8905,plain,
% 1.58/1.69 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8695])).
% 1.58/1.69 tff(8906,plain,
% 1.58/1.69 (op(e3, op(e3, e1)) = op(e3, op(e3, op(e3, e3)))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8905])).
% 1.58/1.69 tff(8907,plain,
% 1.58/1.69 (op(e3, e1) = op(e0, e3)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8903, 772])).
% 1.58/1.69 tff(8908,plain,
% 1.58/1.69 (op(e3, op(e3, e1)) = op(e3, op(e0, e3))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8907])).
% 1.58/1.69 tff(8909,plain,
% 1.58/1.69 (op(e3, op(e0, e3)) = op(e3, op(e3, e1))),
% 1.58/1.69 inference(symmetry,[status(thm)],[8908])).
% 1.58/1.69 tff(8910,plain,
% 1.58/1.69 (op(e3, e0) = op(e3, op(e0, e3))),
% 1.58/1.69 inference(symmetry,[status(thm)],[2418])).
% 1.58/1.69 tff(8911,plain,
% 1.58/1.69 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8897])).
% 1.58/1.69 tff(8912,plain,
% 1.58/1.69 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.58/1.69 inference(transitivity,[status(thm)],[8911, 2234])).
% 1.58/1.69 tff(8913,plain,
% 1.58/1.69 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.58/1.69 inference(monotonicity,[status(thm)],[8912])).
% 1.58/1.69 tff(8914,plain,
% 1.58/1.69 (~(op(e3, e2) = e2)),
% 1.58/1.69 inference(modus_ponens,[status(thm)],[2292, 8913])).
% 1.58/1.69 tff(8915,plain,
% 1.58/1.69 (op(e3, e0) = e2),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[2015, 8914, 126, 82])).
% 1.58/1.69 tff(8916,plain,
% 1.58/1.69 (e2 = op(e3, e0)),
% 1.58/1.69 inference(symmetry,[status(thm)],[8915])).
% 1.58/1.69 tff(8917,plain,
% 1.58/1.69 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.58/1.69 inference(transitivity,[status(thm)],[8916, 8910, 8909, 8906])).
% 1.58/1.69 tff(8918,plain,
% 1.58/1.69 ($false),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[5397, 8917, 8904, 8694])).
% 1.58/1.69 tff(8919,plain,((op(e2, e2) = e3) | (~(op(e0, e3) = e0)) | (op(e3, e1) = e2) | (op(e3, e3) = e2) | (op(e1, e2) = e3) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e1) = e0) | (op(e2, e3) = e0) | (op(e1, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e2) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.69 tff(8920,plain,
% 1.58/1.69 (op(e2, e2) = e3),
% 1.58/1.69 inference(unit_resolution,[status(thm)],[8919, 82, 8691, 126, 75, 7796, 7808, 76, 5425, 7914, 7791, 5436, 8683, 124, 79, 121])).
% 1.58/1.69 tff(8921,plain,
% 1.58/1.69 ((op(e2, e2) = e0) <=> (e3 = op(e0, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8920, 8692])).
% 1.58/1.70 tff(8922,plain,
% 1.58/1.70 ((op(e2, e2) = e0) <=> (op(e0, e3) = e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8921, 1364])).
% 1.58/1.70 tff(8923,plain,
% 1.58/1.70 ((op(e0, e3) = e3) <=> (op(e2, e2) = e0)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8922])).
% 1.58/1.70 tff(8924,plain,
% 1.58/1.70 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e2) = e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8923])).
% 1.58/1.70 tff(8925,plain,
% 1.58/1.70 (~(op(e2, e2) = e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[8690, 8924])).
% 1.58/1.70 tff(8926,plain,
% 1.58/1.70 (op(e2, e0) = e0),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2311, 8925, 7791, 5436])).
% 1.58/1.70 tff(8927,plain,
% 1.58/1.70 (op(e2, e0) = op(e0, e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8926, 8692])).
% 1.58/1.70 tff(8928,plain,
% 1.58/1.70 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8927])).
% 1.58/1.70 tff(8929,plain,
% 1.58/1.70 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8928, 7797])).
% 1.58/1.70 tff(8930,plain,
% 1.58/1.70 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.58/1.70 inference(symmetry,[status(thm)],[8929])).
% 1.58/1.70 tff(8931,plain,
% 1.58/1.70 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8930, 6337])).
% 1.58/1.70 tff(8932,plain,
% 1.58/1.70 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8931])).
% 1.58/1.70 tff(8933,plain,
% 1.58/1.70 (~(op(e0, e2) = op(e2, e0))),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[918, 8932])).
% 1.58/1.70 tff(8934,plain,
% 1.58/1.70 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[6347, 8933])).
% 1.58/1.70 tff(8935,plain,
% 1.58/1.70 ((op(e3, e2) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8344, 395])).
% 1.58/1.70 tff(8936,plain,
% 1.58/1.70 ((~(op(e3, e2) = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8935])).
% 1.58/1.70 tff(8937,plain,
% 1.58/1.70 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8927])).
% 1.58/1.70 tff(8938,plain,
% 1.58/1.70 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8937, 452])).
% 1.58/1.70 tff(8939,plain,
% 1.58/1.70 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = op(e0, e3)))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8938])).
% 1.58/1.70 tff(8940,plain,
% 1.58/1.70 (~(op(e3, e0) = op(e0, e3))),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[747, 8939])).
% 1.58/1.70 tff(8941,plain,
% 1.58/1.70 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8920])).
% 1.58/1.70 tff(8942,plain,
% 1.58/1.70 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8941])).
% 1.58/1.70 tff(8943,plain,
% 1.58/1.70 (~(op(e0, e2) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[2736, 8942])).
% 1.58/1.70 tff(8944,plain,
% 1.58/1.70 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8692])).
% 1.58/1.70 tff(8945,plain,
% 1.58/1.70 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8944])).
% 1.58/1.70 tff(8946,plain,
% 1.58/1.70 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8938, 8945])).
% 1.58/1.70 tff(8947,plain,
% 1.58/1.70 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8946])).
% 1.58/1.70 tff(8948,plain,
% 1.58/1.70 (~(op(e3, e0) = e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[747, 8947])).
% 1.58/1.70 tff(8949,plain,
% 1.58/1.70 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.70 tff(8950,plain,
% 1.58/1.70 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8949])).
% 1.58/1.70 tff(8951,plain,
% 1.58/1.70 (~(op(e1, e1) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[619, 8950])).
% 1.58/1.70 tff(8952,plain,
% 1.58/1.70 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8920])).
% 1.58/1.70 tff(8953,plain,
% 1.58/1.70 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8952])).
% 1.58/1.70 tff(8954,plain,
% 1.58/1.70 (~(op(e2, e1) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[508, 8953])).
% 1.58/1.70 tff(8955,assumption,(op(e3, e2) = e2), introduced(assumption)).
% 1.58/1.70 tff(8956,plain,
% 1.58/1.70 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8955])).
% 1.58/1.70 tff(8957,plain,
% 1.58/1.70 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8956])).
% 1.58/1.70 tff(8958,plain,
% 1.58/1.70 (~(op(e0, e2) = e2)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[1467, 8957])).
% 1.58/1.70 tff(8959,plain,
% 1.58/1.70 (op(e0, e2) = e1),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2745, 8958, 919, 4412])).
% 1.58/1.70 tff(8960,plain,
% 1.58/1.70 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8959])).
% 1.58/1.70 tff(8961,plain,
% 1.58/1.70 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e1))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8960])).
% 1.58/1.70 tff(8962,plain,
% 1.58/1.70 (~(op(e0, e0) = e1)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[3603, 8961])).
% 1.58/1.70 tff(8963,plain,
% 1.58/1.70 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e2)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8955])).
% 1.58/1.70 tff(8964,plain,
% 1.58/1.70 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e2))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8963])).
% 1.58/1.70 tff(8965,plain,
% 1.58/1.70 (~(op(e3, e0) = e2)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[1133, 8964])).
% 1.58/1.70 tff(8966,plain,
% 1.58/1.70 (op(e3, e0) = e3),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[5422, 8965, 8727, 1908])).
% 1.58/1.70 tff(8967,plain,
% 1.58/1.70 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8966])).
% 1.58/1.70 tff(8968,plain,
% 1.58/1.70 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8967])).
% 1.58/1.70 tff(8969,plain,
% 1.58/1.70 (~(op(e0, e0) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[6384, 8968])).
% 1.58/1.70 tff(8970,plain,
% 1.58/1.70 (op(e0, e0) = e2),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[3612, 8969, 8962, 8707])).
% 1.58/1.70 tff(8971,plain,
% 1.58/1.70 (e2 = op(e0, e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[8970, 78])).
% 1.58/1.70 tff(8972,plain,
% 1.58/1.70 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8970])).
% 1.58/1.70 tff(8973,plain,
% 1.58/1.70 (op(e0, e2) = op(e0, op(e0, e0))),
% 1.58/1.70 inference(symmetry,[status(thm)],[8972])).
% 1.58/1.70 tff(8974,plain,
% 1.58/1.70 (e1 = op(e0, e2)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8959])).
% 1.58/1.70 tff(8975,plain,
% 1.58/1.70 (e1 = op(e0, op(e0, e0))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8974, 8973])).
% 1.58/1.70 tff(8976,plain,
% 1.58/1.70 (op(e0, op(e0, e0)) = op(e3, e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8972, 8959, 306])).
% 1.58/1.70 tff(8977,plain,
% 1.58/1.70 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e3, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8976])).
% 1.58/1.70 tff(8978,plain,
% 1.58/1.70 (op(e0, op(e3, e3)) = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.70 inference(symmetry,[status(thm)],[8977])).
% 1.58/1.70 tff(8979,plain,
% 1.58/1.70 ((op(e3, e2) = e0) <=> (e2 = op(e0, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8955, 772])).
% 1.58/1.70 tff(8980,plain,
% 1.58/1.70 ((op(e3, e2) = e0) <=> (op(e0, e3) = e2)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8979, 1681])).
% 1.58/1.70 tff(8981,plain,
% 1.58/1.70 ((op(e0, e3) = e2) <=> (op(e3, e2) = e0)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8980])).
% 1.58/1.70 tff(8982,plain,
% 1.58/1.70 ((~(op(e0, e3) = e2)) <=> (~(op(e3, e2) = e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8981])).
% 1.58/1.70 tff(8983,plain,
% 1.58/1.70 (~(op(e3, e2) = e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[79, 8982])).
% 1.58/1.70 tff(8984,plain,
% 1.58/1.70 (op(e3, e1) = e0),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[5538, 8983, 771, 5528])).
% 1.58/1.70 tff(8985,plain,
% 1.58/1.70 (op(e3, e1) = op(e0, e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[8984, 772])).
% 1.58/1.70 tff(8986,plain,
% 1.58/1.70 ((op(e3, e1) = e3) <=> (op(e0, e3) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8985])).
% 1.58/1.70 tff(8987,plain,
% 1.58/1.70 ((op(e0, e3) = e3) <=> (op(e3, e1) = e3)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8986])).
% 1.58/1.70 tff(8988,plain,
% 1.58/1.70 ((~(op(e0, e3) = e3)) <=> (~(op(e3, e1) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8987])).
% 1.58/1.70 tff(8989,plain,
% 1.58/1.70 (~(op(e3, e1) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[661, 8988])).
% 1.58/1.70 tff(8990,plain,
% 1.58/1.70 (op(e0, e1) = e3),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[1730, 8989, 1291, 3271])).
% 1.58/1.70 tff(8991,plain,
% 1.58/1.70 (e3 = op(e0, e1)),
% 1.58/1.70 inference(symmetry,[status(thm)],[8990])).
% 1.58/1.70 tff(8992,plain,
% 1.58/1.70 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.70 inference(transitivity,[status(thm)],[8991, 8888, 8978])).
% 1.58/1.70 tff(8993,plain,
% 1.58/1.70 ($false),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[842, 8992, 8975, 8971])).
% 1.58/1.70 tff(8994,plain,((~(op(e3, e2) = e2)) | (~(op(e3, e3) = e1)) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e0, e3) = e3) | (~(op(e0, e3) = e0)) | (op(e3, e0) = e0) | (op(e0, e2) = e3) | (op(e3, e0) = op(e0, e3)) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.70 tff(8995,plain,
% 1.58/1.70 (~(op(e3, e2) = e2)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[8994, 8954, 8951, 8684, 8690, 8691, 8948, 8943, 8940, 79])).
% 1.58/1.70 tff(8996,plain,
% 1.58/1.70 (~(op(e2, e3) = op(e3, e2))),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[8995, 8936])).
% 1.58/1.70 tff(8997,plain,
% 1.58/1.70 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[430, 8996])).
% 1.58/1.70 tff(8998,plain,
% 1.58/1.70 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8930])).
% 1.58/1.70 tff(8999,plain,
% 1.58/1.70 (~(op(e2, e0) = op(e0, e2))),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[918, 8998])).
% 1.58/1.70 tff(9000,plain,
% 1.58/1.70 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[6358, 8999])).
% 1.58/1.70 tff(9001,plain,
% 1.58/1.70 (op(op(e0, e3), e3) = e0),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[5461, 8691])).
% 1.58/1.70 tff(9002,plain,
% 1.58/1.70 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.70 tff(9003,plain,
% 1.58/1.70 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9002])).
% 1.58/1.70 tff(9004,plain,
% 1.58/1.70 (~(op(e1, e0) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[110, 9003])).
% 1.58/1.70 tff(9005,plain,
% 1.58/1.70 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8920])).
% 1.58/1.70 tff(9006,plain,
% 1.58/1.70 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9005])).
% 1.58/1.70 tff(9007,plain,
% 1.58/1.70 (~(op(e2, e0) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[2228, 9006])).
% 1.58/1.70 tff(9008,plain,
% 1.58/1.70 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8691])).
% 1.58/1.70 tff(9009,plain,
% 1.58/1.70 (op(e3, e0) = op(e3, op(e0, e3))),
% 1.58/1.70 inference(symmetry,[status(thm)],[9008])).
% 1.58/1.70 tff(9010,plain,
% 1.58/1.70 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9009])).
% 1.58/1.70 tff(9011,plain,
% 1.58/1.70 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.58/1.70 inference(symmetry,[status(thm)],[9010])).
% 1.58/1.70 tff(9012,plain,
% 1.58/1.70 (op(e3, e0) = e2),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2015, 8995, 126, 82])).
% 1.58/1.70 tff(9013,plain,
% 1.58/1.70 (op(e3, op(e0, e3)) = e2),
% 1.58/1.70 inference(transitivity,[status(thm)],[9008, 9012])).
% 1.58/1.70 tff(9014,plain,
% 1.58/1.70 ((op(e3, op(e0, e3)) = e3) <=> (e2 = e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9013])).
% 1.58/1.70 tff(9015,plain,
% 1.58/1.70 ((e2 = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.58/1.70 inference(symmetry,[status(thm)],[9014])).
% 1.58/1.70 tff(9016,plain,
% 1.58/1.70 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[9015, 9011])).
% 1.58/1.70 tff(9017,plain,
% 1.58/1.70 ((~(e2 = e3)) <=> (~(op(e3, e0) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9016])).
% 1.58/1.70 tff(9018,plain,
% 1.58/1.70 (~(op(e3, e0) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[1321, 9017])).
% 1.58/1.70 tff(9019,plain,
% 1.58/1.70 (op(e0, e0) = e3),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2713, 9018, 9007, 9004])).
% 1.58/1.70 tff(9020,plain,
% 1.58/1.70 (op(e0, op(e0, e0)) = op(op(e0, e3), e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8692, 9019])).
% 1.58/1.70 tff(9021,plain,
% 1.58/1.70 (op(e0, op(e0, e0)) = e0),
% 1.58/1.70 inference(transitivity,[status(thm)],[9020, 9001])).
% 1.58/1.70 tff(9022,plain,
% 1.58/1.70 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[5598, 9021])).
% 1.58/1.70 tff(9023,plain,
% 1.58/1.70 ((~(op(e3, e2) = e2)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8344])).
% 1.58/1.70 tff(9024,plain,
% 1.58/1.70 (~(op(e3, e2) = op(e2, e3))),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[8995, 9023])).
% 1.58/1.70 tff(9025,plain,
% 1.58/1.70 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[500, 9024])).
% 1.58/1.70 tff(9026,plain,
% 1.58/1.70 (op(e0, op(e2, e2)) = op(op(e0, e3), e3)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8692, 8920])).
% 1.58/1.70 tff(9027,plain,
% 1.58/1.70 (op(e0, op(e2, e2)) = e0),
% 1.58/1.70 inference(transitivity,[status(thm)],[9026, 9001])).
% 1.58/1.70 tff(9028,plain,
% 1.58/1.70 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[5619, 9027])).
% 1.58/1.70 tff(9029,plain,
% 1.58/1.70 (op(e2, e1) = e1),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2367, 8954, 7791, 7796])).
% 1.58/1.70 tff(9030,plain,
% 1.58/1.70 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9029])).
% 1.58/1.70 tff(9031,plain,
% 1.58/1.70 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.58/1.70 inference(transitivity,[status(thm)],[9030, 5522])).
% 1.58/1.70 tff(9032,plain,
% 1.58/1.70 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 1.58/1.70 inference(symmetry,[status(thm)],[9031])).
% 1.58/1.70 tff(9033,plain,
% 1.58/1.70 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8920])).
% 1.58/1.70 tff(9034,plain,
% 1.58/1.70 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.58/1.70 inference(transitivity,[status(thm)],[9033, 3423])).
% 1.58/1.70 tff(9035,plain,
% 1.58/1.70 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9034])).
% 1.58/1.70 tff(9036,plain,
% 1.58/1.70 (~(op(e3, e2) = e3)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[1546, 9035])).
% 1.58/1.70 tff(9037,plain,
% 1.58/1.70 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8685])).
% 1.58/1.70 tff(9038,plain,
% 1.58/1.70 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.58/1.70 inference(symmetry,[status(thm)],[9037])).
% 1.58/1.70 tff(9039,plain,
% 1.58/1.70 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9038])).
% 1.58/1.70 tff(9040,plain,
% 1.58/1.70 (~(op(e3, e2) = e1)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[1888, 9039])).
% 1.58/1.70 tff(9041,plain,
% 1.58/1.70 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[8926])).
% 1.58/1.70 tff(9042,plain,
% 1.58/1.70 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9041])).
% 1.58/1.70 tff(9043,plain,
% 1.58/1.70 (~(op(e1, e0) = e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[756, 9042])).
% 1.58/1.70 tff(9044,plain,
% 1.58/1.70 (op(e1, e1) = e2),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[2285, 7804, 72, 3785])).
% 1.58/1.70 tff(9045,plain,
% 1.58/1.70 (op(e3, e2) = e0),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[1898, 2386, 930, 1890])).
% 1.58/1.70 tff(9046,plain,
% 1.58/1.70 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9045])).
% 1.58/1.70 tff(9047,plain,
% 1.58/1.70 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9046])).
% 1.58/1.70 tff(9048,plain,
% 1.58/1.70 (~(op(e1, e2) = e0)),
% 1.58/1.70 inference(modus_ponens,[status(thm)],[2292, 9047])).
% 1.58/1.70 tff(9049,plain,
% 1.58/1.70 (op(e1, e1) = e0),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[1830, 9048, 80, 2167])).
% 1.58/1.70 tff(9050,plain,
% 1.58/1.70 (e0 = op(e1, e1)),
% 1.58/1.70 inference(symmetry,[status(thm)],[9049])).
% 1.58/1.70 tff(9051,plain,
% 1.58/1.70 (op(e0, e3) = e2),
% 1.58/1.70 inference(transitivity,[status(thm)],[771, 9050, 9044])).
% 1.58/1.70 tff(9052,plain,
% 1.58/1.70 ($false),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[79, 9051])).
% 1.58/1.70 tff(9053,plain,((op(e3, e2) = e2) | (op(e0, e3) = e2) | (~(op(e0, e3) = e0)) | (op(e1, e3) = e0) | (op(e1, e0) = e0) | (op(e1, e3) = e2) | (op(e1, e2) = e2) | (op(e3, e2) = e1) | (op(e3, e2) = e3) | (op(e3, e3) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.70 tff(9054,plain,
% 1.58/1.70 (op(e1, e2) = e2),
% 1.58/1.70 inference(unit_resolution,[status(thm)],[9053, 8995, 8691, 80, 9043, 72, 79, 9040, 9036, 126, 82])).
% 1.58/1.70 tff(9055,plain,
% 1.58/1.70 ((op(e1, e2) = e1) <=> (e2 = op(e3, e3))),
% 1.58/1.70 inference(monotonicity,[status(thm)],[9054, 8685])).
% 1.58/1.70 tff(9056,plain,
% 1.58/1.70 ((op(e1, e2) = e1) <=> (op(e3, e3) = e2)),
% 1.58/1.70 inference(transitivity,[status(thm)],[9055, 565])).
% 1.58/1.71 tff(9057,plain,
% 1.58/1.71 ((op(e3, e3) = e2) <=> (op(e1, e2) = e1)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9056])).
% 1.58/1.71 tff(9058,plain,
% 1.58/1.71 ((op(e3, e3) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 1.58/1.71 inference(transitivity,[status(thm)],[9057, 9032, 531])).
% 1.58/1.71 tff(9059,plain,
% 1.58/1.71 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9058])).
% 1.58/1.71 tff(9060,plain,
% 1.58/1.71 (~(op(e1, e2) = op(e2, e1))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[126, 9059])).
% 1.58/1.71 tff(9061,plain,
% 1.58/1.71 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[539, 9060])).
% 1.58/1.71 tff(9062,plain,
% 1.58/1.71 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9054])).
% 1.58/1.71 tff(9063,plain,
% 1.58/1.71 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9062])).
% 1.58/1.71 tff(9064,plain,
% 1.58/1.71 (~(op(e0, e2) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[6205, 9063])).
% 1.58/1.71 tff(9065,plain,
% 1.58/1.71 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9012])).
% 1.58/1.71 tff(9066,plain,
% 1.58/1.71 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9065])).
% 1.58/1.71 tff(9067,plain,
% 1.58/1.71 (~(op(e0, e0) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[6384, 9066])).
% 1.58/1.71 tff(9068,plain,
% 1.58/1.71 (op(e0, e1) = e2),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[3652, 9067, 79, 9064])).
% 1.58/1.71 tff(9069,plain,
% 1.58/1.71 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9068])).
% 1.58/1.71 tff(9070,plain,
% 1.58/1.71 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.58/1.71 inference(symmetry,[status(thm)],[9069])).
% 1.58/1.71 tff(9071,plain,
% 1.58/1.71 ((op(e1, e0) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 1.58/1.71 inference(transitivity,[status(thm)],[9070, 596])).
% 1.58/1.71 tff(9072,plain,
% 1.58/1.71 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9071])).
% 1.58/1.71 tff(9073,plain,
% 1.58/1.71 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9012])).
% 1.58/1.71 tff(9074,plain,
% 1.58/1.71 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9073])).
% 1.58/1.71 tff(9075,plain,
% 1.58/1.71 (~(op(e1, e0) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[410, 9074])).
% 1.58/1.71 tff(9076,plain,
% 1.58/1.71 (~(op(e0, e1) = op(e1, e0))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9075, 9072])).
% 1.58/1.71 tff(9077,plain,
% 1.58/1.71 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[609, 9076])).
% 1.58/1.71 tff(9078,plain,
% 1.58/1.71 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.58/1.71 inference(transitivity,[status(thm)],[8938, 453])).
% 1.58/1.71 tff(9079,plain,
% 1.58/1.71 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9078])).
% 1.58/1.71 tff(9080,plain,
% 1.58/1.71 (~(op(e0, e3) = op(e3, e0))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[747, 9079])).
% 1.58/1.71 tff(9081,plain,
% 1.58/1.71 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[496, 9080])).
% 1.58/1.71 tff(9082,plain,
% 1.58/1.71 (op(e2, op(e1, e3)) = op(e2, e3)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.71 tff(9083,plain,
% 1.58/1.71 (op(e2, op(e1, e3)) = e2),
% 1.58/1.71 inference(transitivity,[status(thm)],[9082, 5431])).
% 1.58/1.71 tff(9084,plain,
% 1.58/1.71 (((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)) | (~(op(e2, op(e1, e3)) = e2))),
% 1.58/1.71 inference(tautology,[status(thm)],[])).
% 1.58/1.71 tff(9085,plain,
% 1.58/1.71 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[9084, 9083])).
% 1.58/1.71 tff(9086,plain,
% 1.58/1.71 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8678])).
% 1.58/1.71 tff(9087,plain,
% 1.58/1.71 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9086, 666])).
% 1.58/1.71 tff(9088,plain,
% 1.58/1.71 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9087])).
% 1.58/1.71 tff(9089,plain,
% 1.58/1.71 (~(op(e3, e3) = e3)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[571, 9088])).
% 1.58/1.71 tff(9090,plain,
% 1.58/1.71 (op(e3, e1) = e3),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[422, 9018, 9036, 9089])).
% 1.58/1.71 tff(9091,plain,
% 1.58/1.71 (op(e0, op(e3, e1)) = op(op(e0, e3), e3)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8692, 9090])).
% 1.58/1.71 tff(9092,plain,
% 1.58/1.71 (op(e0, op(e3, e1)) = e0),
% 1.58/1.71 inference(transitivity,[status(thm)],[9091, 9001])).
% 1.58/1.71 tff(9093,plain,
% 1.58/1.71 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[5610, 9092])).
% 1.58/1.71 tff(9094,plain,
% 1.58/1.71 ((op(e3, e3) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 1.58/1.71 inference(transitivity,[status(thm)],[9057, 9032])).
% 1.58/1.71 tff(9095,plain,
% 1.58/1.71 ((~(op(e3, e3) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9094])).
% 1.58/1.71 tff(9096,plain,
% 1.58/1.71 (~(op(e2, e1) = op(e1, e2))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[126, 9095])).
% 1.58/1.71 tff(9097,plain,
% 1.58/1.71 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[557, 9096])).
% 1.58/1.71 tff(9098,plain,
% 1.58/1.71 (op(e1, e0) = e1),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[728, 9075, 9004, 9043])).
% 1.58/1.71 tff(9099,plain,
% 1.58/1.71 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8691])).
% 1.58/1.71 tff(9100,plain,
% 1.58/1.71 (op(e3, e2) = e0),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[1898, 8995, 9040, 9036])).
% 1.58/1.71 tff(9101,plain,
% 1.58/1.71 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9100])).
% 1.58/1.71 tff(9102,plain,
% 1.58/1.71 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9101])).
% 1.58/1.71 tff(9103,plain,
% 1.58/1.71 (~(op(e1, e2) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[2292, 9102])).
% 1.58/1.71 tff(9104,plain,
% 1.58/1.71 (op(e1, e1) = e0),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[1830, 9103, 80, 9043])).
% 1.58/1.71 tff(9105,plain,
% 1.58/1.71 (op(e1, e1) = op(e0, e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9104, 8692])).
% 1.58/1.71 tff(9106,plain,
% 1.58/1.71 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9105])).
% 1.58/1.71 tff(9107,plain,
% 1.58/1.71 (op(e1, op(e1, e1)) = e1),
% 1.58/1.71 inference(transitivity,[status(thm)],[9106, 9099, 9098])).
% 1.58/1.71 tff(9108,plain,
% 1.58/1.71 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[5678, 9107])).
% 1.58/1.71 tff(9109,plain,
% 1.58/1.71 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8684])).
% 1.58/1.71 tff(9110,plain,
% 1.58/1.71 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9109])).
% 1.58/1.71 tff(9111,plain,
% 1.58/1.71 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9110])).
% 1.58/1.71 tff(9112,plain,
% 1.58/1.71 (op(e3, op(e3, e3)) = e3),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9090, 9111])).
% 1.58/1.71 tff(9113,plain,
% 1.58/1.71 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[6277, 9112])).
% 1.58/1.71 tff(9114,plain,
% 1.58/1.71 ((~(op(e1, e0) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9070])).
% 1.58/1.71 tff(9115,plain,
% 1.58/1.71 (~(op(e1, e0) = op(e0, e1))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9075, 9114])).
% 1.58/1.71 tff(9116,plain,
% 1.58/1.71 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[613, 9115])).
% 1.58/1.71 tff(9117,plain,
% 1.58/1.71 ($false),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[5367, 9116, 9113, 9108, 9097, 9093, 9085, 9081, 9077, 9061, 9028, 9025, 9022, 9000, 8997, 8934])).
% 1.58/1.71 tff(9118,plain,((op(e3, e1) = e2) | (op(e1, e3) = e0) | (op(e0, e3) = e2) | (op(e3, e3) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.71 tff(9119,plain,
% 1.58/1.71 (op(e3, e1) = e2),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[9118, 75, 79, 126, 72, 80, 76, 124, 121])).
% 1.58/1.71 tff(9120,plain,
% 1.58/1.71 (op(e3, op(e3, e1)) = op(e3, e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9119])).
% 1.58/1.71 tff(9121,plain,
% 1.58/1.71 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9109])).
% 1.58/1.71 tff(9122,plain,
% 1.58/1.71 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9121, 9120])).
% 1.58/1.71 tff(9123,plain,
% 1.58/1.71 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (e0 = op(e3, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9122])).
% 1.58/1.71 tff(9124,plain,
% 1.58/1.71 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e0)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9123, 4959])).
% 1.58/1.71 tff(9125,plain,
% 1.58/1.71 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9124])).
% 1.58/1.71 tff(9126,plain,
% 1.58/1.71 (e1 = op(e3, e3)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[8684, 658])).
% 1.58/1.71 tff(9127,plain,
% 1.58/1.71 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e1))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9109])).
% 1.58/1.71 tff(9128,plain,
% 1.58/1.71 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e2)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9127, 637])).
% 1.58/1.71 tff(9129,plain,
% 1.58/1.71 ((op(e3, e1) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.58/1.71 inference(symmetry,[status(thm)],[9128])).
% 1.58/1.71 tff(9130,plain,
% 1.58/1.71 (e2 = op(e3, op(e3, e3))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9119, 9129])).
% 1.58/1.71 tff(9131,plain,
% 1.58/1.71 (~(e0 = op(e3, op(e3, op(e3, e3))))),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[2034, 9130, 9126])).
% 1.58/1.71 tff(9132,plain,
% 1.58/1.71 (~(op(e3, e2) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9131, 9125])).
% 1.58/1.71 tff(9133,plain,
% 1.58/1.71 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8692])).
% 1.58/1.71 tff(9134,plain,
% 1.58/1.71 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9133])).
% 1.58/1.71 tff(9135,plain,
% 1.58/1.71 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9134])).
% 1.58/1.71 tff(9136,plain,
% 1.58/1.71 (~(op(e0, e2) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[918, 9135])).
% 1.58/1.71 tff(9137,plain,
% 1.58/1.71 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8692])).
% 1.58/1.71 tff(9138,plain,
% 1.58/1.71 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9137])).
% 1.58/1.71 tff(9139,plain,
% 1.58/1.71 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9138])).
% 1.58/1.71 tff(9140,plain,
% 1.58/1.71 (~(op(e0, e1) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[818, 9139])).
% 1.58/1.71 tff(9141,plain,
% 1.58/1.71 ((op(e3, e1) = e0) <=> (e2 = op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9119, 8692])).
% 1.58/1.71 tff(9142,plain,
% 1.58/1.71 ((op(e3, e1) = e0) <=> (op(e0, e3) = e2)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9141, 1681])).
% 1.58/1.71 tff(9143,plain,
% 1.58/1.71 ((op(e0, e3) = e2) <=> (op(e3, e1) = e0)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9142])).
% 1.58/1.71 tff(9144,plain,
% 1.58/1.71 ((~(op(e0, e3) = e2)) <=> (~(op(e3, e1) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9143])).
% 1.58/1.71 tff(9145,plain,
% 1.58/1.71 (~(op(e3, e1) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[79, 9144])).
% 1.58/1.71 tff(9146,plain,
% 1.58/1.71 (op(e1, e1) = e0),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[292, 9145, 7791, 9140])).
% 1.58/1.71 tff(9147,plain,
% 1.58/1.71 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9146])).
% 1.58/1.71 tff(9148,plain,
% 1.58/1.71 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9147, 67])).
% 1.58/1.71 tff(9149,plain,
% 1.58/1.71 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9148])).
% 1.58/1.71 tff(9150,plain,
% 1.58/1.71 (~(op(e1, e2) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[1604, 9149])).
% 1.58/1.71 tff(9151,plain,
% 1.58/1.71 (op(e2, e2) = e0),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[973, 9150, 9136, 9132])).
% 1.58/1.71 tff(9152,plain,
% 1.58/1.71 (op(e2, e2) = op(e0, e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9151, 8692])).
% 1.58/1.71 tff(9153,plain,
% 1.58/1.71 ((op(e2, e2) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9152, 8685])).
% 1.58/1.71 tff(9154,plain,
% 1.58/1.71 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e2) = e1)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9153])).
% 1.58/1.71 tff(9155,plain,
% 1.58/1.71 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e1))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9154])).
% 1.58/1.71 tff(9156,plain,
% 1.58/1.71 (~(op(e2, e2) = e1)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[1077, 9155])).
% 1.58/1.71 tff(9157,plain,
% 1.58/1.71 (op(e3, e0) = op(e0, e3)),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[5538, 9132, 8691, 9145])).
% 1.58/1.71 tff(9158,plain,
% 1.58/1.71 (op(e0, op(e0, e3)) = op(e0, e0)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8691])).
% 1.58/1.71 tff(9159,plain,
% 1.58/1.71 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e0) = op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9158, 8692])).
% 1.58/1.71 tff(9160,plain,
% 1.58/1.71 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9159])).
% 1.58/1.71 tff(9161,plain,
% 1.58/1.71 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9160])).
% 1.58/1.71 tff(9162,plain,
% 1.58/1.71 (~(op(e0, op(e0, e3)) = e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[3414, 9161])).
% 1.58/1.71 tff(9163,plain,
% 1.58/1.71 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8691])).
% 1.58/1.71 tff(9164,plain,
% 1.58/1.71 (op(e2, e0) = op(e2, op(e0, e3))),
% 1.58/1.71 inference(symmetry,[status(thm)],[9163])).
% 1.58/1.71 tff(9165,plain,
% 1.58/1.71 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9164])).
% 1.58/1.71 tff(9166,plain,
% 1.58/1.71 ((~(op(e2, e0) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9165])).
% 1.58/1.71 tff(9167,plain,
% 1.58/1.71 (~(op(e2, op(e0, e3)) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[5442, 9166])).
% 1.58/1.71 tff(9168,plain,
% 1.58/1.71 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9119])).
% 1.58/1.71 tff(9169,plain,
% 1.58/1.71 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9168, 2234])).
% 1.58/1.71 tff(9170,plain,
% 1.58/1.71 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9169])).
% 1.58/1.71 tff(9171,plain,
% 1.58/1.71 (~(op(e3, e2) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[3429, 9170])).
% 1.58/1.71 tff(9172,plain,
% 1.58/1.71 (op(e3, e2) = e3),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[1898, 9132, 9040, 9171])).
% 1.58/1.71 tff(9173,plain,
% 1.58/1.71 (e3 = op(e3, e2)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9172])).
% 1.58/1.71 tff(9174,plain,
% 1.58/1.71 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e0) = op(e3, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9008, 9173])).
% 1.58/1.71 tff(9175,plain,
% 1.58/1.71 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9174])).
% 1.58/1.71 tff(9176,plain,
% 1.58/1.71 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9175])).
% 1.58/1.71 tff(9177,plain,
% 1.58/1.71 (~(op(e3, op(e0, e3)) = e3)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[1133, 9176])).
% 1.58/1.71 tff(9178,plain,
% 1.58/1.71 (op(e1, op(e0, e3)) = e1),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[4654, 9177, 121, 9167, 9162, 9157])).
% 1.58/1.71 tff(9179,plain,
% 1.58/1.71 (op(e1, e0) = op(e1, op(e0, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[8692])).
% 1.58/1.71 tff(9180,plain,
% 1.58/1.71 (op(e1, e0) = e1),
% 1.58/1.71 inference(transitivity,[status(thm)],[9179, 9178])).
% 1.58/1.71 tff(9181,plain,
% 1.58/1.71 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9180])).
% 1.58/1.71 tff(9182,plain,
% 1.58/1.71 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9181, 5522])).
% 1.58/1.71 tff(9183,plain,
% 1.58/1.71 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9182])).
% 1.58/1.71 tff(9184,plain,
% 1.58/1.71 (~(op(e1, e2) = e1)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[1312, 9183])).
% 1.58/1.71 tff(9185,plain,
% 1.58/1.71 (op(e0, e2) = e1),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[1613, 9184, 9040, 9156])).
% 1.58/1.71 tff(9186,plain,
% 1.58/1.71 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9119])).
% 1.58/1.71 tff(9187,plain,
% 1.58/1.71 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9186])).
% 1.58/1.71 tff(9188,plain,
% 1.58/1.71 (~(op(e3, e0) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[580, 9187])).
% 1.58/1.71 tff(9189,plain,
% 1.58/1.71 (op(e1, e0) = op(e3, e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9179, 9178, 8685])).
% 1.58/1.71 tff(9190,plain,
% 1.58/1.71 ((op(e1, e0) = e2) <=> (op(e3, e3) = e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9189])).
% 1.58/1.71 tff(9191,plain,
% 1.58/1.71 ((op(e3, e3) = e2) <=> (op(e1, e0) = e2)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9190])).
% 1.58/1.71 tff(9192,plain,
% 1.58/1.71 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e0) = e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9191])).
% 1.58/1.71 tff(9193,plain,
% 1.58/1.71 (~(op(e1, e0) = e2)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[126, 9192])).
% 1.58/1.71 tff(9194,plain,
% 1.58/1.71 (op(e0, e0) = e2),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[589, 9193, 5442, 9188])).
% 1.58/1.71 tff(9195,plain,
% 1.58/1.71 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9194])).
% 1.58/1.71 tff(9196,plain,
% 1.58/1.71 (op(e0, op(e0, e0)) = op(e3, e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9195, 9185, 8685])).
% 1.58/1.71 tff(9197,plain,
% 1.58/1.71 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e3, e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9196])).
% 1.58/1.71 tff(9198,plain,
% 1.58/1.71 (op(e0, op(e0, op(e0, e0))) = op(e0, e1)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9197, 8687])).
% 1.58/1.71 tff(9199,plain,
% 1.58/1.71 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (e3 = op(e0, e1))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9198])).
% 1.58/1.71 tff(9200,plain,
% 1.58/1.71 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (op(e0, e1) = e3)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9199, 127])).
% 1.58/1.71 tff(9201,plain,
% 1.58/1.71 ((op(e0, e1) = e3) <=> (e3 = op(e0, op(e0, op(e0, e0))))),
% 1.58/1.71 inference(symmetry,[status(thm)],[9200])).
% 1.58/1.71 tff(9202,plain,
% 1.58/1.71 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e3, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9173])).
% 1.58/1.71 tff(9203,plain,
% 1.58/1.71 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9202])).
% 1.58/1.71 tff(9204,plain,
% 1.58/1.71 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9203])).
% 1.58/1.71 tff(9205,plain,
% 1.58/1.71 (~(op(e0, e2) = e3)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[1467, 9204])).
% 1.58/1.71 tff(9206,plain,
% 1.58/1.71 ((op(e0, e0) = e3) <=> (e2 = op(e3, e2))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9194, 9173])).
% 1.58/1.71 tff(9207,plain,
% 1.58/1.71 ((op(e0, e0) = e3) <=> (op(e3, e2) = e2)),
% 1.58/1.71 inference(transitivity,[status(thm)],[9206, 2234])).
% 1.58/1.71 tff(9208,plain,
% 1.58/1.71 ((op(e3, e2) = e2) <=> (op(e0, e0) = e3)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9207])).
% 1.58/1.71 tff(9209,plain,
% 1.58/1.71 ((~(op(e3, e2) = e2)) <=> (~(op(e0, e0) = e3))),
% 1.58/1.71 inference(monotonicity,[status(thm)],[9208])).
% 1.58/1.71 tff(9210,plain,
% 1.58/1.71 (~(op(e0, e0) = e3)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9171, 9209])).
% 1.58/1.71 tff(9211,plain,
% 1.58/1.71 (op(e0, e1) = e3),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[1495, 9210, 8690, 9205])).
% 1.58/1.71 tff(9212,plain,
% 1.58/1.71 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9211, 9201])).
% 1.58/1.71 tff(9213,plain,
% 1.58/1.71 (e2 = op(e0, e0)),
% 1.58/1.71 inference(modus_ponens,[status(thm)],[9194, 78])).
% 1.58/1.71 tff(9214,plain,
% 1.58/1.71 (op(e0, e2) = op(e0, op(e0, e0))),
% 1.58/1.71 inference(symmetry,[status(thm)],[9195])).
% 1.58/1.71 tff(9215,plain,
% 1.58/1.71 (e1 = op(e0, e2)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9185])).
% 1.58/1.71 tff(9216,plain,
% 1.58/1.71 (e1 = op(e0, op(e0, e0))),
% 1.58/1.71 inference(transitivity,[status(thm)],[9215, 9214])).
% 1.58/1.71 tff(9217,plain,
% 1.58/1.71 (~(e3 = op(e0, op(e0, op(e0, e0))))),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[842, 9216, 9213])).
% 1.58/1.71 tff(9218,plain,
% 1.58/1.71 ($false),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[9217, 9212])).
% 1.58/1.71 tff(9219,plain,((op(e1, e2) = e3) | (op(e3, e3) = e2) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.71 tff(9220,plain,
% 1.58/1.71 (op(e1, e2) = e3),
% 1.58/1.71 inference(unit_resolution,[status(thm)],[9219, 126, 121, 79, 72, 80, 76, 124])).
% 1.58/1.71 tff(9221,plain,
% 1.58/1.71 (e3 = op(e1, e2)),
% 1.58/1.71 inference(symmetry,[status(thm)],[9220])).
% 1.58/1.71 tff(9222,plain,
% 1.58/1.71 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9221])).
% 1.58/1.72 tff(9223,plain,
% 1.58/1.72 ((op(e1, e3) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 1.58/1.72 inference(transitivity,[status(thm)],[9222, 125])).
% 1.58/1.72 tff(9224,plain,
% 1.58/1.72 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9223])).
% 1.58/1.72 tff(9225,plain,
% 1.58/1.72 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9224])).
% 1.58/1.72 tff(9226,plain,
% 1.58/1.72 (~(op(e1, e3) = e3)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1850, 9225])).
% 1.58/1.72 tff(9227,plain,
% 1.58/1.72 (op(e1, e3) = e1),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[104, 9226, 80, 72])).
% 1.58/1.72 tff(9228,plain,
% 1.58/1.72 (e1 = op(e1, e3)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9227])).
% 1.58/1.72 tff(9229,plain,
% 1.58/1.72 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9228])).
% 1.58/1.72 tff(9230,plain,
% 1.58/1.72 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9229])).
% 1.58/1.72 tff(9231,plain,
% 1.58/1.72 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9230])).
% 1.58/1.72 tff(9232,plain,
% 1.58/1.72 (~(op(e1, e1) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[619, 9231])).
% 1.58/1.72 tff(9233,plain,
% 1.58/1.72 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9220])).
% 1.58/1.72 tff(9234,plain,
% 1.58/1.72 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9233])).
% 1.58/1.72 tff(9235,plain,
% 1.58/1.72 (~(op(e1, e1) = e3)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1604, 9234])).
% 1.58/1.72 tff(9236,plain,
% 1.58/1.72 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9221])).
% 1.58/1.72 tff(9237,plain,
% 1.58/1.72 (op(e1, op(e1, e2)) = op(e1, e3)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9236])).
% 1.58/1.72 tff(9238,plain,
% 1.58/1.72 ((op(e1, op(e1, e2)) = e2) <=> (op(e1, e3) = e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9237])).
% 1.58/1.72 tff(9239,plain,
% 1.58/1.72 ((op(e1, e3) = e2) <=> (op(e1, op(e1, e2)) = e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9238])).
% 1.58/1.72 tff(9240,plain,
% 1.58/1.72 ((~(op(e1, e3) = e2)) <=> (~(op(e1, op(e1, e2)) = e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9239])).
% 1.58/1.72 tff(9241,plain,
% 1.58/1.72 (~(op(e1, op(e1, e2)) = e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[72, 9240])).
% 1.58/1.72 tff(9242,plain,
% 1.58/1.72 (op(e0, op(e1, e3)) = op(e0, e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[3724])).
% 1.58/1.72 tff(9243,plain,
% 1.58/1.72 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.72 tff(9244,plain,
% 1.58/1.72 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9243])).
% 1.58/1.72 tff(9245,plain,
% 1.58/1.72 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9244])).
% 1.58/1.72 tff(9246,plain,
% 1.58/1.72 (~(op(e0, e2) = e3)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[6205, 9245])).
% 1.58/1.72 tff(9247,assumption,(~(op(e1, op(e1, e2)) = e2)), introduced(assumption)).
% 1.58/1.72 tff(9248,plain,
% 1.58/1.72 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[3787])).
% 1.58/1.72 tff(9249,plain,
% 1.58/1.72 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9248, 1])).
% 1.58/1.72 tff(9250,plain,
% 1.58/1.72 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9249])).
% 1.58/1.72 tff(9251,plain,
% 1.58/1.72 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9250])).
% 1.58/1.72 tff(9252,plain,
% 1.58/1.72 (~(op(e2, e3) = e0)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[14, 9251])).
% 1.58/1.72 tff(9253,plain,
% 1.58/1.72 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.72 tff(9254,plain,
% 1.58/1.72 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9253])).
% 1.58/1.72 tff(9255,plain,
% 1.58/1.72 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9254])).
% 1.58/1.72 tff(9256,plain,
% 1.58/1.72 (~(op(e1, e0) = e3)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1312, 9255])).
% 1.58/1.72 tff(9257,plain,
% 1.58/1.72 (op(e1, e0) = e0),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[728, 7804, 9256, 3765])).
% 1.58/1.72 tff(9258,plain,
% 1.58/1.72 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9257])).
% 1.58/1.72 tff(9259,plain,
% 1.58/1.72 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9258, 4499])).
% 1.58/1.72 tff(9260,plain,
% 1.58/1.72 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9259])).
% 1.58/1.72 tff(9261,plain,
% 1.58/1.72 (~(op(e2, e0) = e0)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[756, 9260])).
% 1.58/1.72 tff(9262,plain,
% 1.58/1.72 (op(e2, e2) = e0),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[2311, 9261, 2559, 9252])).
% 1.58/1.72 tff(9263,plain,
% 1.58/1.72 (op(e3, op(e2, e2)) = op(e3, e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9262])).
% 1.58/1.72 tff(9264,plain,
% 1.58/1.72 (e0 = op(e2, e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9262])).
% 1.58/1.72 tff(9265,plain,
% 1.58/1.72 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[3787])).
% 1.58/1.72 tff(9266,plain,
% 1.58/1.72 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9265])).
% 1.58/1.72 tff(9267,plain,
% 1.58/1.72 (~(op(e2, e0) = e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[989, 9266])).
% 1.58/1.72 tff(9268,plain,
% 1.58/1.72 ((op(e1, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9269,plain,
% 1.58/1.72 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9268, 502])).
% 1.58/1.72 tff(9270,plain,
% 1.58/1.72 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9269])).
% 1.58/1.72 tff(9271,plain,
% 1.58/1.72 (~(op(e2, e2) = e3)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1273, 9270])).
% 1.58/1.72 tff(9272,plain,
% 1.58/1.72 ((e2 = op(e1, op(e1, e2))) <=> (op(e1, op(e1, e2)) = e2)),
% 1.58/1.72 inference(commutativity,[status(thm)],[])).
% 1.58/1.72 tff(9273,plain,
% 1.58/1.72 (op(e1, op(e1, e2)) = op(e1, e3)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9274,plain,
% 1.58/1.72 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9273])).
% 1.58/1.72 tff(9275,plain,
% 1.58/1.72 (e1 = op(e1, op(e1, e2))),
% 1.58/1.72 inference(transitivity,[status(thm)],[3710, 9274])).
% 1.58/1.72 tff(9276,plain,
% 1.58/1.72 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9277,plain,
% 1.58/1.72 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9276, 1314])).
% 1.58/1.72 tff(9278,plain,
% 1.58/1.72 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9277])).
% 1.58/1.72 tff(9279,plain,
% 1.58/1.72 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9278])).
% 1.58/1.72 tff(9280,plain,
% 1.58/1.72 (~(op(e1, e2) = e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1321, 9279])).
% 1.58/1.72 tff(9281,plain,
% 1.58/1.72 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[3787])).
% 1.58/1.72 tff(9282,plain,
% 1.58/1.72 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9281])).
% 1.58/1.72 tff(9283,plain,
% 1.58/1.72 (~(op(e2, e2) = e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[515, 9282])).
% 1.58/1.72 tff(9284,plain,
% 1.58/1.72 (op(e0, e2) = e2),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1151, 2386, 9283, 9280])).
% 1.58/1.72 tff(9285,plain,
% 1.58/1.72 ((op(e0, e2) = e1) <=> (e2 = op(e1, op(e1, e2)))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9284, 9275])).
% 1.58/1.72 tff(9286,plain,
% 1.58/1.72 ((op(e0, e2) = e1) <=> (op(e1, op(e1, e2)) = e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9285, 9272])).
% 1.58/1.72 tff(9287,plain,
% 1.58/1.72 ((op(e1, op(e1, e2)) = e2) <=> (op(e0, e2) = e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9286])).
% 1.58/1.72 tff(9288,plain,
% 1.58/1.72 ((~(op(e1, op(e1, e2)) = e2)) <=> (~(op(e0, e2) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9287])).
% 1.58/1.72 tff(9289,plain,
% 1.58/1.72 (~(op(e0, e2) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[9247, 9288])).
% 1.58/1.72 tff(9290,plain,
% 1.58/1.72 ((e1 = e3) <=> (e1 = op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.72 tff(9291,plain,
% 1.58/1.72 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9290, 5522])).
% 1.58/1.72 tff(9292,plain,
% 1.58/1.72 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9291])).
% 1.58/1.72 tff(9293,plain,
% 1.58/1.72 (~(op(e1, e2) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[303, 9292])).
% 1.58/1.72 tff(9294,plain,
% 1.58/1.72 ((op(e2, e2) = e1) <=> (e0 = op(e1, e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9262, 3710])).
% 1.58/1.72 tff(9295,plain,
% 1.58/1.72 ((op(e2, e2) = e1) <=> (op(e1, e3) = e0)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9294, 6095])).
% 1.58/1.72 tff(9296,plain,
% 1.58/1.72 ((op(e1, e3) = e0) <=> (op(e2, e2) = e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9295])).
% 1.58/1.72 tff(9297,plain,
% 1.58/1.72 ((~(op(e1, e3) = e0)) <=> (~(op(e2, e2) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9296])).
% 1.58/1.72 tff(9298,plain,
% 1.58/1.72 (~(op(e2, e2) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[80, 9297])).
% 1.58/1.72 tff(9299,plain,
% 1.58/1.72 (op(e3, e2) = e1),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1613, 9298, 9293, 9289])).
% 1.58/1.72 tff(9300,assumption,(op(e2, e2) = e0), introduced(assumption)).
% 1.58/1.72 tff(9301,plain,
% 1.58/1.72 (e0 = op(e2, e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[9300, 995])).
% 1.58/1.72 tff(9302,plain,
% 1.58/1.72 (op(e2, op(e2, e2)) = op(e2, e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9300])).
% 1.58/1.72 tff(9303,plain,
% 1.58/1.72 ((e1 = op(e2, op(e2, e2))) <=> (e1 = op(e2, e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9302])).
% 1.58/1.72 tff(9304,plain,
% 1.58/1.72 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e1)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9303, 16])).
% 1.58/1.72 tff(9305,plain,
% 1.58/1.72 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9304])).
% 1.58/1.72 tff(9306,plain,
% 1.58/1.72 (e1 = op(e2, op(e2, e2))),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[3509, 9305])).
% 1.58/1.72 tff(9307,plain,
% 1.58/1.72 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9302])).
% 1.58/1.72 tff(9308,plain,
% 1.58/1.72 (op(e2, op(e2, e0)) = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9307])).
% 1.58/1.72 tff(9309,plain,
% 1.58/1.72 (e1 = op(e3, e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[5978])).
% 1.58/1.72 tff(9310,plain,
% 1.58/1.72 (op(e2, e0) = op(e3, e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[3509, 9309])).
% 1.58/1.72 tff(9311,plain,
% 1.58/1.72 (op(e2, op(e2, e0)) = op(e2, op(e3, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9310])).
% 1.58/1.72 tff(9312,plain,
% 1.58/1.72 (op(e2, op(e3, e2)) = op(e2, op(e2, e0))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9311])).
% 1.58/1.72 tff(9313,plain,
% 1.58/1.72 (op(e3, e2) = op(e1, e3)),
% 1.58/1.72 inference(transitivity,[status(thm)],[5978, 3710])).
% 1.58/1.72 tff(9314,plain,
% 1.58/1.72 (op(e2, op(e3, e2)) = op(e2, op(e1, e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9313])).
% 1.58/1.72 tff(9315,plain,
% 1.58/1.72 (op(e2, op(e1, e3)) = op(e2, op(e3, e2))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9314])).
% 1.58/1.72 tff(9316,plain,
% 1.58/1.72 (op(e2, e1) = e3),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1559, 3272, 2431, 124])).
% 1.58/1.72 tff(9317,plain,
% 1.58/1.72 (e3 = op(e2, e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9316])).
% 1.58/1.72 tff(9318,plain,
% 1.58/1.72 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.72 inference(transitivity,[status(thm)],[9317, 3884, 9315, 9312, 9308])).
% 1.58/1.72 tff(9319,plain,
% 1.58/1.72 ($false),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1539, 9318, 9306, 9301])).
% 1.58/1.72 tff(9320,plain,((op(e2, e0) = e3) | (~(op(e1, e3) = e1)) | (~(op(e3, e2) = e1)) | (~(op(e2, e2) = e0)) | (op(e2, e2) = e3) | (op(e2, e3) = e3) | (op(e2, e0) = e2) | (op(e2, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.72 tff(9321,plain,
% 1.58/1.72 (op(e2, e0) = e3),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[9320, 9299, 132, 9262, 9271, 124, 9267, 9261])).
% 1.58/1.72 tff(9322,plain,
% 1.58/1.72 (op(op(e2, e0), e0) = op(e3, op(e2, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9321, 9264])).
% 1.58/1.72 tff(9323,plain,
% 1.58/1.72 (op(op(e2, e0), e0) = e2),
% 1.58/1.72 inference(transitivity,[status(thm)],[9322, 9263, 7801])).
% 1.58/1.72 tff(9324,plain,
% 1.58/1.72 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1945, 9323])).
% 1.58/1.72 tff(9325,plain,
% 1.58/1.72 (e1 = op(e3, e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9299])).
% 1.58/1.72 tff(9326,plain,
% 1.58/1.72 (e0 = op(e2, e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9300])).
% 1.58/1.72 tff(9327,plain,
% 1.58/1.72 (op(e3, e3) = op(e2, e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[3066, 9326])).
% 1.58/1.72 tff(9328,plain,
% 1.58/1.72 (op(e3, op(e3, e3)) = op(e3, op(e2, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9327])).
% 1.58/1.72 tff(9329,plain,
% 1.58/1.72 (op(e3, op(e2, e2)) = op(e3, op(e3, e3))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9328])).
% 1.58/1.72 tff(9330,plain,
% 1.58/1.72 (op(e3, op(e2, e2)) = op(e3, e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9300])).
% 1.58/1.72 tff(9331,plain,
% 1.58/1.72 (op(e3, e0) = op(e3, op(e2, e2))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9330])).
% 1.58/1.72 tff(9332,assumption,(op(e3, e0) = e2), introduced(assumption)).
% 1.58/1.72 tff(9333,plain,
% 1.58/1.72 (e2 = op(e3, e0)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9332])).
% 1.58/1.72 tff(9334,plain,
% 1.58/1.72 (e2 = op(e3, op(e3, e3))),
% 1.58/1.72 inference(transitivity,[status(thm)],[9333, 9331, 9329])).
% 1.58/1.72 tff(9335,plain,
% 1.58/1.72 (op(e3, op(e3, e3)) = e2),
% 1.58/1.72 inference(transitivity,[status(thm)],[9328, 9330, 9332])).
% 1.58/1.72 tff(9336,plain,
% 1.58/1.72 (op(e3, op(e3, op(e3, e3))) = op(op(e1, e2), e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2900, 9335])).
% 1.58/1.72 tff(9337,plain,
% 1.58/1.72 (op(op(e1, e2), e2) = op(e3, op(e3, op(e3, e3)))),
% 1.58/1.72 inference(symmetry,[status(thm)],[9336])).
% 1.58/1.72 tff(9338,plain,
% 1.58/1.72 (op(op(e1, e2), e2) = op(e3, e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9339,plain,
% 1.58/1.72 (op(e3, e2) = op(op(e1, e2), e2)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9338])).
% 1.58/1.72 tff(9340,plain,
% 1.58/1.72 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.58/1.72 inference(transitivity,[status(thm)],[9309, 9339, 9337])).
% 1.58/1.72 tff(9341,plain,
% 1.58/1.72 ($false),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[3093, 9340, 9334, 3079])).
% 1.58/1.72 tff(9342,plain,((~(op(e3, e3) = e0)) | (~(op(e3, e2) = e1)) | (~(op(e3, e0) = e2)) | (~(op(e2, e2) = e0)) | (~(op(e1, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.58/1.72 tff(9343,plain,
% 1.58/1.72 (~(op(e3, e3) = e0)),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[9342, 9299, 7801, 9262, 2899])).
% 1.58/1.72 tff(9344,plain,
% 1.58/1.72 (op(e0, e3) = e0),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1098, 9343, 9252, 80])).
% 1.58/1.72 tff(9345,plain,
% 1.58/1.72 (op(e0, op(e1, e2)) = op(e0, e3)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9346,plain,
% 1.58/1.72 ((op(e3, e2) = op(e2, e2)) <=> (op(e2, e2) = op(e3, e2))),
% 1.58/1.72 inference(commutativity,[status(thm)],[])).
% 1.58/1.72 tff(9347,plain,
% 1.58/1.72 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9264])).
% 1.58/1.72 tff(9348,plain,
% 1.58/1.72 ((op(e3, e2) = e0) <=> (op(e2, e2) = op(e3, e2))),
% 1.58/1.72 inference(transitivity,[status(thm)],[9347, 9346])).
% 1.58/1.72 tff(9349,plain,
% 1.58/1.72 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9348])).
% 1.58/1.72 tff(9350,plain,
% 1.58/1.72 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9349])).
% 1.58/1.72 tff(9351,plain,
% 1.58/1.72 (~(op(e3, e2) = e0)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1546, 9350])).
% 1.58/1.72 tff(9352,plain,
% 1.58/1.72 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[7801])).
% 1.58/1.72 tff(9353,plain,
% 1.58/1.72 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9352, 1])).
% 1.58/1.72 tff(9354,plain,
% 1.58/1.72 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9353])).
% 1.58/1.72 tff(9355,plain,
% 1.58/1.72 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9354])).
% 1.58/1.72 tff(9356,plain,
% 1.58/1.72 (~(op(e3, e0) = e0)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[14, 9355])).
% 1.58/1.72 tff(9357,plain,
% 1.58/1.72 (op(e3, e1) = e0),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1916, 9343, 9356, 9351])).
% 1.58/1.72 tff(9358,plain,
% 1.58/1.72 (op(op(e3, e1), e3) = op(e0, op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9357, 2900])).
% 1.58/1.72 tff(9359,plain,
% 1.58/1.72 (op(op(e3, e1), e3) = op(e2, e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9358, 9345, 9344, 9264])).
% 1.58/1.72 tff(9360,plain,
% 1.58/1.72 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e2) = op(e3, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9359, 9325])).
% 1.58/1.72 tff(9361,plain,
% 1.58/1.72 ((op(e2, e2) = op(e3, e2)) <=> (op(op(e3, e1), e3) = e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9360])).
% 1.58/1.72 tff(9362,plain,
% 1.58/1.72 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9361])).
% 1.58/1.72 tff(9363,plain,
% 1.58/1.72 (~(op(op(e3, e1), e3) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[1546, 9362])).
% 1.58/1.72 tff(9364,plain,
% 1.58/1.72 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1050, 9363])).
% 1.58/1.72 tff(9365,plain,
% 1.58/1.72 (op(op(e1, e2), e1) = op(e3, e1)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9366,plain,
% 1.58/1.72 (op(e3, e1) = op(op(e1, e2), e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9365])).
% 1.58/1.72 tff(9367,plain,
% 1.58/1.72 ((op(e3, e1) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9366])).
% 1.58/1.72 tff(9368,plain,
% 1.58/1.72 ((~(op(e3, e1) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9367])).
% 1.58/1.72 tff(9369,plain,
% 1.58/1.72 (~(op(op(e1, e2), e1) = e2)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[82, 9368])).
% 1.58/1.72 tff(9370,plain,
% 1.58/1.72 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[5959, 9369])).
% 1.58/1.72 tff(9371,plain,
% 1.58/1.72 (op(op(e3, e2), e2) = op(e1, e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9299])).
% 1.58/1.72 tff(9372,plain,
% 1.58/1.72 (op(op(e3, e2), e2) = e3),
% 1.58/1.72 inference(transitivity,[status(thm)],[9371, 2899])).
% 1.58/1.72 tff(9373,plain,
% 1.58/1.72 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1339, 9372])).
% 1.58/1.72 tff(9374,plain,
% 1.58/1.72 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9284])).
% 1.58/1.72 tff(9375,plain,
% 1.58/1.72 (op(e0, op(e0, e2)) = e2),
% 1.58/1.72 inference(transitivity,[status(thm)],[9374, 9284])).
% 1.58/1.72 tff(9376,plain,
% 1.58/1.72 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1331, 9375])).
% 1.58/1.72 tff(9377,plain,
% 1.58/1.72 (op(e2, op(e1, e2)) = op(e2, e3)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[2899])).
% 1.58/1.72 tff(9378,plain,
% 1.58/1.72 (op(op(e3, e0), e3) = op(e2, op(e1, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[7801, 2900])).
% 1.58/1.72 tff(9379,plain,
% 1.58/1.72 (op(op(e3, e0), e3) = e2),
% 1.58/1.72 inference(transitivity,[status(thm)],[9378, 9377, 3787])).
% 1.58/1.72 tff(9380,plain,
% 1.58/1.72 ((op(op(e3, e0), e3) = e0) <=> (e2 = e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9379])).
% 1.58/1.72 tff(9381,plain,
% 1.58/1.72 ((op(op(e3, e0), e3) = e0) <=> (e0 = e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9380, 1])).
% 1.58/1.72 tff(9382,plain,
% 1.58/1.72 ((e0 = e2) <=> (op(op(e3, e0), e3) = e0)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9381])).
% 1.58/1.72 tff(9383,plain,
% 1.58/1.72 ((~(e0 = e2)) <=> (~(op(op(e3, e0), e3) = e0))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9382])).
% 1.58/1.72 tff(9384,plain,
% 1.58/1.72 (~(op(op(e3, e0), e3) = e0)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[14, 9383])).
% 1.58/1.72 tff(9385,plain,
% 1.58/1.72 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1764, 9384])).
% 1.58/1.72 tff(9386,plain,
% 1.58/1.72 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9257])).
% 1.58/1.72 tff(9387,plain,
% 1.58/1.72 (op(e1, op(e1, e0)) = e0),
% 1.58/1.72 inference(transitivity,[status(thm)],[9386, 9257])).
% 1.58/1.72 tff(9388,plain,
% 1.58/1.72 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1836, 9387])).
% 1.58/1.72 tff(9389,plain,
% 1.58/1.72 (op(e2, e0) = op(e1, e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9321, 2900])).
% 1.58/1.72 tff(9390,plain,
% 1.58/1.72 ((op(e2, e0) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9389, 9325])).
% 1.58/1.72 tff(9391,plain,
% 1.58/1.72 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e0) = e1)),
% 1.58/1.72 inference(symmetry,[status(thm)],[9390])).
% 1.58/1.72 tff(9392,plain,
% 1.58/1.72 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e0) = e1))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9391])).
% 1.58/1.72 tff(9393,plain,
% 1.58/1.72 (~(op(e2, e0) = e1)),
% 1.58/1.72 inference(modus_ponens,[status(thm)],[2292, 9392])).
% 1.58/1.72 tff(9394,plain,
% 1.58/1.72 (op(e2, e1) = e1),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[345, 9393, 76, 9298])).
% 1.58/1.72 tff(9395,plain,
% 1.58/1.72 (op(e3, e2) = op(e1, e3)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9299, 3710])).
% 1.58/1.72 tff(9396,plain,
% 1.58/1.72 (op(e2, op(e3, e2)) = op(e2, op(e1, e3))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9395])).
% 1.58/1.72 tff(9397,plain,
% 1.58/1.72 (op(e2, e1) = op(e3, e2)),
% 1.58/1.72 inference(transitivity,[status(thm)],[9394, 9325])).
% 1.58/1.72 tff(9398,plain,
% 1.58/1.72 (op(e2, op(e2, e1)) = op(e2, op(e3, e2))),
% 1.58/1.72 inference(monotonicity,[status(thm)],[9397])).
% 1.58/1.72 tff(9399,plain,
% 1.58/1.72 (op(e2, op(e2, e1)) = e1),
% 1.58/1.72 inference(transitivity,[status(thm)],[9398, 9396, 3796, 9394])).
% 1.58/1.72 tff(9400,plain,
% 1.58/1.72 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.58/1.72 inference(unit_resolution,[status(thm)],[1355, 9399])).
% 1.58/1.73 tff(9401,plain,
% 1.58/1.73 (op(e3, op(e1, e3)) = op(op(e1, e2), e1)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900, 132])).
% 1.58/1.73 tff(9402,plain,
% 1.58/1.73 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9395])).
% 1.58/1.73 tff(9403,plain,
% 1.58/1.73 (op(e3, e3) = e3),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1071, 9343, 126, 3811])).
% 1.58/1.73 tff(9404,plain,
% 1.58/1.73 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9403])).
% 1.58/1.73 tff(9405,plain,
% 1.58/1.73 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9404])).
% 1.58/1.73 tff(9406,plain,
% 1.58/1.73 (~(op(e0, e3) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[1077, 9405])).
% 1.58/1.73 tff(9407,plain,
% 1.58/1.73 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9321])).
% 1.58/1.73 tff(9408,plain,
% 1.58/1.73 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9407])).
% 1.58/1.73 tff(9409,plain,
% 1.58/1.73 (~(op(e0, e0) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[359, 9408])).
% 1.58/1.73 tff(9410,plain,
% 1.58/1.73 (op(e0, e1) = e3),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1495, 9409, 9406, 9246])).
% 1.58/1.73 tff(9411,plain,
% 1.58/1.73 (op(op(e0, e1), e1) = op(e3, op(e3, e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9410, 9325])).
% 1.58/1.73 tff(9412,plain,
% 1.58/1.73 (op(op(e0, e1), e1) = e0),
% 1.58/1.73 inference(transitivity,[status(thm)],[9411, 9402, 9401, 9365, 9357])).
% 1.58/1.73 tff(9413,plain,
% 1.58/1.73 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2650, 9412])).
% 1.58/1.73 tff(9414,plain,
% 1.58/1.73 ($false),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1459, 9413, 9400, 9388, 9385, 3342, 1304, 9376, 9373, 9370, 9364, 9324, 3869])).
% 1.58/1.73 tff(9415,plain,((op(e3, e2) = e2) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e1, e3) = e1)) | (~(op(e1, e2) = e3)) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e1, e3) = e0) | (op(e3, e3) = e2) | (op(e2, e1) = e0) | (~(op(e2, e3) = e2)) | (op(e1, op(e1, e2)) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.73 tff(9416,plain,
% 1.58/1.73 (op(e3, e2) = e2),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[9415, 82, 1304, 132, 2899, 76, 124, 80, 126, 2559, 3787, 9247, 3342])).
% 1.58/1.73 tff(9417,plain,
% 1.58/1.73 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9416])).
% 1.58/1.73 tff(9418,plain,
% 1.58/1.73 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9417])).
% 1.58/1.73 tff(9419,plain,
% 1.58/1.73 (~(op(e0, e2) = e2)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[1467, 9418])).
% 1.58/1.73 tff(9420,plain,
% 1.58/1.73 ((e0 = e3) <=> (e0 = op(e1, e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.73 tff(9421,plain,
% 1.58/1.73 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9420, 67])).
% 1.58/1.73 tff(9422,plain,
% 1.58/1.73 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9421])).
% 1.58/1.73 tff(9423,plain,
% 1.58/1.73 (~(op(e1, e2) = e0)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[181, 9422])).
% 1.58/1.73 tff(9424,plain,
% 1.58/1.73 (op(e1, e1) = e0),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1830, 2167, 80, 9423])).
% 1.58/1.73 tff(9425,plain,
% 1.58/1.73 (e0 = op(e1, e1)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[9424, 123])).
% 1.58/1.73 tff(9426,plain,
% 1.58/1.73 (op(e1, e1) = op(e3, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9424, 4451])).
% 1.58/1.73 tff(9427,plain,
% 1.58/1.73 (op(e1, op(e1, e1)) = op(e1, op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9426])).
% 1.58/1.73 tff(9428,plain,
% 1.58/1.73 (op(e1, op(e3, e3)) = op(e1, op(e1, e1))),
% 1.58/1.73 inference(symmetry,[status(thm)],[9427])).
% 1.58/1.73 tff(9429,plain,
% 1.58/1.73 (op(e1, e0) = e2),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[728, 2167, 9256, 929])).
% 1.58/1.73 tff(9430,plain,
% 1.58/1.73 (e2 = op(e1, e0)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9429])).
% 1.58/1.73 tff(9431,plain,
% 1.58/1.73 (e2 = op(e1, op(e1, e1))),
% 1.58/1.73 inference(transitivity,[status(thm)],[9430, 7896, 9428])).
% 1.58/1.73 tff(9432,plain,
% 1.58/1.73 (op(e1, op(e1, e1)) = e2),
% 1.58/1.73 inference(transitivity,[status(thm)],[9427, 4468, 9429])).
% 1.58/1.73 tff(9433,plain,
% 1.58/1.73 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9432])).
% 1.58/1.73 tff(9434,plain,
% 1.58/1.73 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 1.58/1.73 inference(symmetry,[status(thm)],[9433])).
% 1.58/1.73 tff(9435,plain,
% 1.58/1.73 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.58/1.73 inference(transitivity,[status(thm)],[2900, 9434])).
% 1.58/1.73 tff(9436,plain,
% 1.58/1.73 ($false),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2198, 9435, 9431, 9425])).
% 1.58/1.73 tff(9437,plain,((op(e1, e0) = e0) | (~(op(e1, e2) = e3)) | (~(op(e3, e3) = e0)) | (op(e1, e0) = e1) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.73 tff(9438,plain,
% 1.58/1.73 (op(e1, e0) = e0),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[9437, 3066, 2899, 3765, 80])).
% 1.58/1.73 tff(9439,plain,
% 1.58/1.73 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9438])).
% 1.58/1.73 tff(9440,plain,
% 1.58/1.73 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9439, 4499])).
% 1.58/1.73 tff(9441,plain,
% 1.58/1.73 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9440])).
% 1.58/1.73 tff(9442,plain,
% 1.58/1.73 (~(op(e2, e0) = e0)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[756, 9441])).
% 1.58/1.73 tff(9443,plain,
% 1.58/1.73 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e1, e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.73 tff(9444,plain,
% 1.58/1.73 ((op(e2, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 1.58/1.73 inference(transitivity,[status(thm)],[9443, 8066])).
% 1.58/1.73 tff(9445,plain,
% 1.58/1.73 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9444])).
% 1.58/1.73 tff(9446,plain,
% 1.58/1.73 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9445])).
% 1.58/1.73 tff(9447,plain,
% 1.58/1.73 (~(op(e2, e2) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[1273, 9446])).
% 1.58/1.73 tff(9448,plain,
% 1.58/1.73 (op(e2, e2) = e0),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2311, 9442, 2559, 1063])).
% 1.58/1.73 tff(9449,plain,
% 1.58/1.73 (op(e2, e2) = op(e3, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9300, 4451])).
% 1.58/1.73 tff(9450,plain,
% 1.58/1.73 (op(e2, op(e2, e2)) = op(e2, op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9449])).
% 1.58/1.73 tff(9451,plain,
% 1.58/1.73 (op(e2, op(e2, e2)) = op(e2, e0)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9450, 4551])).
% 1.58/1.73 tff(9452,plain,
% 1.58/1.73 ((e1 = op(e2, op(e2, e2))) <=> (e1 = op(e2, e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9451])).
% 1.58/1.73 tff(9453,plain,
% 1.58/1.73 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e1)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9452, 16])).
% 1.58/1.73 tff(9454,plain,
% 1.58/1.73 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 1.58/1.73 inference(symmetry,[status(thm)],[9453])).
% 1.58/1.73 tff(9455,plain,
% 1.58/1.73 (e1 = op(e2, op(e2, e2))),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[3509, 9454])).
% 1.58/1.73 tff(9456,plain,
% 1.58/1.73 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9451])).
% 1.58/1.73 tff(9457,plain,
% 1.58/1.73 (op(e2, op(e2, e0)) = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.73 inference(symmetry,[status(thm)],[9456])).
% 1.58/1.73 tff(9458,plain,
% 1.58/1.73 (op(e2, e0) = op(e1, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[3509, 3710])).
% 1.58/1.73 tff(9459,plain,
% 1.58/1.73 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9458])).
% 1.58/1.73 tff(9460,plain,
% 1.58/1.73 (op(e2, op(e1, e3)) = op(e2, op(e2, e0))),
% 1.58/1.73 inference(symmetry,[status(thm)],[9459])).
% 1.58/1.73 tff(9461,plain,
% 1.58/1.73 (e3 = op(e2, op(e2, op(e2, e2)))),
% 1.58/1.73 inference(transitivity,[status(thm)],[9317, 3884, 9460, 9457])).
% 1.58/1.73 tff(9462,plain,
% 1.58/1.73 ($false),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1539, 9461, 9455, 9301])).
% 1.58/1.73 tff(9463,plain,((op(e2, e0) = e3) | (~(op(e1, e3) = e1)) | (~(op(e3, e3) = e0)) | (~(op(e2, e2) = e0)) | (op(e2, e2) = e3) | (op(e2, e3) = e3) | (op(e2, e0) = e2) | (op(e2, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.73 tff(9464,plain,
% 1.58/1.73 (op(e2, e0) = e3),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[9463, 3066, 132, 9448, 9447, 124, 982, 9442])).
% 1.58/1.73 tff(9465,plain,
% 1.58/1.73 (op(e2, e0) = op(e1, e2)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9464, 2900])).
% 1.58/1.73 tff(9466,plain,
% 1.58/1.73 (op(op(e2, e0), e2) = op(op(e1, e2), e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9465])).
% 1.58/1.73 tff(9467,plain,
% 1.58/1.73 (op(op(e2, e0), e2) = e2),
% 1.58/1.73 inference(transitivity,[status(thm)],[9466, 9338, 8955])).
% 1.58/1.73 tff(9468,plain,
% 1.58/1.73 ((op(op(e2, e0), e2) = e0) <=> (e2 = op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9467, 4451])).
% 1.58/1.73 tff(9469,plain,
% 1.58/1.73 ((op(op(e2, e0), e2) = e0) <=> (op(e3, e3) = e2)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9468, 565])).
% 1.58/1.73 tff(9470,plain,
% 1.58/1.73 ((op(e3, e3) = e2) <=> (op(op(e2, e0), e2) = e0)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9469])).
% 1.58/1.73 tff(9471,plain,
% 1.58/1.73 ((~(op(e3, e3) = e2)) <=> (~(op(op(e2, e0), e2) = e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9470])).
% 1.58/1.73 tff(9472,plain,
% 1.58/1.73 (~(op(op(e2, e0), e2) = e0)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[126, 9471])).
% 1.58/1.73 tff(9473,plain,
% 1.58/1.73 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1379, 9472])).
% 1.58/1.73 tff(9474,plain,
% 1.58/1.73 ((op(e1, e2) = e0) <=> (e3 = op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2899, 4451])).
% 1.58/1.73 tff(9475,plain,
% 1.58/1.73 ((op(e1, e2) = e0) <=> (op(e3, e3) = e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9474, 666])).
% 1.58/1.73 tff(9476,plain,
% 1.58/1.73 ((~(op(e1, e2) = e0)) <=> (~(op(e3, e3) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9475])).
% 1.58/1.73 tff(9477,plain,
% 1.58/1.73 (~(op(e3, e3) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[9423, 9476])).
% 1.58/1.73 tff(9478,plain,
% 1.58/1.73 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e1, e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.73 tff(9479,plain,
% 1.58/1.73 ((op(e3, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 1.58/1.73 inference(transitivity,[status(thm)],[9478, 3635])).
% 1.58/1.73 tff(9480,plain,
% 1.58/1.73 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9479])).
% 1.58/1.73 tff(9481,plain,
% 1.58/1.73 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9480])).
% 1.58/1.73 tff(9482,plain,
% 1.58/1.73 (~(op(e3, e2) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[2292, 9481])).
% 1.58/1.73 tff(9483,plain,
% 1.58/1.73 (op(e3, e0) = op(e3, op(e3, e3))),
% 1.58/1.73 inference(symmetry,[status(thm)],[3067])).
% 1.58/1.73 tff(9484,plain,
% 1.58/1.73 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9483])).
% 1.58/1.73 tff(9485,plain,
% 1.58/1.73 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9484])).
% 1.58/1.73 tff(9486,plain,
% 1.58/1.73 ((e3 = op(e3, op(e3, e3))) <=> (op(e3, op(e3, e3)) = e3)),
% 1.58/1.73 inference(commutativity,[status(thm)],[])).
% 1.58/1.73 tff(9487,plain,
% 1.58/1.73 ((op(e2, e0) = op(e3, e0)) <=> (e3 = op(e3, op(e3, e3)))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9464, 9483])).
% 1.58/1.73 tff(9488,plain,
% 1.58/1.73 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, op(e3, e3)) = e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9487, 9486])).
% 1.58/1.73 tff(9489,plain,
% 1.58/1.73 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9488, 9485])).
% 1.58/1.73 tff(9490,plain,
% 1.58/1.73 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9489])).
% 1.58/1.73 tff(9491,plain,
% 1.58/1.73 (~(op(e3, e0) = e3)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[747, 9490])).
% 1.58/1.73 tff(9492,plain,
% 1.58/1.73 (op(e3, e1) = e3),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[422, 9491, 9482, 9477])).
% 1.58/1.73 tff(9493,plain,
% 1.58/1.73 (op(op(e3, e1), e1) = op(e3, op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9492, 3710])).
% 1.58/1.73 tff(9494,plain,
% 1.58/1.73 (op(op(e3, e1), e1) = e3),
% 1.58/1.73 inference(transitivity,[status(thm)],[9493, 9401, 9365, 9492])).
% 1.58/1.73 tff(9495,plain,
% 1.58/1.73 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2416, 9494])).
% 1.58/1.73 tff(9496,plain,
% 1.58/1.73 (op(e3, op(e3, e2)) = op(op(e1, e2), e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900, 8955])).
% 1.58/1.73 tff(9497,plain,
% 1.58/1.73 (op(e3, op(e3, e2)) = e2),
% 1.58/1.73 inference(transitivity,[status(thm)],[9496, 9338, 8955])).
% 1.58/1.73 tff(9498,plain,
% 1.58/1.73 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1904, 9497])).
% 1.58/1.73 tff(9499,plain,
% 1.58/1.73 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.73 tff(9500,plain,
% 1.58/1.73 (e1 = op(e1, op(e1, e2))),
% 1.58/1.73 inference(transitivity,[status(thm)],[3710, 9499])).
% 1.58/1.73 tff(9501,plain,
% 1.58/1.73 ((op(e3, e2) = e1) <=> (e2 = op(e1, op(e1, e2)))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[8955, 9500])).
% 1.58/1.73 tff(9502,plain,
% 1.58/1.73 ((op(e3, e2) = e1) <=> (op(e1, op(e1, e2)) = e2)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9501, 9272])).
% 1.58/1.73 tff(9503,plain,
% 1.58/1.73 ((op(e1, op(e1, e2)) = e2) <=> (op(e3, e2) = e1)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9502])).
% 1.58/1.73 tff(9504,plain,
% 1.58/1.73 ((~(op(e1, op(e1, e2)) = e2)) <=> (~(op(e3, e2) = e1))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9503])).
% 1.58/1.73 tff(9505,plain,
% 1.58/1.73 (~(op(e3, e2) = e1)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[9247, 9504])).
% 1.58/1.73 tff(9506,plain,
% 1.58/1.73 (op(e2, e2) = op(e3, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9448, 4451])).
% 1.58/1.73 tff(9507,plain,
% 1.58/1.73 ((op(e2, e2) = e1) <=> (op(e3, e3) = op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9506, 3710])).
% 1.58/1.73 tff(9508,plain,
% 1.58/1.73 ((op(e2, e2) = e1) <=> (op(e1, e3) = op(e3, e3))),
% 1.58/1.73 inference(transitivity,[status(thm)],[9507, 1659])).
% 1.58/1.73 tff(9509,plain,
% 1.58/1.73 ((op(e1, e3) = op(e3, e3)) <=> (op(e2, e2) = e1)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9508])).
% 1.58/1.73 tff(9510,plain,
% 1.58/1.73 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e1))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9509])).
% 1.58/1.73 tff(9511,plain,
% 1.58/1.73 (~(op(e2, e2) = e1)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[571, 9510])).
% 1.58/1.73 tff(9512,plain,
% 1.58/1.73 (op(e0, e2) = e1),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1613, 9511, 9293, 9505])).
% 1.58/1.73 tff(9513,plain,
% 1.58/1.73 (op(op(e0, e2), e0) = op(e1, op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9512, 4451])).
% 1.58/1.73 tff(9514,plain,
% 1.58/1.73 (op(op(e0, e2), e0) = op(e3, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9513, 4468, 9438, 4451])).
% 1.58/1.73 tff(9515,plain,
% 1.58/1.73 ((op(op(e0, e2), e0) = e2) <=> (op(e3, e3) = e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9514])).
% 1.58/1.73 tff(9516,plain,
% 1.58/1.73 ((op(e3, e3) = e2) <=> (op(op(e0, e2), e0) = e2)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9515])).
% 1.58/1.73 tff(9517,plain,
% 1.58/1.73 ((~(op(e3, e3) = e2)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9516])).
% 1.58/1.73 tff(9518,plain,
% 1.58/1.73 (~(op(op(e0, e2), e0) = e2)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[126, 9517])).
% 1.58/1.73 tff(9519,plain,
% 1.58/1.73 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2446, 9518])).
% 1.58/1.73 tff(9520,plain,
% 1.58/1.73 ((op(e1, e0) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9438])).
% 1.58/1.73 tff(9521,plain,
% 1.58/1.73 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9520, 122])).
% 1.58/1.73 tff(9522,plain,
% 1.58/1.73 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9521])).
% 1.58/1.73 tff(9523,plain,
% 1.58/1.73 (~(op(e1, e1) = e0)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[737, 9522])).
% 1.58/1.73 tff(9524,plain,
% 1.58/1.73 (op(e0, e1) = e0),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[292, 9523, 2559, 4476])).
% 1.58/1.73 tff(9525,plain,
% 1.58/1.73 (op(op(e0, e1), e1) = op(e0, op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9524, 3710])).
% 1.58/1.73 tff(9526,plain,
% 1.58/1.73 (op(op(e0, e1), e1) = e0),
% 1.58/1.73 inference(transitivity,[status(thm)],[9525, 3788, 9524])).
% 1.58/1.73 tff(9527,plain,
% 1.58/1.73 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[2650, 9526])).
% 1.58/1.73 tff(9528,plain,
% 1.58/1.73 (op(e1, e0) = op(e3, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9438, 4451])).
% 1.58/1.73 tff(9529,plain,
% 1.58/1.73 (op(e1, op(e1, e0)) = op(e1, op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9528])).
% 1.58/1.73 tff(9530,plain,
% 1.58/1.73 (op(e1, op(e1, e0)) = e0),
% 1.58/1.73 inference(transitivity,[status(thm)],[9529, 4468, 9438])).
% 1.58/1.73 tff(9531,plain,
% 1.58/1.73 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1836, 9530])).
% 1.58/1.73 tff(9532,plain,
% 1.58/1.73 ((op(e2, e0) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9465, 3710])).
% 1.58/1.73 tff(9533,plain,
% 1.58/1.73 ((op(e1, e2) = op(e1, e3)) <=> (op(e2, e0) = e1)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9532])).
% 1.58/1.73 tff(9534,plain,
% 1.58/1.73 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e2, e0) = e1))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9533])).
% 1.58/1.73 tff(9535,plain,
% 1.58/1.73 (~(op(e2, e0) = e1)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[1850, 9534])).
% 1.58/1.73 tff(9536,plain,
% 1.58/1.73 (op(e2, e1) = e1),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[345, 9535, 76, 9511])).
% 1.58/1.73 tff(9537,plain,
% 1.58/1.73 (op(e2, e1) = op(e1, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9536, 3710])).
% 1.58/1.73 tff(9538,plain,
% 1.58/1.73 (op(e2, op(e2, e1)) = op(e2, op(e1, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9537])).
% 1.58/1.73 tff(9539,plain,
% 1.58/1.73 (op(e2, op(e2, e1)) = e1),
% 1.58/1.73 inference(transitivity,[status(thm)],[9538, 3796, 9536])).
% 1.58/1.73 tff(9540,plain,
% 1.58/1.73 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1355, 9539])).
% 1.58/1.73 tff(9541,plain,
% 1.58/1.73 (op(op(e1, e3), e3) = e1),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[137, 132])).
% 1.58/1.73 tff(9542,plain,
% 1.58/1.73 ((op(e1, e0) = e2) <=> (op(e3, e3) = e2)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9528])).
% 1.58/1.73 tff(9543,plain,
% 1.58/1.73 ((op(e3, e3) = e2) <=> (op(e1, e0) = e2)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9542])).
% 1.58/1.73 tff(9544,plain,
% 1.58/1.73 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e0) = e2))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9543])).
% 1.58/1.73 tff(9545,plain,
% 1.58/1.73 (~(op(e1, e0) = e2)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[126, 9544])).
% 1.58/1.73 tff(9546,plain,
% 1.58/1.73 (op(e0, e0) = e2),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[589, 9545, 982, 8965])).
% 1.58/1.73 tff(9547,plain,
% 1.58/1.73 ((op(e0, e0) = e1) <=> (e2 = op(e1, op(e1, e2)))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9546, 9500])).
% 1.58/1.73 tff(9548,plain,
% 1.58/1.73 ((op(e0, e0) = e1) <=> (op(e1, op(e1, e2)) = e2)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9547, 9272])).
% 1.58/1.73 tff(9549,plain,
% 1.58/1.73 ((op(e1, op(e1, e2)) = e2) <=> (op(e0, e0) = e1)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9548])).
% 1.58/1.73 tff(9550,plain,
% 1.58/1.73 ((~(op(e1, op(e1, e2)) = e2)) <=> (~(op(e0, e0) = e1))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9549])).
% 1.58/1.73 tff(9551,plain,
% 1.58/1.73 (~(op(e0, e0) = e1)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[9247, 9550])).
% 1.58/1.73 tff(9552,plain,
% 1.58/1.73 (op(e3, e0) = e1),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1480, 9535, 3765, 9551])).
% 1.58/1.73 tff(9553,plain,
% 1.58/1.73 (op(e3, e0) = op(e1, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9552, 3710])).
% 1.58/1.73 tff(9554,plain,
% 1.58/1.73 (op(op(e3, e0), e3) = op(op(e1, e3), e3)),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9553])).
% 1.58/1.73 tff(9555,plain,
% 1.58/1.73 (op(op(e3, e0), e3) = op(e1, e3)),
% 1.58/1.73 inference(transitivity,[status(thm)],[9554, 9541, 3710])).
% 1.58/1.73 tff(9556,plain,
% 1.58/1.73 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e3) = op(e3, e3))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9555, 4451])).
% 1.58/1.73 tff(9557,plain,
% 1.58/1.73 ((op(e1, e3) = op(e3, e3)) <=> (op(op(e3, e0), e3) = e0)),
% 1.58/1.73 inference(symmetry,[status(thm)],[9556])).
% 1.58/1.73 tff(9558,plain,
% 1.58/1.73 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(op(e3, e0), e3) = e0))),
% 1.58/1.73 inference(monotonicity,[status(thm)],[9557])).
% 1.58/1.73 tff(9559,plain,
% 1.58/1.73 (~(op(op(e3, e0), e3) = e0)),
% 1.58/1.73 inference(modus_ponens,[status(thm)],[571, 9558])).
% 1.58/1.73 tff(9560,plain,
% 1.58/1.73 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1764, 9559])).
% 1.58/1.73 tff(9561,plain,
% 1.58/1.73 ($false),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[1459, 9560, 9540, 9531, 9527, 3342, 1304, 9519, 9498, 1358, 9495, 9473, 1347])).
% 1.58/1.73 tff(9562,plain,((~(op(e3, e3) = e0)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e1, e3) = e1)) | (~(op(e1, e2) = e3)) | (op(e2, e3) = e1) | (op(e3, e3) = e2) | (~(op(e3, e2) = e2)) | (op(e2, e3) = e3) | (op(e2, e0) = e2) | (op(e1, op(e1, e2)) = e2) | (op(e2, e1) = e0) | (op(e2, e3) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.73 tff(9563,plain,
% 1.58/1.73 (~(op(e3, e3) = e0)),
% 1.58/1.73 inference(unit_resolution,[status(thm)],[9562, 9370, 1304, 3342, 3869, 132, 2899, 76, 126, 9416, 124, 9267, 9247, 2559, 9252, 80])).
% 1.58/1.74 tff(9564,plain,
% 1.58/1.74 (op(e0, e3) = e0),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[1098, 9563, 9252, 80])).
% 1.58/1.74 tff(9565,plain,
% 1.58/1.74 (e0 = op(e0, e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9564])).
% 1.58/1.74 tff(9566,plain,
% 1.58/1.74 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9565])).
% 1.58/1.74 tff(9567,plain,
% 1.58/1.74 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9566])).
% 1.58/1.74 tff(9568,plain,
% 1.58/1.74 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9567])).
% 1.58/1.74 tff(9569,plain,
% 1.58/1.74 (~(op(e0, e2) = e0)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[918, 9568])).
% 1.58/1.74 tff(9570,plain,
% 1.58/1.74 (op(e0, e2) = e1),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2745, 9569, 9419, 9246])).
% 1.58/1.74 tff(9571,plain,
% 1.58/1.74 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9416])).
% 1.58/1.74 tff(9572,plain,
% 1.58/1.74 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9571])).
% 1.58/1.74 tff(9573,plain,
% 1.58/1.74 (~(op(e3, e0) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1133, 9572])).
% 1.58/1.74 tff(9574,plain,
% 1.58/1.74 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[3710])).
% 1.58/1.74 tff(9575,plain,
% 1.58/1.74 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9574])).
% 1.58/1.74 tff(9576,plain,
% 1.58/1.74 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9575])).
% 1.58/1.74 tff(9577,plain,
% 1.58/1.74 (~(op(e1, e1) = e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[619, 9576])).
% 1.58/1.74 tff(9578,plain,
% 1.58/1.74 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.74 tff(9579,plain,
% 1.58/1.74 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9578])).
% 1.58/1.74 tff(9580,plain,
% 1.58/1.74 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9579])).
% 1.58/1.74 tff(9581,plain,
% 1.58/1.74 (~(op(e1, e1) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1604, 9580])).
% 1.58/1.74 tff(9582,plain,
% 1.58/1.74 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e1, e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2900])).
% 1.58/1.74 tff(9583,plain,
% 1.58/1.74 ((op(e1, e3) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9582, 125])).
% 1.58/1.74 tff(9584,plain,
% 1.58/1.74 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9583])).
% 1.58/1.74 tff(9585,plain,
% 1.58/1.74 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9584])).
% 1.58/1.74 tff(9586,plain,
% 1.58/1.74 (~(op(e1, e3) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1850, 9585])).
% 1.58/1.74 tff(9587,plain,
% 1.58/1.74 (op(e1, e0) = e0),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2200, 9564, 9256, 9586, 9581, 3765, 9577])).
% 1.58/1.74 tff(9588,plain,
% 1.58/1.74 (op(e1, e0) = op(e0, e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9587, 9565])).
% 1.58/1.74 tff(9589,plain,
% 1.58/1.74 ((op(e1, e0) = e2) <=> (op(e0, e3) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9588])).
% 1.58/1.74 tff(9590,plain,
% 1.58/1.74 ((op(e0, e3) = e2) <=> (op(e1, e0) = e2)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9589])).
% 1.58/1.74 tff(9591,plain,
% 1.58/1.74 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e0) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9590])).
% 1.58/1.74 tff(9592,plain,
% 1.58/1.74 (~(op(e1, e0) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[79, 9591])).
% 1.58/1.74 tff(9593,plain,
% 1.58/1.74 (op(e0, e0) = e2),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[589, 9592, 9267, 9573])).
% 1.58/1.74 tff(9594,plain,
% 1.58/1.74 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9593])).
% 1.58/1.74 tff(9595,plain,
% 1.58/1.74 (op(e0, op(e0, e0)) = op(e1, e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9594, 9570, 3710])).
% 1.58/1.74 tff(9596,plain,
% 1.58/1.74 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9595])).
% 1.58/1.74 tff(9597,plain,
% 1.58/1.74 (op(e0, op(e0, op(e0, e0))) = op(e0, e1)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9596, 9242])).
% 1.58/1.74 tff(9598,plain,
% 1.58/1.74 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (e3 = op(e0, e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9597])).
% 1.58/1.74 tff(9599,plain,
% 1.58/1.74 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (op(e0, e1) = e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9598, 127])).
% 1.58/1.74 tff(9600,plain,
% 1.58/1.74 ((op(e0, e1) = e3) <=> (e3 = op(e0, op(e0, op(e0, e0))))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9599])).
% 1.58/1.74 tff(9601,plain,
% 1.58/1.74 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9593])).
% 1.58/1.74 tff(9602,plain,
% 1.58/1.74 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9601, 4838])).
% 1.58/1.74 tff(9603,plain,
% 1.58/1.74 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9602])).
% 1.58/1.74 tff(9604,plain,
% 1.58/1.74 (~(op(e0, e1) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[811, 9603])).
% 1.58/1.74 tff(9605,plain,
% 1.58/1.74 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[3724, 9564])).
% 1.58/1.74 tff(9606,plain,
% 1.58/1.74 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9605, 3726])).
% 1.58/1.74 tff(9607,plain,
% 1.58/1.74 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9606])).
% 1.58/1.74 tff(9608,plain,
% 1.58/1.74 (~(op(e0, e1) = e0)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[818, 9607])).
% 1.58/1.74 tff(9609,plain,
% 1.58/1.74 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9570])).
% 1.58/1.74 tff(9610,plain,
% 1.58/1.74 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9609])).
% 1.58/1.74 tff(9611,plain,
% 1.58/1.74 (~(op(e0, e1) = e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[2102, 9610])).
% 1.58/1.74 tff(9612,plain,
% 1.58/1.74 (op(e0, e1) = e3),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[829, 9611, 9608, 9604])).
% 1.58/1.74 tff(9613,plain,
% 1.58/1.74 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[9612, 9600])).
% 1.58/1.74 tff(9614,plain,
% 1.58/1.74 (e2 = op(e0, e0)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[9593, 78])).
% 1.58/1.74 tff(9615,plain,
% 1.58/1.74 (op(e0, e2) = op(e0, op(e0, e0))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9594])).
% 1.58/1.74 tff(9616,plain,
% 1.58/1.74 (e1 = op(e0, e2)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9570])).
% 1.58/1.74 tff(9617,plain,
% 1.58/1.74 (e1 = op(e0, op(e0, e0))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9616, 9615])).
% 1.58/1.74 tff(9618,plain,
% 1.58/1.74 (~(e3 = op(e0, op(e0, op(e0, e0))))),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[842, 9617, 9614])).
% 1.58/1.74 tff(9619,plain,
% 1.58/1.74 ($false),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[9618, 9613])).
% 1.58/1.74 tff(9620,plain,((op(e3, e1) = e2) | (~(op(e1, e3) = e1)) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~(op(e1, e2) = e3)) | (op(e2, e3) = e1) | (op(e3, e3) = e2) | (op(e2, e3) = e3) | (op(e1, op(e1, e2)) = e2) | (op(e2, e1) = e0) | (~(op(e2, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.58/1.74 tff(9621,plain,
% 1.58/1.74 (op(e3, e1) = e2),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[9620, 9227, 79, 80, 5425, 5469, 9220, 76, 126, 124, 9241, 7791, 5431])).
% 1.58/1.74 tff(9622,plain,
% 1.58/1.74 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9621])).
% 1.58/1.74 tff(9623,plain,
% 1.58/1.74 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9622])).
% 1.58/1.74 tff(9624,plain,
% 1.58/1.74 (~(op(e1, e1) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[945, 9623])).
% 1.58/1.74 tff(9625,plain,
% 1.58/1.74 (op(e1, e1) = e0),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[630, 9624, 9235, 9232])).
% 1.58/1.74 tff(9626,plain,
% 1.58/1.74 (e0 = op(e1, e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[9625, 123])).
% 1.58/1.74 tff(9627,plain,
% 1.58/1.74 (op(e1, op(e1, e1)) = op(e1, e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9625])).
% 1.58/1.74 tff(9628,plain,
% 1.58/1.74 (op(e1, e0) = op(e1, op(e1, e1))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9627])).
% 1.58/1.74 tff(9629,plain,
% 1.58/1.74 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9220])).
% 1.58/1.74 tff(9630,plain,
% 1.58/1.74 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9629, 1314])).
% 1.58/1.74 tff(9631,plain,
% 1.58/1.74 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9630])).
% 1.58/1.74 tff(9632,plain,
% 1.58/1.74 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9631])).
% 1.58/1.74 tff(9633,plain,
% 1.58/1.74 (~(op(e1, e2) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1321, 9632])).
% 1.58/1.74 tff(9634,plain,
% 1.58/1.74 (op(e1, e0) = e2),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2285, 9624, 72, 9633])).
% 1.58/1.74 tff(9635,plain,
% 1.58/1.74 (e2 = op(e1, e0)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9634])).
% 1.58/1.74 tff(9636,plain,
% 1.58/1.74 (e2 = op(e1, op(e1, e1))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9635, 9628])).
% 1.58/1.74 tff(9637,plain,
% 1.58/1.74 (op(e1, op(e1, e1)) = e2),
% 1.58/1.74 inference(transitivity,[status(thm)],[9627, 9634])).
% 1.58/1.74 tff(9638,plain,
% 1.58/1.74 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9637])).
% 1.58/1.74 tff(9639,plain,
% 1.58/1.74 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9638])).
% 1.58/1.74 tff(9640,plain,
% 1.58/1.74 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9221, 9639])).
% 1.58/1.74 tff(9641,plain,
% 1.58/1.74 ($false),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2198, 9640, 9636, 9626])).
% 1.58/1.74 tff(9642,plain,((op(e3, e3) = e2) | (op(e1, e3) = e2) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.74 tff(9643,plain,
% 1.58/1.74 (op(e3, e3) = e2),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[9642, 72, 79, 80, 76, 124, 121])).
% 1.58/1.74 tff(9644,plain,
% 1.58/1.74 ((op(e3, e3) = e3) <=> (e2 = e3)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9643])).
% 1.58/1.74 tff(9645,plain,
% 1.58/1.74 ((e2 = e3) <=> (op(e3, e3) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9644])).
% 1.58/1.74 tff(9646,plain,
% 1.58/1.74 ((~(e2 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9645])).
% 1.58/1.74 tff(9647,plain,
% 1.58/1.74 (~(op(e3, e3) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1321, 9646])).
% 1.58/1.74 tff(9648,plain,
% 1.58/1.74 (e2 = op(e3, e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9643])).
% 1.58/1.74 tff(9649,plain,
% 1.58/1.74 ((e1 = e2) <=> (e1 = op(e3, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9648])).
% 1.58/1.74 tff(9650,plain,
% 1.58/1.74 ((e1 = e2) <=> (op(e3, e3) = e1)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9649, 657])).
% 1.58/1.74 tff(9651,plain,
% 1.58/1.74 ((~(e1 = e2)) <=> (~(op(e3, e3) = e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9650])).
% 1.58/1.74 tff(9652,plain,
% 1.58/1.74 (~(op(e3, e3) = e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[708, 9651])).
% 1.58/1.74 tff(9653,plain,
% 1.58/1.74 (op(e1, e3) = e1),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[151, 9652, 121, 76])).
% 1.58/1.74 tff(9654,plain,
% 1.58/1.74 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9653])).
% 1.58/1.74 tff(9655,plain,
% 1.58/1.74 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9654])).
% 1.58/1.74 tff(9656,plain,
% 1.58/1.74 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9655])).
% 1.58/1.74 tff(9657,plain,
% 1.58/1.74 (~(op(e1, e3) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[303, 9656])).
% 1.58/1.74 tff(9658,plain,
% 1.58/1.74 (op(e0, e3) = e3),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[480, 9657, 124, 9647])).
% 1.58/1.74 tff(9659,plain,
% 1.58/1.74 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9643])).
% 1.58/1.74 tff(9660,plain,
% 1.58/1.74 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9659])).
% 1.58/1.74 tff(9661,plain,
% 1.58/1.74 (~(op(e2, e3) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[368, 9660])).
% 1.58/1.74 tff(9662,plain,
% 1.58/1.74 (op(e2, e3) = e0),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[206, 9661, 76, 124])).
% 1.58/1.74 tff(9663,plain,
% 1.58/1.74 (op(op(e0, e3), e0) = op(e3, e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[1869])).
% 1.58/1.74 tff(9664,plain,
% 1.58/1.74 ((e1 = e2) <=> (e1 = op(e3, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2834])).
% 1.58/1.74 tff(9665,plain,
% 1.58/1.74 ((e1 = e2) <=> (op(e3, e3) = e1)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9664, 657])).
% 1.58/1.74 tff(9666,plain,
% 1.58/1.74 ((~(e1 = e2)) <=> (~(op(e3, e3) = e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9665])).
% 1.58/1.74 tff(9667,plain,
% 1.58/1.74 (~(op(e3, e3) = e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[708, 9666])).
% 1.58/1.74 tff(9668,plain,
% 1.58/1.74 (op(e1, e3) = e1),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[151, 9667, 121, 76])).
% 1.58/1.74 tff(9669,plain,
% 1.58/1.74 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9668])).
% 1.58/1.74 tff(9670,plain,
% 1.58/1.74 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9669])).
% 1.58/1.74 tff(9671,plain,
% 1.58/1.74 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9670])).
% 1.58/1.74 tff(9672,plain,
% 1.58/1.74 (~(op(e1, e3) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[303, 9671])).
% 1.58/1.74 tff(9673,plain,
% 1.58/1.74 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9668])).
% 1.58/1.74 tff(9674,plain,
% 1.58/1.74 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9673])).
% 1.58/1.74 tff(9675,plain,
% 1.58/1.74 (~(op(e1, e2) = e1)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1850, 9674])).
% 1.58/1.74 tff(9676,plain,
% 1.58/1.74 (op(e1, e1) = e3),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[7135, 2891, 2812, 4515, 75, 1080])).
% 1.58/1.74 tff(9677,plain,
% 1.58/1.74 (e3 = op(e1, e1)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9676])).
% 1.58/1.74 tff(9678,plain,
% 1.58/1.74 (op(e0, e3) = e2),
% 1.58/1.74 inference(transitivity,[status(thm)],[1869, 9677, 2891])).
% 1.58/1.74 tff(9679,plain,
% 1.58/1.74 ($false),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[79, 9678])).
% 1.58/1.74 tff(9680,plain,((~(op(e1, e1) = e2)) | (op(e0, e3) = e2) | (~(op(e0, e3) = e3)) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e1) | (op(e1, e2) = e3) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.58/1.74 tff(9681,plain,
% 1.58/1.74 (~(op(e1, e1) = e2)),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[9680, 75, 1869, 2812, 9675, 79, 9672])).
% 1.58/1.74 tff(9682,plain,
% 1.58/1.74 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2812])).
% 1.58/1.74 tff(9683,plain,
% 1.58/1.74 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9682])).
% 1.58/1.74 tff(9684,plain,
% 1.58/1.74 (~(op(e3, e1) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[437, 9683])).
% 1.58/1.74 tff(9685,plain,
% 1.58/1.74 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[1870])).
% 1.58/1.74 tff(9686,plain,
% 1.58/1.74 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9685])).
% 1.58/1.74 tff(9687,plain,
% 1.58/1.74 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9686])).
% 1.58/1.74 tff(9688,plain,
% 1.58/1.74 (~(op(e0, e2) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[918, 9687])).
% 1.58/1.74 tff(9689,plain,
% 1.58/1.74 (op(e3, e2) = e3),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2111, 2431, 75, 9688])).
% 1.58/1.74 tff(9690,plain,
% 1.58/1.74 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2812])).
% 1.58/1.74 tff(9691,plain,
% 1.58/1.74 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9690])).
% 1.58/1.74 tff(9692,plain,
% 1.58/1.74 (~(op(e2, e3) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[368, 9691])).
% 1.58/1.74 tff(9693,plain,
% 1.58/1.74 ((e0 = e2) <=> (e0 = op(e3, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2834])).
% 1.58/1.74 tff(9694,plain,
% 1.58/1.74 ((e0 = e2) <=> (op(e3, e3) = e0)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9693, 3077])).
% 1.58/1.74 tff(9695,plain,
% 1.58/1.74 ((~(e0 = e2)) <=> (~(op(e3, e3) = e0))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9694])).
% 1.58/1.74 tff(9696,plain,
% 1.58/1.74 (~(op(e3, e3) = e0)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[14, 9695])).
% 1.58/1.74 tff(9697,plain,
% 1.58/1.74 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e2)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2812])).
% 1.58/1.74 tff(9698,plain,
% 1.58/1.74 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9697])).
% 1.58/1.74 tff(9699,plain,
% 1.58/1.74 (~(op(e3, e2) = e2)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1888, 9698])).
% 1.58/1.74 tff(9700,plain,
% 1.58/1.74 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e2) = e3)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[2814])).
% 1.58/1.74 tff(9701,plain,
% 1.58/1.74 ((op(e3, e2) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9700])).
% 1.58/1.74 tff(9702,plain,
% 1.58/1.74 (op(e3, op(e3, e3)) = e3),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[9689, 9701])).
% 1.58/1.74 tff(9703,plain,
% 1.58/1.74 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[6277, 9702])).
% 1.58/1.74 tff(9704,plain,
% 1.58/1.74 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[1870])).
% 1.58/1.74 tff(9705,plain,
% 1.58/1.74 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9704])).
% 1.58/1.74 tff(9706,plain,
% 1.58/1.74 (op(e3, e2) = op(e0, e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[856, 1870])).
% 1.58/1.74 tff(9707,plain,
% 1.58/1.74 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9706])).
% 1.58/1.74 tff(9708,plain,
% 1.58/1.74 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9707, 9705])).
% 1.58/1.74 tff(9709,plain,
% 1.58/1.74 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9708])).
% 1.58/1.74 tff(9710,plain,
% 1.58/1.74 (~(op(e3, e0) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[1133, 9709])).
% 1.58/1.74 tff(9711,plain,
% 1.58/1.74 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[1870])).
% 1.58/1.74 tff(9712,plain,
% 1.58/1.74 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9711])).
% 1.58/1.74 tff(9713,plain,
% 1.58/1.74 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9712])).
% 1.58/1.74 tff(9714,plain,
% 1.58/1.74 (~(op(e0, e0) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[3414, 9713])).
% 1.58/1.74 tff(9715,plain,
% 1.58/1.74 ((op(e1, e0) = e3) <=> (e2 = op(e0, e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[8406, 1870])).
% 1.58/1.74 tff(9716,plain,
% 1.58/1.74 ((op(e1, e0) = e3) <=> (op(e0, e3) = e2)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9715, 1681])).
% 1.58/1.74 tff(9717,plain,
% 1.58/1.74 ((op(e0, e3) = e2) <=> (op(e1, e0) = e3)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9716])).
% 1.58/1.74 tff(9718,plain,
% 1.58/1.74 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e0) = e3))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9717])).
% 1.58/1.74 tff(9719,plain,
% 1.58/1.74 (~(op(e1, e0) = e3)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[79, 9718])).
% 1.58/1.74 tff(9720,plain,
% 1.58/1.74 (op(e2, e0) = e3),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[2713, 9719, 9714, 9710])).
% 1.58/1.74 tff(9721,plain,
% 1.58/1.74 (op(e2, e0) = op(e0, e3)),
% 1.58/1.74 inference(transitivity,[status(thm)],[9720, 1870])).
% 1.58/1.74 tff(9722,plain,
% 1.58/1.74 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9721])).
% 1.58/1.74 tff(9723,plain,
% 1.58/1.74 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9722, 7797])).
% 1.58/1.74 tff(9724,plain,
% 1.58/1.74 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9723])).
% 1.58/1.74 tff(9725,plain,
% 1.58/1.74 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9724, 6337])).
% 1.58/1.74 tff(9726,plain,
% 1.58/1.74 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9725])).
% 1.58/1.74 tff(9727,plain,
% 1.58/1.74 (~(op(e0, e2) = op(e2, e0))),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[918, 9726])).
% 1.58/1.74 tff(9728,plain,
% 1.58/1.74 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.58/1.74 inference(unit_resolution,[status(thm)],[6347, 9727])).
% 1.58/1.74 tff(9729,plain,
% 1.58/1.74 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[251])).
% 1.58/1.74 tff(9730,plain,
% 1.58/1.74 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.58/1.74 inference(symmetry,[status(thm)],[9729])).
% 1.58/1.74 tff(9731,plain,
% 1.58/1.74 ((op(e3, e2) = e0) <=> (op(e0, e3) = e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9706])).
% 1.58/1.74 tff(9732,plain,
% 1.58/1.74 ((op(e0, e3) = e0) <=> (op(e3, e2) = e0)),
% 1.58/1.74 inference(symmetry,[status(thm)],[9731])).
% 1.58/1.74 tff(9733,plain,
% 1.58/1.74 ((op(e0, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.58/1.74 inference(transitivity,[status(thm)],[9732, 9730, 395])).
% 1.58/1.74 tff(9734,plain,
% 1.58/1.74 ((~(op(e0, e3) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9733])).
% 1.58/1.74 tff(9735,plain,
% 1.58/1.74 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e0)),
% 1.58/1.74 inference(monotonicity,[status(thm)],[251])).
% 1.58/1.74 tff(9736,plain,
% 1.58/1.74 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e0))),
% 1.58/1.74 inference(monotonicity,[status(thm)],[9735])).
% 1.58/1.74 tff(9737,plain,
% 1.58/1.74 (~(op(e0, e3) = e0)),
% 1.58/1.74 inference(modus_ponens,[status(thm)],[964, 9736])).
% 1.58/1.74 tff(9738,plain,
% 1.58/1.74 (~(op(e2, e3) = op(e3, e2))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[9737, 9734])).
% 1.58/1.75 tff(9739,plain,
% 1.58/1.75 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[430, 9738])).
% 1.58/1.75 tff(9740,plain,
% 1.58/1.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9724])).
% 1.58/1.75 tff(9741,plain,
% 1.58/1.75 (~(op(e2, e0) = op(e0, e2))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[918, 9740])).
% 1.58/1.75 tff(9742,plain,
% 1.58/1.75 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[6358, 9741])).
% 1.58/1.75 tff(9743,plain,
% 1.58/1.75 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[3710])).
% 1.58/1.75 tff(9744,plain,
% 1.58/1.75 ((op(e2, e0) = e1) <=> (op(e0, e3) = e1)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9721])).
% 1.58/1.75 tff(9745,plain,
% 1.58/1.75 ((op(e0, e3) = e1) <=> (op(e2, e0) = e1)),
% 1.58/1.75 inference(symmetry,[status(thm)],[9744])).
% 1.58/1.75 tff(9746,plain,
% 1.58/1.75 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9745])).
% 1.58/1.75 tff(9747,plain,
% 1.58/1.75 (~(op(e2, e0) = e1)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[121, 9746])).
% 1.58/1.75 tff(9748,plain,
% 1.58/1.75 ((op(e3, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9706])).
% 1.58/1.75 tff(9749,plain,
% 1.58/1.75 ((op(e0, e3) = e1) <=> (op(e3, e2) = e1)),
% 1.58/1.75 inference(symmetry,[status(thm)],[9748])).
% 1.58/1.75 tff(9750,plain,
% 1.58/1.75 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9749])).
% 1.58/1.75 tff(9751,plain,
% 1.58/1.75 (~(op(e3, e2) = e1)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[121, 9750])).
% 1.58/1.75 tff(9752,plain,
% 1.58/1.75 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e2) = e0))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9732])).
% 1.58/1.75 tff(9753,plain,
% 1.58/1.75 (~(op(e3, e2) = e0)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[9737, 9752])).
% 1.58/1.75 tff(9754,plain,
% 1.58/1.75 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[856])).
% 1.58/1.75 tff(9755,plain,
% 1.58/1.75 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9754])).
% 1.58/1.75 tff(9756,plain,
% 1.58/1.75 (~(op(e3, e1) = e3)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[3429, 9755])).
% 1.58/1.75 tff(9757,plain,
% 1.58/1.75 (op(e1, e2) = e0),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[1859, 3785, 75, 2232])).
% 1.58/1.75 tff(9758,plain,
% 1.58/1.75 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e0)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9757])).
% 1.58/1.75 tff(9759,plain,
% 1.58/1.75 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e0))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9758])).
% 1.58/1.75 tff(9760,plain,
% 1.58/1.75 (~(op(e1, e1) = e0)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[1604, 9759])).
% 1.58/1.75 tff(9761,plain,
% 1.58/1.75 ((op(e0, e2) = op(e0, e3)) <=> (op(op(e2, e3), e2) = e3)),
% 1.58/1.75 inference(transitivity,[status(thm)],[9686, 5090])).
% 1.58/1.75 tff(9762,plain,
% 1.58/1.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9761])).
% 1.58/1.75 tff(9763,plain,
% 1.58/1.75 (~(op(op(e2, e3), e2) = e3)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[918, 9762])).
% 1.58/1.75 tff(9764,plain,
% 1.58/1.75 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[1934, 9763])).
% 1.58/1.75 tff(9765,plain,
% 1.58/1.75 (op(e2, op(e0, e3)) = op(e2, e3)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[1869])).
% 1.58/1.75 tff(9766,plain,
% 1.58/1.75 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9721])).
% 1.58/1.75 tff(9767,plain,
% 1.58/1.75 (op(e2, op(e2, e0)) = e0),
% 1.58/1.75 inference(transitivity,[status(thm)],[9766, 9765, 251])).
% 1.58/1.75 tff(9768,plain,
% 1.58/1.75 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2653, 9767])).
% 1.58/1.75 tff(9769,plain,
% 1.58/1.75 (op(e1, op(e1, e2)) = op(e1, e0)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9757])).
% 1.58/1.75 tff(9770,plain,
% 1.58/1.75 (op(e1, op(e1, e2)) = e2),
% 1.58/1.75 inference(transitivity,[status(thm)],[9769, 8406])).
% 1.58/1.75 tff(9771,plain,
% 1.58/1.75 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[2377, 9770])).
% 1.58/1.75 tff(9772,plain,
% 1.58/1.75 (op(op(e3, e2), e2) = e3),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[7919, 856])).
% 1.58/1.75 tff(9773,plain,
% 1.58/1.75 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[1339, 9772])).
% 1.58/1.75 tff(9774,plain,
% 1.58/1.75 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[8406])).
% 1.58/1.75 tff(9775,plain,
% 1.58/1.75 (op(e1, op(e1, e0)) = e0),
% 1.58/1.75 inference(transitivity,[status(thm)],[9774, 9757])).
% 1.58/1.75 tff(9776,plain,
% 1.58/1.75 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[1836, 9775])).
% 1.58/1.75 tff(9777,plain,
% 1.58/1.75 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e0)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9757])).
% 1.58/1.75 tff(9778,plain,
% 1.58/1.75 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e0))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9777])).
% 1.58/1.75 tff(9779,plain,
% 1.58/1.75 (~(op(e0, e2) = e0)),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[6205, 9778])).
% 1.58/1.75 tff(9780,plain,
% 1.58/1.75 ((op(e0, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.58/1.75 inference(transitivity,[status(thm)],[9732, 9730])).
% 1.58/1.75 tff(9781,plain,
% 1.58/1.75 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9780])).
% 1.58/1.75 tff(9782,plain,
% 1.58/1.75 (~(op(e3, e2) = op(e2, e3))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[9737, 9781])).
% 1.58/1.75 tff(9783,plain,
% 1.58/1.75 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[500, 9782])).
% 1.58/1.75 tff(9784,plain,
% 1.58/1.75 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e0)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9757])).
% 1.58/1.75 tff(9785,plain,
% 1.58/1.75 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 1.58/1.75 inference(symmetry,[status(thm)],[9784])).
% 1.58/1.75 tff(9786,plain,
% 1.58/1.75 ((op(e2, e1) = e0) <=> (op(e1, e2) = op(e2, e1))),
% 1.58/1.75 inference(transitivity,[status(thm)],[9785, 531])).
% 1.58/1.75 tff(9787,plain,
% 1.58/1.75 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9786])).
% 1.58/1.75 tff(9788,plain,
% 1.58/1.75 (~(op(e1, e2) = op(e2, e1))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[2559, 9787])).
% 1.58/1.75 tff(9789,plain,
% 1.58/1.75 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[539, 9788])).
% 1.58/1.75 tff(9790,plain,
% 1.58/1.75 (op(e3, op(e1, e0)) = op(e3, e2)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[8406])).
% 1.58/1.75 tff(9791,plain,
% 1.58/1.75 (op(e3, op(e1, e0)) = e3),
% 1.58/1.75 inference(transitivity,[status(thm)],[9790, 856])).
% 1.58/1.75 tff(9792,plain,
% 1.58/1.75 (((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)) | (~(op(e3, op(e1, e0)) = e3))),
% 1.58/1.75 inference(tautology,[status(thm)],[])).
% 1.58/1.75 tff(9793,plain,
% 1.58/1.75 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[9792, 9791])).
% 1.58/1.75 tff(9794,plain,
% 1.58/1.75 ((op(e3, e0) = op(e3, e2)) <=> (op(e0, e3) = op(e3, e0))),
% 1.58/1.75 inference(transitivity,[status(thm)],[9707, 453])).
% 1.58/1.75 tff(9795,plain,
% 1.58/1.75 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.58/1.75 inference(monotonicity,[status(thm)],[9794])).
% 1.58/1.75 tff(9796,plain,
% 1.58/1.75 (~(op(e0, e3) = op(e3, e0))),
% 1.58/1.75 inference(modus_ponens,[status(thm)],[1133, 9795])).
% 1.58/1.75 tff(9797,plain,
% 1.58/1.75 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[496, 9796])).
% 1.58/1.75 tff(9798,plain,
% 1.58/1.75 (op(e1, op(e0, e3)) = op(e1, e3)),
% 1.58/1.75 inference(monotonicity,[status(thm)],[1869])).
% 1.58/1.75 tff(9799,plain,
% 1.58/1.75 (op(e1, e1) = e3),
% 1.58/1.75 inference(unit_resolution,[status(thm)],[630, 9760, 68, 2165])).
% 1.58/1.75 tff(9800,plain,
% 1.58/1.75 (op(e1, e1) = op(e0, e3)),
% 1.58/1.75 inference(transitivity,[status(thm)],[9799, 1870])).
% 1.65/1.75 tff(9801,plain,
% 1.65/1.75 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9800])).
% 1.65/1.75 tff(9802,plain,
% 1.65/1.75 (op(e1, op(e1, e1)) = e1),
% 1.65/1.75 inference(transitivity,[status(thm)],[9801, 9798, 132])).
% 1.65/1.75 tff(9803,plain,
% 1.65/1.75 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[5678, 9802])).
% 1.65/1.75 tff(9804,plain,
% 1.65/1.75 ((~(op(e2, e1) = e0)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9785])).
% 1.65/1.75 tff(9805,plain,
% 1.65/1.75 (~(op(e2, e1) = op(e1, e2))),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[2559, 9804])).
% 1.65/1.75 tff(9806,plain,
% 1.65/1.75 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[557, 9805])).
% 1.65/1.75 tff(9807,plain,
% 1.65/1.75 (op(e0, e2) = e2),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[2745, 4484, 7053, 9688])).
% 1.65/1.75 tff(9808,plain,
% 1.65/1.75 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9807])).
% 1.65/1.75 tff(9809,plain,
% 1.65/1.75 (op(e0, op(e0, e2)) = e2),
% 1.65/1.75 inference(transitivity,[status(thm)],[9808, 9807])).
% 1.65/1.75 tff(9810,plain,
% 1.65/1.75 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1331, 9809])).
% 1.65/1.75 tff(9811,plain,
% 1.65/1.75 (op(e2, e2) = e1),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1613, 4484, 2232, 930])).
% 1.65/1.75 tff(9812,plain,
% 1.65/1.75 ((e2 = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 1.65/1.75 inference(commutativity,[status(thm)],[])).
% 1.65/1.75 tff(9813,plain,
% 1.65/1.75 ((op(e1, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[920])).
% 1.65/1.75 tff(9814,plain,
% 1.65/1.75 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 1.65/1.75 inference(transitivity,[status(thm)],[9813, 9812])).
% 1.65/1.75 tff(9815,plain,
% 1.65/1.75 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9814])).
% 1.65/1.75 tff(9816,plain,
% 1.65/1.75 (~(op(e2, e0) = e2)),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[756, 9815])).
% 1.65/1.75 tff(9817,plain,
% 1.65/1.75 ((op(e0, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9807])).
% 1.65/1.75 tff(9818,plain,
% 1.65/1.75 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.65/1.75 inference(transitivity,[status(thm)],[9817, 81])).
% 1.65/1.75 tff(9819,plain,
% 1.65/1.75 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9818])).
% 1.65/1.75 tff(9820,plain,
% 1.65/1.75 (~(op(e2, e2) = e2)),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[2736, 9819])).
% 1.65/1.75 tff(9821,plain,
% 1.65/1.75 (op(e2, e1) = e2),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[2088, 9820, 4382, 9816])).
% 1.65/1.75 tff(9822,plain,
% 1.65/1.75 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9821])).
% 1.65/1.75 tff(9823,plain,
% 1.65/1.75 (op(e2, op(e2, e1)) = e1),
% 1.65/1.75 inference(transitivity,[status(thm)],[9822, 9811])).
% 1.65/1.75 tff(9824,plain,
% 1.65/1.75 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1355, 9823])).
% 1.65/1.75 tff(9825,plain,
% 1.65/1.75 (op(e3, e1) = e1),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[446, 183, 82, 2839])).
% 1.65/1.75 tff(9826,plain,
% 1.65/1.75 (op(e3, op(e3, e1)) = op(e3, e1)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9825])).
% 1.65/1.75 tff(9827,plain,
% 1.65/1.75 (op(e3, op(e3, e1)) = e1),
% 1.65/1.75 inference(transitivity,[status(thm)],[9826, 9825])).
% 1.65/1.75 tff(9828,plain,
% 1.65/1.75 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[2594, 9827])).
% 1.65/1.75 tff(9829,plain,
% 1.65/1.75 (op(e3, e0) = e0),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1916, 183, 656, 85])).
% 1.65/1.75 tff(9830,plain,
% 1.65/1.75 (op(e3, op(e3, e0)) = op(op(e0, e3), e0)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[1870, 9829])).
% 1.65/1.75 tff(9831,plain,
% 1.65/1.75 (op(e3, op(e3, e0)) = e0),
% 1.65/1.75 inference(transitivity,[status(thm)],[9830, 9663, 9829])).
% 1.65/1.75 tff(9832,plain,
% 1.65/1.75 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1345, 9831])).
% 1.65/1.75 tff(9833,plain,
% 1.65/1.75 (op(e0, e1) = e0),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[292, 183, 2559, 84])).
% 1.65/1.75 tff(9834,plain,
% 1.65/1.75 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9833])).
% 1.65/1.75 tff(9835,plain,
% 1.65/1.75 (op(op(e0, e1), e1) = e0),
% 1.65/1.75 inference(transitivity,[status(thm)],[9834, 9833])).
% 1.65/1.75 tff(9836,plain,
% 1.65/1.75 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[2650, 9835])).
% 1.65/1.75 tff(9837,plain,
% 1.65/1.75 ($false),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[1459, 9836, 9832, 1357, 1936, 3342, 1304, 1363, 3341, 1358, 9828, 2421, 1347])).
% 1.65/1.75 tff(9838,plain,((op(e3, e1) = e0) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e0, e3) = e3)) | (op(e2, e1) = e0) | (op(e1, e1) = e0) | (op(e3, e1) = e2) | (op(e3, e1) = e3) | (op(e3, e3) = e0) | (op(e3, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.75 tff(9839,plain,
% 1.65/1.75 (op(e3, e1) = e0),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[9838, 9824, 1357, 3342, 1304, 9810, 3341, 1358, 2421, 1347, 1869, 2559, 84, 82, 2839, 656, 85])).
% 1.65/1.75 tff(9840,plain,
% 1.65/1.75 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9839])).
% 1.65/1.75 tff(9841,plain,
% 1.65/1.75 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9840])).
% 1.65/1.75 tff(9842,plain,
% 1.65/1.75 (~(op(e0, e1) = e0)),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[3046, 9841])).
% 1.65/1.75 tff(9843,plain,
% 1.65/1.75 (op(e0, e0) = e0),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[3976, 9842, 1087, 7053])).
% 1.65/1.75 tff(9844,plain,
% 1.65/1.75 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9843])).
% 1.65/1.75 tff(9845,plain,
% 1.65/1.75 (op(e0, op(e0, e0)) = e0),
% 1.65/1.75 inference(transitivity,[status(thm)],[9844, 9843])).
% 1.65/1.75 tff(9846,assumption,((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)), introduced(assumption)).
% 1.65/1.75 tff(9847,plain,
% 1.65/1.75 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e1) = e2)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[3796])).
% 1.65/1.75 tff(9848,plain,
% 1.65/1.75 ((op(e2, e1) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 1.65/1.75 inference(symmetry,[status(thm)],[9847])).
% 1.65/1.75 tff(9849,plain,
% 1.65/1.75 (op(e2, op(e1, e3)) = e2),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[9821, 9848])).
% 1.65/1.75 tff(9850,plain,
% 1.65/1.75 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[9084, 9849])).
% 1.65/1.75 tff(9851,plain,
% 1.65/1.75 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9811])).
% 1.65/1.75 tff(9852,plain,
% 1.65/1.75 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, e1) = e2)),
% 1.65/1.75 inference(monotonicity,[status(thm)],[9851])).
% 1.65/1.75 tff(9853,plain,
% 1.65/1.75 ((op(e2, e1) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 1.65/1.75 inference(symmetry,[status(thm)],[9852])).
% 1.65/1.75 tff(9854,plain,
% 1.65/1.75 (op(e2, op(e2, e2)) = e2),
% 1.65/1.75 inference(modus_ponens,[status(thm)],[9821, 9853])).
% 1.65/1.75 tff(9855,plain,
% 1.65/1.75 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.65/1.75 inference(unit_resolution,[status(thm)],[528, 9854])).
% 1.65/1.75 tff(9856,plain,
% 1.65/1.75 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.65/1.75 inference(monotonicity,[status(thm)],[920])).
% 1.65/1.75 tff(9857,plain,
% 1.65/1.75 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.65/1.75 inference(transitivity,[status(thm)],[9856, 4838])).
% 1.65/1.76 tff(9858,plain,
% 1.65/1.76 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.65/1.76 inference(symmetry,[status(thm)],[9857])).
% 1.65/1.76 tff(9859,plain,
% 1.65/1.76 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9807])).
% 1.65/1.76 tff(9860,plain,
% 1.65/1.76 ((op(e0, e1) = op(e0, e2)) <=> (op(e1, e0) = op(e0, e1))),
% 1.65/1.76 inference(transitivity,[status(thm)],[9859, 9858])).
% 1.65/1.76 tff(9861,plain,
% 1.65/1.76 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9860])).
% 1.65/1.76 tff(9862,plain,
% 1.65/1.76 (~(op(e1, e0) = op(e0, e1))),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[2102, 9861])).
% 1.65/1.76 tff(9863,plain,
% 1.65/1.76 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[613, 9862])).
% 1.65/1.76 tff(9864,plain,
% 1.65/1.76 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[132])).
% 1.65/1.76 tff(9865,plain,
% 1.65/1.76 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.65/1.76 inference(symmetry,[status(thm)],[9864])).
% 1.65/1.76 tff(9866,plain,
% 1.65/1.76 ((op(e3, e1) = e1) <=> (e0 = e1)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9839])).
% 1.65/1.76 tff(9867,plain,
% 1.65/1.76 ((e0 = e1) <=> (op(e3, e1) = e1)),
% 1.65/1.76 inference(symmetry,[status(thm)],[9866])).
% 1.65/1.76 tff(9868,plain,
% 1.65/1.76 ((e0 = e1) <=> (op(e1, e3) = op(e3, e1))),
% 1.65/1.76 inference(transitivity,[status(thm)],[9867, 9865, 6290])).
% 1.65/1.76 tff(9869,plain,
% 1.65/1.76 ((~(e0 = e1)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9868])).
% 1.65/1.76 tff(9870,plain,
% 1.65/1.76 (~(op(e1, e3) = op(e3, e1))),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[26, 9869])).
% 1.65/1.76 tff(9871,plain,
% 1.65/1.76 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[6307, 9870])).
% 1.65/1.76 tff(9872,plain,
% 1.65/1.76 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[5367, 9871, 6688, 5680, 6689, 9863, 5670, 5681, 5673, 9855, 5671, 9850, 5674, 5668, 9846])).
% 1.65/1.76 tff(9873,plain,
% 1.65/1.76 (~(op(e0, op(e0, e0)) = e0)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[5598, 9872])).
% 1.65/1.76 tff(9874,plain,
% 1.65/1.76 ($false),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[9873, 9845])).
% 1.65/1.76 tff(9875,plain,((op(e0, e2) = e1) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (op(e0, e3) = e0) | (op(e0, e2) = e0) | (~(op(e1, e3) = e1)) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e0, e3) = e3)) | (op(e2, e1) = e0) | (op(e1, e1) = e0) | (op(e3, e1) = e2) | (op(e3, e1) = e3) | (op(e3, e3) = e0) | (op(e3, e2) = e0) | (op(e2, e3) = e2) | (~(op(e1, e0) = e2)) | (op(e3, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.76 tff(9876,plain,
% 1.65/1.76 (op(e0, e2) = e1),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[9875, 9806, 6688, 9803, 9797, 9793, 9789, 9783, 9742, 9739, 9728, 9737, 9779, 132, 9776, 5469, 1304, 9773, 9771, 9768, 9764, 1869, 2559, 9760, 82, 9756, 656, 9753, 4382, 8406, 9751])).
% 1.65/1.76 tff(9877,plain,
% 1.65/1.76 ((op(e0, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9876])).
% 1.65/1.76 tff(9878,plain,
% 1.65/1.76 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9877, 316])).
% 1.65/1.76 tff(9879,plain,
% 1.65/1.76 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9878])).
% 1.65/1.76 tff(9880,plain,
% 1.65/1.76 (~(op(e2, e2) = e1)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[2736, 9879])).
% 1.65/1.76 tff(9881,plain,
% 1.65/1.76 (op(e2, e1) = e1),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[345, 9880, 76, 9747])).
% 1.65/1.76 tff(9882,plain,
% 1.65/1.76 ((op(e2, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9881])).
% 1.65/1.76 tff(9883,plain,
% 1.65/1.76 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9882, 7793])).
% 1.65/1.76 tff(9884,plain,
% 1.65/1.76 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 1.65/1.76 inference(transitivity,[status(thm)],[9883, 9743])).
% 1.65/1.76 tff(9885,plain,
% 1.65/1.76 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9884])).
% 1.65/1.76 tff(9886,plain,
% 1.65/1.76 (~(op(e3, e1) = op(e1, e3))),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[402, 9885])).
% 1.65/1.76 tff(9887,plain,
% 1.65/1.76 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[6362, 9886])).
% 1.65/1.76 tff(9888,plain,
% 1.65/1.76 ((op(e0, e2) = e2) <=> (e1 = e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9876])).
% 1.65/1.76 tff(9889,plain,
% 1.65/1.76 ((e1 = e2) <=> (op(e0, e2) = e2)),
% 1.65/1.76 inference(symmetry,[status(thm)],[9888])).
% 1.65/1.76 tff(9890,plain,
% 1.65/1.76 ((~(e1 = e2)) <=> (~(op(e0, e2) = e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9889])).
% 1.65/1.76 tff(9891,plain,
% 1.65/1.76 (~(op(e0, e2) = e2)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[708, 9890])).
% 1.65/1.76 tff(9892,plain,
% 1.65/1.76 (op(e2, e2) = e2),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[1151, 9891, 2386, 3785])).
% 1.65/1.76 tff(9893,plain,
% 1.65/1.76 (op(e2, op(e2, e2)) = op(e2, e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9892])).
% 1.65/1.76 tff(9894,plain,
% 1.65/1.76 (op(e2, op(e2, e2)) = e2),
% 1.65/1.76 inference(transitivity,[status(thm)],[9893, 9892])).
% 1.65/1.76 tff(9895,plain,
% 1.65/1.76 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[528, 9894])).
% 1.65/1.76 tff(9896,plain,
% 1.65/1.76 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[8406])).
% 1.65/1.76 tff(9897,plain,
% 1.65/1.76 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9896])).
% 1.65/1.76 tff(9898,plain,
% 1.65/1.76 (~(op(e0, e0) = e2)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[2471, 9897])).
% 1.65/1.76 tff(9899,plain,
% 1.65/1.76 (op(e0, e1) = e2),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[3652, 9891, 79, 9898])).
% 1.65/1.76 tff(9900,plain,
% 1.65/1.76 (op(e2, op(e0, e1)) = op(e2, e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9899])).
% 1.65/1.76 tff(9901,plain,
% 1.65/1.76 (op(e2, op(e0, e1)) = e2),
% 1.65/1.76 inference(transitivity,[status(thm)],[9900, 9892])).
% 1.65/1.76 tff(9902,plain,
% 1.65/1.76 (((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)) | (~(op(e2, op(e0, e1)) = e2))),
% 1.65/1.76 inference(tautology,[status(thm)],[])).
% 1.65/1.76 tff(9903,plain,
% 1.65/1.76 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[9902, 9901])).
% 1.65/1.76 tff(9904,plain,
% 1.65/1.76 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 1.65/1.76 inference(transitivity,[status(thm)],[9883, 9743, 6290])).
% 1.65/1.76 tff(9905,plain,
% 1.65/1.76 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9904])).
% 1.65/1.76 tff(9906,plain,
% 1.65/1.76 (~(op(e1, e3) = op(e3, e1))),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[402, 9905])).
% 1.65/1.76 tff(9907,plain,
% 1.65/1.76 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[6307, 9906])).
% 1.65/1.76 tff(9908,plain,
% 1.65/1.76 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9876])).
% 1.65/1.76 tff(9909,plain,
% 1.65/1.76 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e1))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9908])).
% 1.65/1.76 tff(9910,plain,
% 1.65/1.76 (~(op(e0, e0) = e1)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[3603, 9909])).
% 1.65/1.76 tff(9911,plain,
% 1.65/1.76 (op(e0, e0) = e0),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[3612, 9910, 9714, 9898])).
% 1.65/1.76 tff(9912,plain,
% 1.65/1.76 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9911])).
% 1.65/1.76 tff(9913,plain,
% 1.65/1.76 (op(e0, op(e0, e0)) = e0),
% 1.65/1.76 inference(transitivity,[status(thm)],[9912, 9911])).
% 1.65/1.76 tff(9914,plain,
% 1.65/1.76 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[5598, 9913])).
% 1.65/1.76 tff(9915,plain,
% 1.65/1.76 ($false),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[5367, 9914, 9907, 6688, 9806, 9803, 9903, 9797, 9793, 9789, 9895, 9783, 9887, 9742, 9739, 9728])).
% 1.65/1.76 tff(9916,plain,((op(e1, e2) = e2) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~(op(e1, e3) = e1)) | (op(e2, e3) = e1) | (op(e0, e3) = e2) | (op(e3, e2) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e0, e3) = e3)) | (op(e2, e1) = e0) | (op(e3, e1) = e2) | (op(e3, e3) = e0) | (op(e2, e3) = e2) | (~(op(e2, e3) = e0)) | (op(e0, e3) = e1) | (op(e1, e1) = e2) | (~(op(e3, e2) = e3)) | (op(e1, e3) = e2) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.76 tff(9917,plain,
% 1.65/1.76 (op(e1, e2) = e2),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[9916, 9703, 9668, 76, 79, 9699, 1304, 1869, 7791, 9684, 9696, 9692, 251, 121, 9681, 9689, 72, 75])).
% 1.65/1.76 tff(9918,plain,
% 1.65/1.76 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9917])).
% 1.65/1.76 tff(9919,plain,
% 1.65/1.76 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9918, 81])).
% 1.65/1.76 tff(9920,plain,
% 1.65/1.76 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9919])).
% 1.65/1.76 tff(9921,plain,
% 1.65/1.76 (~(op(e2, e2) = e2)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[1273, 9920])).
% 1.65/1.76 tff(9922,plain,
% 1.65/1.76 (op(e2, e2) = e1),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[524, 9921, 5023, 2431])).
% 1.65/1.76 tff(9923,plain,
% 1.65/1.76 (e1 = op(e2, e2)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[9922, 317])).
% 1.65/1.76 tff(9924,plain,
% 1.65/1.76 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9922])).
% 1.65/1.76 tff(9925,plain,
% 1.65/1.76 ((e3 = op(e2, op(e2, e2))) <=> (e3 = op(e2, e1))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9924])).
% 1.65/1.76 tff(9926,plain,
% 1.65/1.76 ((e3 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e3)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9925, 1262])).
% 1.65/1.76 tff(9927,plain,
% 1.65/1.76 ((op(e2, e1) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.65/1.76 inference(symmetry,[status(thm)],[9926])).
% 1.65/1.76 tff(9928,plain,
% 1.65/1.76 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9689])).
% 1.65/1.76 tff(9929,plain,
% 1.65/1.76 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9928])).
% 1.65/1.76 tff(9930,plain,
% 1.65/1.76 (~(op(e3, e1) = e3)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[3429, 9929])).
% 1.65/1.76 tff(9931,plain,
% 1.65/1.76 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[1870])).
% 1.65/1.76 tff(9932,plain,
% 1.65/1.76 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 1.65/1.76 inference(symmetry,[status(thm)],[9931])).
% 1.65/1.76 tff(9933,plain,
% 1.65/1.76 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9932])).
% 1.65/1.76 tff(9934,plain,
% 1.65/1.76 (~(op(e0, e1) = e3)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[818, 9933])).
% 1.65/1.76 tff(9935,plain,
% 1.65/1.76 ((op(e1, e2) = e0) <=> (e2 = e0)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9917])).
% 1.65/1.76 tff(9936,plain,
% 1.65/1.76 ((op(e1, e2) = e0) <=> (e0 = e2)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9935, 1])).
% 1.65/1.76 tff(9937,plain,
% 1.65/1.76 ((e0 = e2) <=> (op(e1, e2) = e0)),
% 1.65/1.76 inference(symmetry,[status(thm)],[9936])).
% 1.65/1.76 tff(9938,plain,
% 1.65/1.76 ((~(e0 = e2)) <=> (~(op(e1, e2) = e0))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9937])).
% 1.65/1.76 tff(9939,plain,
% 1.65/1.76 (~(op(e1, e2) = e0)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[14, 9938])).
% 1.65/1.76 tff(9940,plain,
% 1.65/1.76 (op(e3, e2) = op(e0, e3)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9689, 1870])).
% 1.65/1.76 tff(9941,plain,
% 1.65/1.76 ((op(e3, e2) = e0) <=> (op(e0, e3) = e0)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9940])).
% 1.65/1.76 tff(9942,plain,
% 1.65/1.76 ((op(e0, e3) = e0) <=> (op(e3, e2) = e0)),
% 1.65/1.76 inference(symmetry,[status(thm)],[9941])).
% 1.65/1.76 tff(9943,plain,
% 1.65/1.76 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e2) = e0))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9942])).
% 1.65/1.76 tff(9944,plain,
% 1.65/1.76 (~(op(e3, e2) = e0)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[9737, 9943])).
% 1.65/1.76 tff(9945,plain,
% 1.65/1.76 (op(e0, e2) = e0),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[973, 9939, 5023, 9944])).
% 1.65/1.76 tff(9946,plain,
% 1.65/1.76 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9945])).
% 1.65/1.76 tff(9947,plain,
% 1.65/1.76 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9946])).
% 1.65/1.76 tff(9948,plain,
% 1.65/1.76 (~(op(e0, e1) = e0)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[2102, 9947])).
% 1.65/1.76 tff(9949,plain,
% 1.65/1.76 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = op(e0, e3))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9940])).
% 1.65/1.76 tff(9950,plain,
% 1.65/1.76 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 1.65/1.76 inference(transitivity,[status(thm)],[9949, 9705])).
% 1.65/1.76 tff(9951,plain,
% 1.65/1.76 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9950])).
% 1.65/1.76 tff(9952,plain,
% 1.65/1.76 (~(op(e3, e0) = e3)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[1133, 9951])).
% 1.65/1.76 tff(9953,plain,
% 1.65/1.76 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[2812])).
% 1.65/1.76 tff(9954,plain,
% 1.65/1.76 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9953])).
% 1.65/1.76 tff(9955,plain,
% 1.65/1.76 (~(op(e3, e0) = e2)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[157, 9954])).
% 1.65/1.76 tff(9956,plain,
% 1.65/1.76 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9668])).
% 1.65/1.76 tff(9957,plain,
% 1.65/1.76 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9956])).
% 1.65/1.76 tff(9958,plain,
% 1.65/1.76 (~(op(e1, e1) = e1)),
% 1.65/1.76 inference(modus_ponens,[status(thm)],[619, 9957])).
% 1.65/1.76 tff(9959,plain,
% 1.65/1.76 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9917])).
% 1.65/1.76 tff(9960,plain,
% 1.65/1.76 (op(e1, op(e1, e2)) = e2),
% 1.65/1.76 inference(transitivity,[status(thm)],[9959, 9917])).
% 1.65/1.76 tff(9961,plain,
% 1.65/1.76 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[2377, 9960])).
% 1.65/1.76 tff(9962,plain,
% 1.65/1.76 (op(op(e3, e2), e2) = e3),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[7919, 9689])).
% 1.65/1.76 tff(9963,plain,
% 1.65/1.76 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.65/1.76 inference(unit_resolution,[status(thm)],[1339, 9962])).
% 1.65/1.76 tff(9964,plain,
% 1.65/1.76 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.65/1.76 inference(monotonicity,[status(thm)],[9945])).
% 1.65/1.77 tff(9965,plain,
% 1.65/1.77 (op(op(e0, e2), e2) = e0),
% 1.65/1.77 inference(transitivity,[status(thm)],[9964, 9945])).
% 1.65/1.77 tff(9966,plain,
% 1.65/1.77 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1956, 9965])).
% 1.65/1.77 tff(9967,plain,
% 1.65/1.77 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[1869])).
% 1.65/1.77 tff(9968,plain,
% 1.65/1.77 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9967])).
% 1.65/1.77 tff(9969,plain,
% 1.65/1.77 (~(op(e0, e0) = e3)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[3414, 9968])).
% 1.65/1.77 tff(9970,plain,
% 1.65/1.77 ((op(e1, e0) = e3) <=> (e0 = op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[3352, 1870])).
% 1.65/1.77 tff(9971,plain,
% 1.65/1.77 ((op(e1, e0) = e3) <=> (op(e0, e3) = e0)),
% 1.65/1.77 inference(transitivity,[status(thm)],[9970, 1079])).
% 1.65/1.77 tff(9972,plain,
% 1.65/1.77 ((op(e0, e3) = e0) <=> (op(e1, e0) = e3)),
% 1.65/1.77 inference(symmetry,[status(thm)],[9971])).
% 1.65/1.77 tff(9973,plain,
% 1.65/1.77 ((~(op(e0, e3) = e0)) <=> (~(op(e1, e0) = e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9972])).
% 1.65/1.77 tff(9974,plain,
% 1.65/1.77 (~(op(e1, e0) = e3)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[9737, 9973])).
% 1.65/1.77 tff(9975,plain,
% 1.65/1.77 (op(e2, e0) = e3),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[2713, 9974, 9969, 2410])).
% 1.65/1.77 tff(9976,plain,
% 1.65/1.77 (op(e2, e0) = op(e0, e3)),
% 1.65/1.77 inference(transitivity,[status(thm)],[9975, 1870])).
% 1.65/1.77 tff(9977,plain,
% 1.65/1.77 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9976])).
% 1.65/1.77 tff(9978,plain,
% 1.65/1.77 (op(e2, op(e2, e0)) = e0),
% 1.65/1.77 inference(transitivity,[status(thm)],[9977, 9765, 251])).
% 1.65/1.77 tff(9979,plain,
% 1.65/1.77 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[2653, 9978])).
% 1.65/1.77 tff(9980,plain,
% 1.65/1.77 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[307])).
% 1.65/1.77 tff(9981,plain,
% 1.65/1.77 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9980])).
% 1.65/1.77 tff(9982,plain,
% 1.65/1.77 (~(op(e2, e1) = e1)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[508, 9981])).
% 1.65/1.77 tff(9983,plain,
% 1.65/1.77 (op(e3, e1) = e0),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[292, 84, 2559, 3849])).
% 1.65/1.77 tff(9984,plain,
% 1.65/1.77 ((op(e3, e1) = e1) <=> (e0 = e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9983])).
% 1.65/1.77 tff(9985,plain,
% 1.65/1.77 ((e0 = e1) <=> (op(e3, e1) = e1)),
% 1.65/1.77 inference(symmetry,[status(thm)],[9984])).
% 1.65/1.77 tff(9986,plain,
% 1.65/1.77 ((~(e0 = e1)) <=> (~(op(e3, e1) = e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9985])).
% 1.65/1.77 tff(9987,plain,
% 1.65/1.77 (~(op(e3, e1) = e1)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[26, 9986])).
% 1.65/1.77 tff(9988,plain,
% 1.65/1.77 (op(e0, e1) = e1),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1252, 9987, 1266, 9982])).
% 1.65/1.77 tff(9989,plain,
% 1.65/1.77 (op(e0, op(e0, e1)) = op(e0, e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9988])).
% 1.65/1.77 tff(9990,plain,
% 1.65/1.77 (op(e0, op(e0, e1)) = e1),
% 1.65/1.77 inference(transitivity,[status(thm)],[9989, 9988])).
% 1.65/1.77 tff(9991,plain,
% 1.65/1.77 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[2449, 9990])).
% 1.65/1.77 tff(9992,plain,
% 1.65/1.77 (op(op(e3, e1), e3) = op(e0, op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9983, 1870])).
% 1.65/1.77 tff(9993,plain,
% 1.65/1.77 (op(op(e3, e1), e3) = op(e0, e3)),
% 1.65/1.77 inference(transitivity,[status(thm)],[9992, 1906])).
% 1.65/1.77 tff(9994,plain,
% 1.65/1.77 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9993])).
% 1.65/1.77 tff(9995,plain,
% 1.65/1.77 ((op(e0, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 1.65/1.77 inference(symmetry,[status(thm)],[9994])).
% 1.65/1.77 tff(9996,plain,
% 1.65/1.77 ((~(op(e0, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9995])).
% 1.65/1.77 tff(9997,plain,
% 1.65/1.77 (~(op(op(e3, e1), e3) = e1)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[121, 9996])).
% 1.65/1.77 tff(9998,plain,
% 1.65/1.77 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1050, 9997])).
% 1.65/1.77 tff(9999,plain,
% 1.65/1.77 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[3352])).
% 1.65/1.77 tff(10000,plain,
% 1.65/1.77 (op(e1, op(e1, e0)) = e0),
% 1.65/1.77 inference(transitivity,[status(thm)],[9999, 3352])).
% 1.65/1.77 tff(10001,plain,
% 1.65/1.77 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1836, 10000])).
% 1.65/1.77 tff(10002,plain,
% 1.65/1.77 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[3352])).
% 1.65/1.77 tff(10003,plain,
% 1.65/1.77 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10002, 8115])).
% 1.65/1.77 tff(10004,plain,
% 1.65/1.77 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10003])).
% 1.65/1.77 tff(10005,plain,
% 1.65/1.77 (~(op(e3, e0) = e0)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[410, 10004])).
% 1.65/1.77 tff(10006,plain,
% 1.65/1.77 (op(e3, e0) = e1),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[5422, 10005, 3786, 2410])).
% 1.65/1.77 tff(10007,plain,
% 1.65/1.77 (op(e3, op(e3, e0)) = op(e3, e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10006])).
% 1.65/1.77 tff(10008,plain,
% 1.65/1.77 (op(e3, op(e3, e0)) = e0),
% 1.65/1.77 inference(transitivity,[status(thm)],[10007, 9983])).
% 1.65/1.77 tff(10009,plain,
% 1.65/1.77 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1345, 10008])).
% 1.65/1.77 tff(10010,plain,
% 1.65/1.77 (op(e1, e1) = e3),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[630, 84, 68, 1266])).
% 1.65/1.77 tff(10011,plain,
% 1.65/1.77 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10010])).
% 1.65/1.77 tff(10012,plain,
% 1.65/1.77 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10011, 1262])).
% 1.65/1.77 tff(10013,plain,
% 1.65/1.77 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10012])).
% 1.65/1.77 tff(10014,plain,
% 1.65/1.77 (~(op(e2, e1) = e3)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[225, 10013])).
% 1.65/1.77 tff(10015,plain,
% 1.65/1.77 (op(e2, e1) = e2),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[2367, 10014, 2559, 9982])).
% 1.65/1.77 tff(10016,plain,
% 1.65/1.77 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10015])).
% 1.65/1.77 tff(10017,plain,
% 1.65/1.77 (op(e2, op(e2, e1)) = e1),
% 1.65/1.77 inference(transitivity,[status(thm)],[10016, 307])).
% 1.65/1.77 tff(10018,plain,
% 1.65/1.77 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1355, 10017])).
% 1.65/1.77 tff(10019,plain,
% 1.65/1.77 ($false),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1459, 10018, 10009, 10001, 9998, 3342, 1304, 1363, 3341, 1358, 9991, 9979, 9764])).
% 1.65/1.77 tff(10020,plain,((op(e1, e1) = e0) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~(op(e2, e2) = e1)) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e3)) | (op(e1, e1) = e1) | (op(e2, e1) = e0) | (op(e3, e0) = e2) | (op(e3, e0) = e3) | (op(e0, e3) = e1) | (op(e0, e1) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e0) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.77 tff(10021,plain,
% 1.65/1.77 (op(e1, e1) = e0),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[10020, 9966, 1304, 5469, 9963, 9961, 9922, 251, 1869, 9958, 7791, 9955, 9952, 121, 9948, 9681, 80, 9939])).
% 1.65/1.77 tff(10022,plain,
% 1.65/1.77 ((op(e1, e1) = e3) <=> (e0 = op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10021, 1870])).
% 1.65/1.77 tff(10023,plain,
% 1.65/1.77 ((op(e1, e1) = e3) <=> (op(e0, e3) = e0)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10022, 1079])).
% 1.65/1.77 tff(10024,plain,
% 1.65/1.77 ((op(e0, e3) = e0) <=> (op(e1, e1) = e3)),
% 1.65/1.77 inference(symmetry,[status(thm)],[10023])).
% 1.65/1.77 tff(10025,plain,
% 1.65/1.77 ((~(op(e0, e3) = e0)) <=> (~(op(e1, e1) = e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10024])).
% 1.65/1.77 tff(10026,plain,
% 1.65/1.77 (~(op(e1, e1) = e3)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[9737, 10025])).
% 1.65/1.77 tff(10027,plain,
% 1.65/1.77 (op(e2, e1) = e3),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1730, 10026, 9934, 9930])).
% 1.65/1.77 tff(10028,plain,
% 1.65/1.77 (e3 = op(e2, op(e2, e2))),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[10027, 9927])).
% 1.65/1.77 tff(10029,plain,
% 1.65/1.77 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[9924])).
% 1.65/1.77 tff(10030,plain,
% 1.65/1.77 (op(e2, op(e2, e1)) = op(e2, op(e2, op(e2, e2)))),
% 1.65/1.77 inference(symmetry,[status(thm)],[10029])).
% 1.65/1.77 tff(10031,plain,
% 1.65/1.77 (op(e2, e1) = op(e0, e3)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10027, 1870])).
% 1.65/1.77 tff(10032,plain,
% 1.65/1.77 (op(e2, op(e2, e1)) = op(e2, op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10031])).
% 1.65/1.77 tff(10033,plain,
% 1.65/1.77 (op(e2, op(e0, e3)) = op(e2, op(e2, e1))),
% 1.65/1.77 inference(symmetry,[status(thm)],[10032])).
% 1.65/1.77 tff(10034,plain,
% 1.65/1.77 (op(e2, e3) = op(e2, op(e0, e3))),
% 1.65/1.77 inference(symmetry,[status(thm)],[9765])).
% 1.65/1.77 tff(10035,plain,
% 1.65/1.77 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.65/1.77 inference(transitivity,[status(thm)],[252, 10034, 10033, 10030])).
% 1.65/1.77 tff(10036,plain,
% 1.65/1.77 ($false),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[334, 10035, 10028, 9923])).
% 1.65/1.77 tff(10037,plain,((op(e2, e2) = e3) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e3)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.77 tff(10038,plain,
% 1.65/1.77 (op(e2, e2) = e3),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[10037, 75, 1869, 1304, 121, 80, 76, 79, 72, 251, 2812])).
% 1.65/1.77 tff(10039,plain,
% 1.65/1.77 (op(e2, e2) = op(e0, e3)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10038, 1870])).
% 1.65/1.77 tff(10040,plain,
% 1.65/1.77 ((op(e2, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10039])).
% 1.65/1.77 tff(10041,plain,
% 1.65/1.77 ((op(e0, e3) = e1) <=> (op(e2, e2) = e1)),
% 1.65/1.77 inference(symmetry,[status(thm)],[10040])).
% 1.65/1.77 tff(10042,plain,
% 1.65/1.77 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e2) = e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10041])).
% 1.65/1.77 tff(10043,plain,
% 1.65/1.77 (~(op(e2, e2) = e1)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[121, 10042])).
% 1.65/1.77 tff(10044,plain,
% 1.65/1.77 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10039])).
% 1.65/1.77 tff(10045,plain,
% 1.65/1.77 (op(e2, op(e2, e2)) = e0),
% 1.65/1.77 inference(transitivity,[status(thm)],[10044, 9765, 251])).
% 1.65/1.77 tff(10046,plain,
% 1.65/1.77 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10045])).
% 1.65/1.77 tff(10047,plain,
% 1.65/1.77 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (e1 = op(e2, e0))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10046])).
% 1.65/1.77 tff(10048,plain,
% 1.65/1.77 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 1.65/1.77 inference(transitivity,[status(thm)],[10047, 16])).
% 1.65/1.77 tff(10049,plain,
% 1.65/1.77 ((~(e1 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e0) = e1))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10048])).
% 1.65/1.77 tff(10050,plain,
% 1.65/1.77 (e3 = op(e2, e2)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[10038, 1796])).
% 1.65/1.77 tff(10051,plain,
% 1.65/1.77 (op(e2, op(e0, e3)) = op(e2, op(e2, e2))),
% 1.65/1.77 inference(symmetry,[status(thm)],[10044])).
% 1.65/1.77 tff(10052,plain,
% 1.65/1.77 (e0 = op(e2, op(e2, e2))),
% 1.65/1.77 inference(transitivity,[status(thm)],[252, 10034, 10051])).
% 1.65/1.77 tff(10053,plain,
% 1.65/1.77 (~(e1 = op(e2, op(e2, op(e2, e2))))),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[1810, 10052, 10050])).
% 1.65/1.77 tff(10054,plain,
% 1.65/1.77 (~(op(e2, e0) = e1)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[10053, 10049])).
% 1.65/1.77 tff(10055,plain,
% 1.65/1.77 (op(e2, e1) = e1),
% 1.65/1.77 inference(unit_resolution,[status(thm)],[345, 10054, 76, 10043])).
% 1.65/1.77 tff(10056,plain,
% 1.65/1.77 ((op(e2, e1) = e2) <=> (e1 = e2)),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10055])).
% 1.65/1.77 tff(10057,plain,
% 1.65/1.77 ((e1 = e2) <=> (op(e2, e1) = e2)),
% 1.65/1.77 inference(symmetry,[status(thm)],[10056])).
% 1.65/1.77 tff(10058,plain,
% 1.65/1.77 ((~(e1 = e2)) <=> (~(op(e2, e1) = e2))),
% 1.65/1.77 inference(monotonicity,[status(thm)],[10057])).
% 1.65/1.77 tff(10059,plain,
% 1.65/1.77 (~(op(e2, e1) = e2)),
% 1.65/1.77 inference(modus_ponens,[status(thm)],[708, 10058])).
% 1.65/1.77 tff(10060,plain,
% 1.65/1.77 (op(e0, e1) = e2),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[1993, 10059, 9684, 9681])).
% 1.67/1.77 tff(10061,plain,
% 1.67/1.77 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10060])).
% 1.67/1.77 tff(10062,plain,
% 1.67/1.77 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10061, 1])).
% 1.67/1.77 tff(10063,plain,
% 1.67/1.77 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 1.67/1.77 inference(symmetry,[status(thm)],[10062])).
% 1.67/1.77 tff(10064,plain,
% 1.67/1.77 ((~(e0 = e2)) <=> (~(op(e0, e1) = e0))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10063])).
% 1.67/1.77 tff(10065,plain,
% 1.67/1.77 (~(op(e0, e1) = e0)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[14, 10064])).
% 1.67/1.77 tff(10066,plain,
% 1.67/1.77 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10038])).
% 1.67/1.77 tff(10067,plain,
% 1.67/1.77 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10066, 3423])).
% 1.67/1.77 tff(10068,plain,
% 1.67/1.77 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10067])).
% 1.67/1.77 tff(10069,plain,
% 1.67/1.77 (~(op(e3, e2) = e3)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[1546, 10068])).
% 1.67/1.77 tff(10070,plain,
% 1.67/1.77 ((e1 = op(e3, op(e3, e3))) <=> (e1 = op(e3, e2))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[2814])).
% 1.67/1.77 tff(10071,plain,
% 1.67/1.77 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e1)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10070, 7171])).
% 1.67/1.77 tff(10072,plain,
% 1.67/1.77 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 1.67/1.77 inference(symmetry,[status(thm)],[10071])).
% 1.67/1.77 tff(10073,plain,
% 1.67/1.77 ((op(e3, e1) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[4731])).
% 1.67/1.77 tff(10074,plain,
% 1.67/1.77 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10073, 4959])).
% 1.67/1.77 tff(10075,plain,
% 1.67/1.77 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10074])).
% 1.67/1.77 tff(10076,plain,
% 1.67/1.77 (~(op(e3, e2) = e0)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[3429, 10075])).
% 1.67/1.77 tff(10077,plain,
% 1.67/1.77 (op(e3, e2) = e1),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[1898, 10076, 1890, 9699])).
% 1.67/1.77 tff(10078,plain,
% 1.67/1.77 (e1 = op(e3, op(e3, e3))),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[10077, 10072])).
% 1.67/1.77 tff(10079,plain,
% 1.67/1.77 (op(e3, op(e3, e2)) = op(e3, op(e3, op(e3, e3)))),
% 1.67/1.77 inference(symmetry,[status(thm)],[6490])).
% 1.67/1.77 tff(10080,plain,
% 1.67/1.77 (op(e3, op(e3, e2)) = op(e3, e1)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10077])).
% 1.67/1.77 tff(10081,plain,
% 1.67/1.77 (op(e3, e1) = op(e3, op(e3, e2))),
% 1.67/1.77 inference(symmetry,[status(thm)],[10080])).
% 1.67/1.77 tff(10082,plain,
% 1.67/1.77 (e0 = op(e3, op(e3, op(e3, e3)))),
% 1.67/1.77 inference(transitivity,[status(thm)],[4734, 10081, 10079])).
% 1.67/1.77 tff(10083,plain,
% 1.67/1.77 ($false),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[2852, 10082, 10078, 2813])).
% 1.67/1.77 tff(10084,plain,((~(op(e3, e1) = e0)) | (~(op(e3, e3) = e2)) | (op(e3, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.77 tff(10085,plain,
% 1.67/1.77 (~(op(e3, e1) = e0)),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[10084, 10069, 2812])).
% 1.67/1.77 tff(10086,plain,
% 1.67/1.77 (op(e1, e1) = e0),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[292, 10085, 7791, 10065])).
% 1.67/1.77 tff(10087,plain,
% 1.67/1.77 (op(e3, op(e1, e1)) = op(op(e0, e3), e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[1870, 10086])).
% 1.67/1.77 tff(10088,plain,
% 1.67/1.77 (e0 = op(e1, e1)),
% 1.67/1.77 inference(symmetry,[status(thm)],[10086])).
% 1.67/1.77 tff(10089,plain,
% 1.67/1.77 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[251])).
% 1.67/1.77 tff(10090,plain,
% 1.67/1.77 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10089])).
% 1.67/1.77 tff(10091,plain,
% 1.67/1.77 (~(op(e2, e0) = e0)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[989, 10090])).
% 1.67/1.77 tff(10092,plain,
% 1.67/1.77 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10038])).
% 1.67/1.77 tff(10093,plain,
% 1.67/1.77 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10092])).
% 1.67/1.77 tff(10094,plain,
% 1.67/1.77 (~(op(e2, e0) = e3)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[2228, 10093])).
% 1.67/1.77 tff(10095,plain,
% 1.67/1.77 (op(e2, e0) = e2),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[765, 10054, 10094, 10091])).
% 1.67/1.77 tff(10096,plain,
% 1.67/1.77 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10095])).
% 1.67/1.77 tff(10097,plain,
% 1.67/1.77 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10096])).
% 1.67/1.77 tff(10098,plain,
% 1.67/1.77 (~(op(e1, e0) = e2)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[756, 10097])).
% 1.67/1.77 tff(10099,plain,
% 1.67/1.77 (op(e1, e2) = e2),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[2285, 10098, 72, 9681])).
% 1.67/1.77 tff(10100,plain,
% 1.67/1.77 ((op(e1, e2) = e0) <=> (e2 = e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10099])).
% 1.67/1.77 tff(10101,plain,
% 1.67/1.77 ((op(e1, e2) = e0) <=> (e0 = e2)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10100, 1])).
% 1.67/1.77 tff(10102,plain,
% 1.67/1.77 ((e0 = e2) <=> (op(e1, e2) = e0)),
% 1.67/1.77 inference(symmetry,[status(thm)],[10101])).
% 1.67/1.77 tff(10103,plain,
% 1.67/1.77 ((~(e0 = e2)) <=> (~(op(e1, e2) = e0))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10102])).
% 1.67/1.77 tff(10104,plain,
% 1.67/1.77 (~(op(e1, e2) = e0)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[14, 10103])).
% 1.67/1.77 tff(10105,plain,
% 1.67/1.77 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[1869])).
% 1.67/1.77 tff(10106,plain,
% 1.67/1.77 ((op(e0, e2) = op(e0, e3)) <=> (op(op(e2, e3), e2) = e3)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10105, 5090])).
% 1.67/1.77 tff(10107,plain,
% 1.67/1.77 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10106])).
% 1.67/1.77 tff(10108,plain,
% 1.67/1.77 (~(op(op(e2, e3), e2) = e3)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[918, 10107])).
% 1.67/1.77 tff(10109,plain,
% 1.67/1.77 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[1934, 10108])).
% 1.67/1.77 tff(10110,plain,
% 1.67/1.77 (op(op(e2, e0), e0) = op(e2, e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10095])).
% 1.67/1.77 tff(10111,plain,
% 1.67/1.77 (op(op(e2, e0), e0) = e2),
% 1.67/1.77 inference(transitivity,[status(thm)],[10110, 10095])).
% 1.67/1.77 tff(10112,plain,
% 1.67/1.77 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[1945, 10111])).
% 1.67/1.77 tff(10113,plain,
% 1.67/1.77 (op(op(e0, e1), e0) = op(e2, e0)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10060])).
% 1.67/1.77 tff(10114,plain,
% 1.67/1.77 (op(op(e0, e1), e0) = e2),
% 1.67/1.77 inference(transitivity,[status(thm)],[10113, 10095])).
% 1.67/1.77 tff(10115,plain,
% 1.67/1.77 ((op(op(e0, e1), e0) = e1) <=> (e2 = e1)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10114])).
% 1.67/1.77 tff(10116,plain,
% 1.67/1.77 ((op(op(e0, e1), e0) = e1) <=> (e1 = e2)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10115, 69])).
% 1.67/1.77 tff(10117,plain,
% 1.67/1.77 ((e1 = e2) <=> (op(op(e0, e1), e0) = e1)),
% 1.67/1.77 inference(symmetry,[status(thm)],[10116])).
% 1.67/1.77 tff(10118,plain,
% 1.67/1.77 ((~(e1 = e2)) <=> (~(op(op(e0, e1), e0) = e1))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10117])).
% 1.67/1.77 tff(10119,plain,
% 1.67/1.77 (~(op(op(e0, e1), e0) = e1)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[708, 10118])).
% 1.67/1.77 tff(10120,plain,
% 1.67/1.77 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[1461, 10119])).
% 1.67/1.77 tff(10121,plain,
% 1.67/1.77 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10099])).
% 1.67/1.77 tff(10122,plain,
% 1.67/1.77 (op(e1, op(e1, e2)) = e2),
% 1.67/1.77 inference(transitivity,[status(thm)],[10121, 10099])).
% 1.67/1.77 tff(10123,plain,
% 1.67/1.77 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[2377, 10122])).
% 1.67/1.77 tff(10124,plain,
% 1.67/1.77 ((op(e2, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10055])).
% 1.67/1.77 tff(10125,plain,
% 1.67/1.77 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.67/1.77 inference(transitivity,[status(thm)],[10124, 7793])).
% 1.67/1.77 tff(10126,plain,
% 1.67/1.77 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.67/1.77 inference(monotonicity,[status(thm)],[10125])).
% 1.67/1.77 tff(10127,plain,
% 1.67/1.77 (~(op(e3, e1) = e1)),
% 1.67/1.77 inference(modus_ponens,[status(thm)],[402, 10126])).
% 1.67/1.77 tff(10128,plain,
% 1.67/1.77 (op(e3, e1) = e3),
% 1.67/1.77 inference(unit_resolution,[status(thm)],[446, 10085, 9684, 10127])).
% 1.67/1.77 tff(10129,plain,
% 1.67/1.77 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10128])).
% 1.67/1.78 tff(10130,plain,
% 1.67/1.78 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10129])).
% 1.67/1.78 tff(10131,plain,
% 1.67/1.78 (~(op(e1, e1) = e3)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[945, 10130])).
% 1.67/1.78 tff(10132,plain,
% 1.67/1.78 (op(e1, e0) = e3),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[247, 10131, 9672, 75])).
% 1.67/1.78 tff(10133,plain,
% 1.67/1.78 (op(op(e1, e0), e1) = op(e3, e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10132])).
% 1.67/1.78 tff(10134,plain,
% 1.67/1.78 (op(op(e1, e0), e1) = e3),
% 1.67/1.78 inference(transitivity,[status(thm)],[10133, 10128])).
% 1.67/1.78 tff(10135,plain,
% 1.67/1.78 ((op(op(e1, e0), e1) = e0) <=> (e3 = op(e1, e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10134, 10088])).
% 1.67/1.78 tff(10136,plain,
% 1.67/1.78 ((op(op(e1, e0), e1) = e0) <=> (op(e1, e1) = e3)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10135, 1112])).
% 1.67/1.78 tff(10137,plain,
% 1.67/1.78 ((op(e1, e1) = e3) <=> (op(op(e1, e0), e1) = e0)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10136])).
% 1.67/1.78 tff(10138,plain,
% 1.67/1.78 ((~(op(e1, e1) = e3)) <=> (~(op(op(e1, e0), e1) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10137])).
% 1.67/1.78 tff(10139,plain,
% 1.67/1.78 (~(op(op(e1, e0), e1) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[10131, 10138])).
% 1.67/1.78 tff(10140,plain,
% 1.67/1.78 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1302, 10139])).
% 1.67/1.78 tff(10141,plain,
% 1.67/1.78 (op(op(e3, e1), e1) = op(e3, e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10128])).
% 1.67/1.78 tff(10142,plain,
% 1.67/1.78 (op(op(e3, e1), e1) = e3),
% 1.67/1.78 inference(transitivity,[status(thm)],[10141, 10128])).
% 1.67/1.78 tff(10143,plain,
% 1.67/1.78 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[2416, 10142])).
% 1.67/1.78 tff(10144,plain,
% 1.67/1.78 (op(e2, op(e2, e1)) = op(e2, e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10055])).
% 1.67/1.78 tff(10145,plain,
% 1.67/1.78 (op(e2, op(e2, e1)) = e1),
% 1.67/1.78 inference(transitivity,[status(thm)],[10144, 10055])).
% 1.67/1.78 tff(10146,plain,
% 1.67/1.78 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1355, 10145])).
% 1.67/1.78 tff(10147,plain,
% 1.67/1.78 (op(e3, e2) = e1),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1898, 85, 1890, 2386])).
% 1.67/1.78 tff(10148,plain,
% 1.67/1.78 (op(op(e3, e2), e3) = op(e1, op(e0, e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10147, 1870])).
% 1.67/1.78 tff(10149,plain,
% 1.67/1.78 (op(op(e3, e2), e3) = e1),
% 1.67/1.78 inference(transitivity,[status(thm)],[10148, 9798, 132])).
% 1.67/1.78 tff(10150,plain,
% 1.67/1.78 ((op(op(e3, e2), e3) = e2) <=> (e1 = e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10149])).
% 1.67/1.78 tff(10151,plain,
% 1.67/1.78 ((e1 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10150])).
% 1.67/1.78 tff(10152,plain,
% 1.67/1.78 ((~(e1 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10151])).
% 1.67/1.78 tff(10153,plain,
% 1.67/1.78 (~(op(op(e3, e2), e3) = e2)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[708, 10152])).
% 1.67/1.78 tff(10154,plain,
% 1.67/1.78 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[2408, 10153])).
% 1.67/1.78 tff(10155,plain,
% 1.67/1.78 (op(e0, e2) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[973, 85, 17, 1947])).
% 1.67/1.78 tff(10156,plain,
% 1.67/1.78 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10155])).
% 1.67/1.78 tff(10157,plain,
% 1.67/1.78 (op(op(e0, e2), e2) = e0),
% 1.67/1.78 inference(transitivity,[status(thm)],[10156, 10155])).
% 1.67/1.78 tff(10158,plain,
% 1.67/1.78 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1956, 10157])).
% 1.67/1.78 tff(10159,plain,
% 1.67/1.78 (op(e3, e0) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1916, 85, 656, 183])).
% 1.67/1.78 tff(10160,plain,
% 1.67/1.78 (op(e3, op(e1, e1)) = op(op(e0, e3), e0)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[1870, 249])).
% 1.67/1.78 tff(10161,plain,
% 1.67/1.78 (e0 = op(e1, e1)),
% 1.67/1.78 inference(symmetry,[status(thm)],[249])).
% 1.67/1.78 tff(10162,plain,
% 1.67/1.78 (op(e3, e0) = op(e1, e1)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10159, 10161])).
% 1.67/1.78 tff(10163,plain,
% 1.67/1.78 (op(e3, op(e3, e0)) = op(e3, op(e1, e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10162])).
% 1.67/1.78 tff(10164,plain,
% 1.67/1.78 (op(e3, op(e3, e0)) = e0),
% 1.67/1.78 inference(transitivity,[status(thm)],[10163, 10160, 9663, 10159])).
% 1.67/1.78 tff(10165,plain,
% 1.67/1.78 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1345, 10164])).
% 1.67/1.78 tff(10166,plain,
% 1.67/1.78 ($false),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1459, 10165, 10158, 1936, 1275, 3342, 1304, 1357, 10154, 1358, 4549, 2421, 1347])).
% 1.67/1.78 tff(10167,plain,((op(e3, e2) = e0) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e1, e3) = e1)) | (~(op(e0, e3) = e3)) | (~(op(e1, e1) = e0)) | (op(e3, e3) = e0) | (op(e3, e1) = e0) | (op(e2, e2) = e0) | (op(e1, e2) = e0) | (op(e3, e2) = e3) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.78 tff(10168,plain,
% 1.67/1.78 (op(e3, e2) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[10167, 10146, 10143, 5469, 1304, 10140, 10123, 10120, 10112, 10109, 9668, 1869, 10086, 9696, 10085, 5023, 10104, 10069, 9699])).
% 1.67/1.78 tff(10169,plain,
% 1.67/1.78 (op(e3, e2) = op(e1, e1)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10168, 10088])).
% 1.67/1.78 tff(10170,plain,
% 1.67/1.78 (op(e3, op(e3, e2)) = op(e3, op(e1, e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10169])).
% 1.67/1.78 tff(10171,plain,
% 1.67/1.78 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.67/1.78 inference(transitivity,[status(thm)],[6490, 10170, 10087, 9663])).
% 1.67/1.78 tff(10172,plain,
% 1.67/1.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10171])).
% 1.67/1.78 tff(10173,plain,
% 1.67/1.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10172, 6411])).
% 1.67/1.78 tff(10174,plain,
% 1.67/1.78 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10173])).
% 1.67/1.78 tff(10175,plain,
% 1.67/1.78 (e0 = op(e3, op(e3, e3))),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[10168, 6497])).
% 1.67/1.78 tff(10176,plain,
% 1.67/1.78 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[5879, 10175, 2813])).
% 1.67/1.78 tff(10177,plain,
% 1.67/1.78 (~(op(e3, e0) = e1)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[10176, 10174])).
% 1.67/1.78 tff(10178,plain,
% 1.67/1.78 ((op(e3, e2) = e1) <=> (op(e1, e1) = e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10169])).
% 1.67/1.78 tff(10179,plain,
% 1.67/1.78 ((op(e1, e1) = e1) <=> (op(e3, e2) = e1)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10178])).
% 1.67/1.78 tff(10180,plain,
% 1.67/1.78 ((~(op(e1, e1) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10179])).
% 1.67/1.78 tff(10181,plain,
% 1.67/1.78 (~(op(e3, e2) = e1)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[9958, 10180])).
% 1.67/1.78 tff(10182,plain,
% 1.67/1.78 (op(e3, e0) = e1),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[939, 10181, 9667, 10127])).
% 1.67/1.78 tff(10183,plain,
% 1.67/1.78 ($false),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[10182, 10177])).
% 1.67/1.78 tff(10184,plain,((op(e1, e2) = e3) | (~(op(e0, e3) = e3)) | (~(op(e3, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e3) = e2) | (op(e2, e3) = e1) | (~(op(e2, e3) = e0)) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.78 tff(10185,plain,
% 1.67/1.78 (op(e1, e2) = e3),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[10184, 9658, 9643, 5425, 72, 76, 9662, 121, 80, 79])).
% 1.67/1.78 tff(10186,plain,
% 1.67/1.78 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e0)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[9662])).
% 1.67/1.78 tff(10187,plain,
% 1.67/1.78 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10186])).
% 1.67/1.78 tff(10188,plain,
% 1.67/1.78 (~(op(e0, e3) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[964, 10187])).
% 1.67/1.78 tff(10189,plain,
% 1.67/1.78 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[9662])).
% 1.67/1.78 tff(10190,plain,
% 1.67/1.78 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10189])).
% 1.67/1.78 tff(10191,plain,
% 1.67/1.78 (~(op(e2, e0) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[989, 10190])).
% 1.67/1.78 tff(10192,plain,
% 1.67/1.78 (op(op(e2, e3), e2) = op(e0, e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[9662])).
% 1.67/1.78 tff(10193,plain,
% 1.67/1.78 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e2) = e3)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10192])).
% 1.67/1.78 tff(10194,plain,
% 1.67/1.78 ((op(e0, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10193])).
% 1.67/1.78 tff(10195,plain,
% 1.67/1.78 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[9658])).
% 1.67/1.78 tff(10196,plain,
% 1.67/1.78 ((op(e0, e2) = op(e0, e3)) <=> (op(op(e2, e3), e2) = e3)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10195, 10194])).
% 1.67/1.78 tff(10197,plain,
% 1.67/1.78 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10196])).
% 1.67/1.78 tff(10198,plain,
% 1.67/1.78 (~(op(op(e2, e3), e2) = e3)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[918, 10197])).
% 1.67/1.78 tff(10199,plain,
% 1.67/1.78 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1934, 10198])).
% 1.67/1.78 tff(10200,plain,
% 1.67/1.78 ((e0 = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 1.67/1.78 inference(commutativity,[status(thm)],[])).
% 1.67/1.78 tff(10201,plain,
% 1.67/1.78 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[2899])).
% 1.67/1.78 tff(10202,plain,
% 1.67/1.78 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10201, 3423])).
% 1.67/1.78 tff(10203,plain,
% 1.67/1.78 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10202])).
% 1.67/1.78 tff(10204,plain,
% 1.67/1.78 (~(op(e3, e2) = e3)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[2292, 10203])).
% 1.67/1.78 tff(10205,plain,
% 1.67/1.78 (~(op(e3, e1) = e0)),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[10084, 10204, 2812])).
% 1.67/1.78 tff(10206,plain,
% 1.67/1.78 (op(e0, e1) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[292, 84, 7791, 10205])).
% 1.67/1.78 tff(10207,plain,
% 1.67/1.78 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10206])).
% 1.67/1.78 tff(10208,plain,
% 1.67/1.78 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10207, 10200])).
% 1.67/1.78 tff(10209,plain,
% 1.67/1.78 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10208])).
% 1.67/1.78 tff(10210,plain,
% 1.67/1.78 (~(op(e0, e2) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[2102, 10209])).
% 1.67/1.78 tff(10211,plain,
% 1.67/1.78 (op(e1, e2) = op(e0, e3)),
% 1.67/1.78 inference(transitivity,[status(thm)],[2899, 1870])).
% 1.67/1.78 tff(10212,plain,
% 1.67/1.78 ((op(e1, e2) = e0) <=> (op(e0, e3) = e0)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10211])).
% 1.67/1.78 tff(10213,plain,
% 1.67/1.78 ((op(e0, e3) = e0) <=> (op(e1, e2) = e0)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10212])).
% 1.67/1.78 tff(10214,plain,
% 1.67/1.78 ((~(op(e0, e3) = e0)) <=> (~(op(e1, e2) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10213])).
% 1.67/1.78 tff(10215,plain,
% 1.67/1.78 (~(op(e1, e2) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[1087, 10214])).
% 1.67/1.78 tff(10216,plain,
% 1.67/1.78 (op(e1, e0) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1830, 84, 80, 10215])).
% 1.67/1.78 tff(10217,plain,
% 1.67/1.78 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10216])).
% 1.67/1.78 tff(10218,plain,
% 1.67/1.78 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10217, 8115])).
% 1.67/1.78 tff(10219,plain,
% 1.67/1.78 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10218])).
% 1.67/1.78 tff(10220,plain,
% 1.67/1.78 (~(op(e3, e0) = e0)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[410, 10219])).
% 1.67/1.78 tff(10221,plain,
% 1.67/1.78 (op(e3, e2) = e0),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1916, 10220, 9696, 10205])).
% 1.67/1.78 tff(10222,plain,
% 1.67/1.78 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[2899])).
% 1.67/1.78 tff(10223,plain,
% 1.67/1.78 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10222])).
% 1.67/1.78 tff(10224,plain,
% 1.67/1.78 (~(op(e1, e1) = e3)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[1604, 10223])).
% 1.67/1.78 tff(10225,plain,
% 1.67/1.78 ((e1 = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 1.67/1.78 inference(commutativity,[status(thm)],[])).
% 1.67/1.78 tff(10226,plain,
% 1.67/1.78 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10221])).
% 1.67/1.78 tff(10227,plain,
% 1.67/1.78 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10226])).
% 1.67/1.78 tff(10228,plain,
% 1.67/1.78 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10227])).
% 1.67/1.78 tff(10229,plain,
% 1.67/1.78 (~(op(e3, e2) = e1)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[26, 10228])).
% 1.67/1.78 tff(10230,plain,
% 1.67/1.78 (op(e3, op(e3, e2)) = op(op(e0, e3), e0)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[1870, 10221])).
% 1.67/1.78 tff(10231,plain,
% 1.67/1.78 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.67/1.78 inference(transitivity,[status(thm)],[6490, 10230, 9663])).
% 1.67/1.78 tff(10232,plain,
% 1.67/1.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10231])).
% 1.67/1.78 tff(10233,plain,
% 1.67/1.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10232, 6411])).
% 1.67/1.78 tff(10234,plain,
% 1.67/1.78 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10233])).
% 1.67/1.78 tff(10235,plain,
% 1.67/1.78 (e0 = op(e3, op(e3, e3))),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[10221, 6497])).
% 1.67/1.78 tff(10236,plain,
% 1.67/1.78 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[5879, 10235, 2813])).
% 1.67/1.78 tff(10237,plain,
% 1.67/1.78 (~(op(e3, e0) = e1)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[10236, 10234])).
% 1.67/1.78 tff(10238,plain,
% 1.67/1.78 (op(e3, e1) = e1),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[939, 10237, 9667, 10229])).
% 1.67/1.78 tff(10239,plain,
% 1.67/1.78 ((op(e3, e1) = e3) <=> (e1 = op(e0, e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10238, 1870])).
% 1.67/1.78 tff(10240,plain,
% 1.67/1.78 ((op(e3, e1) = e3) <=> (op(e0, e3) = e1)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10239, 10225])).
% 1.67/1.78 tff(10241,plain,
% 1.67/1.78 ((op(e0, e3) = e1) <=> (op(e3, e1) = e3)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10240])).
% 1.67/1.78 tff(10242,plain,
% 1.67/1.78 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e1) = e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10241])).
% 1.67/1.78 tff(10243,plain,
% 1.67/1.78 (~(op(e3, e1) = e3)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[121, 10242])).
% 1.67/1.78 tff(10244,plain,
% 1.67/1.78 (op(e2, e1) = e3),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[1730, 10243, 9934, 10224])).
% 1.67/1.78 tff(10245,plain,
% 1.67/1.78 (op(op(e2, e1), e2) = op(e3, e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10244])).
% 1.67/1.78 tff(10246,plain,
% 1.67/1.78 (op(op(e2, e1), e2) = e0),
% 1.67/1.78 inference(transitivity,[status(thm)],[10245, 10221])).
% 1.67/1.78 tff(10247,plain,
% 1.67/1.78 ((op(op(e2, e1), e2) = e1) <=> (e0 = e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10246])).
% 1.67/1.78 tff(10248,plain,
% 1.67/1.78 ((e0 = e1) <=> (op(op(e2, e1), e2) = e1)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10247])).
% 1.67/1.78 tff(10249,plain,
% 1.67/1.78 ((~(e0 = e1)) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10248])).
% 1.67/1.78 tff(10250,plain,
% 1.67/1.78 (~(op(op(e2, e1), e2) = e1)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[26, 10249])).
% 1.67/1.78 tff(10251,plain,
% 1.67/1.78 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[5808, 10250])).
% 1.67/1.78 tff(10252,plain,
% 1.67/1.78 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10206])).
% 1.67/1.78 tff(10253,plain,
% 1.67/1.78 (op(op(e0, e1), e1) = e0),
% 1.67/1.78 inference(transitivity,[status(thm)],[10252, 10206])).
% 1.67/1.78 tff(10254,plain,
% 1.67/1.78 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[2650, 10253])).
% 1.67/1.78 tff(10255,plain,
% 1.67/1.78 ((op(op(e1, e2), e1) = e2) <=> (op(e3, e1) = e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[9365])).
% 1.67/1.78 tff(10256,plain,
% 1.67/1.78 ((op(e3, e1) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 1.67/1.78 inference(symmetry,[status(thm)],[10255])).
% 1.67/1.78 tff(10257,plain,
% 1.67/1.78 ((~(op(e3, e1) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10256])).
% 1.67/1.78 tff(10258,plain,
% 1.67/1.78 (~(op(op(e1, e2), e1) = e2)),
% 1.67/1.78 inference(modus_ponens,[status(thm)],[9684, 10257])).
% 1.67/1.78 tff(10259,plain,
% 1.67/1.78 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.67/1.78 inference(unit_resolution,[status(thm)],[5959, 10258])).
% 1.67/1.78 tff(10260,plain,
% 1.67/1.78 (op(op(e3, e2), e3) = op(e0, op(e0, e3))),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10221, 1870])).
% 1.67/1.78 tff(10261,plain,
% 1.67/1.78 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.67/1.78 inference(transitivity,[status(thm)],[10260, 1906])).
% 1.67/1.78 tff(10262,plain,
% 1.67/1.78 ((op(op(e3, e2), e3) = e2) <=> (op(e0, e3) = e2)),
% 1.67/1.78 inference(monotonicity,[status(thm)],[10261])).
% 1.67/1.78 tff(10263,plain,
% 1.67/1.79 ((op(e0, e3) = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10262])).
% 1.67/1.79 tff(10264,plain,
% 1.67/1.79 ((~(op(e0, e3) = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10263])).
% 1.67/1.79 tff(10265,plain,
% 1.67/1.79 (~(op(op(e3, e2), e3) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[79, 10264])).
% 1.67/1.79 tff(10266,plain,
% 1.67/1.79 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2408, 10265])).
% 1.67/1.79 tff(10267,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = op(e1, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10216])).
% 1.67/1.79 tff(10268,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = e0),
% 1.67/1.79 inference(transitivity,[status(thm)],[10267, 10216])).
% 1.67/1.79 tff(10269,plain,
% 1.67/1.79 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1836, 10268])).
% 1.67/1.79 tff(10270,plain,
% 1.67/1.79 (op(e3, op(e3, e1)) = op(e3, e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10238])).
% 1.67/1.79 tff(10271,plain,
% 1.67/1.79 (op(e3, op(e3, e1)) = e1),
% 1.67/1.79 inference(transitivity,[status(thm)],[10270, 10238])).
% 1.67/1.79 tff(10272,plain,
% 1.67/1.79 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2594, 10271])).
% 1.67/1.79 tff(10273,plain,
% 1.67/1.79 (op(e3, e0) = e3),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[5422, 10237, 9955, 10220])).
% 1.67/1.79 tff(10274,plain,
% 1.67/1.79 (op(e3, e0) = op(e0, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10273, 1870])).
% 1.67/1.79 tff(10275,plain,
% 1.67/1.79 (op(op(e3, e0), e0) = op(op(e0, e3), e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10274])).
% 1.67/1.79 tff(10276,plain,
% 1.67/1.79 (op(op(e3, e0), e0) = e3),
% 1.67/1.79 inference(transitivity,[status(thm)],[10275, 9663, 10273])).
% 1.67/1.79 tff(10277,plain,
% 1.67/1.79 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[4026, 10276])).
% 1.67/1.79 tff(10278,plain,
% 1.67/1.79 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10273])).
% 1.67/1.79 tff(10279,plain,
% 1.67/1.79 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10278])).
% 1.67/1.79 tff(10280,plain,
% 1.67/1.79 (~(op(e2, e0) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[747, 10279])).
% 1.67/1.79 tff(10281,plain,
% 1.67/1.79 (op(op(e2, e0), e2) = op(e1, e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[767])).
% 1.67/1.79 tff(10282,plain,
% 1.67/1.79 (op(e1, e2) = op(op(e2, e0), e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10281])).
% 1.67/1.79 tff(10283,plain,
% 1.67/1.79 (op(e0, e3) = e0),
% 1.67/1.79 inference(transitivity,[status(thm)],[1869, 2900, 10282, 7965])).
% 1.67/1.79 tff(10284,plain,
% 1.67/1.79 ($false),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1087, 10283])).
% 1.67/1.79 tff(10285,plain,((~(op(e2, e0) = e1)) | (op(e0, e3) = e0) | (~(op(op(e2, e0), e2) = e0)) | (~(op(e1, e2) = e3)) | (~(op(e0, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.79 tff(10286,plain,
% 1.67/1.79 (~(op(e2, e0) = e1)),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10285, 7959, 1087, 2899, 1869])).
% 1.67/1.79 tff(10287,plain,
% 1.67/1.79 (op(e2, e0) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[765, 10286, 3272, 983])).
% 1.67/1.79 tff(10288,plain,
% 1.67/1.79 (op(op(e2, e0), e0) = op(e2, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10287])).
% 1.67/1.79 tff(10289,plain,
% 1.67/1.79 (op(op(e2, e0), e0) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10288, 10287])).
% 1.67/1.79 tff(10290,plain,
% 1.67/1.79 (~(op(op(e2, e0), e0) = e2)),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1945, 7958])).
% 1.67/1.79 tff(10291,plain,
% 1.67/1.79 ($false),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10290, 10289])).
% 1.67/1.79 tff(10292,plain,(((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))) | (op(e2, e0) = e3) | (op(e2, e0) = e0) | (op(e0, e3) = e0) | (~(op(e1, e2) = e3)) | (~(op(e0, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.79 tff(10293,plain,
% 1.67/1.79 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10292, 10280, 983, 1087, 2899, 1869])).
% 1.67/1.79 tff(10294,plain,
% 1.67/1.79 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1459, 10293, 10277, 10272, 5469, 1304, 10269, 10266, 10259, 10254, 10251, 1347])).
% 1.67/1.79 tff(10295,plain,
% 1.67/1.79 (op(op(e0, e2), e0) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2446, 10294])).
% 1.67/1.79 tff(10296,assumption,(op(op(e0, e2), e0) = e2), introduced(assumption)).
% 1.67/1.79 tff(10297,plain,
% 1.67/1.79 (op(op(e0, e2), e0) = op(e1, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[8026])).
% 1.67/1.79 tff(10298,plain,
% 1.67/1.79 (op(e1, e0) = op(op(e0, e2), e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10297])).
% 1.67/1.79 tff(10299,plain,
% 1.67/1.79 (e0 = op(e1, e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[6142])).
% 1.67/1.79 tff(10300,plain,
% 1.67/1.79 (e0 = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10299, 10298, 10296])).
% 1.67/1.79 tff(10301,plain,
% 1.67/1.79 ($false),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[14, 10300])).
% 1.67/1.79 tff(10302,plain,((~(op(e0, e2) = e1)) | (~(op(op(e0, e2), e0) = e2)) | (~(op(e1, e0) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.79 tff(10303,plain,
% 1.67/1.79 (~(op(e0, e2) = e1)),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10302, 10295, 10216])).
% 1.67/1.79 tff(10304,plain,
% 1.67/1.79 (op(e0, e2) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2745, 10303, 10210, 9688])).
% 1.67/1.79 tff(10305,plain,
% 1.67/1.79 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10304])).
% 1.67/1.79 tff(10306,plain,
% 1.67/1.79 (op(e0, op(e0, e2)) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10305, 10304])).
% 1.67/1.79 tff(10307,plain,
% 1.67/1.79 (~(op(e0, op(e0, e2)) = e2)),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1331, 10294])).
% 1.67/1.79 tff(10308,plain,
% 1.67/1.79 ($false),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10307, 10306])).
% 1.67/1.79 tff(10309,plain,((op(e1, e1) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e0) = e0) | (op(e0, e3) = e0) | (~(op(e1, e2) = e3)) | (~(op(e0, e3) = e3)) | (op(e0, e3) = e1) | (~(op(e3, e3) = e2)) | (op(e0, e3) = e2) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.79 tff(10310,plain,
% 1.67/1.79 (op(e1, e1) = e0),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10309, 10199, 5425, 10191, 10188, 10185, 9658, 121, 9643, 79, 80])).
% 1.67/1.79 tff(10311,plain,
% 1.67/1.79 (e0 = op(e1, e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[10310, 123])).
% 1.67/1.79 tff(10312,plain,
% 1.67/1.79 (op(e1, op(e1, e1)) = op(e1, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10310])).
% 1.67/1.79 tff(10313,plain,
% 1.67/1.79 ((e2 = op(e1, op(e1, e1))) <=> (e2 = op(e1, e0))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10312])).
% 1.67/1.79 tff(10314,plain,
% 1.67/1.79 ((e2 = op(e1, op(e1, e1))) <=> (op(e1, e0) = e2)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10313, 2154])).
% 1.67/1.79 tff(10315,plain,
% 1.67/1.79 ((op(e1, e0) = e2) <=> (e2 = op(e1, op(e1, e1)))),
% 1.67/1.79 inference(symmetry,[status(thm)],[10314])).
% 1.67/1.79 tff(10316,plain,
% 1.67/1.79 (e3 = op(e0, e3)),
% 1.67/1.79 inference(symmetry,[status(thm)],[9658])).
% 1.67/1.79 tff(10317,plain,
% 1.67/1.79 (op(e1, e2) = op(e0, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10185, 10316])).
% 1.67/1.79 tff(10318,plain,
% 1.67/1.79 ((op(e1, e2) = e2) <=> (op(e0, e3) = e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10317])).
% 1.67/1.79 tff(10319,plain,
% 1.67/1.79 ((op(e0, e3) = e2) <=> (op(e1, e2) = e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10318])).
% 1.67/1.79 tff(10320,plain,
% 1.67/1.79 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e2) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10319])).
% 1.67/1.79 tff(10321,plain,
% 1.67/1.79 (~(op(e1, e2) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[79, 10320])).
% 1.67/1.79 tff(10322,plain,
% 1.67/1.79 ((op(e1, e1) = e2) <=> (e0 = e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10310])).
% 1.67/1.79 tff(10323,plain,
% 1.67/1.79 ((e0 = e2) <=> (op(e1, e1) = e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10322])).
% 1.67/1.79 tff(10324,plain,
% 1.67/1.79 ((~(e0 = e2)) <=> (~(op(e1, e1) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10323])).
% 1.67/1.79 tff(10325,plain,
% 1.67/1.79 (~(op(e1, e1) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[14, 10324])).
% 1.67/1.79 tff(10326,plain,
% 1.67/1.79 (op(e1, e0) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2285, 10325, 72, 10321])).
% 1.67/1.79 tff(10327,plain,
% 1.67/1.79 (e2 = op(e1, op(e1, e1))),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[10326, 10315])).
% 1.67/1.79 tff(10328,plain,
% 1.67/1.79 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e0))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10312])).
% 1.67/1.79 tff(10329,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = op(e1, op(e1, op(e1, e1)))),
% 1.67/1.79 inference(symmetry,[status(thm)],[10328])).
% 1.67/1.79 tff(10330,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10326])).
% 1.67/1.79 tff(10331,plain,
% 1.67/1.79 (op(e1, e2) = op(e1, op(e1, e0))),
% 1.67/1.79 inference(symmetry,[status(thm)],[10330])).
% 1.67/1.79 tff(10332,plain,
% 1.67/1.79 (e3 = op(e1, e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10185])).
% 1.67/1.79 tff(10333,plain,
% 1.67/1.79 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.67/1.79 inference(transitivity,[status(thm)],[10332, 10331, 10329])).
% 1.67/1.79 tff(10334,plain,
% 1.67/1.79 ($false),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2198, 10333, 10327, 10311])).
% 1.67/1.79 tff(10335,plain,((op(e1, e3) = e2) | (op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.79 tff(10336,plain,
% 1.67/1.79 (op(e0, e3) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[10335, 121, 119, 72, 76, 80])).
% 1.67/1.79 tff(10337,plain,
% 1.67/1.79 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10336])).
% 1.67/1.79 tff(10338,plain,
% 1.67/1.79 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10337, 120])).
% 1.67/1.79 tff(10339,plain,
% 1.67/1.79 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10338])).
% 1.67/1.79 tff(10340,plain,
% 1.67/1.79 (~(op(e2, e3) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[964, 10339])).
% 1.67/1.79 tff(10341,plain,
% 1.67/1.79 (op(e2, e3) = e0),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[206, 10340, 76, 119])).
% 1.67/1.79 tff(10342,plain,
% 1.67/1.79 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10341])).
% 1.67/1.79 tff(10343,plain,
% 1.67/1.79 (op(e3, e0) = op(e3, op(e2, e3))),
% 1.67/1.79 inference(symmetry,[status(thm)],[10342])).
% 1.67/1.79 tff(10344,plain,
% 1.67/1.79 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10343])).
% 1.67/1.79 tff(10345,plain,
% 1.67/1.79 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10344])).
% 1.67/1.79 tff(10346,plain,
% 1.67/1.79 (e0 = op(e2, e3)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10341])).
% 1.67/1.79 tff(10347,plain,
% 1.67/1.79 (op(e3, e3) = e1),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[151, 121, 76, 87])).
% 1.67/1.79 tff(10348,plain,
% 1.67/1.79 ((op(e3, e3) = e0) <=> (e1 = e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10347])).
% 1.67/1.79 tff(10349,plain,
% 1.67/1.79 ((op(e3, e3) = e0) <=> (e0 = e1)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10348, 18])).
% 1.67/1.79 tff(10350,plain,
% 1.67/1.79 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10349])).
% 1.67/1.79 tff(10351,plain,
% 1.67/1.79 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10350])).
% 1.67/1.79 tff(10352,plain,
% 1.67/1.79 (~(op(e3, e3) = e0)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[26, 10351])).
% 1.67/1.79 tff(10353,plain,
% 1.67/1.79 (e2 = op(e0, e3)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10336])).
% 1.67/1.79 tff(10354,plain,
% 1.67/1.79 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[105])).
% 1.67/1.79 tff(10355,plain,
% 1.67/1.79 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10354])).
% 1.67/1.79 tff(10356,plain,
% 1.67/1.79 (~(op(e1, e1) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[619, 10355])).
% 1.67/1.79 tff(10357,plain,
% 1.67/1.79 (op(e1, e1) = e1),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[630, 10356, 68, 84])).
% 1.67/1.79 tff(10358,plain,
% 1.67/1.79 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10357])).
% 1.67/1.79 tff(10359,plain,
% 1.67/1.79 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10358, 7793])).
% 1.67/1.79 tff(10360,plain,
% 1.67/1.79 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10359])).
% 1.67/1.79 tff(10361,plain,
% 1.67/1.79 (~(op(e3, e1) = e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[945, 10360])).
% 1.67/1.79 tff(10362,plain,
% 1.67/1.79 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[105])).
% 1.67/1.79 tff(10363,plain,
% 1.67/1.79 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10362])).
% 1.67/1.79 tff(10364,plain,
% 1.67/1.79 (~(op(e0, e3) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[64, 10363])).
% 1.67/1.79 tff(10365,plain,
% 1.67/1.79 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10357])).
% 1.67/1.79 tff(10366,plain,
% 1.67/1.79 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10365])).
% 1.67/1.79 tff(10367,plain,
% 1.67/1.79 (~(op(e1, e0) = e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[737, 10366])).
% 1.67/1.79 tff(10368,plain,
% 1.67/1.79 (op(e1, op(e1, e3)) = e3),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[169, 105])).
% 1.67/1.79 tff(10369,plain,
% 1.67/1.79 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[162, 10368])).
% 1.67/1.79 tff(10370,plain,
% 1.67/1.79 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[2560])).
% 1.67/1.79 tff(10371,plain,
% 1.67/1.79 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10370])).
% 1.67/1.79 tff(10372,plain,
% 1.67/1.79 (op(e3, e0) = op(e3, op(e2, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[252])).
% 1.67/1.79 tff(10373,plain,
% 1.67/1.79 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10372])).
% 1.67/1.79 tff(10374,plain,
% 1.67/1.79 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[305])).
% 1.67/1.79 tff(10375,plain,
% 1.67/1.79 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10374])).
% 1.67/1.79 tff(10376,plain,
% 1.67/1.79 (~(op(e3, e0) = e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[157, 10375])).
% 1.67/1.79 tff(10377,plain,
% 1.67/1.79 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[2560])).
% 1.67/1.79 tff(10378,plain,
% 1.67/1.79 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10377])).
% 1.67/1.79 tff(10379,plain,
% 1.67/1.79 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10378])).
% 1.67/1.79 tff(10380,plain,
% 1.67/1.79 (~(op(e0, e1) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[818, 10379])).
% 1.67/1.79 tff(10381,plain,
% 1.67/1.79 (op(e2, e1) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1993, 82, 68, 10380])).
% 1.67/1.79 tff(10382,plain,
% 1.67/1.79 (op(e2, e1) = op(e0, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10381, 2560])).
% 1.67/1.79 tff(10383,plain,
% 1.67/1.79 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10382])).
% 1.67/1.79 tff(10384,plain,
% 1.67/1.79 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10383])).
% 1.67/1.79 tff(10385,plain,
% 1.67/1.79 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10384])).
% 1.67/1.79 tff(10386,plain,
% 1.67/1.79 (~(op(e2, e1) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[661, 10385])).
% 1.67/1.79 tff(10387,plain,
% 1.67/1.79 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10381])).
% 1.67/1.79 tff(10388,plain,
% 1.67/1.79 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10387])).
% 1.67/1.79 tff(10389,plain,
% 1.67/1.79 (~(op(e2, e0) = e2)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[1966, 10388])).
% 1.67/1.79 tff(10390,plain,
% 1.67/1.79 (op(e2, e0) = e3),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[3293, 10389, 2, 251, 10386, 124])).
% 1.67/1.79 tff(10391,plain,
% 1.67/1.79 ((op(e2, e0) = e1) <=> (e3 = e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10390])).
% 1.67/1.79 tff(10392,plain,
% 1.67/1.79 ((op(e2, e0) = e1) <=> (e1 = e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10391, 128])).
% 1.67/1.79 tff(10393,plain,
% 1.67/1.79 ((e1 = e3) <=> (op(e2, e0) = e1)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10392])).
% 1.67/1.79 tff(10394,plain,
% 1.67/1.79 ((~(e1 = e3)) <=> (~(op(e2, e0) = e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10393])).
% 1.67/1.79 tff(10395,plain,
% 1.67/1.79 (~(op(e2, e0) = e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[303, 10394])).
% 1.67/1.79 tff(10396,plain,
% 1.67/1.79 (op(e0, e0) = e1),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1480, 10395, 10376, 929])).
% 1.67/1.79 tff(10397,plain,
% 1.67/1.79 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10390])).
% 1.67/1.79 tff(10398,plain,
% 1.67/1.79 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10397])).
% 1.67/1.79 tff(10399,plain,
% 1.67/1.79 (~(op(e0, e0) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[359, 10398])).
% 1.67/1.79 tff(10400,plain,
% 1.67/1.79 (op(op(e2, e1), e1) = op(e2, e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10381])).
% 1.67/1.79 tff(10401,plain,
% 1.67/1.79 (op(op(e2, e1), e1) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10400, 10381])).
% 1.67/1.79 tff(10402,plain,
% 1.67/1.79 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2371, 10401])).
% 1.67/1.79 tff(10403,plain,
% 1.67/1.79 (op(e2, op(e2, e0)) = op(op(e0, e3), e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[2560, 10390])).
% 1.67/1.79 tff(10404,plain,
% 1.67/1.79 (op(e2, op(e2, e0)) = e0),
% 1.67/1.79 inference(transitivity,[status(thm)],[10403, 3277, 251])).
% 1.67/1.79 tff(10405,plain,
% 1.67/1.79 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2653, 10404])).
% 1.67/1.79 tff(10406,assumption,(op(e0, e0) = e1), introduced(assumption)).
% 1.67/1.79 tff(10407,plain,
% 1.67/1.79 (op(e0, e1) = e0),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[292, 183, 3346, 84])).
% 1.67/1.79 tff(10408,plain,
% 1.67/1.79 (op(e0, op(e0, e1)) = op(e0, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10407])).
% 1.67/1.79 tff(10409,plain,
% 1.67/1.79 (op(e0, op(e0, e1)) = e1),
% 1.67/1.79 inference(transitivity,[status(thm)],[10408, 10406])).
% 1.67/1.79 tff(10410,plain,
% 1.67/1.79 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2449, 10409])).
% 1.67/1.79 tff(10411,plain,
% 1.67/1.79 ((op(e3, e3) = e0) <=> (e1 = e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[305])).
% 1.67/1.79 tff(10412,plain,
% 1.67/1.79 ((op(e3, e3) = e0) <=> (e0 = e1)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10411, 18])).
% 1.67/1.79 tff(10413,plain,
% 1.67/1.79 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10412])).
% 1.67/1.79 tff(10414,plain,
% 1.67/1.79 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10413])).
% 1.67/1.79 tff(10415,plain,
% 1.67/1.79 (~(op(e3, e3) = e0)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[26, 10414])).
% 1.67/1.79 tff(10416,plain,
% 1.67/1.79 (op(e3, e0) = e0),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1916, 183, 85, 10415])).
% 1.67/1.79 tff(10417,plain,
% 1.67/1.79 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10416])).
% 1.67/1.79 tff(10418,plain,
% 1.67/1.79 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10417])).
% 1.67/1.79 tff(10419,plain,
% 1.67/1.79 (~(op(e1, e0) = e0)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[410, 10418])).
% 1.67/1.79 tff(10420,plain,
% 1.67/1.79 (op(e1, e2) = e0),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1830, 10419, 80, 84])).
% 1.67/1.79 tff(10421,plain,
% 1.67/1.79 (op(e1, op(e0, e3)) = op(e1, e2)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[2])).
% 1.67/1.79 tff(10422,plain,
% 1.67/1.79 (op(e1, e0) = e2),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[728, 10419, 2168, 929])).
% 1.67/1.79 tff(10423,plain,
% 1.67/1.79 (op(e1, e0) = op(e0, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10422, 2560])).
% 1.67/1.79 tff(10424,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = op(e1, op(e0, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10423])).
% 1.67/1.79 tff(10425,plain,
% 1.67/1.79 (op(e1, op(e1, e0)) = e0),
% 1.67/1.79 inference(transitivity,[status(thm)],[10424, 10421, 10420])).
% 1.67/1.79 tff(10426,plain,
% 1.67/1.79 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1836, 10425])).
% 1.67/1.79 tff(10427,plain,
% 1.67/1.79 (op(e1, e2) = op(e2, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10420, 252])).
% 1.67/1.79 tff(10428,plain,
% 1.67/1.79 (op(e1, op(e1, e2)) = op(e1, op(e2, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10427])).
% 1.67/1.79 tff(10429,plain,
% 1.67/1.79 (op(e1, op(e1, e2)) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10428, 256, 10422])).
% 1.67/1.79 tff(10430,plain,
% 1.67/1.79 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2377, 10429])).
% 1.67/1.79 tff(10431,plain,
% 1.67/1.79 ((op(op(e0, e3), e3) = e0) <=> (op(e2, e3) = e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[3277])).
% 1.67/1.79 tff(10432,plain,
% 1.67/1.79 ((op(e2, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 1.67/1.79 inference(symmetry,[status(thm)],[10431])).
% 1.67/1.79 tff(10433,plain,
% 1.67/1.79 (op(op(e0, e3), e3) = e0),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[251, 10432])).
% 1.67/1.79 tff(10434,plain,
% 1.67/1.79 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1361, 10433])).
% 1.67/1.79 tff(10435,plain,
% 1.67/1.79 (op(e3, e1) = e3),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[446, 183, 2826, 82])).
% 1.67/1.79 tff(10436,plain,
% 1.67/1.79 (op(e3, op(e3, e1)) = op(e3, e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10435])).
% 1.67/1.79 tff(10437,plain,
% 1.67/1.79 (op(e3, op(e3, e1)) = e1),
% 1.67/1.79 inference(transitivity,[status(thm)],[10436, 305])).
% 1.67/1.79 tff(10438,plain,
% 1.67/1.79 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[2594, 10437])).
% 1.67/1.79 tff(10439,plain,
% 1.67/1.79 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[251])).
% 1.67/1.79 tff(10440,plain,
% 1.67/1.79 (op(e3, e0) = op(e2, e3)),
% 1.67/1.79 inference(transitivity,[status(thm)],[10416, 252])).
% 1.67/1.79 tff(10441,plain,
% 1.67/1.79 (op(e3, op(e3, e0)) = op(e3, op(e2, e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10440])).
% 1.67/1.79 tff(10442,plain,
% 1.67/1.79 (op(e3, op(e3, e0)) = e0),
% 1.67/1.79 inference(transitivity,[status(thm)],[10441, 10439, 10416])).
% 1.67/1.79 tff(10443,plain,
% 1.67/1.79 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1345, 10442])).
% 1.67/1.79 tff(10444,plain,
% 1.67/1.79 (op(op(e2, e3), e3) = op(e0, e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[251])).
% 1.67/1.79 tff(10445,plain,
% 1.67/1.79 (op(op(e2, e3), e3) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10444, 2])).
% 1.67/1.79 tff(10446,plain,
% 1.67/1.79 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1288, 10445])).
% 1.67/1.79 tff(10447,assumption,(~(op(e0, e0) = e3)), introduced(assumption)).
% 1.67/1.79 tff(10448,plain,
% 1.67/1.79 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10435])).
% 1.67/1.79 tff(10449,plain,
% 1.67/1.79 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10448])).
% 1.67/1.79 tff(10450,plain,
% 1.67/1.79 (~(op(e0, e1) = e3)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[3046, 10449])).
% 1.67/1.79 tff(10451,plain,
% 1.67/1.79 (op(e0, e2) = e3),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1495, 10450, 661, 10447])).
% 1.67/1.79 tff(10452,plain,
% 1.67/1.79 (op(e0, op(e0, e2)) = op(op(e2, e3), e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[252, 10451])).
% 1.67/1.79 tff(10453,plain,
% 1.67/1.79 (op(e0, op(e0, e2)) = e2),
% 1.67/1.79 inference(transitivity,[status(thm)],[10452, 10444, 2])).
% 1.67/1.79 tff(10454,plain,
% 1.67/1.79 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.67/1.79 inference(unit_resolution,[status(thm)],[1331, 10453])).
% 1.67/1.79 tff(10455,plain,
% 1.67/1.79 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[305])).
% 1.67/1.79 tff(10456,plain,
% 1.67/1.79 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10455])).
% 1.67/1.79 tff(10457,plain,
% 1.67/1.79 (~(op(e3, e2) = e1)),
% 1.67/1.79 inference(modus_ponens,[status(thm)],[1888, 10456])).
% 1.67/1.79 tff(10458,plain,
% 1.67/1.79 (op(e3, e2) = op(e3, op(e0, e3))),
% 1.67/1.79 inference(symmetry,[status(thm)],[857])).
% 1.67/1.79 tff(10459,plain,
% 1.67/1.79 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.67/1.79 inference(monotonicity,[status(thm)],[10458])).
% 1.67/1.79 tff(10460,plain,
% 1.67/1.80 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10459])).
% 1.67/1.80 tff(10461,plain,
% 1.67/1.80 ((e3 = op(e3, op(e0, e3))) <=> (op(e3, op(e0, e3)) = e3)),
% 1.67/1.80 inference(commutativity,[status(thm)],[])).
% 1.67/1.80 tff(10462,plain,
% 1.67/1.80 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, op(e0, e3)))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10435, 10458])).
% 1.67/1.80 tff(10463,plain,
% 1.67/1.80 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10462, 10461])).
% 1.67/1.80 tff(10464,plain,
% 1.67/1.80 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10463, 10460])).
% 1.67/1.80 tff(10465,plain,
% 1.67/1.80 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10464])).
% 1.67/1.80 tff(10466,plain,
% 1.67/1.80 (~(op(e3, e2) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[3429, 10465])).
% 1.67/1.80 tff(10467,plain,
% 1.67/1.80 (op(e3, e2) = e2),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1898, 10466, 85, 10457])).
% 1.67/1.80 tff(10468,plain,
% 1.67/1.80 (op(e3, e2) = op(e0, e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10467, 2560])).
% 1.67/1.80 tff(10469,plain,
% 1.67/1.80 (op(e3, op(e3, e2)) = op(e3, op(e0, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10468])).
% 1.67/1.80 tff(10470,plain,
% 1.67/1.80 (op(e3, op(e3, e2)) = e2),
% 1.67/1.80 inference(transitivity,[status(thm)],[10469, 857, 10467])).
% 1.67/1.80 tff(10471,plain,
% 1.67/1.80 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1904, 10470])).
% 1.67/1.80 tff(10472,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1459, 10471, 10454, 10446, 2421, 1936, 1304, 10443, 10438, 10434, 10430, 10426, 10410])).
% 1.67/1.80 tff(10473,plain,((op(e3, e1) = e0) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e0, e3) = e2)) | (~(op(e2, e3) = e0)) | (op(e1, e0) = e3) | (op(e1, e0) = e1) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e3, e2) = e0) | (op(e0, e3) = e3) | (op(e0, e0) = e3) | (~(op(e0, e0) = e1)) | (~(op(e3, e3) = e1)) | (op(e3, e1) = e1) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10474,plain,
% 1.67/1.80 (op(e3, e1) = e0),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10473, 10405, 10402, 1304, 2, 251, 2168, 929, 80, 84, 85, 661, 10399, 10396, 305, 2826, 82])).
% 1.67/1.80 tff(10475,plain,
% 1.67/1.80 (op(e3, e1) = op(e2, e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10474, 252])).
% 1.67/1.80 tff(10476,plain,
% 1.67/1.80 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10475])).
% 1.67/1.80 tff(10477,plain,
% 1.67/1.80 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.67/1.80 inference(transitivity,[status(thm)],[8729, 10476, 10373])).
% 1.67/1.80 tff(10478,plain,
% 1.67/1.80 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e0, e3) = op(e3, e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[2560, 10477])).
% 1.67/1.80 tff(10479,plain,
% 1.67/1.80 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = op(e0, e3))),
% 1.67/1.80 inference(transitivity,[status(thm)],[10478, 452])).
% 1.67/1.80 tff(10480,plain,
% 1.67/1.80 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10479, 10371])).
% 1.67/1.80 tff(10481,plain,
% 1.67/1.80 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10480])).
% 1.67/1.80 tff(10482,plain,
% 1.67/1.80 (e0 = op(e3, op(e3, e3))),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[10474, 8736])).
% 1.67/1.80 tff(10483,plain,
% 1.67/1.80 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[5397, 10482, 6771])).
% 1.67/1.80 tff(10484,plain,
% 1.67/1.80 (~(op(e3, e0) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[10483, 10481])).
% 1.67/1.80 tff(10485,plain,
% 1.67/1.80 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10372])).
% 1.67/1.80 tff(10486,plain,
% 1.67/1.80 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10485])).
% 1.67/1.80 tff(10487,plain,
% 1.67/1.80 ((e3 = op(e3, op(e2, e3))) <=> (op(e3, op(e2, e3)) = e3)),
% 1.67/1.80 inference(commutativity,[status(thm)],[])).
% 1.67/1.80 tff(10488,plain,
% 1.67/1.80 ((op(e2, e0) = op(e3, e0)) <=> (e3 = op(e3, op(e2, e3)))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10390, 10372])).
% 1.67/1.80 tff(10489,plain,
% 1.67/1.80 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, op(e2, e3)) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10488, 10487])).
% 1.67/1.80 tff(10490,plain,
% 1.67/1.80 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10489, 10486])).
% 1.67/1.80 tff(10491,plain,
% 1.67/1.80 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10490])).
% 1.67/1.80 tff(10492,plain,
% 1.67/1.80 (~(op(e3, e0) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[747, 10491])).
% 1.67/1.80 tff(10493,plain,
% 1.67/1.80 (e0 = op(e3, e1)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10474])).
% 1.67/1.80 tff(10494,plain,
% 1.67/1.80 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10493])).
% 1.67/1.80 tff(10495,plain,
% 1.67/1.80 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e0)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10494])).
% 1.67/1.80 tff(10496,plain,
% 1.67/1.80 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10495])).
% 1.67/1.80 tff(10497,plain,
% 1.67/1.80 (~(op(e3, e0) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[580, 10496])).
% 1.67/1.80 tff(10498,plain,
% 1.67/1.80 (op(e3, e0) = e2),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[5422, 10497, 10376, 10492])).
% 1.67/1.80 tff(10499,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10498, 10484])).
% 1.67/1.80 tff(10500,plain,((op(e3, e1) = e2) | (~(op(e2, e3) = e0)) | (~(op(e3, e3) = e1)) | (~(op(e0, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e0) = e3) | (op(e1, e0) = e1) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e3, e2) = e0) | (op(e0, e3) = e3) | (op(e3, e1) = e1) | (op(e2, e3) = e3) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10501,plain,
% 1.67/1.80 (op(e3, e1) = e2),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10500, 10341, 10347, 10336, 10369, 111, 10367, 80, 84, 85, 10364, 10361, 119, 68])).
% 1.67/1.80 tff(10502,plain,
% 1.67/1.80 (op(e3, e1) = op(e0, e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10501, 10353])).
% 1.67/1.80 tff(10503,plain,
% 1.67/1.80 ((op(e3, e1) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10502, 10346])).
% 1.67/1.80 tff(10504,plain,
% 1.67/1.80 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e1) = e0)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10503])).
% 1.67/1.80 tff(10505,plain,
% 1.67/1.80 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10504])).
% 1.67/1.80 tff(10506,plain,
% 1.67/1.80 (~(op(e3, e1) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[964, 10505])).
% 1.67/1.80 tff(10507,plain,
% 1.67/1.80 (op(e3, e0) = e0),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1916, 10506, 85, 10352])).
% 1.67/1.80 tff(10508,plain,
% 1.67/1.80 (op(e3, op(e2, e3)) = op(e2, e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10342, 10507, 10346])).
% 1.67/1.80 tff(10509,plain,
% 1.67/1.80 ((op(e3, op(e2, e3)) = e3) <=> (op(e2, e3) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10508])).
% 1.67/1.80 tff(10510,plain,
% 1.67/1.80 ((op(e2, e3) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10509])).
% 1.67/1.80 tff(10511,plain,
% 1.67/1.80 ((op(e2, e3) = e3) <=> (op(e3, e0) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10510, 10345])).
% 1.67/1.80 tff(10512,plain,
% 1.67/1.80 ((~(op(e2, e3) = e3)) <=> (~(op(e3, e0) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10511])).
% 1.67/1.80 tff(10513,plain,
% 1.67/1.80 (~(op(e3, e0) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[119, 10512])).
% 1.67/1.80 tff(10514,plain,
% 1.67/1.80 (op(e2, e0) = op(op(e0, e3), e0)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10353])).
% 1.67/1.80 tff(10515,plain,
% 1.67/1.80 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10514])).
% 1.67/1.80 tff(10516,plain,
% 1.67/1.80 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10515])).
% 1.67/1.80 tff(10517,plain,
% 1.67/1.80 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10346])).
% 1.67/1.80 tff(10518,plain,
% 1.67/1.80 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10517])).
% 1.67/1.80 tff(10519,plain,
% 1.67/1.80 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10518])).
% 1.67/1.80 tff(10520,plain,
% 1.67/1.80 (~(op(e2, e1) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[197, 10519])).
% 1.67/1.80 tff(10521,plain,
% 1.67/1.80 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10357])).
% 1.67/1.80 tff(10522,plain,
% 1.67/1.80 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10521, 2355])).
% 1.67/1.80 tff(10523,plain,
% 1.67/1.80 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10522])).
% 1.67/1.80 tff(10524,plain,
% 1.67/1.80 (~(op(e2, e1) = e1)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[225, 10523])).
% 1.67/1.80 tff(10525,plain,
% 1.67/1.80 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10501])).
% 1.67/1.80 tff(10526,plain,
% 1.67/1.80 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10525])).
% 1.67/1.80 tff(10527,plain,
% 1.67/1.80 (~(op(e2, e1) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[402, 10526])).
% 1.67/1.80 tff(10528,plain,
% 1.67/1.80 (op(e2, e1) = e3),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[2367, 10527, 10524, 10520])).
% 1.67/1.80 tff(10529,plain,
% 1.67/1.80 ((op(e2, e0) = op(e2, e1)) <=> (op(op(e0, e3), e0) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10514, 10528])).
% 1.67/1.80 tff(10530,plain,
% 1.67/1.80 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10529, 10516])).
% 1.67/1.80 tff(10531,plain,
% 1.67/1.80 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10530])).
% 1.67/1.80 tff(10532,plain,
% 1.67/1.80 (~(op(e2, e0) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[1966, 10531])).
% 1.67/1.80 tff(10533,plain,
% 1.67/1.80 (op(e0, e0) = e3),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[2713, 10532, 10513, 111])).
% 1.67/1.80 tff(10534,plain,
% 1.67/1.80 (e3 = op(e0, e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[10533, 71])).
% 1.67/1.80 tff(10535,plain,
% 1.67/1.80 (e3 = op(e2, e1)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10528])).
% 1.67/1.80 tff(10536,plain,
% 1.67/1.80 (op(e0, e0) = op(e2, e1)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10533, 10535])).
% 1.67/1.80 tff(10537,plain,
% 1.67/1.80 (op(e0, op(e0, e0)) = op(e0, op(e2, e1))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10536])).
% 1.67/1.80 tff(10538,plain,
% 1.67/1.80 (op(e0, op(e2, e1)) = op(e0, op(e0, e0))),
% 1.67/1.80 inference(symmetry,[status(thm)],[10537])).
% 1.67/1.80 tff(10539,plain,
% 1.67/1.80 (op(e0, op(e2, e1)) = op(op(e2, e3), e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10346, 10528])).
% 1.67/1.80 tff(10540,plain,
% 1.67/1.80 (op(op(e2, e3), e3) = op(e0, op(e2, e1))),
% 1.67/1.80 inference(symmetry,[status(thm)],[10539])).
% 1.67/1.80 tff(10541,plain,
% 1.67/1.80 (op(op(e2, e3), e3) = op(e0, e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10341])).
% 1.67/1.80 tff(10542,plain,
% 1.67/1.80 (op(e0, e3) = op(op(e2, e3), e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10541])).
% 1.67/1.80 tff(10543,plain,
% 1.67/1.80 (e2 = op(e0, op(e0, e0))),
% 1.67/1.80 inference(transitivity,[status(thm)],[10353, 10542, 10540, 10538])).
% 1.67/1.80 tff(10544,plain,
% 1.67/1.80 (op(e0, op(e0, e0)) = e2),
% 1.67/1.80 inference(transitivity,[status(thm)],[10537, 10539, 10541, 10336])).
% 1.67/1.80 tff(10545,plain,
% 1.67/1.80 (op(e0, op(e0, op(e0, e0))) = op(op(e2, e3), e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10346, 10544])).
% 1.67/1.80 tff(10546,plain,
% 1.67/1.80 (op(op(e2, e3), e2) = op(e0, op(e0, op(e0, e0)))),
% 1.67/1.80 inference(symmetry,[status(thm)],[10545])).
% 1.67/1.80 tff(10547,plain,
% 1.67/1.80 (op(op(e2, e3), e2) = op(e0, op(e0, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10341, 10353])).
% 1.67/1.80 tff(10548,plain,
% 1.67/1.80 (op(e0, op(e0, e3)) = op(op(e2, e3), e2)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10547])).
% 1.67/1.80 tff(10549,plain,
% 1.67/1.80 (op(e0, op(e0, e3)) = op(e0, e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10336])).
% 1.67/1.80 tff(10550,plain,
% 1.67/1.80 (op(e0, e2) = op(e0, op(e0, e3))),
% 1.67/1.80 inference(symmetry,[status(thm)],[10549])).
% 1.67/1.80 tff(10551,plain,
% 1.67/1.80 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10550])).
% 1.67/1.80 tff(10552,plain,
% 1.67/1.80 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10551])).
% 1.67/1.80 tff(10553,plain,
% 1.67/1.80 (op(e0, e1) = e0),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[292, 10506, 10520, 84])).
% 1.67/1.80 tff(10554,plain,
% 1.67/1.80 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, op(e0, e3)))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10553, 10550])).
% 1.67/1.80 tff(10555,plain,
% 1.67/1.80 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10554, 2239])).
% 1.67/1.80 tff(10556,plain,
% 1.67/1.80 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10555, 10552])).
% 1.67/1.80 tff(10557,plain,
% 1.67/1.80 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10556])).
% 1.67/1.80 tff(10558,plain,
% 1.67/1.80 (~(op(e0, e2) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[2102, 10557])).
% 1.67/1.80 tff(10559,plain,
% 1.67/1.80 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10353])).
% 1.67/1.80 tff(10560,plain,
% 1.67/1.80 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10559])).
% 1.67/1.80 tff(10561,plain,
% 1.67/1.80 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10560])).
% 1.67/1.80 tff(10562,plain,
% 1.67/1.80 (~(op(e0, e2) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[918, 10561])).
% 1.67/1.80 tff(10563,plain,
% 1.67/1.80 ((op(e0, e2) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10550])).
% 1.67/1.80 tff(10564,plain,
% 1.67/1.80 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e2) = e3)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10563])).
% 1.67/1.80 tff(10565,plain,
% 1.67/1.80 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10347])).
% 1.67/1.80 tff(10566,plain,
% 1.67/1.80 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10565])).
% 1.67/1.80 tff(10567,plain,
% 1.67/1.80 (~(op(e3, e2) = e1)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[1888, 10566])).
% 1.67/1.80 tff(10568,plain,
% 1.67/1.80 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10501])).
% 1.67/1.80 tff(10569,plain,
% 1.67/1.80 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10568, 2234])).
% 1.67/1.80 tff(10570,plain,
% 1.67/1.80 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10569])).
% 1.67/1.80 tff(10571,plain,
% 1.67/1.80 (~(op(e3, e2) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[3429, 10570])).
% 1.67/1.80 tff(10572,plain,
% 1.67/1.80 (op(e3, e2) = e3),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1898, 10571, 85, 10567])).
% 1.67/1.80 tff(10573,plain,
% 1.67/1.80 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, op(e0, e3)) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10550, 10572])).
% 1.67/1.80 tff(10574,plain,
% 1.67/1.80 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10573, 10564])).
% 1.67/1.80 tff(10575,plain,
% 1.67/1.80 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10574])).
% 1.67/1.80 tff(10576,plain,
% 1.67/1.80 (~(op(e0, e2) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[1467, 10575])).
% 1.67/1.80 tff(10577,plain,
% 1.67/1.80 (op(e0, e2) = e1),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[2745, 10576, 10562, 10558])).
% 1.67/1.80 tff(10578,plain,
% 1.67/1.80 (e1 = op(e0, e2)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10577])).
% 1.67/1.80 tff(10579,plain,
% 1.67/1.80 (e1 = op(e0, op(e0, op(e0, e0)))),
% 1.67/1.80 inference(transitivity,[status(thm)],[10578, 10550, 10548, 10546])).
% 1.67/1.80 tff(10580,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[2760, 10579, 10543, 10534])).
% 1.67/1.80 tff(10581,plain,((op(e0, e3) = e1) | (op(e3, e2) = e0) | (op(e1, e1) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e2) | (op(e2, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10582,plain,
% 1.67/1.80 (op(e0, e3) = e1),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10581, 87, 84, 80, 68, 76, 72, 85])).
% 1.67/1.80 tff(10583,plain,
% 1.67/1.80 ((op(e0, e3) = e2) <=> (e1 = e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10582])).
% 1.67/1.80 tff(10584,plain,
% 1.67/1.80 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10583])).
% 1.67/1.80 tff(10585,plain,
% 1.67/1.80 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10584])).
% 1.67/1.80 tff(10586,plain,
% 1.67/1.80 (~(op(e0, e3) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[708, 10585])).
% 1.67/1.80 tff(10587,plain,
% 1.67/1.80 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[2812])).
% 1.67/1.80 tff(10588,plain,
% 1.67/1.80 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10587])).
% 1.67/1.80 tff(10589,plain,
% 1.67/1.80 (~(op(e1, e3) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[571, 10588])).
% 1.67/1.80 tff(10590,plain,
% 1.67/1.80 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[2812])).
% 1.67/1.80 tff(10591,plain,
% 1.67/1.80 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10590])).
% 1.67/1.80 tff(10592,plain,
% 1.67/1.80 (~(op(e0, e3) = e2)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[1077, 10591])).
% 1.67/1.80 tff(10593,plain,
% 1.67/1.80 (op(e1, e3) = e0),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[104, 170, 72, 138])).
% 1.67/1.80 tff(10594,plain,
% 1.67/1.80 (~(op(e0, e3) = e1)),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1223, 10593, 131])).
% 1.67/1.80 tff(10595,plain,
% 1.67/1.80 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10593])).
% 1.67/1.80 tff(10596,plain,
% 1.67/1.80 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10595])).
% 1.67/1.80 tff(10597,plain,
% 1.67/1.80 (~(op(e0, e3) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[64, 10596])).
% 1.67/1.80 tff(10598,plain,
% 1.67/1.80 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10593])).
% 1.67/1.80 tff(10599,plain,
% 1.67/1.80 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.67/1.80 inference(transitivity,[status(thm)],[10598, 86])).
% 1.67/1.80 tff(10600,plain,
% 1.67/1.80 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10599])).
% 1.67/1.80 tff(10601,plain,
% 1.67/1.80 (~(op(e2, e3) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[118, 10600])).
% 1.67/1.80 tff(10602,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[1105, 10601, 10597, 656, 161, 10594, 79])).
% 1.67/1.80 tff(10603,plain,(((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e3, e3) = e0) | (op(e0, e3) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10604,plain,
% 1.67/1.80 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10603, 9696, 10592, 10589])).
% 1.67/1.80 tff(10605,plain,
% 1.67/1.80 (op(e1, e1) = e2),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[630, 1291, 84, 1266])).
% 1.67/1.80 tff(10606,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[7135, 10605, 1291, 75, 2812, 4515, 1080])).
% 1.67/1.80 tff(10607,plain,((op(e1, e1) = e3) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e1) | (op(e1, e3) = e3) | (op(e1, e1) = e0) | (op(e1, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10608,plain,
% 1.67/1.80 ($false),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10607, 2232, 2165, 2812, 75, 84, 1291, 2045])).
% 1.67/1.80 tff(10609,plain,((~(op(e1, e3) = e1)) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (op(e1, e1) = e0) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.80 tff(10610,plain,
% 1.67/1.80 (~(op(e1, e3) = e1)),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[10609, 1291, 75, 84, 2812])).
% 1.67/1.80 tff(10611,plain,
% 1.67/1.80 ((op(e2, e3) = op(e2, e2)) <=> (op(e2, e2) = op(e2, e3))),
% 1.67/1.80 inference(commutativity,[status(thm)],[])).
% 1.67/1.80 tff(10612,plain,
% 1.67/1.80 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e2, e2))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.80 tff(10613,plain,
% 1.67/1.80 ((op(e2, e3) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 1.67/1.80 inference(transitivity,[status(thm)],[10612, 10611])).
% 1.67/1.80 tff(10614,plain,
% 1.67/1.80 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.67/1.80 inference(symmetry,[status(thm)],[10613])).
% 1.67/1.80 tff(10615,plain,
% 1.67/1.80 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10614])).
% 1.67/1.80 tff(10616,plain,
% 1.67/1.80 (~(op(e2, e3) = e0)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[515, 10615])).
% 1.67/1.80 tff(10617,plain,
% 1.67/1.80 (op(e2, e3) = e3),
% 1.67/1.80 inference(unit_resolution,[status(thm)],[206, 10616, 9692, 76])).
% 1.67/1.80 tff(10618,plain,
% 1.67/1.80 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10617])).
% 1.67/1.80 tff(10619,plain,
% 1.67/1.80 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 1.67/1.80 inference(monotonicity,[status(thm)],[10618])).
% 1.67/1.80 tff(10620,plain,
% 1.67/1.80 (~(op(e2, e1) = e3)),
% 1.67/1.80 inference(modus_ponens,[status(thm)],[197, 10619])).
% 1.67/1.80 tff(10621,plain,
% 1.67/1.81 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e2))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.81 tff(10622,plain,
% 1.67/1.81 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e0)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10621])).
% 1.67/1.81 tff(10623,plain,
% 1.67/1.81 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10622])).
% 1.67/1.81 tff(10624,plain,
% 1.67/1.81 (~(op(e2, e1) = e0)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[508, 10623])).
% 1.67/1.81 tff(10625,plain,
% 1.67/1.81 ((op(e2, e1) = op(e2, e0)) <=> (op(e2, e0) = op(e2, e1))),
% 1.67/1.81 inference(commutativity,[status(thm)],[])).
% 1.67/1.81 tff(10626,plain,
% 1.67/1.81 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e2))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.81 tff(10627,plain,
% 1.67/1.81 ((op(e3, e2) = e0) <=> (op(e2, e2) = op(e3, e2))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10626, 9346])).
% 1.67/1.81 tff(10628,plain,
% 1.67/1.81 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10627])).
% 1.67/1.81 tff(10629,plain,
% 1.67/1.81 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10628])).
% 1.67/1.81 tff(10630,plain,
% 1.67/1.81 (~(op(e3, e2) = e0)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[1546, 10629])).
% 1.67/1.81 tff(10631,plain,
% 1.67/1.81 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10617])).
% 1.67/1.81 tff(10632,plain,
% 1.67/1.81 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10631])).
% 1.67/1.81 tff(10633,plain,
% 1.67/1.81 (~(op(e1, e3) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[118, 10632])).
% 1.67/1.81 tff(10634,plain,
% 1.67/1.81 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.81 tff(10635,plain,
% 1.67/1.81 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10634])).
% 1.67/1.81 tff(10636,plain,
% 1.67/1.81 (~(op(e2, e2) = e1)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[26, 10635])).
% 1.67/1.81 tff(10637,plain,
% 1.67/1.81 (op(e2, e1) = e1),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[345, 1349, 76, 10636])).
% 1.67/1.81 tff(10638,plain,
% 1.67/1.81 ((op(e2, op(e2, e2)) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.67/1.81 inference(commutativity,[status(thm)],[])).
% 1.67/1.81 tff(10639,plain,
% 1.67/1.81 (op(e2, e0) = op(e2, op(e2, e2))),
% 1.67/1.81 inference(symmetry,[status(thm)],[9302])).
% 1.67/1.81 tff(10640,plain,
% 1.67/1.81 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e2)) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10639])).
% 1.67/1.81 tff(10641,plain,
% 1.67/1.81 ((op(e2, e0) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10640, 10638])).
% 1.67/1.81 tff(10642,plain,
% 1.67/1.81 ((e3 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e3)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10641])).
% 1.67/1.81 tff(10643,plain,
% 1.67/1.81 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, op(e2, e2)) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10639, 10617])).
% 1.67/1.81 tff(10644,plain,
% 1.67/1.81 ((op(e2, e0) = op(e2, e3)) <=> (e3 = op(e2, op(e2, e2)))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10643, 10638])).
% 1.67/1.81 tff(10645,plain,
% 1.67/1.81 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10644, 10642])).
% 1.67/1.81 tff(10646,plain,
% 1.67/1.81 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10645])).
% 1.67/1.81 tff(10647,plain,
% 1.67/1.81 (~(op(e2, e0) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[989, 10646])).
% 1.67/1.81 tff(10648,plain,
% 1.67/1.81 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e2))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.81 tff(10649,plain,
% 1.67/1.81 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e0)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10648])).
% 1.67/1.81 tff(10650,plain,
% 1.67/1.81 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10649])).
% 1.67/1.81 tff(10651,plain,
% 1.67/1.81 (~(op(e2, e0) = e0)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[2228, 10650])).
% 1.67/1.81 tff(10652,plain,
% 1.67/1.81 (op(e2, e0) = e2),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[765, 1349, 10651, 10647])).
% 1.67/1.81 tff(10653,plain,
% 1.67/1.81 (op(e0, e3) = e0),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[1098, 80, 9696, 10616])).
% 1.67/1.81 tff(10654,assumption,(op(e2, e1) = e1), introduced(assumption)).
% 1.67/1.81 tff(10655,plain,
% 1.67/1.81 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10654])).
% 1.67/1.81 tff(10656,plain,
% 1.67/1.81 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10655])).
% 1.67/1.81 tff(10657,plain,
% 1.67/1.81 (~(op(e1, e1) = e1)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[225, 10656])).
% 1.67/1.81 tff(10658,plain,
% 1.67/1.81 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[6778])).
% 1.67/1.81 tff(10659,plain,
% 1.67/1.81 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10658])).
% 1.67/1.81 tff(10660,plain,
% 1.67/1.81 (~(op(e1, e3) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[118, 10659])).
% 1.67/1.81 tff(10661,plain,
% 1.67/1.81 (op(e1, e3) = e1),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[104, 80, 10589, 10660])).
% 1.67/1.81 tff(10662,plain,
% 1.67/1.81 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10661])).
% 1.67/1.81 tff(10663,plain,
% 1.67/1.81 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10662])).
% 1.67/1.81 tff(10664,plain,
% 1.67/1.81 (~(op(e1, e2) = e1)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[1850, 10663])).
% 1.67/1.81 tff(10665,plain,
% 1.67/1.81 (op(e1, e1) = e3),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10607, 10664, 2812, 75, 10660, 84, 10657])).
% 1.67/1.81 tff(10666,plain,
% 1.67/1.81 (op(e0, op(e1, e1)) = op(e0, e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10665])).
% 1.67/1.81 tff(10667,plain,
% 1.67/1.81 (e3 = op(e1, e1)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10665])).
% 1.67/1.81 tff(10668,plain,
% 1.67/1.81 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e2, e2))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[9326])).
% 1.67/1.81 tff(10669,plain,
% 1.67/1.81 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e0)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10668])).
% 1.67/1.81 tff(10670,plain,
% 1.67/1.81 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10669])).
% 1.67/1.81 tff(10671,plain,
% 1.67/1.81 (~(op(e1, e2) = e0)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[1273, 10670])).
% 1.67/1.81 tff(10672,plain,
% 1.67/1.81 (op(e1, e0) = e0),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[1830, 80, 10671, 84])).
% 1.67/1.81 tff(10673,plain,
% 1.67/1.81 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10672])).
% 1.67/1.81 tff(10674,plain,
% 1.67/1.81 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10673, 8115])).
% 1.67/1.81 tff(10675,plain,
% 1.67/1.81 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10674])).
% 1.67/1.81 tff(10676,plain,
% 1.67/1.81 (~(op(e3, e0) = e0)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[410, 10675])).
% 1.67/1.81 tff(10677,plain,
% 1.67/1.81 (op(e3, e1) = e0),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[1916, 10676, 9696, 10630])).
% 1.67/1.81 tff(10678,plain,
% 1.67/1.81 (op(e3, e2) = e3),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10084, 10677, 2812])).
% 1.67/1.81 tff(10679,plain,
% 1.67/1.81 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10678])).
% 1.67/1.81 tff(10680,plain,
% 1.67/1.81 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10679])).
% 1.67/1.81 tff(10681,plain,
% 1.67/1.81 (~(op(e0, e2) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[1467, 10680])).
% 1.67/1.81 tff(10682,plain,
% 1.67/1.81 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[6778])).
% 1.67/1.81 tff(10683,plain,
% 1.67/1.81 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10682])).
% 1.67/1.81 tff(10684,plain,
% 1.67/1.81 (~(op(e0, e3) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[964, 10683])).
% 1.67/1.81 tff(10685,plain,
% 1.67/1.81 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10667])).
% 1.67/1.81 tff(10686,plain,
% 1.67/1.81 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10685])).
% 1.67/1.81 tff(10687,plain,
% 1.67/1.81 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10686])).
% 1.67/1.81 tff(10688,plain,
% 1.67/1.81 (~(op(e0, e1) = e3)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[792, 10687])).
% 1.67/1.81 tff(10689,plain,
% 1.67/1.81 (op(e0, e0) = e3),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[1495, 10688, 10684, 10681])).
% 1.67/1.81 tff(10690,plain,
% 1.67/1.81 (op(e0, e0) = op(e1, e1)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10689, 10667])).
% 1.67/1.81 tff(10691,plain,
% 1.67/1.81 (op(e0, op(e0, e0)) = op(e0, op(e1, e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10690])).
% 1.67/1.81 tff(10692,plain,
% 1.67/1.81 (op(e0, op(e0, e0)) = e0),
% 1.67/1.81 inference(transitivity,[status(thm)],[10691, 10666, 10653])).
% 1.67/1.81 tff(10693,plain,
% 1.67/1.81 (op(e3, op(e2, e0)) = op(e3, e2)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[1940])).
% 1.67/1.81 tff(10694,plain,
% 1.67/1.81 ((op(e3, op(e2, e0)) = e3) <=> (op(e3, e2) = e3)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10693])).
% 1.67/1.81 tff(10695,plain,
% 1.67/1.81 ((op(e3, e2) = e3) <=> (op(e3, op(e2, e0)) = e3)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10694])).
% 1.67/1.81 tff(10696,plain,
% 1.67/1.81 (op(e3, op(e2, e0)) = e3),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10678, 10695])).
% 1.67/1.81 tff(10697,plain,
% 1.67/1.81 (((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)) | (~(op(e3, op(e2, e0)) = e3))),
% 1.67/1.81 inference(tautology,[status(thm)],[])).
% 1.67/1.81 tff(10698,plain,
% 1.67/1.81 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10697, 10696])).
% 1.67/1.81 tff(10699,plain,
% 1.67/1.81 (op(e3, e2) = op(e1, e1)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10678, 10667])).
% 1.67/1.81 tff(10700,plain,
% 1.67/1.81 (op(e0, op(e3, e2)) = op(e0, op(e1, e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10699])).
% 1.67/1.81 tff(10701,plain,
% 1.67/1.81 (op(e0, op(e3, e2)) = e0),
% 1.67/1.81 inference(transitivity,[status(thm)],[10700, 10666, 10653])).
% 1.67/1.81 tff(10702,plain,
% 1.67/1.81 (((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)) | (~(op(e0, op(e3, e2)) = e0))),
% 1.67/1.81 inference(tautology,[status(thm)],[])).
% 1.67/1.81 tff(10703,plain,
% 1.67/1.81 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10702, 10701])).
% 1.67/1.81 tff(10704,plain,
% 1.67/1.81 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[1997])).
% 1.67/1.81 tff(10705,plain,
% 1.67/1.81 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10704, 6336])).
% 1.67/1.81 tff(10706,plain,
% 1.67/1.81 (op(e1, e2) = e2),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[1859, 10664, 75, 10671])).
% 1.67/1.81 tff(10707,plain,
% 1.67/1.81 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10706])).
% 1.67/1.81 tff(10708,plain,
% 1.67/1.81 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10707, 10705])).
% 1.67/1.81 tff(10709,plain,
% 1.67/1.81 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10708])).
% 1.67/1.81 tff(10710,plain,
% 1.67/1.81 (~(op(e2, e0) = op(e0, e2))),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[6205, 10709])).
% 1.67/1.81 tff(10711,plain,
% 1.67/1.81 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[6358, 10710])).
% 1.67/1.81 tff(10712,plain,
% 1.67/1.81 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10661])).
% 1.67/1.81 tff(10713,plain,
% 1.67/1.81 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.67/1.81 inference(symmetry,[status(thm)],[10712])).
% 1.67/1.81 tff(10714,plain,
% 1.67/1.81 ((~(op(e3, e1) = e1)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10713])).
% 1.67/1.81 tff(10715,plain,
% 1.67/1.81 ((op(e2, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10654])).
% 1.67/1.81 tff(10716,plain,
% 1.67/1.81 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10715, 7793])).
% 1.67/1.81 tff(10717,plain,
% 1.67/1.81 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10716])).
% 1.67/1.81 tff(10718,plain,
% 1.67/1.81 (~(op(e3, e1) = e1)),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[402, 10717])).
% 1.67/1.81 tff(10719,plain,
% 1.67/1.81 (~(op(e3, e1) = op(e1, e3))),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10718, 10714])).
% 1.67/1.81 tff(10720,plain,
% 1.67/1.81 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[6362, 10719])).
% 1.67/1.81 tff(10721,plain,
% 1.67/1.81 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e3) = e1)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[6910])).
% 1.67/1.81 tff(10722,plain,
% 1.67/1.81 ((op(e1, e3) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.67/1.81 inference(symmetry,[status(thm)],[10721])).
% 1.67/1.81 tff(10723,plain,
% 1.67/1.81 (op(e1, op(e2, e3)) = e1),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10661, 10722])).
% 1.67/1.81 tff(10724,plain,
% 1.67/1.81 (((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)) | (~(op(e1, op(e2, e3)) = e1))),
% 1.67/1.81 inference(tautology,[status(thm)],[])).
% 1.67/1.81 tff(10725,plain,
% 1.67/1.81 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10724, 10723])).
% 1.67/1.81 tff(10726,plain,
% 1.67/1.81 (op(e3, op(e3, e3)) = e3),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10678, 9701])).
% 1.67/1.81 tff(10727,plain,
% 1.67/1.81 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[6277, 10726])).
% 1.67/1.81 tff(10728,plain,
% 1.67/1.81 ((op(e3, e1) = e1) <=> (op(e1, e3) = op(e3, e1))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10713, 6290])).
% 1.67/1.81 tff(10729,plain,
% 1.67/1.81 ((~(op(e3, e1) = e1)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10728])).
% 1.67/1.81 tff(10730,plain,
% 1.67/1.81 (~(op(e1, e3) = op(e3, e1))),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10718, 10729])).
% 1.67/1.81 tff(10731,plain,
% 1.67/1.81 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[6307, 10730])).
% 1.67/1.81 tff(10732,plain,
% 1.67/1.81 (op(e1, e0) = op(e2, e2)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10672, 9326])).
% 1.67/1.81 tff(10733,plain,
% 1.67/1.81 (op(e2, op(e1, e0)) = op(e2, op(e2, e2))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10732])).
% 1.67/1.81 tff(10734,plain,
% 1.67/1.81 (op(e2, op(e1, e0)) = e2),
% 1.67/1.81 inference(transitivity,[status(thm)],[10733, 9302, 1940])).
% 1.67/1.81 tff(10735,plain,
% 1.67/1.81 (((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)) | (~(op(e2, op(e1, e0)) = e2))),
% 1.67/1.81 inference(tautology,[status(thm)],[])).
% 1.67/1.81 tff(10736,plain,
% 1.67/1.81 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[10735, 10734])).
% 1.67/1.81 tff(10737,plain,
% 1.67/1.81 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10653])).
% 1.67/1.81 tff(10738,plain,
% 1.67/1.81 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.67/1.81 inference(symmetry,[status(thm)],[10737])).
% 1.67/1.81 tff(10739,plain,
% 1.67/1.81 ((op(e3, e0) = e0) <=> (op(e0, e3) = op(e3, e0))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10738, 453])).
% 1.67/1.81 tff(10740,plain,
% 1.67/1.81 ((~(op(e3, e0) = e0)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10739])).
% 1.67/1.81 tff(10741,plain,
% 1.67/1.81 (~(op(e0, e3) = op(e3, e0))),
% 1.67/1.81 inference(modus_ponens,[status(thm)],[10676, 10740])).
% 1.67/1.81 tff(10742,plain,
% 1.67/1.81 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.67/1.81 inference(unit_resolution,[status(thm)],[496, 10741])).
% 1.67/1.81 tff(10743,plain,
% 1.67/1.81 ((op(e1, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10672])).
% 1.67/1.81 tff(10744,plain,
% 1.67/1.81 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 1.67/1.81 inference(transitivity,[status(thm)],[10743, 5637])).
% 1.67/1.81 tff(10745,plain,
% 1.67/1.81 ((op(e0, e1) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 1.67/1.81 inference(symmetry,[status(thm)],[10744])).
% 1.67/1.81 tff(10746,plain,
% 1.67/1.81 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.67/1.81 inference(monotonicity,[status(thm)],[10653])).
% 1.67/1.81 tff(10747,plain,
% 1.67/1.81 ((op(e0, e1) = op(e0, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 1.67/1.81 inference(transitivity,[status(thm)],[10746, 10745])).
% 1.67/1.82 tff(10748,plain,
% 1.67/1.82 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10747])).
% 1.67/1.82 tff(10749,plain,
% 1.67/1.82 (~(op(e1, e0) = op(e0, e1))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[818, 10748])).
% 1.67/1.82 tff(10750,plain,
% 1.67/1.82 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[613, 10749])).
% 1.67/1.82 tff(10751,plain,
% 1.67/1.82 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10654])).
% 1.67/1.82 tff(10752,plain,
% 1.67/1.82 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.67/1.82 inference(transitivity,[status(thm)],[10751, 5522])).
% 1.67/1.82 tff(10753,plain,
% 1.67/1.82 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 1.67/1.82 inference(symmetry,[status(thm)],[10752])).
% 1.67/1.82 tff(10754,plain,
% 1.67/1.82 ((op(e1, e2) = op(e1, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 1.67/1.82 inference(transitivity,[status(thm)],[10662, 10753])).
% 1.67/1.82 tff(10755,plain,
% 1.67/1.82 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10754])).
% 1.67/1.82 tff(10756,plain,
% 1.67/1.82 (~(op(e2, e1) = op(e1, e2))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[1850, 10755])).
% 1.67/1.82 tff(10757,plain,
% 1.67/1.82 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[557, 10756])).
% 1.67/1.82 tff(10758,plain,
% 1.67/1.82 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 1.67/1.82 inference(transitivity,[status(thm)],[10662, 10753, 531])).
% 1.67/1.82 tff(10759,plain,
% 1.67/1.82 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10758])).
% 1.67/1.82 tff(10760,plain,
% 1.67/1.82 (~(op(e1, e2) = op(e2, e1))),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[1850, 10759])).
% 1.67/1.82 tff(10761,plain,
% 1.67/1.82 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[539, 10760])).
% 1.67/1.82 tff(10762,plain,
% 1.67/1.82 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10639])).
% 1.67/1.82 tff(10763,plain,
% 1.67/1.82 (op(e2, op(e2, e2)) = e2),
% 1.67/1.82 inference(modus_ponens,[status(thm)],[1940, 10762])).
% 1.67/1.82 tff(10764,plain,
% 1.67/1.82 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[528, 10763])).
% 1.67/1.82 tff(10765,plain,
% 1.67/1.82 (op(e0, op(e1, e1)) = e0),
% 1.67/1.82 inference(transitivity,[status(thm)],[10666, 10653])).
% 1.67/1.82 tff(10766,plain,
% 1.67/1.82 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[635, 10765])).
% 1.67/1.82 tff(10767,plain,
% 1.67/1.82 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[5367, 10766, 10764, 10761, 10757, 10750, 10742, 10736, 10731, 10727, 10725, 10720, 10711, 10703, 10698])).
% 1.67/1.82 tff(10768,plain,
% 1.67/1.82 (~(op(e0, op(e0, e0)) = e0)),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[5598, 10767])).
% 1.67/1.82 tff(10769,plain,
% 1.67/1.82 ($false),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[10768, 10692])).
% 1.67/1.82 tff(10770,plain,((op(e1, e3) = e0) | (~(op(e2, e0) = e2)) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (op(e1, e1) = e0) | (~(op(e2, e2) = e0)) | (~(op(e2, e1) = e1)) | (~(op(e2, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.67/1.82 tff(10771,plain,
% 1.67/1.82 (op(e1, e3) = e0),
% 1.67/1.82 inference(unit_resolution,[status(thm)],[10770, 10652, 2812, 75, 84, 9300, 10637, 10617])).
% 1.67/1.82 tff(10772,plain,
% 1.67/1.82 (op(e1, e3) = op(e2, e2)),
% 1.67/1.82 inference(transitivity,[status(thm)],[10771, 9326])).
% 1.67/1.82 tff(10773,plain,
% 1.67/1.82 ((op(e1, e3) = e1) <=> (op(e2, e2) = e1)),
% 1.67/1.82 inference(monotonicity,[status(thm)],[10772])).
% 1.67/1.82 tff(10774,plain,
% 1.67/1.82 ((op(e2, e2) = e1) <=> (op(e1, e3) = e1)),
% 1.67/1.82 inference(symmetry,[status(thm)],[10773])).
% 1.67/1.82 tff(10775,plain,
% 1.67/1.82 ((~(op(e2, e2) = e1)) <=> (~(op(e1, e3) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10774])).
% 1.72/1.82 tff(10776,plain,
% 1.72/1.82 (~(op(e1, e3) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[10636, 10775])).
% 1.72/1.82 tff(10777,plain,
% 1.72/1.82 (op(e0, e3) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[151, 10776, 9667, 76])).
% 1.72/1.82 tff(10778,plain,
% 1.72/1.82 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10777])).
% 1.72/1.82 tff(10779,plain,
% 1.72/1.82 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10778])).
% 1.72/1.82 tff(10780,plain,
% 1.72/1.82 (~(op(e0, e2) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[918, 10779])).
% 1.72/1.82 tff(10781,plain,
% 1.72/1.82 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10637])).
% 1.72/1.82 tff(10782,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10781])).
% 1.72/1.82 tff(10783,plain,
% 1.72/1.82 (~(op(e1, e1) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[225, 10782])).
% 1.72/1.82 tff(10784,plain,
% 1.72/1.82 ((op(e2, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10637])).
% 1.72/1.82 tff(10785,plain,
% 1.72/1.82 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10784, 7793])).
% 1.72/1.82 tff(10786,plain,
% 1.72/1.82 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10785])).
% 1.72/1.82 tff(10787,plain,
% 1.72/1.82 (~(op(e3, e1) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[402, 10786])).
% 1.72/1.82 tff(10788,plain,
% 1.72/1.82 (op(e1, e1) = e3),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[10607, 4515, 2812, 75, 1080, 84, 1266])).
% 1.72/1.82 tff(10789,plain,
% 1.72/1.82 (e3 = op(e1, e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10788])).
% 1.72/1.82 tff(10790,plain,
% 1.72/1.82 (op(e3, e2) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[1613, 4515, 1348, 4484])).
% 1.72/1.82 tff(10791,plain,
% 1.72/1.82 ((op(e3, e2) = e3) <=> (e1 = op(e1, e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10790, 10789])).
% 1.72/1.82 tff(10792,plain,
% 1.72/1.82 ((op(e3, e2) = e3) <=> (op(e1, e1) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10791, 8462])).
% 1.72/1.82 tff(10793,plain,
% 1.72/1.82 ((op(e1, e1) = e1) <=> (op(e3, e2) = e3)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10792])).
% 1.72/1.82 tff(10794,plain,
% 1.72/1.82 ((~(op(e1, e1) = e1)) <=> (~(op(e3, e2) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10793])).
% 1.72/1.82 tff(10795,plain,
% 1.72/1.82 (~(op(e3, e2) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1266, 10794])).
% 1.72/1.82 tff(10796,plain,
% 1.72/1.82 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10788])).
% 1.72/1.82 tff(10797,plain,
% 1.72/1.82 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10796, 396])).
% 1.72/1.82 tff(10798,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10797])).
% 1.72/1.82 tff(10799,plain,
% 1.72/1.82 (~(op(e3, e1) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[945, 10798])).
% 1.72/1.82 tff(10800,plain,
% 1.72/1.82 (op(e3, e1) = e0),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[446, 10799, 2826, 9684])).
% 1.72/1.82 tff(10801,plain,
% 1.72/1.82 ($false),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[10084, 10800, 10795, 2812])).
% 1.72/1.82 tff(10802,plain,((op(e1, e2) = e1) | (~(op(e3, e3) = e2)) | (op(e3, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e2) = e1) | (op(e0, e2) = e1) | (op(e1, e2) = e3) | (op(e1, e3) = e3) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.82 tff(10803,plain,
% 1.72/1.82 (op(e1, e2) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[10802, 10787, 2812, 10783, 10636, 10780, 75, 10633, 84])).
% 1.72/1.82 tff(10804,plain,
% 1.72/1.82 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10803])).
% 1.72/1.82 tff(10805,plain,
% 1.72/1.82 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10804, 7171])).
% 1.72/1.82 tff(10806,plain,
% 1.72/1.82 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10805])).
% 1.72/1.82 tff(10807,plain,
% 1.72/1.82 (~(op(e3, e2) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[2292, 10806])).
% 1.72/1.82 tff(10808,plain,
% 1.72/1.82 (op(e3, e2) = e3),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[1898, 10807, 10630, 9699])).
% 1.72/1.82 tff(10809,plain,
% 1.72/1.82 (e3 = op(e3, e2)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10808])).
% 1.72/1.82 tff(10810,plain,
% 1.72/1.82 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10808])).
% 1.72/1.82 tff(10811,plain,
% 1.72/1.82 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10810])).
% 1.72/1.82 tff(10812,plain,
% 1.72/1.82 (~(op(e3, e1) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[3429, 10811])).
% 1.72/1.82 tff(10813,plain,
% 1.72/1.82 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10652])).
% 1.72/1.82 tff(10814,plain,
% 1.72/1.82 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10813])).
% 1.72/1.82 tff(10815,plain,
% 1.72/1.82 (~(op(e1, e0) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[756, 10814])).
% 1.72/1.82 tff(10816,plain,
% 1.72/1.82 ((op(e1, e2) = e2) <=> (e1 = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10803])).
% 1.72/1.82 tff(10817,plain,
% 1.72/1.82 ((e1 = e2) <=> (op(e1, e2) = e2)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10816])).
% 1.72/1.82 tff(10818,plain,
% 1.72/1.82 ((~(e1 = e2)) <=> (~(op(e1, e2) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10817])).
% 1.72/1.82 tff(10819,plain,
% 1.72/1.82 (~(op(e1, e2) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[708, 10818])).
% 1.72/1.82 tff(10820,plain,
% 1.72/1.82 (op(e1, e1) = e2),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[2285, 10819, 10589, 10815])).
% 1.72/1.82 tff(10821,plain,
% 1.72/1.82 ((op(e1, e1) = e3) <=> (e2 = e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10820])).
% 1.72/1.82 tff(10822,plain,
% 1.72/1.82 ((e2 = e3) <=> (op(e1, e1) = e3)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10821])).
% 1.72/1.82 tff(10823,plain,
% 1.72/1.82 ((~(e2 = e3)) <=> (~(op(e1, e1) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10822])).
% 1.72/1.82 tff(10824,plain,
% 1.72/1.82 (~(op(e1, e1) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1321, 10823])).
% 1.72/1.82 tff(10825,plain,
% 1.72/1.82 (op(e0, e1) = e3),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[1730, 10824, 10812, 10620])).
% 1.72/1.82 tff(10826,plain,
% 1.72/1.82 (e1 = op(e0, e3)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10777])).
% 1.72/1.82 tff(10827,plain,
% 1.72/1.82 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10826])).
% 1.72/1.82 tff(10828,plain,
% 1.72/1.82 (op(e3, e0) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[939, 10807, 9667, 10787])).
% 1.72/1.82 tff(10829,plain,
% 1.72/1.82 (op(e3, e0) = op(e0, e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[10828, 10827])).
% 1.72/1.82 tff(10830,plain,
% 1.72/1.82 (op(e0, e1) = e0),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[4953, 10829, 1304, 10771, 10783, 10777, 10812])).
% 1.72/1.82 tff(10831,plain,
% 1.72/1.82 (e0 = op(e0, e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10830])).
% 1.72/1.82 tff(10832,plain,
% 1.72/1.82 (op(e2, e2) = op(e3, e2)),
% 1.72/1.82 inference(transitivity,[status(thm)],[9300, 10831, 10825, 10809])).
% 1.72/1.82 tff(10833,plain,
% 1.72/1.82 ($false),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[1546, 10832])).
% 1.72/1.82 tff(10834,plain,((op(e2, e0) = e1) | (~(op(e2, e2) = e0)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (op(e1, e1) = e0) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.82 tff(10835,plain,
% 1.72/1.82 (op(e2, e0) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[10834, 84, 1304, 2812, 75, 9300, 76])).
% 1.72/1.82 tff(10836,plain,
% 1.72/1.82 (e1 = op(e2, e0)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10835])).
% 1.72/1.82 tff(10837,plain,
% 1.72/1.82 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e0))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10836])).
% 1.72/1.82 tff(10838,plain,
% 1.72/1.82 ((op(e2, e1) = e1) <=> (op(e2, e0) = op(e2, e1))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10837, 10625])).
% 1.72/1.82 tff(10839,plain,
% 1.72/1.82 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10838])).
% 1.72/1.82 tff(10840,plain,
% 1.72/1.82 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10839])).
% 1.72/1.82 tff(10841,plain,
% 1.72/1.82 (~(op(e2, e1) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1966, 10840])).
% 1.72/1.82 tff(10842,plain,
% 1.72/1.82 (op(e2, e1) = e2),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[2367, 10841, 10624, 10620])).
% 1.72/1.82 tff(10843,plain,
% 1.72/1.82 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10842])).
% 1.72/1.82 tff(10844,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10843])).
% 1.72/1.82 tff(10845,plain,
% 1.72/1.82 (~(op(e1, e1) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[225, 10844])).
% 1.72/1.82 tff(10846,plain,
% 1.72/1.82 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[9300])).
% 1.72/1.82 tff(10847,plain,
% 1.72/1.82 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10846, 4959])).
% 1.72/1.82 tff(10848,plain,
% 1.72/1.82 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10847])).
% 1.72/1.82 tff(10849,plain,
% 1.72/1.82 (~(op(e3, e2) = e0)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1546, 10848])).
% 1.72/1.82 tff(10850,plain,
% 1.72/1.82 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[7832])).
% 1.72/1.82 tff(10851,plain,
% 1.72/1.82 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10850])).
% 1.72/1.82 tff(10852,plain,
% 1.72/1.82 (~(op(e1, e0) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1312, 10851])).
% 1.72/1.82 tff(10853,plain,
% 1.72/1.82 (op(e1, op(e2, e2)) = op(e1, e0)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[9300])).
% 1.72/1.82 tff(10854,plain,
% 1.72/1.82 (op(e1, e0) = op(e1, op(e2, e2))),
% 1.72/1.82 inference(symmetry,[status(thm)],[10853])).
% 1.72/1.82 tff(10855,plain,
% 1.72/1.82 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e2)) = e1)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10854])).
% 1.72/1.82 tff(10856,plain,
% 1.72/1.82 ((op(e1, op(e2, e2)) = e1) <=> (op(e1, e0) = e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10855])).
% 1.72/1.82 tff(10857,plain,
% 1.72/1.82 ((op(e1, op(e2, e2)) = e1) <=> (op(e1, e0) = op(e2, e0))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10853, 768])).
% 1.72/1.82 tff(10858,plain,
% 1.72/1.82 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, op(e2, e2)) = e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10857])).
% 1.72/1.82 tff(10859,plain,
% 1.72/1.82 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10858, 10856])).
% 1.72/1.82 tff(10860,plain,
% 1.72/1.82 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10859])).
% 1.72/1.82 tff(10861,plain,
% 1.72/1.82 (~(op(e1, e0) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[756, 10860])).
% 1.72/1.82 tff(10862,plain,
% 1.72/1.82 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e0))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[768])).
% 1.72/1.82 tff(10863,plain,
% 1.72/1.82 ((op(e2, e1) = e1) <=> (op(e2, e0) = op(e2, e1))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10862, 10625])).
% 1.72/1.82 tff(10864,plain,
% 1.72/1.82 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10863])).
% 1.72/1.82 tff(10865,plain,
% 1.72/1.82 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10864])).
% 1.72/1.82 tff(10866,plain,
% 1.72/1.82 (~(op(e2, e1) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[1966, 10865])).
% 1.72/1.82 tff(10867,plain,
% 1.72/1.82 (op(e2, e1) = e2),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[2367, 10866, 10624, 10620])).
% 1.72/1.82 tff(10868,plain,
% 1.72/1.82 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10867])).
% 1.72/1.82 tff(10869,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10868])).
% 1.72/1.82 tff(10870,plain,
% 1.72/1.82 (~(op(e1, e1) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[225, 10869])).
% 1.72/1.82 tff(10871,plain,
% 1.72/1.82 (op(e2, e0) = op(e2, op(e2, e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[9326])).
% 1.72/1.82 tff(10872,plain,
% 1.72/1.82 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, op(e2, e2)) = e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10871, 10617])).
% 1.72/1.82 tff(10873,plain,
% 1.72/1.82 ((op(e2, e0) = op(e2, e3)) <=> (e3 = op(e2, op(e2, e2)))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10872, 10638])).
% 1.72/1.82 tff(10874,plain,
% 1.72/1.82 ((~(op(e2, e0) = op(e2, e3))) <=> (~(e3 = op(e2, op(e2, e2))))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10873])).
% 1.72/1.82 tff(10875,plain,
% 1.72/1.82 (~(e3 = op(e2, op(e2, e2)))),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[989, 10874])).
% 1.72/1.82 tff(10876,plain,
% 1.72/1.82 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10867])).
% 1.72/1.82 tff(10877,plain,
% 1.72/1.82 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10876])).
% 1.72/1.82 tff(10878,plain,
% 1.72/1.82 (~(op(e0, e1) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[606, 10877])).
% 1.72/1.82 tff(10879,plain,
% 1.72/1.82 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[7832])).
% 1.72/1.82 tff(10880,plain,
% 1.72/1.82 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10879])).
% 1.72/1.82 tff(10881,plain,
% 1.72/1.82 (~(op(e0, e2) = e2)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[6205, 10880])).
% 1.72/1.82 tff(10882,plain,
% 1.72/1.82 (op(e0, e0) = e2),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[3652, 10881, 10592, 10878])).
% 1.72/1.82 tff(10883,plain,
% 1.72/1.82 ((e3 = op(e0, op(e0, e0))) <=> (e3 = op(e0, e2))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[2381])).
% 1.72/1.82 tff(10884,plain,
% 1.72/1.82 ((e3 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e3)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10883, 4221])).
% 1.72/1.82 tff(10885,plain,
% 1.72/1.82 ((op(e0, e2) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 1.72/1.82 inference(symmetry,[status(thm)],[10884])).
% 1.72/1.82 tff(10886,plain,
% 1.72/1.82 ((e0 = e3) <=> (op(e2, e2) = e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[9326])).
% 1.72/1.82 tff(10887,plain,
% 1.72/1.82 ((~(e0 = e3)) <=> (~(op(e2, e2) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10886])).
% 1.72/1.82 tff(10888,plain,
% 1.72/1.82 (~(op(e2, e2) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[181, 10887])).
% 1.72/1.82 tff(10889,plain,
% 1.72/1.82 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[5523])).
% 1.72/1.82 tff(10890,plain,
% 1.72/1.82 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10889, 7793])).
% 1.72/1.82 tff(10891,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10890])).
% 1.72/1.82 tff(10892,plain,
% 1.72/1.82 (~(op(e3, e1) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[945, 10891])).
% 1.72/1.82 tff(10893,plain,
% 1.72/1.82 (op(e3, e2) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[939, 10892, 926, 6136])).
% 1.72/1.82 tff(10894,plain,
% 1.72/1.82 (op(e3, e2) = op(e2, op(e2, e2))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10893, 768, 10871])).
% 1.72/1.82 tff(10895,plain,
% 1.72/1.82 ((op(e3, e2) = e3) <=> (op(e2, op(e2, e2)) = e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10894])).
% 1.72/1.82 tff(10896,plain,
% 1.72/1.82 ((op(e3, e2) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10895, 10638])).
% 1.72/1.82 tff(10897,plain,
% 1.72/1.82 ((e3 = op(e2, op(e2, e2))) <=> (op(e3, e2) = e3)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10896])).
% 1.72/1.82 tff(10898,plain,
% 1.72/1.82 ((~(e3 = op(e2, op(e2, e2)))) <=> (~(op(e3, e2) = e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10897])).
% 1.72/1.82 tff(10899,assumption,(~(e3 = op(e2, op(e2, e2)))), introduced(assumption)).
% 1.72/1.82 tff(10900,plain,
% 1.72/1.82 (~(op(e3, e2) = e3)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[10899, 10898])).
% 1.72/1.82 tff(10901,plain,
% 1.72/1.82 (op(e0, e2) = e3),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[2111, 10900, 10888, 75])).
% 1.72/1.82 tff(10902,plain,
% 1.72/1.82 (e3 = op(e0, op(e0, e0))),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[10901, 10885])).
% 1.72/1.82 tff(10903,plain,
% 1.72/1.82 (op(e0, op(e0, e2)) = op(e0, e3)),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10901])).
% 1.72/1.82 tff(10904,plain,
% 1.72/1.82 (op(e0, e3) = op(e0, op(e0, e2))),
% 1.72/1.82 inference(symmetry,[status(thm)],[10903])).
% 1.72/1.82 tff(10905,plain,
% 1.72/1.82 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[5523])).
% 1.72/1.82 tff(10906,plain,
% 1.72/1.82 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 1.72/1.82 inference(transitivity,[status(thm)],[10905, 28])).
% 1.72/1.82 tff(10907,plain,
% 1.72/1.82 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 1.72/1.82 inference(monotonicity,[status(thm)],[10906])).
% 1.72/1.82 tff(10908,plain,
% 1.72/1.82 (~(op(e1, e3) = e1)),
% 1.72/1.82 inference(modus_ponens,[status(thm)],[619, 10907])).
% 1.72/1.82 tff(10909,plain,
% 1.72/1.82 (op(e0, e3) = e1),
% 1.72/1.82 inference(unit_resolution,[status(thm)],[151, 10908, 926, 76])).
% 1.72/1.82 tff(10910,plain,
% 1.72/1.82 (e1 = op(e0, e3)),
% 1.72/1.82 inference(symmetry,[status(thm)],[10909])).
% 1.72/1.82 tff(10911,plain,
% 1.72/1.82 (e1 = op(e0, op(e0, op(e0, e0)))),
% 1.72/1.82 inference(transitivity,[status(thm)],[10910, 10904, 8607])).
% 1.72/1.82 tff(10912,plain,
% 1.72/1.82 ((~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0))))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0)))))),
% 1.72/1.82 inference(rewrite,[status(thm)],[])).
% 1.72/1.83 tff(10913,plain,
% 1.72/1.83 (((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0))))))),
% 1.72/1.83 inference(rewrite,[status(thm)],[])).
% 1.72/1.83 tff(10914,plain,
% 1.72/1.83 ((~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0)))))))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10913])).
% 1.72/1.83 tff(10915,plain,
% 1.72/1.83 ((~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0)))))),
% 1.72/1.83 inference(transitivity,[status(thm)],[10914, 10912])).
% 1.72/1.83 tff(10916,plain,
% 1.72/1.83 ((~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))))),
% 1.72/1.83 inference(rewrite,[status(thm)],[])).
% 1.72/1.83 tff(10917,plain,
% 1.72/1.83 ((~(((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0))) & (e1 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0))))))),
% 1.72/1.83 inference(rewrite,[status(thm)],[])).
% 1.72/1.83 tff(10918,axiom,(~(((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0))) & (e1 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax11')).
% 1.72/1.83 tff(10919,plain,
% 1.72/1.83 (~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10918, 10917])).
% 1.72/1.83 tff(10920,plain,
% 1.72/1.83 (~((e3 = op(e0, op(e0, e0))) & (e2 = op(e0, e0)) & (e1 = op(e0, op(e0, op(e0, e0)))))),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10919, 10916])).
% 1.72/1.83 tff(10921,plain,
% 1.72/1.83 ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, op(e0, e0))))) | (~(e3 = op(e0, op(e0, e0))))),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10920, 10915])).
% 1.72/1.83 tff(10922,plain,
% 1.72/1.83 ($false),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[10921, 10911, 10902, 8486])).
% 1.72/1.83 tff(10923,plain,((~(op(e1, e1) = e1)) | (~(op(e0, e0) = e2)) | (op(e1, e2) = e3) | (e3 = op(e2, op(e2, e2))) | (~(op(e2, e0) = e1)) | (~(op(e2, e2) = e0)) | (op(e3, e3) = e1) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.83 tff(10924,plain,
% 1.72/1.83 (~(op(e1, e1) = e1)),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[10923, 10882, 75, 10875, 767, 9300, 9667, 76])).
% 1.72/1.83 tff(10925,plain,
% 1.72/1.83 (op(e1, e1) = e3),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[630, 10924, 84, 10870])).
% 1.72/1.83 tff(10926,plain,
% 1.72/1.83 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10925])).
% 1.72/1.83 tff(10927,plain,
% 1.72/1.83 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10926])).
% 1.72/1.83 tff(10928,plain,
% 1.72/1.83 (~(op(e1, e0) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[737, 10927])).
% 1.72/1.83 tff(10929,plain,
% 1.72/1.83 (op(e1, e0) = e0),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[728, 10928, 10861, 10852])).
% 1.72/1.83 tff(10930,plain,
% 1.72/1.83 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10929])).
% 1.72/1.83 tff(10931,plain,
% 1.72/1.83 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.72/1.83 inference(transitivity,[status(thm)],[10930, 8115])).
% 1.72/1.83 tff(10932,plain,
% 1.72/1.83 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10931])).
% 1.72/1.83 tff(10933,plain,
% 1.72/1.83 (~(op(e3, e0) = e0)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[410, 10932])).
% 1.72/1.83 tff(10934,plain,
% 1.72/1.83 ((op(e0, e0) = e3) <=> (e2 = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10882])).
% 1.72/1.83 tff(10935,plain,
% 1.72/1.83 ((e2 = e3) <=> (op(e0, e0) = e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10934])).
% 1.72/1.83 tff(10936,plain,
% 1.72/1.83 ((~(e2 = e3)) <=> (~(op(e0, e0) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10935])).
% 1.72/1.83 tff(10937,plain,
% 1.72/1.83 (~(op(e0, e0) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[1321, 10936])).
% 1.72/1.83 tff(10938,plain,
% 1.72/1.83 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10617])).
% 1.72/1.83 tff(10939,plain,
% 1.72/1.83 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10938])).
% 1.72/1.83 tff(10940,plain,
% 1.72/1.83 (~(op(e0, e3) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[964, 10939])).
% 1.72/1.83 tff(10941,plain,
% 1.72/1.83 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10925])).
% 1.72/1.83 tff(10942,plain,
% 1.72/1.83 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10941])).
% 1.72/1.83 tff(10943,plain,
% 1.72/1.83 (~(op(e0, e1) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[792, 10942])).
% 1.72/1.83 tff(10944,plain,
% 1.72/1.83 (op(e0, e2) = e3),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1495, 10943, 10940, 10937])).
% 1.72/1.83 tff(10945,plain,
% 1.72/1.83 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10944])).
% 1.72/1.83 tff(10946,plain,
% 1.72/1.83 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.72/1.83 inference(transitivity,[status(thm)],[10945, 3423])).
% 1.72/1.83 tff(10947,plain,
% 1.72/1.83 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10946])).
% 1.72/1.83 tff(10948,plain,
% 1.72/1.83 (~(op(e3, e2) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[1467, 10947])).
% 1.72/1.83 tff(10949,plain,
% 1.72/1.83 (~(op(e3, e1) = e0)),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[10084, 10948, 2812])).
% 1.72/1.83 tff(10950,plain,
% 1.72/1.83 ($false),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1916, 10949, 10933, 9696, 10849])).
% 1.72/1.83 tff(10951,plain,((~(op(e1, e2) = e2)) | (~(op(e3, e3) = e2)) | (op(e1, e1) = e0) | (op(e1, e2) = e3) | (~(op(e2, e0) = e1)) | (~(op(e2, e2) = e0)) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.83 tff(10952,plain,
% 1.72/1.83 (~(op(e1, e2) = e2)),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[10951, 84, 2812, 75, 10835, 9300, 76])).
% 1.72/1.83 tff(10953,plain,
% 1.72/1.83 (op(e1, e2) = e1),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1859, 10952, 75, 10671])).
% 1.72/1.83 tff(10954,plain,
% 1.72/1.83 (e1 = op(e1, e2)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10953])).
% 1.72/1.83 tff(10955,plain,
% 1.72/1.83 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10954])).
% 1.72/1.83 tff(10956,plain,
% 1.72/1.83 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10955])).
% 1.72/1.83 tff(10957,plain,
% 1.72/1.83 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10956])).
% 1.72/1.83 tff(10958,plain,
% 1.72/1.83 (~(op(e1, e1) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[1604, 10957])).
% 1.72/1.83 tff(10959,plain,
% 1.72/1.83 (op(e1, e1) = e3),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[630, 10958, 84, 10845])).
% 1.72/1.83 tff(10960,plain,
% 1.72/1.83 (e3 = op(e1, e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10959, 1740])).
% 1.72/1.83 tff(10961,plain,
% 1.72/1.83 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10959])).
% 1.72/1.83 tff(10962,plain,
% 1.72/1.83 (op(e1, e3) = op(e1, op(e1, e1))),
% 1.72/1.83 inference(symmetry,[status(thm)],[10961])).
% 1.72/1.83 tff(10963,plain,
% 1.72/1.83 ((op(e1, e3) = e1) <=> (op(e1, e3) = op(e1, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10954])).
% 1.72/1.83 tff(10964,plain,
% 1.72/1.83 ((op(e1, e3) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.72/1.83 inference(transitivity,[status(thm)],[10963, 125])).
% 1.72/1.83 tff(10965,plain,
% 1.72/1.83 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10964])).
% 1.72/1.83 tff(10966,plain,
% 1.72/1.83 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10965])).
% 1.72/1.83 tff(10967,plain,
% 1.72/1.83 (~(op(e1, e3) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[1850, 10966])).
% 1.72/1.83 tff(10968,plain,
% 1.72/1.83 (op(e1, e3) = e0),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[104, 10967, 10589, 10633])).
% 1.72/1.83 tff(10969,plain,
% 1.72/1.83 (e0 = op(e1, e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10968])).
% 1.72/1.83 tff(10970,plain,
% 1.72/1.83 (e0 = op(e1, op(e1, e1))),
% 1.72/1.83 inference(transitivity,[status(thm)],[10969, 10962])).
% 1.72/1.83 tff(10971,plain,
% 1.72/1.83 (op(e1, op(e1, e1)) = e0),
% 1.72/1.83 inference(transitivity,[status(thm)],[10961, 10968])).
% 1.72/1.83 tff(10972,plain,
% 1.72/1.83 (op(e1, op(e1, op(e1, e1))) = op(op(e2, e0), e0)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10836, 10971])).
% 1.72/1.83 tff(10973,plain,
% 1.72/1.83 (op(op(e2, e0), e0) = op(e1, op(e1, op(e1, e1)))),
% 1.72/1.83 inference(symmetry,[status(thm)],[10972])).
% 1.72/1.83 tff(10974,plain,
% 1.72/1.83 (op(op(e2, e0), e0) = op(e1, op(e2, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10835, 9326])).
% 1.72/1.83 tff(10975,plain,
% 1.72/1.83 (op(e1, op(e2, e2)) = op(op(e2, e0), e0)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10974])).
% 1.72/1.83 tff(10976,plain,
% 1.72/1.83 (op(e1, e0) = e2),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[2285, 10952, 10589, 10845])).
% 1.72/1.83 tff(10977,plain,
% 1.72/1.83 (e2 = op(e1, e0)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10976])).
% 1.72/1.83 tff(10978,plain,
% 1.72/1.83 (e2 = op(e1, op(e1, op(e1, e1)))),
% 1.72/1.83 inference(transitivity,[status(thm)],[10977, 10854, 10975, 10973])).
% 1.72/1.83 tff(10979,plain,
% 1.72/1.83 ($false),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[3009, 10978, 10970, 10960])).
% 1.72/1.83 tff(10980,plain,((op(e1, e1) = e0) | (~(op(e2, e2) = e0)) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (op(e2, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.83 tff(10981,plain,
% 1.72/1.83 (op(e1, e1) = e0),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[10980, 9300, 75, 2812, 76, 1304])).
% 1.72/1.83 tff(10982,plain,
% 1.72/1.83 (op(e1, e1) = op(e2, e2)),
% 1.72/1.83 inference(transitivity,[status(thm)],[10981, 9326])).
% 1.72/1.83 tff(10983,plain,
% 1.72/1.83 ((op(e1, e1) = e2) <=> (op(e2, e2) = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10982])).
% 1.72/1.83 tff(10984,plain,
% 1.72/1.83 ((op(e2, e2) = e2) <=> (op(e1, e1) = e2)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10983])).
% 1.72/1.83 tff(10985,plain,
% 1.72/1.83 ((~(op(e2, e2) = e2)) <=> (~(op(e1, e1) = e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10984])).
% 1.72/1.83 tff(10986,plain,
% 1.72/1.83 ((op(e2, e2) = e2) <=> (e0 = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[9300])).
% 1.72/1.83 tff(10987,plain,
% 1.72/1.83 ((e0 = e2) <=> (op(e2, e2) = e2)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10986])).
% 1.72/1.83 tff(10988,plain,
% 1.72/1.83 ((~(e0 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10987])).
% 1.72/1.83 tff(10989,plain,
% 1.72/1.83 (~(op(e2, e2) = e2)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[14, 10988])).
% 1.72/1.83 tff(10990,plain,
% 1.72/1.83 (~(op(e1, e1) = e2)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10989, 10985])).
% 1.72/1.83 tff(10991,plain,
% 1.72/1.83 ((op(e1, e1) = e3) <=> (op(e2, e2) = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10982])).
% 1.72/1.83 tff(10992,plain,
% 1.72/1.83 ((op(e2, e2) = e3) <=> (op(e1, e1) = e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10991])).
% 1.72/1.83 tff(10993,plain,
% 1.72/1.83 ((~(op(e2, e2) = e3)) <=> (~(op(e1, e1) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10992])).
% 1.72/1.83 tff(10994,plain,
% 1.72/1.83 (~(op(e1, e1) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10888, 10993])).
% 1.72/1.83 tff(10995,plain,
% 1.72/1.83 (op(e1, e0) = e3),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[247, 10994, 10633, 75])).
% 1.72/1.83 tff(10996,plain,
% 1.72/1.83 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10995])).
% 1.72/1.83 tff(10997,plain,
% 1.72/1.83 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 1.72/1.83 inference(transitivity,[status(thm)],[10996, 1314])).
% 1.72/1.83 tff(10998,plain,
% 1.72/1.83 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10997])).
% 1.72/1.83 tff(10999,plain,
% 1.72/1.83 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10998])).
% 1.72/1.83 tff(11000,plain,
% 1.72/1.83 (~(op(e1, e0) = e2)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[1321, 10999])).
% 1.72/1.83 tff(11001,plain,
% 1.72/1.83 (op(e1, e2) = e2),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[2285, 11000, 10589, 10990])).
% 1.72/1.83 tff(11002,plain,
% 1.72/1.83 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11001])).
% 1.72/1.83 tff(11003,plain,
% 1.72/1.83 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11002])).
% 1.72/1.83 tff(11004,plain,
% 1.72/1.83 (~(op(e0, e2) = e2)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[6205, 11003])).
% 1.72/1.83 tff(11005,plain,
% 1.72/1.83 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10981])).
% 1.72/1.83 tff(11006,plain,
% 1.72/1.83 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11005, 5470])).
% 1.72/1.83 tff(11007,plain,
% 1.72/1.83 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11006])).
% 1.72/1.83 tff(11008,plain,
% 1.72/1.83 (~(op(e3, e1) = e0)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[945, 11007])).
% 1.72/1.83 tff(11009,plain,
% 1.72/1.83 (op(e3, e0) = e0),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1916, 11008, 9696, 10849])).
% 1.72/1.83 tff(11010,plain,
% 1.72/1.83 ((op(e1, e1) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10981])).
% 1.72/1.83 tff(11011,plain,
% 1.72/1.83 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11010, 6095])).
% 1.72/1.83 tff(11012,plain,
% 1.72/1.83 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11011])).
% 1.72/1.83 tff(11013,plain,
% 1.72/1.83 (~(op(e1, e3) = e0)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[619, 11012])).
% 1.72/1.83 tff(11014,plain,
% 1.72/1.83 (op(e0, e3) = e0),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1098, 11013, 9696, 10616])).
% 1.72/1.83 tff(11015,plain,
% 1.72/1.83 (op(e0, e3) = op(e2, e2)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11014, 9326])).
% 1.72/1.83 tff(11016,plain,
% 1.72/1.83 (op(e3, op(e0, e3)) = op(e3, op(e2, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11015])).
% 1.72/1.83 tff(11017,plain,
% 1.72/1.83 (op(e3, op(e0, e3)) = op(e2, e2)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11016, 9330, 11009, 9326])).
% 1.72/1.83 tff(11018,plain,
% 1.72/1.83 ((op(e3, op(e0, e3)) = e3) <=> (op(e2, e2) = e3)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11017])).
% 1.72/1.83 tff(11019,plain,
% 1.72/1.83 ((op(e2, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11018])).
% 1.72/1.83 tff(11020,plain,
% 1.72/1.83 ((~(op(e2, e2) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11019])).
% 1.72/1.83 tff(11021,plain,
% 1.72/1.83 (~(op(e3, op(e0, e3)) = e3)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10888, 11020])).
% 1.72/1.83 tff(11022,plain,
% 1.72/1.83 (op(e1, e3) = e1),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[104, 11013, 10589, 10633])).
% 1.72/1.83 tff(11023,plain,
% 1.72/1.83 (e1 = op(e1, e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11022])).
% 1.72/1.83 tff(11024,plain,
% 1.72/1.83 (op(e1, op(e0, e3)) = op(e1, op(e2, e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11015])).
% 1.72/1.83 tff(11025,plain,
% 1.72/1.83 (op(e1, op(e0, e3)) = e3),
% 1.72/1.83 inference(transitivity,[status(thm)],[11024, 10853, 10995])).
% 1.72/1.83 tff(11026,plain,
% 1.72/1.83 ((op(e1, op(e0, e3)) = e1) <=> (e3 = op(e1, e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11025, 11023])).
% 1.72/1.83 tff(11027,plain,
% 1.72/1.83 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e3)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11026, 3230])).
% 1.72/1.83 tff(11028,plain,
% 1.72/1.83 ((op(e1, e3) = e3) <=> (op(e1, op(e0, e3)) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11027])).
% 1.72/1.83 tff(11029,plain,
% 1.72/1.83 ((~(op(e1, e3) = e3)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11028])).
% 1.72/1.83 tff(11030,plain,
% 1.72/1.83 (~(op(e1, op(e0, e3)) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10633, 11029])).
% 1.72/1.83 tff(11031,plain,
% 1.72/1.83 (op(e0, op(e0, e3)) = op(e0, e0)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11014])).
% 1.72/1.83 tff(11032,plain,
% 1.72/1.83 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e0) = e0)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11031])).
% 1.72/1.83 tff(11033,plain,
% 1.72/1.83 ((op(e0, e0) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11032])).
% 1.72/1.83 tff(11034,plain,
% 1.72/1.83 ((~(op(e0, e0) = e0)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11033])).
% 1.72/1.83 tff(11035,plain,
% 1.72/1.83 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e0)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11009])).
% 1.72/1.83 tff(11036,plain,
% 1.72/1.83 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e0))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11035])).
% 1.72/1.83 tff(11037,plain,
% 1.72/1.83 (~(op(e0, e0) = e0)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[6384, 11036])).
% 1.72/1.83 tff(11038,plain,
% 1.72/1.83 (~(op(e0, op(e0, e3)) = e0)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[11037, 11034])).
% 1.72/1.83 tff(11039,plain,
% 1.72/1.83 (op(e3, e0) = op(e0, e3)),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[5538, 11014, 11008, 10849])).
% 1.72/1.83 tff(11040,plain,
% 1.72/1.83 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11023])).
% 1.72/1.83 tff(11041,plain,
% 1.72/1.83 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11040])).
% 1.72/1.83 tff(11042,plain,
% 1.72/1.83 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11041])).
% 1.72/1.83 tff(11043,plain,
% 1.72/1.83 (~(op(e0, e3) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[64, 11042])).
% 1.72/1.83 tff(11044,plain,
% 1.72/1.83 (op(e2, op(e0, e3)) = e2),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[2487, 11043, 11039, 10940, 11022, 11038, 11013, 10994, 11030, 11021, 9696])).
% 1.72/1.83 tff(11045,plain,
% 1.72/1.83 (e0 = op(e0, e3)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11014])).
% 1.72/1.83 tff(11046,plain,
% 1.72/1.83 (op(e2, e2) = op(e0, e3)),
% 1.72/1.83 inference(transitivity,[status(thm)],[9300, 11045])).
% 1.72/1.83 tff(11047,plain,
% 1.72/1.83 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11046])).
% 1.72/1.83 tff(11048,plain,
% 1.72/1.83 (op(e2, e0) = e2),
% 1.72/1.83 inference(transitivity,[status(thm)],[10871, 11047, 11044])).
% 1.72/1.83 tff(11049,plain,
% 1.72/1.83 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11048])).
% 1.72/1.83 tff(11050,plain,
% 1.72/1.83 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11049])).
% 1.72/1.83 tff(11051,plain,
% 1.72/1.83 (~(op(e0, e0) = e2)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[359, 11050])).
% 1.72/1.83 tff(11052,plain,
% 1.72/1.83 (op(e0, e1) = e2),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[3652, 11051, 10592, 11004])).
% 1.72/1.83 tff(11053,plain,
% 1.72/1.83 (op(e0, op(e1, e3)) = op(e0, e1)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11022])).
% 1.72/1.83 tff(11054,plain,
% 1.72/1.83 ((e1 = op(e1, op(e2, e2))) <=> (op(e1, op(e2, e2)) = e1)),
% 1.72/1.83 inference(commutativity,[status(thm)],[])).
% 1.72/1.83 tff(11055,plain,
% 1.72/1.83 (e3 = op(e1, e0)),
% 1.72/1.83 inference(symmetry,[status(thm)],[10995])).
% 1.72/1.83 tff(11056,plain,
% 1.72/1.83 (e3 = op(e1, op(e2, e2))),
% 1.72/1.83 inference(transitivity,[status(thm)],[11055, 10854])).
% 1.72/1.83 tff(11057,plain,
% 1.72/1.83 ((e1 = e3) <=> (e1 = op(e1, op(e2, e2)))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11056])).
% 1.72/1.83 tff(11058,plain,
% 1.72/1.83 ((e1 = e3) <=> (op(e1, op(e2, e2)) = e1)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11057, 11054])).
% 1.72/1.83 tff(11059,plain,
% 1.72/1.83 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11058, 10856])).
% 1.72/1.83 tff(11060,plain,
% 1.72/1.83 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11059])).
% 1.72/1.83 tff(11061,plain,
% 1.72/1.83 (~(op(e1, e0) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[303, 11060])).
% 1.72/1.83 tff(11062,plain,
% 1.72/1.83 (op(e3, e0) = op(e2, e2)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11009, 9326])).
% 1.72/1.83 tff(11063,plain,
% 1.72/1.83 ((op(e3, e0) = e1) <=> (op(e2, e2) = e1)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11062])).
% 1.72/1.83 tff(11064,plain,
% 1.72/1.83 ((op(e2, e2) = e1) <=> (op(e3, e0) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11063])).
% 1.72/1.83 tff(11065,plain,
% 1.72/1.83 ((~(op(e2, e2) = e1)) <=> (~(op(e3, e0) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11064])).
% 1.72/1.83 tff(11066,plain,
% 1.72/1.83 (~(op(e3, e0) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10636, 11065])).
% 1.72/1.83 tff(11067,plain,
% 1.72/1.83 ((op(e2, op(e2, e2)) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 1.72/1.83 inference(commutativity,[status(thm)],[])).
% 1.72/1.83 tff(11068,plain,
% 1.72/1.83 ((op(e2, e0) = e1) <=> (op(e2, op(e2, e2)) = e1)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[10871])).
% 1.72/1.83 tff(11069,plain,
% 1.72/1.83 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 1.72/1.83 inference(transitivity,[status(thm)],[11068, 11067])).
% 1.72/1.83 tff(11070,plain,
% 1.72/1.83 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e1)),
% 1.72/1.83 inference(symmetry,[status(thm)],[11069])).
% 1.72/1.83 tff(11071,plain,
% 1.72/1.83 (op(e2, op(e2, e2)) = e2),
% 1.72/1.83 inference(transitivity,[status(thm)],[11047, 11044])).
% 1.72/1.83 tff(11072,plain,
% 1.72/1.83 ((e1 = op(e2, op(e2, e2))) <=> (op(e1, e3) = e2)),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11023, 11071])).
% 1.72/1.83 tff(11073,plain,
% 1.72/1.83 ((op(e1, e3) = e2) <=> (e1 = op(e2, op(e2, e2)))),
% 1.72/1.83 inference(symmetry,[status(thm)],[11072])).
% 1.72/1.83 tff(11074,plain,
% 1.72/1.83 ((op(e1, e3) = e2) <=> (op(e2, e0) = e1)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11073, 11070])).
% 1.72/1.83 tff(11075,plain,
% 1.72/1.83 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e1))),
% 1.72/1.83 inference(monotonicity,[status(thm)],[11074])).
% 1.72/1.83 tff(11076,plain,
% 1.72/1.83 (~(op(e2, e0) = e1)),
% 1.72/1.83 inference(modus_ponens,[status(thm)],[10589, 11075])).
% 1.72/1.83 tff(11077,plain,
% 1.72/1.83 (op(e0, e0) = e1),
% 1.72/1.83 inference(unit_resolution,[status(thm)],[1480, 11076, 11066, 11061])).
% 1.72/1.83 tff(11078,plain,
% 1.72/1.83 (op(e0, e0) = op(e1, e3)),
% 1.72/1.83 inference(transitivity,[status(thm)],[11077, 11023])).
% 1.72/1.83 tff(11079,plain,
% 1.72/1.83 (op(e0, op(e0, e0)) = op(e0, op(e1, e3))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11078])).
% 1.72/1.84 tff(11080,plain,
% 1.72/1.84 (op(e0, op(e0, e0)) = e2),
% 1.72/1.84 inference(transitivity,[status(thm)],[11079, 11053, 11052])).
% 1.72/1.84 tff(11081,plain,
% 1.72/1.84 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11080])).
% 1.72/1.84 tff(11082,plain,
% 1.72/1.84 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (e3 = op(e0, e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11081])).
% 1.72/1.84 tff(11083,plain,
% 1.72/1.84 ((e3 = op(e0, op(e0, op(e0, e0)))) <=> (op(e0, e2) = e3)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11082, 4221])).
% 1.72/1.84 tff(11084,plain,
% 1.72/1.84 ((op(e0, e2) = e3) <=> (e3 = op(e0, op(e0, op(e0, e0))))),
% 1.72/1.84 inference(symmetry,[status(thm)],[11083])).
% 1.72/1.84 tff(11085,plain,
% 1.72/1.84 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[9300])).
% 1.72/1.84 tff(11086,plain,
% 1.72/1.84 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11085])).
% 1.72/1.84 tff(11087,plain,
% 1.72/1.84 (~(op(e0, e2) = e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[2736, 11086])).
% 1.72/1.84 tff(11088,plain,
% 1.72/1.84 ((op(e0, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11077])).
% 1.72/1.84 tff(11089,plain,
% 1.72/1.84 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11088, 697])).
% 1.72/1.84 tff(11090,plain,
% 1.72/1.84 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11089])).
% 1.72/1.84 tff(11091,plain,
% 1.72/1.84 (~(op(e0, e2) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[3603, 11090])).
% 1.72/1.84 tff(11092,plain,
% 1.72/1.84 (op(e0, e2) = e3),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[2745, 11091, 11087, 11004])).
% 1.72/1.84 tff(11093,plain,
% 1.72/1.84 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[11092, 11084])).
% 1.72/1.84 tff(11094,plain,
% 1.72/1.84 (e1 = op(e0, e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[11077, 74])).
% 1.72/1.84 tff(11095,plain,
% 1.72/1.84 (op(e0, op(e1, e3)) = op(e0, op(e0, e0))),
% 1.72/1.84 inference(symmetry,[status(thm)],[11079])).
% 1.72/1.84 tff(11096,plain,
% 1.72/1.84 (op(e0, e1) = op(e0, op(e1, e3))),
% 1.72/1.84 inference(symmetry,[status(thm)],[11053])).
% 1.72/1.84 tff(11097,plain,
% 1.72/1.84 (e2 = op(e0, e1)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11052])).
% 1.72/1.84 tff(11098,plain,
% 1.72/1.84 (e2 = op(e0, op(e0, e0))),
% 1.72/1.84 inference(transitivity,[status(thm)],[11097, 11096, 11095])).
% 1.72/1.84 tff(11099,plain,
% 1.72/1.84 (~(e3 = op(e0, op(e0, op(e0, e0))))),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[3582, 11098, 11094])).
% 1.72/1.84 tff(11100,plain,
% 1.72/1.84 ($false),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[11099, 11093])).
% 1.72/1.84 tff(11101,plain,((~(op(e2, e2) = e0)) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (op(e2, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.84 tff(11102,plain,
% 1.72/1.84 (~(op(e2, e2) = e0)),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[11101, 76, 2812, 75, 1304])).
% 1.72/1.84 tff(11103,plain,
% 1.72/1.84 (op(e1, e3) = e3),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[104, 80, 10589, 87])).
% 1.72/1.84 tff(11104,plain,
% 1.72/1.84 (e3 = op(e1, e3)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11103])).
% 1.72/1.84 tff(11105,plain,
% 1.72/1.84 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11104])).
% 1.72/1.84 tff(11106,plain,
% 1.72/1.84 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11105])).
% 1.72/1.84 tff(11107,plain,
% 1.72/1.84 (op(e0, e3) = e1),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[151, 87, 9667, 76])).
% 1.72/1.84 tff(11108,plain,
% 1.72/1.84 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11107])).
% 1.72/1.84 tff(11109,plain,
% 1.72/1.84 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11108, 18])).
% 1.72/1.84 tff(11110,plain,
% 1.72/1.84 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11109])).
% 1.72/1.84 tff(11111,plain,
% 1.72/1.84 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11110])).
% 1.72/1.84 tff(11112,plain,
% 1.72/1.84 (~(op(e0, e3) = e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[26, 11111])).
% 1.72/1.84 tff(11113,plain,
% 1.72/1.84 (op(e2, e3) = e0),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1098, 80, 9696, 11112])).
% 1.72/1.84 tff(11114,plain,
% 1.72/1.84 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11107])).
% 1.72/1.84 tff(11115,plain,
% 1.72/1.84 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11114])).
% 1.72/1.84 tff(11116,plain,
% 1.72/1.84 (~(op(e0, e0) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[3414, 11115])).
% 1.72/1.84 tff(11117,plain,
% 1.72/1.84 (op(e3, op(e3, e2)) = op(e3, e0)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[5819])).
% 1.72/1.84 tff(11118,plain,
% 1.72/1.84 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.72/1.84 inference(transitivity,[status(thm)],[6490, 11117])).
% 1.72/1.84 tff(11119,plain,
% 1.72/1.84 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11118])).
% 1.72/1.84 tff(11120,plain,
% 1.72/1.84 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11119, 6411])).
% 1.72/1.84 tff(11121,plain,
% 1.72/1.84 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11120])).
% 1.72/1.84 tff(11122,plain,
% 1.72/1.84 (e0 = op(e3, op(e3, e3))),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[5819, 6497])).
% 1.72/1.84 tff(11123,plain,
% 1.72/1.84 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[5879, 11122, 2813])).
% 1.72/1.84 tff(11124,plain,
% 1.72/1.84 (~(op(e3, e0) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[11123, 11121])).
% 1.72/1.84 tff(11125,plain,
% 1.72/1.84 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[6665])).
% 1.72/1.84 tff(11126,plain,
% 1.72/1.84 (~(op(e1, e2) = e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[2292, 11125])).
% 1.72/1.84 tff(11127,plain,
% 1.72/1.84 (op(e1, e0) = e0),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1830, 11126, 84, 80])).
% 1.72/1.84 tff(11128,plain,
% 1.72/1.84 ((op(e1, e0) = e1) <=> (e0 = e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11127])).
% 1.72/1.84 tff(11129,plain,
% 1.72/1.84 ((e0 = e1) <=> (op(e1, e0) = e1)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11128])).
% 1.72/1.84 tff(11130,plain,
% 1.72/1.84 ((~(e0 = e1)) <=> (~(op(e1, e0) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11129])).
% 1.72/1.84 tff(11131,plain,
% 1.72/1.84 (~(op(e1, e0) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[26, 11130])).
% 1.72/1.84 tff(11132,plain,
% 1.72/1.84 ($false),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1480, 11131, 11124, 1349, 2379])).
% 1.72/1.84 tff(11133,plain,((~(op(e3, e2) = e0)) | (op(e2, e0) = e1) | (op(e0, e0) = e1) | (~(op(e3, e3) = e2)) | (op(e1, e1) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.84 tff(11134,plain,
% 1.72/1.84 (~(op(e3, e2) = e0)),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[11133, 80, 11116, 2812, 84, 1349])).
% 1.72/1.84 tff(11135,plain,
% 1.72/1.84 (e3 = op(e1, e3)),
% 1.72/1.84 inference(symmetry,[status(thm)],[164])).
% 1.72/1.84 tff(11136,plain,
% 1.72/1.84 (op(e3, e2) = e1),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1898, 1890, 85, 9699])).
% 1.72/1.84 tff(11137,plain,
% 1.72/1.84 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11136])).
% 1.72/1.84 tff(11138,plain,
% 1.72/1.84 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11137])).
% 1.72/1.84 tff(11139,plain,
% 1.72/1.84 (~(op(e2, e2) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[1546, 11138])).
% 1.72/1.84 tff(11140,plain,
% 1.72/1.84 (op(e2, e1) = e1),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[345, 11139, 76, 1349])).
% 1.72/1.84 tff(11141,plain,
% 1.72/1.84 ((op(e2, e1) = e3) <=> (e1 = op(e1, e3))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11140, 11135])).
% 1.72/1.84 tff(11142,plain,
% 1.72/1.84 ((op(e2, e1) = e3) <=> (op(e1, e3) = e1)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11141, 28])).
% 1.72/1.84 tff(11143,plain,
% 1.72/1.84 ((op(e1, e3) = e1) <=> (op(e2, e1) = e3)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11142])).
% 1.72/1.84 tff(11144,plain,
% 1.72/1.84 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e1) = e3))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11143])).
% 1.72/1.84 tff(11145,plain,
% 1.72/1.84 (~(op(e2, e1) = e3)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[87, 11144])).
% 1.72/1.84 tff(11146,plain,
% 1.72/1.84 (~(op(e3, e1) = e0)),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[10084, 1890, 2812])).
% 1.72/1.84 tff(11147,plain,
% 1.72/1.84 (op(e3, e0) = e0),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1916, 11146, 9696, 85])).
% 1.72/1.84 tff(11148,plain,
% 1.72/1.84 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[251])).
% 1.72/1.84 tff(11149,plain,
% 1.72/1.84 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11148])).
% 1.72/1.84 tff(11150,plain,
% 1.72/1.84 (~(op(e2, e1) = e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[197, 11149])).
% 1.72/1.84 tff(11151,plain,
% 1.72/1.84 (op(e0, e1) = e0),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[292, 11146, 84, 11150])).
% 1.72/1.84 tff(11152,plain,
% 1.72/1.84 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11151])).
% 1.72/1.84 tff(11153,plain,
% 1.72/1.84 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11152])).
% 1.72/1.84 tff(11154,plain,
% 1.72/1.84 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11153])).
% 1.72/1.84 tff(11155,plain,
% 1.72/1.84 (~(op(e0, e1) = e2)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[14, 11154])).
% 1.72/1.84 tff(11156,plain,
% 1.72/1.84 ((op(e2, e1) = e2) <=> (e1 = e2)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11140])).
% 1.72/1.84 tff(11157,plain,
% 1.72/1.84 ((e1 = e2) <=> (op(e2, e1) = e2)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11156])).
% 1.72/1.84 tff(11158,plain,
% 1.72/1.84 ((~(e1 = e2)) <=> (~(op(e2, e1) = e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11157])).
% 1.72/1.84 tff(11159,plain,
% 1.72/1.84 (~(op(e2, e1) = e2)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[708, 11158])).
% 1.72/1.84 tff(11160,plain,
% 1.72/1.84 (op(e1, e1) = e2),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1993, 11159, 9684, 11155])).
% 1.72/1.84 tff(11161,plain,
% 1.72/1.84 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11136])).
% 1.72/1.84 tff(11162,plain,
% 1.72/1.84 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e1))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11161])).
% 1.72/1.84 tff(11163,plain,
% 1.72/1.84 (~(op(e3, e1) = e1)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[3429, 11162])).
% 1.72/1.84 tff(11164,plain,
% 1.72/1.84 (op(e3, e1) = e3),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[446, 11163, 11146, 9684])).
% 1.72/1.84 tff(11165,plain,
% 1.72/1.84 (op(op(e1, e3), e1) = op(e3, e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[164])).
% 1.72/1.84 tff(11166,plain,
% 1.72/1.84 (op(e3, e1) = op(e1, e3)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11164, 11135])).
% 1.72/1.84 tff(11167,plain,
% 1.72/1.84 (op(op(e3, e1), e1) = op(op(e1, e3), e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11166])).
% 1.72/1.84 tff(11168,plain,
% 1.72/1.84 (op(op(e3, e1), e1) = e3),
% 1.72/1.84 inference(transitivity,[status(thm)],[11167, 11165, 11164])).
% 1.72/1.84 tff(11169,plain,
% 1.72/1.84 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[2416, 11168])).
% 1.72/1.84 tff(11170,plain,
% 1.72/1.84 (op(e2, op(e2, e1)) = op(e2, e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11140])).
% 1.72/1.84 tff(11171,plain,
% 1.72/1.84 (op(e2, op(e2, e1)) = e1),
% 1.72/1.84 inference(transitivity,[status(thm)],[11170, 11140])).
% 1.72/1.84 tff(11172,plain,
% 1.72/1.84 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[1355, 11171])).
% 1.72/1.84 tff(11173,plain,
% 1.72/1.84 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11151])).
% 1.72/1.84 tff(11174,plain,
% 1.72/1.84 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 1.72/1.84 inference(transitivity,[status(thm)],[11173, 10200])).
% 1.72/1.84 tff(11175,plain,
% 1.72/1.84 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11174])).
% 1.72/1.84 tff(11176,plain,
% 1.72/1.84 (~(op(e0, e2) = e0)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[2102, 11175])).
% 1.72/1.84 tff(11177,plain,
% 1.72/1.84 (op(e1, e2) = e0),
% 1.72/1.84 inference(unit_resolution,[status(thm)],[973, 11176, 11102, 85])).
% 1.72/1.84 tff(11178,plain,
% 1.72/1.84 (op(op(e1, e2), e1) = op(e0, e1)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11177])).
% 1.72/1.84 tff(11179,plain,
% 1.72/1.84 (op(op(e1, e2), e1) = e0),
% 1.72/1.84 inference(transitivity,[status(thm)],[11178, 11151])).
% 1.72/1.84 tff(11180,plain,
% 1.72/1.84 ((op(op(e1, e2), e1) = e2) <=> (e0 = e2)),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11179])).
% 1.72/1.84 tff(11181,plain,
% 1.72/1.84 ((e0 = e2) <=> (op(op(e1, e2), e1) = e2)),
% 1.72/1.84 inference(symmetry,[status(thm)],[11180])).
% 1.72/1.84 tff(11182,plain,
% 1.72/1.84 ((~(e0 = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 1.72/1.84 inference(monotonicity,[status(thm)],[11181])).
% 1.72/1.84 tff(11183,plain,
% 1.72/1.84 (~(op(op(e1, e2), e1) = e2)),
% 1.72/1.84 inference(modus_ponens,[status(thm)],[14, 11182])).
% 1.72/1.84 tff(11184,plain,
% 1.72/1.84 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[5959, 11183])).
% 1.74/1.84 tff(11185,plain,
% 1.74/1.84 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11151])).
% 1.74/1.84 tff(11186,plain,
% 1.74/1.84 (op(op(e0, e1), e1) = e0),
% 1.74/1.84 inference(transitivity,[status(thm)],[11185, 11151])).
% 1.74/1.84 tff(11187,plain,
% 1.74/1.84 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2650, 11186])).
% 1.74/1.84 tff(11188,plain,
% 1.74/1.84 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11136])).
% 1.74/1.84 tff(11189,plain,
% 1.74/1.84 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11188])).
% 1.74/1.84 tff(11190,plain,
% 1.74/1.84 (~(op(e3, e0) = e1)),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[1133, 11189])).
% 1.74/1.84 tff(11191,plain,
% 1.74/1.84 (op(e1, e0) = e1),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[1480, 11190, 1349, 11116])).
% 1.74/1.84 tff(11192,plain,
% 1.74/1.84 (op(op(e1, e0), e0) = op(e1, e0)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11191])).
% 1.74/1.84 tff(11193,plain,
% 1.74/1.84 (op(op(e1, e0), e0) = e1),
% 1.74/1.84 inference(transitivity,[status(thm)],[11192, 11191])).
% 1.74/1.84 tff(11194,plain,
% 1.74/1.84 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[3015, 11193])).
% 1.74/1.84 tff(11195,plain,
% 1.74/1.84 (op(op(e0, e3), e0) = op(e1, e0)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11107])).
% 1.74/1.84 tff(11196,plain,
% 1.74/1.84 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11195])).
% 1.74/1.84 tff(11197,plain,
% 1.74/1.84 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11196])).
% 1.74/1.84 tff(11198,plain,
% 1.74/1.84 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11135])).
% 1.74/1.84 tff(11199,plain,
% 1.74/1.84 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11198])).
% 1.74/1.84 tff(11200,plain,
% 1.74/1.84 ((op(e1, e0) = op(e1, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 1.74/1.84 inference(transitivity,[status(thm)],[11199, 11197])).
% 1.74/1.84 tff(11201,plain,
% 1.74/1.84 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11200])).
% 1.74/1.84 tff(11202,plain,
% 1.74/1.84 (~(op(op(e0, e3), e0) = e3)),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[110, 11201])).
% 1.74/1.84 tff(11203,plain,
% 1.74/1.84 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2635, 11202])).
% 1.74/1.84 tff(11204,plain,
% 1.74/1.84 (op(e1, op(e1, e3)) = e3),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[169, 164])).
% 1.74/1.84 tff(11205,plain,
% 1.74/1.84 (op(op(e3, e2), e3) = op(e1, op(e1, e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11136, 11135])).
% 1.74/1.84 tff(11206,plain,
% 1.74/1.84 (op(op(e3, e2), e3) = op(e1, e3)),
% 1.74/1.84 inference(transitivity,[status(thm)],[11205, 11204, 11135])).
% 1.74/1.84 tff(11207,plain,
% 1.74/1.84 ((op(op(e3, e2), e3) = e2) <=> (op(e1, e3) = e2)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11206])).
% 1.74/1.84 tff(11208,plain,
% 1.74/1.84 ((op(e1, e3) = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11207])).
% 1.74/1.84 tff(11209,plain,
% 1.74/1.84 ((~(op(e1, e3) = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11208])).
% 1.74/1.84 tff(11210,plain,
% 1.74/1.84 (~(op(op(e3, e2), e3) = e2)),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[10589, 11209])).
% 1.74/1.84 tff(11211,plain,
% 1.74/1.84 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2408, 11210])).
% 1.74/1.84 tff(11212,plain,
% 1.74/1.84 (op(e2, op(e2, e3)) = op(e2, e0)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[251])).
% 1.74/1.84 tff(11213,plain,
% 1.74/1.84 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e0) = e3)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11212])).
% 1.74/1.84 tff(11214,plain,
% 1.74/1.84 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11213])).
% 1.74/1.84 tff(11215,plain,
% 1.74/1.84 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e1, e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11135])).
% 1.74/1.84 tff(11216,plain,
% 1.74/1.84 ((op(e2, e3) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 1.74/1.84 inference(transitivity,[status(thm)],[11215, 1687])).
% 1.74/1.84 tff(11217,plain,
% 1.74/1.84 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11216])).
% 1.74/1.84 tff(11218,plain,
% 1.74/1.84 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11217])).
% 1.74/1.84 tff(11219,plain,
% 1.74/1.84 (~(op(e2, e3) = e3)),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[118, 11218])).
% 1.74/1.84 tff(11220,plain,
% 1.74/1.84 (op(e2, e0) = e3),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[1559, 2431, 11219, 3271])).
% 1.74/1.84 tff(11221,plain,
% 1.74/1.84 (op(e2, op(e2, e3)) = e3),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[11220, 11214])).
% 1.74/1.84 tff(11222,plain,
% 1.74/1.84 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2344, 11221])).
% 1.74/1.84 tff(11223,assumption,(op(e3, e0) = e0), introduced(assumption)).
% 1.74/1.84 tff(11224,plain,
% 1.74/1.84 (op(e3, op(e3, e0)) = op(e3, e0)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11223])).
% 1.74/1.84 tff(11225,plain,
% 1.74/1.84 (op(e3, op(e3, e0)) = e0),
% 1.74/1.84 inference(transitivity,[status(thm)],[11224, 11223])).
% 1.74/1.84 tff(11226,plain,
% 1.74/1.84 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[1345, 11225])).
% 1.74/1.84 tff(11227,plain,
% 1.74/1.84 (op(e2, op(e1, e3)) = op(e2, e3)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[164])).
% 1.74/1.84 tff(11228,plain,
% 1.74/1.84 (op(e2, e0) = op(e1, e3)),
% 1.74/1.84 inference(transitivity,[status(thm)],[11220, 11135])).
% 1.74/1.84 tff(11229,plain,
% 1.74/1.84 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11228])).
% 1.74/1.84 tff(11230,plain,
% 1.74/1.84 (op(e2, op(e2, e0)) = e0),
% 1.74/1.84 inference(transitivity,[status(thm)],[11229, 11227, 251])).
% 1.74/1.84 tff(11231,plain,
% 1.74/1.84 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2653, 11230])).
% 1.74/1.84 tff(11232,plain,
% 1.74/1.84 (op(op(e0, e2), e0) = e0),
% 1.74/1.84 inference(transitivity,[status(thm)],[5991, 11223])).
% 1.74/1.84 tff(11233,plain,
% 1.74/1.84 ((op(op(e0, e2), e0) = e2) <=> (e0 = op(e1, e1))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11232, 4872])).
% 1.74/1.84 tff(11234,plain,
% 1.74/1.84 ((op(op(e0, e2), e0) = e2) <=> (op(e1, e1) = e0)),
% 1.74/1.84 inference(transitivity,[status(thm)],[11233, 122])).
% 1.74/1.84 tff(11235,plain,
% 1.74/1.84 ((op(e1, e1) = e0) <=> (op(op(e0, e2), e0) = e2)),
% 1.74/1.84 inference(symmetry,[status(thm)],[11234])).
% 1.74/1.84 tff(11236,plain,
% 1.74/1.84 ((~(op(e1, e1) = e0)) <=> (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11235])).
% 1.74/1.84 tff(11237,plain,
% 1.74/1.84 (~(op(op(e0, e2), e0) = e2)),
% 1.74/1.84 inference(modus_ponens,[status(thm)],[84, 11236])).
% 1.74/1.84 tff(11238,plain,
% 1.74/1.84 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[2446, 11237])).
% 1.74/1.84 tff(11239,plain,
% 1.74/1.84 ($false),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[1459, 11238, 11231, 3341, 11226, 3342, 1304, 1357, 4549, 1358, 1936, 1275, 11222])).
% 1.74/1.84 tff(11240,plain,((op(e2, e2) = e3) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e1, e1) = e0) | (~(op(e1, e1) = e2)) | (~(op(e3, e0) = e0)) | (~(op(e2, e3) = e0)) | (~(op(e1, e3) = e3)) | (op(e3, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.84 tff(11241,plain,
% 1.74/1.84 (op(e2, e2) = e3),
% 1.74/1.84 inference(unit_resolution,[status(thm)],[11240, 11211, 11203, 1304, 11194, 11187, 11184, 11172, 11169, 84, 11160, 11147, 251, 164, 1890, 75, 11145])).
% 1.74/1.84 tff(11242,plain,
% 1.74/1.84 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.74/1.84 inference(monotonicity,[status(thm)],[11241])).
% 1.74/1.85 tff(11243,plain,
% 1.74/1.85 ((op(e0, e2) = op(e2, e2)) <=> (op(op(e2, e3), e2) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11242, 5090])).
% 1.74/1.85 tff(11244,plain,
% 1.74/1.85 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11243])).
% 1.74/1.85 tff(11245,plain,
% 1.74/1.85 (~(op(op(e2, e3), e2) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[2736, 11244])).
% 1.74/1.85 tff(11246,plain,
% 1.74/1.85 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1934, 11245])).
% 1.74/1.85 tff(11247,plain,
% 1.74/1.85 (op(e3, op(e3, e0)) = op(e3, e0)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11147])).
% 1.74/1.85 tff(11248,plain,
% 1.74/1.85 (op(e3, op(e3, e0)) = e0),
% 1.74/1.85 inference(transitivity,[status(thm)],[11247, 11147])).
% 1.74/1.85 tff(11249,plain,
% 1.74/1.85 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1345, 11248])).
% 1.74/1.85 tff(11250,plain,
% 1.74/1.85 (e2 = op(e1, e1)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11160])).
% 1.74/1.85 tff(11251,plain,
% 1.74/1.85 (op(e2, e2) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11241, 11135])).
% 1.74/1.85 tff(11252,plain,
% 1.74/1.85 ((op(e2, e2) = e2) <=> (op(e1, e3) = op(e1, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11251, 11250])).
% 1.74/1.85 tff(11253,plain,
% 1.74/1.85 ((op(e2, e2) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 1.74/1.85 inference(transitivity,[status(thm)],[11252, 5020])).
% 1.74/1.85 tff(11254,plain,
% 1.74/1.85 ((op(e1, e1) = op(e1, e3)) <=> (op(e2, e2) = e2)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11253])).
% 1.74/1.85 tff(11255,plain,
% 1.74/1.85 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e2, e2) = e2))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11254])).
% 1.74/1.85 tff(11256,plain,
% 1.74/1.85 (~(op(e2, e2) = e2)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[619, 11255])).
% 1.74/1.85 tff(11257,plain,
% 1.74/1.85 (op(e2, e0) = e2),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2088, 11256, 9692, 11159])).
% 1.74/1.85 tff(11258,plain,
% 1.74/1.85 (op(op(e2, e0), e0) = op(e2, e0)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11257])).
% 1.74/1.85 tff(11259,plain,
% 1.74/1.85 (op(op(e2, e0), e0) = e2),
% 1.74/1.85 inference(transitivity,[status(thm)],[11258, 11257])).
% 1.74/1.85 tff(11260,plain,
% 1.74/1.85 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1945, 11259])).
% 1.74/1.85 tff(11261,plain,
% 1.74/1.85 ((op(e1, e2) = e2) <=> (e0 = e2)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11177])).
% 1.74/1.85 tff(11262,plain,
% 1.74/1.85 ((e0 = e2) <=> (op(e1, e2) = e2)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11261])).
% 1.74/1.85 tff(11263,plain,
% 1.74/1.85 ((~(e0 = e2)) <=> (~(op(e1, e2) = e2))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11262])).
% 1.74/1.85 tff(11264,plain,
% 1.74/1.85 (~(op(e1, e2) = e2)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[14, 11263])).
% 1.74/1.85 tff(11265,plain,
% 1.74/1.85 (op(e0, e2) = e2),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1151, 11256, 9699, 11264])).
% 1.74/1.85 tff(11266,plain,
% 1.74/1.85 (op(e0, op(e1, e1)) = op(e0, e2)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11160])).
% 1.74/1.85 tff(11267,plain,
% 1.74/1.85 (op(e0, e2) = op(e1, e1)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11265, 11250])).
% 1.74/1.85 tff(11268,plain,
% 1.74/1.85 (op(e0, op(e0, e2)) = op(e0, op(e1, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11267])).
% 1.74/1.85 tff(11269,plain,
% 1.74/1.85 (op(e0, op(e0, e2)) = e2),
% 1.74/1.85 inference(transitivity,[status(thm)],[11268, 11266, 11265])).
% 1.74/1.85 tff(11270,plain,
% 1.74/1.85 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1331, 11269])).
% 1.74/1.85 tff(11271,plain,
% 1.74/1.85 ($false),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1459, 11270, 11260, 11211, 11249, 11203, 1304, 11194, 11187, 11184, 11172, 11169, 11246])).
% 1.74/1.85 tff(11272,plain,((op(e3, e2) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e2, e3) = e0)) | (~(op(e1, e3) = e3)) | (op(e1, e1) = e0) | (op(e1, e2) = e3) | (op(e1, e3) = e1) | (op(e3, e2) = e0) | (op(e2, e0) = e1) | (op(e2, e3) = e1) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.85 tff(11273,plain,
% 1.74/1.85 (op(e3, e2) = e3),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[11272, 11134, 11113, 11103, 84, 75, 87, 1304, 1349, 76, 2812])).
% 1.74/1.85 tff(11274,plain,
% 1.74/1.85 (op(e3, e2) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11273, 11104])).
% 1.74/1.85 tff(11275,plain,
% 1.74/1.85 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11274])).
% 1.74/1.85 tff(11276,plain,
% 1.74/1.85 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11275, 11106])).
% 1.74/1.85 tff(11277,plain,
% 1.74/1.85 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11276])).
% 1.74/1.85 tff(11278,plain,
% 1.74/1.85 (~(op(e3, e1) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[3429, 11277])).
% 1.74/1.85 tff(11279,plain,
% 1.74/1.85 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11107])).
% 1.74/1.85 tff(11280,plain,
% 1.74/1.85 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11279])).
% 1.74/1.85 tff(11281,plain,
% 1.74/1.85 (~(op(e0, e2) = e1)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[918, 11280])).
% 1.74/1.85 tff(11282,plain,
% 1.74/1.85 (op(e3, e2) = e3),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[11272, 85, 251, 164, 84, 75, 87, 1304, 1349, 76, 2812])).
% 1.74/1.85 tff(11283,plain,
% 1.74/1.85 (op(e3, e2) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11282, 11135])).
% 1.74/1.85 tff(11284,plain,
% 1.74/1.85 ((op(e3, e2) = e1) <=> (op(e1, e3) = e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11283])).
% 1.74/1.85 tff(11285,plain,
% 1.74/1.85 ((op(e1, e3) = e1) <=> (op(e3, e2) = e1)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11284])).
% 1.74/1.85 tff(11286,plain,
% 1.74/1.85 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11285])).
% 1.74/1.85 tff(11287,plain,
% 1.74/1.85 (~(op(e3, e2) = e1)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[87, 11286])).
% 1.74/1.85 tff(11288,plain,
% 1.74/1.85 (op(e2, e2) = e1),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1613, 11287, 11281, 4515])).
% 1.74/1.85 tff(11289,plain,
% 1.74/1.85 (e1 = op(e2, e2)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[11288, 317])).
% 1.74/1.85 tff(11290,plain,
% 1.74/1.85 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11288])).
% 1.74/1.85 tff(11291,plain,
% 1.74/1.85 ((e3 = op(e2, op(e2, e2))) <=> (e3 = op(e2, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11290])).
% 1.74/1.85 tff(11292,plain,
% 1.74/1.85 ((e3 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11291, 1262])).
% 1.74/1.85 tff(11293,plain,
% 1.74/1.85 ((op(e2, e1) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.74/1.85 inference(symmetry,[status(thm)],[11292])).
% 1.74/1.85 tff(11294,plain,
% 1.74/1.85 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11288])).
% 1.74/1.85 tff(11295,plain,
% 1.74/1.85 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11294])).
% 1.74/1.85 tff(11296,plain,
% 1.74/1.85 (~(op(e2, e1) = e1)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[508, 11295])).
% 1.74/1.85 tff(11297,plain,
% 1.74/1.85 (op(e3, op(e3, e3)) = e3),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[11282, 9701])).
% 1.74/1.85 tff(11298,plain,
% 1.74/1.85 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[6277, 11297])).
% 1.74/1.85 tff(11299,plain,
% 1.74/1.85 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11135])).
% 1.74/1.85 tff(11300,plain,
% 1.74/1.85 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11299])).
% 1.74/1.85 tff(11301,plain,
% 1.74/1.85 (op(e3, e2) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[856, 11135])).
% 1.74/1.85 tff(11302,plain,
% 1.74/1.85 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11301])).
% 1.74/1.85 tff(11303,plain,
% 1.74/1.85 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11302, 11300])).
% 1.74/1.85 tff(11304,plain,
% 1.74/1.85 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11303])).
% 1.74/1.85 tff(11305,plain,
% 1.74/1.85 (~(op(e3, e1) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[3429, 11304])).
% 1.74/1.85 tff(11306,plain,
% 1.74/1.85 (op(e1, e1) = e1),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[630, 68, 84, 1291])).
% 1.74/1.85 tff(11307,plain,
% 1.74/1.85 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11306])).
% 1.74/1.85 tff(11308,plain,
% 1.74/1.85 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11307, 7793])).
% 1.74/1.85 tff(11309,plain,
% 1.74/1.85 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11308])).
% 1.74/1.85 tff(11310,plain,
% 1.74/1.85 (~(op(e3, e1) = e1)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[945, 11309])).
% 1.74/1.85 tff(11311,plain,
% 1.74/1.85 (op(e3, e1) = e0),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[446, 11310, 11305, 82])).
% 1.74/1.85 tff(11312,plain,
% 1.74/1.85 (e0 = op(e3, e1)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11311])).
% 1.74/1.85 tff(11313,plain,
% 1.74/1.85 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[19])).
% 1.74/1.85 tff(11314,plain,
% 1.74/1.85 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11313])).
% 1.74/1.85 tff(11315,plain,
% 1.74/1.85 (~(op(e0, e2) = e1)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[918, 11314])).
% 1.74/1.85 tff(11316,plain,
% 1.74/1.85 (op(e2, e2) = e1),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1613, 930, 11315, 4515])).
% 1.74/1.85 tff(11317,plain,
% 1.74/1.85 ((op(e2, e2) = e2) <=> (e1 = e2)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11316])).
% 1.74/1.85 tff(11318,plain,
% 1.74/1.85 ((e1 = e2) <=> (op(e2, e2) = e2)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11317])).
% 1.74/1.85 tff(11319,plain,
% 1.74/1.85 ((~(e1 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11318])).
% 1.74/1.85 tff(11320,plain,
% 1.74/1.85 (~(op(e2, e2) = e2)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[708, 11319])).
% 1.74/1.85 tff(11321,plain,
% 1.74/1.85 ((op(e0, e2) = op(e3, e2)) <=> (op(op(e2, e3), e2) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[1463, 5090])).
% 1.74/1.85 tff(11322,plain,
% 1.74/1.85 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11321])).
% 1.74/1.85 tff(11323,plain,
% 1.74/1.85 (~(op(op(e2, e3), e2) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[1467, 11322])).
% 1.74/1.85 tff(11324,plain,
% 1.74/1.85 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1934, 11323])).
% 1.74/1.85 tff(11325,plain,
% 1.74/1.85 (op(e3, e0) = e1),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[939, 11310, 926, 930])).
% 1.74/1.85 tff(11326,plain,
% 1.74/1.85 (op(e3, op(e3, e1)) = op(e3, e0)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11311])).
% 1.74/1.85 tff(11327,plain,
% 1.74/1.85 (op(e3, op(e3, e1)) = e1),
% 1.74/1.85 inference(transitivity,[status(thm)],[11326, 11325])).
% 1.74/1.85 tff(11328,plain,
% 1.74/1.85 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2594, 11327])).
% 1.74/1.85 tff(11329,plain,
% 1.74/1.85 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e3, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11312])).
% 1.74/1.85 tff(11330,plain,
% 1.74/1.85 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11329])).
% 1.74/1.85 tff(11331,plain,
% 1.74/1.85 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11330])).
% 1.74/1.85 tff(11332,plain,
% 1.74/1.85 (~(op(e0, e1) = e0)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[3046, 11331])).
% 1.74/1.85 tff(11333,plain,
% 1.74/1.85 (op(e0, e1) = e3),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[5000, 11332, 19, 1468])).
% 1.74/1.85 tff(11334,plain,
% 1.74/1.85 (op(e0, e1) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11333, 11135])).
% 1.74/1.85 tff(11335,plain,
% 1.74/1.85 ((op(e0, e1) = e2) <=> (op(e1, e3) = e2)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11334])).
% 1.74/1.85 tff(11336,plain,
% 1.74/1.85 ((op(e1, e3) = e2) <=> (op(e0, e1) = e2)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11335])).
% 1.74/1.85 tff(11337,plain,
% 1.74/1.85 ((~(op(e1, e3) = e2)) <=> (~(op(e0, e1) = e2))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11336])).
% 1.74/1.85 tff(11338,plain,
% 1.74/1.85 (~(op(e0, e1) = e2)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[72, 11337])).
% 1.74/1.85 tff(11339,plain,
% 1.74/1.85 (op(e2, e1) = e2),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1993, 11338, 82, 68])).
% 1.74/1.85 tff(11340,plain,
% 1.74/1.85 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11339])).
% 1.74/1.85 tff(11341,plain,
% 1.74/1.85 (op(e2, op(e2, e1)) = e1),
% 1.74/1.85 inference(transitivity,[status(thm)],[11340, 11316])).
% 1.74/1.85 tff(11342,plain,
% 1.74/1.85 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1355, 11341])).
% 1.74/1.85 tff(11343,plain,
% 1.74/1.85 (op(e0, op(e1, e3)) = op(e0, e3)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[164])).
% 1.74/1.85 tff(11344,plain,
% 1.74/1.85 (op(op(e3, e1), e3) = op(e0, op(e1, e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11311, 11135])).
% 1.74/1.85 tff(11345,plain,
% 1.74/1.85 (op(e0, op(e0, e1)) = op(op(e3, e1), e3)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11312, 11333])).
% 1.74/1.85 tff(11346,plain,
% 1.74/1.85 (op(e0, op(e0, e1)) = e1),
% 1.74/1.85 inference(transitivity,[status(thm)],[11345, 11344, 11343, 19])).
% 1.74/1.85 tff(11347,plain,
% 1.74/1.85 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2449, 11346])).
% 1.74/1.85 tff(11348,plain,
% 1.74/1.85 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11333])).
% 1.74/1.85 tff(11349,plain,
% 1.74/1.85 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11348, 1262])).
% 1.74/1.85 tff(11350,plain,
% 1.74/1.85 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11349])).
% 1.74/1.85 tff(11351,plain,
% 1.74/1.85 (~(op(e2, e1) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[606, 11350])).
% 1.74/1.85 tff(11352,plain,
% 1.74/1.85 (op(e2, e0) = e3),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1559, 11351, 11219, 1547])).
% 1.74/1.85 tff(11353,plain,
% 1.74/1.85 (op(e2, e0) = op(e1, e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11352, 11135])).
% 1.74/1.85 tff(11354,plain,
% 1.74/1.85 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11353])).
% 1.74/1.85 tff(11355,plain,
% 1.74/1.85 (op(e2, op(e2, e0)) = e0),
% 1.74/1.85 inference(transitivity,[status(thm)],[11354, 11227, 251])).
% 1.74/1.85 tff(11356,plain,
% 1.74/1.85 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2653, 11355])).
% 1.74/1.85 tff(11357,plain,
% 1.74/1.85 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[5069])).
% 1.74/1.85 tff(11358,plain,
% 1.74/1.85 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.74/1.85 inference(symmetry,[status(thm)],[11357])).
% 1.74/1.85 tff(11359,plain,
% 1.74/1.85 ((op(e1, e0) = op(e1, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11199, 11358])).
% 1.74/1.85 tff(11360,plain,
% 1.74/1.85 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11359])).
% 1.74/1.85 tff(11361,plain,
% 1.74/1.85 (~(op(op(e0, e3), e0) = e3)),
% 1.74/1.85 inference(modus_ponens,[status(thm)],[110, 11360])).
% 1.74/1.85 tff(11362,plain,
% 1.74/1.85 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2635, 11361])).
% 1.74/1.85 tff(11363,plain,
% 1.74/1.85 (op(e3, op(e3, e0)) = op(op(e1, e3), e1)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11135, 11325])).
% 1.74/1.85 tff(11364,plain,
% 1.74/1.85 (op(e3, op(e3, e0)) = e0),
% 1.74/1.85 inference(transitivity,[status(thm)],[11363, 11165, 11311])).
% 1.74/1.85 tff(11365,plain,
% 1.74/1.85 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1345, 11364])).
% 1.74/1.85 tff(11366,plain,
% 1.74/1.85 (op(e1, op(e3, e1)) = op(e1, e0)),
% 1.74/1.85 inference(monotonicity,[status(thm)],[4731])).
% 1.74/1.85 tff(11367,plain,
% 1.74/1.85 (op(e1, e2) = e0),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1859, 3785, 75, 4515])).
% 1.74/1.85 tff(11368,plain,
% 1.74/1.85 (op(e1, e2) = op(e3, e1)),
% 1.74/1.85 inference(transitivity,[status(thm)],[11367, 4734])).
% 1.74/1.85 tff(11369,plain,
% 1.74/1.85 (op(e1, op(e1, e2)) = op(e1, op(e3, e1))),
% 1.74/1.85 inference(monotonicity,[status(thm)],[11368])).
% 1.74/1.85 tff(11370,plain,
% 1.74/1.85 (op(e1, op(e1, e2)) = e2),
% 1.74/1.85 inference(transitivity,[status(thm)],[11369, 11366, 8406])).
% 1.74/1.85 tff(11371,plain,
% 1.74/1.85 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[2377, 11370])).
% 1.74/1.85 tff(11372,plain,
% 1.74/1.85 (op(e1, op(e1, e0)) = e0),
% 1.74/1.85 inference(transitivity,[status(thm)],[9774, 11367])).
% 1.74/1.85 tff(11373,plain,
% 1.74/1.85 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1836, 11372])).
% 1.74/1.85 tff(11374,plain,
% 1.74/1.85 (op(e0, e2) = e2),
% 1.74/1.85 inference(unit_resolution,[status(thm)],[1151, 3785, 2386, 5548])).
% 1.74/1.85 tff(11375,plain,
% 1.74/1.86 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11374])).
% 1.74/1.86 tff(11376,plain,
% 1.74/1.86 (op(e0, op(e0, e2)) = e2),
% 1.74/1.86 inference(transitivity,[status(thm)],[11375, 11374])).
% 1.74/1.86 tff(11377,plain,
% 1.74/1.86 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[1331, 11376])).
% 1.74/1.86 tff(11378,plain,
% 1.74/1.86 ($false),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[1459, 11377, 11373, 3341, 1926, 3342, 1304, 2421, 4549, 11371, 1936, 1275, 1347])).
% 1.74/1.86 tff(11379,plain,((op(e1, e2) = e2) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e3, e1) = e0)) | (op(e3, e2) = e2) | (op(e2, e2) = e2) | (op(e1, e3) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e3) | (op(e1, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.86 tff(11380,plain,
% 1.74/1.86 (op(e1, e2) = e2),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11379, 11365, 9773, 11362, 1304, 11356, 11347, 11342, 11328, 11324, 11311, 2386, 11320, 72, 68, 75, 4515])).
% 1.74/1.86 tff(11381,plain,
% 1.74/1.86 ((op(e1, e2) = e0) <=> (e2 = op(e3, e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11380, 11312])).
% 1.74/1.86 tff(11382,plain,
% 1.74/1.86 ((op(e1, e2) = e0) <=> (op(e3, e1) = e2)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11381, 637])).
% 1.74/1.86 tff(11383,plain,
% 1.74/1.86 ((op(e3, e1) = e2) <=> (op(e1, e2) = e0)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11382])).
% 1.74/1.86 tff(11384,plain,
% 1.74/1.86 ((~(op(e3, e1) = e2)) <=> (~(op(e1, e2) = e0))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11383])).
% 1.74/1.86 tff(11385,plain,
% 1.74/1.86 (~(op(e1, e2) = e0)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[82, 11384])).
% 1.74/1.86 tff(11386,plain,
% 1.74/1.86 (op(e0, e2) = e0),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[973, 11385, 17, 85])).
% 1.74/1.86 tff(11387,plain,
% 1.74/1.86 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11380])).
% 1.74/1.86 tff(11388,plain,
% 1.74/1.86 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11387])).
% 1.74/1.86 tff(11389,plain,
% 1.74/1.86 (~(op(e0, e2) = e2)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[6205, 11388])).
% 1.74/1.86 tff(11390,plain,
% 1.74/1.86 (op(e0, e0) = e2),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[3652, 11389, 79, 11338])).
% 1.74/1.86 tff(11391,plain,
% 1.74/1.86 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11390])).
% 1.74/1.86 tff(11392,plain,
% 1.74/1.86 (op(e0, op(e0, e0)) = e0),
% 1.74/1.86 inference(transitivity,[status(thm)],[11391, 11386])).
% 1.74/1.86 tff(11393,plain,
% 1.74/1.86 ((op(e2, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11352])).
% 1.74/1.86 tff(11394,plain,
% 1.74/1.86 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11393, 4221])).
% 1.74/1.86 tff(11395,plain,
% 1.74/1.86 ((op(e0, e2) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 1.74/1.86 inference(symmetry,[status(thm)],[11394])).
% 1.74/1.86 tff(11396,plain,
% 1.74/1.86 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 1.74/1.86 inference(transitivity,[status(thm)],[11395, 6337])).
% 1.74/1.86 tff(11397,plain,
% 1.74/1.86 ((~(op(e0, e2) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11396])).
% 1.74/1.86 tff(11398,plain,
% 1.74/1.86 (~(op(e0, e2) = op(e2, e0))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[1468, 11397])).
% 1.74/1.86 tff(11399,plain,
% 1.74/1.86 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6347, 11398])).
% 1.74/1.86 tff(11400,plain,
% 1.74/1.86 ((op(e3, e2) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.74/1.86 inference(transitivity,[status(thm)],[9730, 395])).
% 1.74/1.86 tff(11401,plain,
% 1.74/1.86 ((~(op(e3, e2) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11400])).
% 1.74/1.86 tff(11402,plain,
% 1.74/1.86 (~(op(e2, e3) = op(e3, e2))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[85, 11401])).
% 1.74/1.86 tff(11403,plain,
% 1.74/1.86 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[430, 11402])).
% 1.74/1.86 tff(11404,plain,
% 1.74/1.86 ((~(op(e0, e2) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11395])).
% 1.74/1.86 tff(11405,plain,
% 1.74/1.86 (~(op(e2, e0) = op(e0, e2))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[1468, 11404])).
% 1.74/1.86 tff(11406,plain,
% 1.74/1.86 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6358, 11405])).
% 1.74/1.86 tff(11407,plain,
% 1.74/1.86 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11302])).
% 1.74/1.86 tff(11408,plain,
% 1.74/1.86 (~(op(e3, e1) = op(e1, e3))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[3429, 11407])).
% 1.74/1.86 tff(11409,plain,
% 1.74/1.86 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6362, 11408])).
% 1.74/1.86 tff(11410,plain,
% 1.74/1.86 ((~(op(e3, e2) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[9730])).
% 1.74/1.86 tff(11411,plain,
% 1.74/1.86 (~(op(e3, e2) = op(e2, e3))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[85, 11410])).
% 1.74/1.86 tff(11412,plain,
% 1.74/1.86 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[500, 11411])).
% 1.74/1.86 tff(11413,plain,
% 1.74/1.86 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = op(e1, e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11334])).
% 1.74/1.86 tff(11414,plain,
% 1.74/1.86 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 1.74/1.86 inference(symmetry,[status(thm)],[11413])).
% 1.74/1.86 tff(11415,plain,
% 1.74/1.86 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11414])).
% 1.74/1.86 tff(11416,plain,
% 1.74/1.86 (~(op(e1, e0) = op(e0, e1))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[110, 11415])).
% 1.74/1.86 tff(11417,plain,
% 1.74/1.86 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[613, 11416])).
% 1.74/1.86 tff(11418,plain,
% 1.74/1.86 ((op(e1, e0) = op(e1, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 1.74/1.86 inference(transitivity,[status(thm)],[11414, 596])).
% 1.74/1.86 tff(11419,plain,
% 1.74/1.86 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11418])).
% 1.74/1.86 tff(11420,plain,
% 1.74/1.86 (~(op(e0, e1) = op(e1, e0))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[110, 11419])).
% 1.74/1.86 tff(11421,plain,
% 1.74/1.86 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[609, 11420])).
% 1.74/1.86 tff(11422,plain,
% 1.74/1.86 (op(e1, op(e3, e0)) = op(e1, e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11325])).
% 1.74/1.86 tff(11423,plain,
% 1.74/1.86 (op(e1, op(e3, e0)) = e1),
% 1.74/1.86 inference(transitivity,[status(thm)],[11422, 11306])).
% 1.74/1.86 tff(11424,plain,
% 1.74/1.86 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[8474, 11423])).
% 1.74/1.86 tff(11425,plain,
% 1.74/1.86 (op(e1, op(e2, e2)) = op(e1, e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11316])).
% 1.74/1.86 tff(11426,plain,
% 1.74/1.86 ((op(e1, op(e2, e2)) = e1) <=> (op(e1, e1) = e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11425])).
% 1.74/1.86 tff(11427,plain,
% 1.74/1.86 ((op(e1, e1) = e1) <=> (op(e1, op(e2, e2)) = e1)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11426])).
% 1.74/1.86 tff(11428,plain,
% 1.74/1.86 (op(e1, op(e2, e2)) = e1),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[11306, 11427])).
% 1.74/1.86 tff(11429,plain,
% 1.74/1.86 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6714, 11428])).
% 1.74/1.86 tff(11430,plain,
% 1.74/1.86 (op(e3, op(e2, e1)) = op(e3, e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11339])).
% 1.74/1.86 tff(11431,plain,
% 1.74/1.86 (op(e3, op(e2, e1)) = e3),
% 1.74/1.86 inference(transitivity,[status(thm)],[11430, 856])).
% 1.74/1.86 tff(11432,plain,
% 1.74/1.86 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6334, 11431])).
% 1.74/1.86 tff(11433,plain,
% 1.74/1.86 (op(e1, op(e1, e1)) = op(e1, e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11306])).
% 1.74/1.86 tff(11434,plain,
% 1.74/1.86 (op(e1, op(e1, e1)) = e1),
% 1.74/1.86 inference(transitivity,[status(thm)],[11433, 11306])).
% 1.74/1.86 tff(11435,plain,
% 1.74/1.86 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[5678, 11434])).
% 1.74/1.86 tff(11436,plain,
% 1.74/1.86 ((op(e3, e1) = op(e3, e2)) <=> (op(e1, e3) = op(e3, e1))),
% 1.74/1.86 inference(transitivity,[status(thm)],[11302, 6290])).
% 1.74/1.86 tff(11437,plain,
% 1.74/1.86 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11436])).
% 1.74/1.86 tff(11438,plain,
% 1.74/1.86 (~(op(e1, e3) = op(e3, e1))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[3429, 11437])).
% 1.74/1.86 tff(11439,plain,
% 1.74/1.86 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[6307, 11438])).
% 1.74/1.86 tff(11440,plain,
% 1.74/1.86 (op(e3, op(e1, e2)) = op(e3, e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11380])).
% 1.74/1.86 tff(11441,plain,
% 1.74/1.86 (op(e3, op(e1, e2)) = e3),
% 1.74/1.86 inference(transitivity,[status(thm)],[11440, 856])).
% 1.74/1.86 tff(11442,plain,
% 1.74/1.86 (((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)) | (~(op(e3, op(e1, e2)) = e3))),
% 1.74/1.86 inference(tautology,[status(thm)],[])).
% 1.74/1.86 tff(11443,plain,
% 1.74/1.86 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11442, 11441])).
% 1.74/1.86 tff(11444,plain,
% 1.74/1.86 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[5367, 11443, 11439, 11435, 11432, 11429, 11424, 11421, 6688, 11417, 11412, 11409, 11406, 11403, 11399])).
% 1.74/1.86 tff(11445,plain,
% 1.74/1.86 (~(op(e0, op(e0, e0)) = e0)),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[5598, 11444])).
% 1.74/1.86 tff(11446,plain,
% 1.74/1.86 ($false),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11445, 11392])).
% 1.74/1.86 tff(11447,plain,((op(e1, e1) = e2) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (op(e0, e3) = e2) | (op(e2, e2) = e0) | (op(e3, e2) = e0) | (~(op(e3, e2) = e3)) | (op(e3, e1) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e3, e2) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e2) = e1) | (~(op(e2, e3) = e0)) | (~(op(e1, e3) = e3)) | (~(op(e0, e3) = e1)) | (op(e3, e3) = e1) | (op(e3, e2) = e1) | (op(e1, e1) = e0) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.86 tff(11448,plain,
% 1.74/1.86 (op(e1, e1) = e2),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11447, 11298, 10592, 11102, 85, 11282, 9684, 1304, 9699, 10589, 75, 4515, 251, 164, 11107, 9667, 11287, 84, 1291])).
% 1.74/1.86 tff(11449,plain,
% 1.74/1.86 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11448])).
% 1.74/1.86 tff(11450,plain,
% 1.74/1.86 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11449, 1960])).
% 1.74/1.86 tff(11451,plain,
% 1.74/1.86 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11450])).
% 1.74/1.86 tff(11452,plain,
% 1.74/1.86 (~(op(e2, e1) = e2)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[225, 11451])).
% 1.74/1.86 tff(11453,plain,
% 1.74/1.86 (op(e2, e1) = e3),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[2367, 11452, 11150, 11296])).
% 1.74/1.86 tff(11454,plain,
% 1.74/1.86 (e3 = op(e2, op(e2, e2))),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[11453, 11293])).
% 1.74/1.86 tff(11455,plain,
% 1.74/1.86 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11290])).
% 1.74/1.86 tff(11456,plain,
% 1.74/1.86 (op(e2, op(e2, e1)) = op(e2, op(e2, op(e2, e2)))),
% 1.74/1.86 inference(symmetry,[status(thm)],[11455])).
% 1.74/1.86 tff(11457,plain,
% 1.74/1.86 (op(e2, e1) = op(e1, e3)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11453, 11135])).
% 1.74/1.86 tff(11458,plain,
% 1.74/1.86 (op(e2, op(e2, e1)) = op(e2, op(e1, e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11457])).
% 1.74/1.86 tff(11459,plain,
% 1.74/1.86 (op(e2, op(e1, e3)) = op(e2, op(e2, e1))),
% 1.74/1.86 inference(symmetry,[status(thm)],[11458])).
% 1.74/1.86 tff(11460,plain,
% 1.74/1.86 (op(e2, e3) = op(e2, op(e1, e3))),
% 1.74/1.86 inference(symmetry,[status(thm)],[11227])).
% 1.74/1.86 tff(11461,plain,
% 1.74/1.86 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.74/1.86 inference(transitivity,[status(thm)],[252, 11460, 11459, 11456])).
% 1.74/1.86 tff(11462,plain,
% 1.74/1.86 ($false),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[334, 11461, 11454, 11289])).
% 1.74/1.86 tff(11463,plain,((op(e3, e2) = e0) | (~(op(e2, e3) = e0)) | (~(op(e1, e3) = e3)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e2) = e3) | (op(e1, e2) = e1) | (op(e1, e1) = e0) | (op(e1, e1) = e3) | (op(e1, e3) = e1) | (~(op(e3, e3) = e2)) | (op(e2, e0) = e1) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.86 tff(11464,plain,
% 1.74/1.86 (op(e1, e2) = e1),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11463, 11134, 11103, 1304, 75, 11113, 84, 1291, 87, 2812, 1349, 76])).
% 1.74/1.86 tff(11465,plain,
% 1.74/1.86 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11464])).
% 1.74/1.86 tff(11466,plain,
% 1.74/1.86 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11465, 316])).
% 1.74/1.86 tff(11467,plain,
% 1.74/1.86 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11466])).
% 1.74/1.86 tff(11468,plain,
% 1.74/1.86 (~(op(e2, e2) = e1)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[1273, 11467])).
% 1.74/1.86 tff(11469,plain,
% 1.74/1.86 (op(e2, e1) = e1),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[345, 11468, 76, 1349])).
% 1.74/1.86 tff(11470,plain,
% 1.74/1.86 ((op(e2, e1) = e2) <=> (e1 = e2)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11469])).
% 1.74/1.86 tff(11471,plain,
% 1.74/1.86 ((e1 = e2) <=> (op(e2, e1) = e2)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11470])).
% 1.74/1.86 tff(11472,plain,
% 1.74/1.86 ((~(e1 = e2)) <=> (~(op(e2, e1) = e2))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11471])).
% 1.74/1.86 tff(11473,plain,
% 1.74/1.86 (~(op(e2, e1) = e2)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[708, 11472])).
% 1.74/1.86 tff(11474,plain,
% 1.74/1.86 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11464])).
% 1.74/1.86 tff(11475,plain,
% 1.74/1.86 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11474])).
% 1.74/1.86 tff(11476,plain,
% 1.74/1.86 (~(op(e1, e1) = e1)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[1604, 11475])).
% 1.74/1.86 tff(11477,plain,
% 1.74/1.86 (e1 = op(e0, e3)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11107])).
% 1.74/1.86 tff(11478,plain,
% 1.74/1.86 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11477])).
% 1.74/1.86 tff(11479,plain,
% 1.74/1.86 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11464])).
% 1.74/1.86 tff(11480,plain,
% 1.74/1.86 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11479])).
% 1.74/1.86 tff(11481,plain,
% 1.74/1.86 (~(op(e1, e0) = e1)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[1312, 11480])).
% 1.74/1.86 tff(11482,plain,
% 1.74/1.86 (op(e3, e0) = e1),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[1480, 11481, 1349, 11116])).
% 1.74/1.86 tff(11483,plain,
% 1.74/1.86 (op(e3, e0) = op(e0, e3)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[11482, 11478])).
% 1.74/1.86 tff(11484,plain,
% 1.74/1.86 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11464])).
% 1.74/1.86 tff(11485,plain,
% 1.74/1.86 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11484, 18])).
% 1.74/1.86 tff(11486,plain,
% 1.74/1.86 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11485])).
% 1.74/1.86 tff(11487,plain,
% 1.74/1.86 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11486])).
% 1.74/1.86 tff(11488,plain,
% 1.74/1.86 (~(op(e1, e2) = e0)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[26, 11487])).
% 1.74/1.86 tff(11489,plain,
% 1.74/1.86 (op(e0, e2) = e0),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[973, 11488, 11102, 11134])).
% 1.74/1.86 tff(11490,plain,
% 1.74/1.86 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11489])).
% 1.74/1.86 tff(11491,plain,
% 1.74/1.86 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11490])).
% 1.74/1.86 tff(11492,plain,
% 1.74/1.86 (~(op(e0, e1) = e0)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[2102, 11491])).
% 1.74/1.86 tff(11493,plain,
% 1.74/1.86 ($false),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[5154, 11492, 11483, 11107, 1304, 80, 9696, 11476, 11473, 11278])).
% 1.74/1.86 tff(11494,plain,((op(e1, e3) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e0) = e1) | (op(e2, e3) = e1) | (op(e1, e2) = e3) | (op(e1, e1) = e0) | (op(e1, e1) = e3) | (op(e1, e3) = e1) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.86 tff(11495,plain,
% 1.74/1.86 (op(e1, e3) = e0),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[11494, 87, 1349, 76, 75, 84, 1291, 1304, 2812])).
% 1.74/1.86 tff(11496,plain,
% 1.74/1.86 (e0 = op(e1, e3)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11495])).
% 1.74/1.86 tff(11497,plain,
% 1.74/1.86 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11496])).
% 1.74/1.86 tff(11498,plain,
% 1.74/1.86 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11497])).
% 1.74/1.86 tff(11499,plain,
% 1.74/1.86 (~(op(e1, e3) = e3)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[181, 11498])).
% 1.74/1.86 tff(11500,plain,
% 1.74/1.86 (op(e1, e0) = e3),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[247, 11499, 1291, 75])).
% 1.74/1.86 tff(11501,plain,
% 1.74/1.86 ((op(e1, e0) = e1) <=> (e3 = e1)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11500])).
% 1.74/1.86 tff(11502,plain,
% 1.74/1.86 ((op(e1, e0) = e1) <=> (e1 = e3)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11501, 128])).
% 1.74/1.86 tff(11503,plain,
% 1.74/1.86 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11502])).
% 1.74/1.86 tff(11504,plain,
% 1.74/1.86 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11503])).
% 1.74/1.86 tff(11505,plain,
% 1.74/1.86 (~(op(e1, e0) = e1)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[303, 11504])).
% 1.74/1.86 tff(11506,plain,
% 1.74/1.86 (op(e3, e0) = e1),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[1480, 11505, 1349, 11116])).
% 1.74/1.86 tff(11507,plain,
% 1.74/1.86 ((op(e3, e0) = e0) <=> (e1 = op(e1, e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11506, 11496])).
% 1.74/1.86 tff(11508,plain,
% 1.74/1.86 ((op(e3, e0) = e0) <=> (op(e1, e3) = e1)),
% 1.74/1.86 inference(transitivity,[status(thm)],[11507, 28])).
% 1.74/1.86 tff(11509,plain,
% 1.74/1.86 ((op(e1, e3) = e1) <=> (op(e3, e0) = e0)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11508])).
% 1.74/1.86 tff(11510,plain,
% 1.74/1.86 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e0) = e0))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11509])).
% 1.74/1.86 tff(11511,plain,
% 1.74/1.86 (~(op(e3, e0) = e0)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[87, 11510])).
% 1.74/1.86 tff(11512,plain,
% 1.74/1.86 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e1, e3))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11496])).
% 1.74/1.86 tff(11513,plain,
% 1.74/1.86 ((op(e2, e3) = e0) <=> (op(e1, e3) = op(e2, e3))),
% 1.74/1.86 inference(transitivity,[status(thm)],[11512, 1687])).
% 1.74/1.86 tff(11514,plain,
% 1.74/1.86 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.74/1.86 inference(symmetry,[status(thm)],[11513])).
% 1.74/1.86 tff(11515,plain,
% 1.74/1.86 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11514])).
% 1.74/1.86 tff(11516,plain,
% 1.74/1.86 (~(op(e2, e3) = e0)),
% 1.74/1.86 inference(modus_ponens,[status(thm)],[118, 11515])).
% 1.74/1.86 tff(11517,plain,
% 1.74/1.86 (op(e2, e3) = e3),
% 1.74/1.86 inference(unit_resolution,[status(thm)],[206, 11516, 9692, 76])).
% 1.74/1.86 tff(11518,plain,
% 1.74/1.86 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 1.74/1.86 inference(monotonicity,[status(thm)],[11517])).
% 1.74/1.87 tff(11519,plain,
% 1.74/1.87 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11518])).
% 1.74/1.87 tff(11520,plain,
% 1.74/1.87 (~(op(e2, e0) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[989, 11519])).
% 1.74/1.87 tff(11521,plain,
% 1.74/1.87 (op(e2, op(e2, e3)) = op(e2, e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11517])).
% 1.74/1.87 tff(11522,plain,
% 1.74/1.87 (op(e2, op(e2, e3)) = e3),
% 1.74/1.87 inference(transitivity,[status(thm)],[11521, 11517])).
% 1.74/1.87 tff(11523,plain,
% 1.74/1.87 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2344, 11522])).
% 1.74/1.87 tff(11524,plain,
% 1.74/1.87 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[4681])).
% 1.74/1.87 tff(11525,plain,
% 1.74/1.87 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[19])).
% 1.74/1.87 tff(11526,plain,
% 1.74/1.87 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11525])).
% 1.74/1.87 tff(11527,plain,
% 1.74/1.87 (~(op(e0, e0) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[3414, 11526])).
% 1.74/1.87 tff(11528,plain,
% 1.74/1.87 ((op(e1, e0) = e1) <=> (e3 = e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[258])).
% 1.74/1.87 tff(11529,plain,
% 1.74/1.87 ((op(e1, e0) = e1) <=> (e1 = e3)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11528, 128])).
% 1.74/1.87 tff(11530,plain,
% 1.74/1.87 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11529])).
% 1.74/1.87 tff(11531,plain,
% 1.74/1.87 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11530])).
% 1.74/1.87 tff(11532,plain,
% 1.74/1.87 (~(op(e1, e0) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[303, 11531])).
% 1.74/1.87 tff(11533,plain,
% 1.74/1.87 (op(e3, e0) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1480, 11532, 1349, 11527])).
% 1.74/1.87 tff(11534,plain,
% 1.74/1.87 (op(e3, e0) = op(e0, e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[11533, 11524])).
% 1.74/1.87 tff(11535,plain,
% 1.74/1.87 (op(e3, e1) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1916, 85, 656, 1908])).
% 1.74/1.87 tff(11536,plain,
% 1.74/1.87 (op(e3, op(e3, e1)) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[4813, 11535, 19, 11534])).
% 1.74/1.87 tff(11537,plain,
% 1.74/1.87 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2594, 11536])).
% 1.74/1.87 tff(11538,plain,
% 1.74/1.87 (op(e0, op(e1, e0)) = op(op(e1, e3), e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[2909, 258])).
% 1.74/1.87 tff(11539,plain,
% 1.74/1.87 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[259])).
% 1.74/1.87 tff(11540,plain,
% 1.74/1.87 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11539])).
% 1.74/1.87 tff(11541,plain,
% 1.74/1.87 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11540])).
% 1.74/1.87 tff(11542,plain,
% 1.74/1.87 (~(op(e0, e0) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[2471, 11541])).
% 1.74/1.87 tff(11543,plain,
% 1.74/1.87 ((op(e0, e3) = e3) <=> (e1 = e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[19])).
% 1.74/1.87 tff(11544,plain,
% 1.74/1.87 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11543])).
% 1.74/1.87 tff(11545,plain,
% 1.74/1.87 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11544])).
% 1.74/1.87 tff(11546,plain,
% 1.74/1.87 (~(op(e0, e3) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[303, 11545])).
% 1.74/1.87 tff(11547,plain,
% 1.74/1.87 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11533])).
% 1.74/1.87 tff(11548,plain,
% 1.74/1.87 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11547, 7171])).
% 1.74/1.87 tff(11549,plain,
% 1.74/1.87 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11548])).
% 1.74/1.87 tff(11550,plain,
% 1.74/1.87 (~(op(e3, e2) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1133, 11549])).
% 1.74/1.87 tff(11551,plain,
% 1.74/1.87 (op(e3, e2) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1898, 85, 11550, 2386])).
% 1.74/1.87 tff(11552,plain,
% 1.74/1.87 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11551])).
% 1.74/1.87 tff(11553,plain,
% 1.74/1.87 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11552])).
% 1.74/1.87 tff(11554,plain,
% 1.74/1.87 (~(op(e0, e2) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1467, 11553])).
% 1.74/1.87 tff(11555,plain,
% 1.74/1.87 (op(e0, e1) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1495, 11554, 11546, 11542])).
% 1.74/1.87 tff(11556,plain,
% 1.74/1.87 (op(e0, e1) = op(e1, e0)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11555, 259])).
% 1.74/1.87 tff(11557,plain,
% 1.74/1.87 (op(e0, op(e0, e1)) = op(e0, op(e1, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11556])).
% 1.74/1.87 tff(11558,plain,
% 1.74/1.87 (op(e0, op(e0, e1)) = e1),
% 1.74/1.87 inference(transitivity,[status(thm)],[11557, 11538, 4820])).
% 1.74/1.87 tff(11559,plain,
% 1.74/1.87 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2449, 11558])).
% 1.74/1.87 tff(11560,plain,
% 1.74/1.87 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11535])).
% 1.74/1.87 tff(11561,plain,
% 1.74/1.87 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11560])).
% 1.74/1.87 tff(11562,plain,
% 1.74/1.87 (~(op(e2, e1) = e0)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[402, 11561])).
% 1.74/1.87 tff(11563,plain,
% 1.74/1.87 (op(e2, op(e2, e0)) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[4933, 11562, 1349, 1219, 3272, 11535])).
% 1.74/1.87 tff(11564,plain,
% 1.74/1.87 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2653, 11563])).
% 1.74/1.87 tff(11565,plain,
% 1.74/1.87 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[2909])).
% 1.74/1.87 tff(11566,plain,
% 1.74/1.87 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11565])).
% 1.74/1.87 tff(11567,plain,
% 1.74/1.87 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11566])).
% 1.74/1.87 tff(11568,plain,
% 1.74/1.87 (~(op(e1, e2) = e0)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1850, 11567])).
% 1.74/1.87 tff(11569,plain,
% 1.74/1.87 (op(e0, e2) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[973, 85, 17, 11568])).
% 1.74/1.87 tff(11570,plain,
% 1.74/1.87 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11569])).
% 1.74/1.87 tff(11571,plain,
% 1.74/1.87 (op(op(e0, e2), e2) = e0),
% 1.74/1.87 inference(transitivity,[status(thm)],[11570, 11569])).
% 1.74/1.87 tff(11572,plain,
% 1.74/1.87 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1956, 11571])).
% 1.74/1.87 tff(11573,plain,
% 1.74/1.87 (op(op(e3, e2), e2) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[7919, 11551])).
% 1.74/1.87 tff(11574,plain,
% 1.74/1.87 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1339, 11573])).
% 1.74/1.87 tff(11575,plain,
% 1.74/1.87 ((op(op(e0, e3), e3) = e0) <=> (op(e1, e3) = e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[4735])).
% 1.74/1.87 tff(11576,plain,
% 1.74/1.87 ((op(e1, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11575])).
% 1.74/1.87 tff(11577,plain,
% 1.74/1.87 (op(op(e0, e3), e3) = e0),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1219, 11576])).
% 1.74/1.87 tff(11578,plain,
% 1.74/1.87 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1361, 11577])).
% 1.74/1.87 tff(11579,plain,
% 1.74/1.87 (op(e1, op(e1, e3)) = op(e1, e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[1219])).
% 1.74/1.87 tff(11580,plain,
% 1.74/1.87 (op(op(e3, e0), e0) = op(e1, op(e1, e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11533, 2909])).
% 1.74/1.87 tff(11581,plain,
% 1.74/1.87 (op(op(e3, e0), e0) = e3),
% 1.74/1.87 inference(transitivity,[status(thm)],[11580, 11579, 258])).
% 1.74/1.87 tff(11582,plain,
% 1.74/1.87 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[4026, 11581])).
% 1.74/1.87 tff(11583,plain,
% 1.74/1.87 (op(e1, op(e1, e0)) = e0),
% 1.74/1.87 inference(transitivity,[status(thm)],[781, 1219])).
% 1.74/1.87 tff(11584,plain,
% 1.74/1.87 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1836, 11583])).
% 1.74/1.87 tff(11585,plain,
% 1.74/1.87 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11551])).
% 1.74/1.87 tff(11586,plain,
% 1.74/1.87 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11585])).
% 1.74/1.87 tff(11587,plain,
% 1.74/1.87 (~(op(e3, e1) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[3429, 11586])).
% 1.74/1.87 tff(11588,plain,
% 1.74/1.87 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11569])).
% 1.74/1.87 tff(11589,plain,
% 1.74/1.87 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11588])).
% 1.74/1.87 tff(11590,plain,
% 1.74/1.87 (~(op(e0, e1) = e0)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[2102, 11589])).
% 1.74/1.87 tff(11591,plain,
% 1.74/1.87 (op(e1, e1) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[4953, 11590, 1304, 1219, 11534, 19, 11587])).
% 1.74/1.87 tff(11592,plain,
% 1.74/1.87 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11591])).
% 1.74/1.87 tff(11593,plain,
% 1.74/1.87 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11592, 2355])).
% 1.74/1.87 tff(11594,plain,
% 1.74/1.87 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11593])).
% 1.74/1.87 tff(11595,plain,
% 1.74/1.87 (~(op(e2, e1) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[225, 11594])).
% 1.74/1.87 tff(11596,plain,
% 1.74/1.87 (op(e2, e2) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[345, 11595, 76, 1349])).
% 1.74/1.87 tff(11597,plain,
% 1.74/1.87 ((op(e0, e1) = e2) <=> (op(e1, e0) = e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11556])).
% 1.74/1.87 tff(11598,plain,
% 1.74/1.87 ((op(e1, e0) = e2) <=> (op(e0, e1) = e2)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11597])).
% 1.74/1.87 tff(11599,plain,
% 1.74/1.87 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e1) = e2))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11598])).
% 1.74/1.87 tff(11600,plain,
% 1.74/1.87 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[258])).
% 1.74/1.87 tff(11601,plain,
% 1.74/1.87 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11600, 1314])).
% 1.74/1.87 tff(11602,plain,
% 1.74/1.87 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11601])).
% 1.74/1.87 tff(11603,plain,
% 1.74/1.87 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11602])).
% 1.74/1.87 tff(11604,plain,
% 1.74/1.87 (~(op(e1, e0) = e2)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1321, 11603])).
% 1.74/1.87 tff(11605,plain,
% 1.74/1.87 (~(op(e0, e1) = e2)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[11604, 11599])).
% 1.74/1.87 tff(11606,plain,
% 1.74/1.87 ((op(e1, e1) = e2) <=> (e1 = e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11591])).
% 1.74/1.87 tff(11607,plain,
% 1.74/1.87 ((e1 = e2) <=> (op(e1, e1) = e2)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11606])).
% 1.74/1.87 tff(11608,plain,
% 1.74/1.87 ((~(e1 = e2)) <=> (~(op(e1, e1) = e2))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11607])).
% 1.74/1.87 tff(11609,plain,
% 1.74/1.87 (~(op(e1, e1) = e2)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[708, 11608])).
% 1.74/1.87 tff(11610,plain,
% 1.74/1.87 (op(e2, e1) = e2),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1993, 11609, 82, 11605])).
% 1.74/1.87 tff(11611,plain,
% 1.74/1.87 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11610])).
% 1.74/1.87 tff(11612,plain,
% 1.74/1.87 (op(e2, op(e2, e1)) = e1),
% 1.74/1.87 inference(transitivity,[status(thm)],[11611, 11596])).
% 1.74/1.87 tff(11613,plain,
% 1.74/1.87 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1355, 11612])).
% 1.74/1.87 tff(11614,plain,
% 1.74/1.87 (op(e1, e2) = e2),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2285, 11609, 72, 11604])).
% 1.74/1.87 tff(11615,plain,
% 1.74/1.87 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11614])).
% 1.74/1.87 tff(11616,plain,
% 1.74/1.87 (op(e1, op(e1, e2)) = e2),
% 1.74/1.87 inference(transitivity,[status(thm)],[11615, 11614])).
% 1.74/1.87 tff(11617,plain,
% 1.74/1.87 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2377, 11616])).
% 1.74/1.87 tff(11618,plain,
% 1.74/1.87 ($false),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1459, 11617, 11613, 11584, 11582, 11578, 1304, 11574, 11572, 11564, 11559, 11537, 1347])).
% 1.74/1.87 tff(11619,plain,((op(e3, e2) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e1, e3) = e2) | (op(e3, e1) = e2) | (~(op(e1, e0) = e3)) | (~(op(e1, e3) = e0)) | (op(e2, e0) = e3) | (~(op(e0, e3) = e1)) | (op(e3, e3) = e0) | (op(e3, e0) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.87 tff(11620,plain,
% 1.74/1.87 (op(e3, e2) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[11619, 11523, 1304, 76, 1349, 10589, 9684, 11500, 11495, 11520, 11107, 9696, 11511, 11102, 9699])).
% 1.74/1.87 tff(11621,plain,
% 1.74/1.87 (e0 = op(e3, op(e3, e3))),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[11620, 6497])).
% 1.74/1.87 tff(11622,plain,
% 1.74/1.87 (e3 = op(e1, e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11500])).
% 1.74/1.87 tff(11623,plain,
% 1.74/1.87 (op(e3, op(e3, e2)) = op(op(e1, e0), e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11622, 11620])).
% 1.74/1.87 tff(11624,plain,
% 1.74/1.87 (op(op(e1, e0), e0) = op(e3, op(e3, e2))),
% 1.74/1.87 inference(symmetry,[status(thm)],[11623])).
% 1.74/1.87 tff(11625,plain,
% 1.74/1.87 (op(op(e1, e0), e0) = op(e3, op(e1, e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11500, 11496])).
% 1.74/1.87 tff(11626,plain,
% 1.74/1.87 (op(e3, op(e1, e3)) = op(op(e1, e0), e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11625])).
% 1.74/1.87 tff(11627,plain,
% 1.74/1.87 (op(e3, op(e1, e3)) = op(e3, e0)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11495])).
% 1.74/1.87 tff(11628,plain,
% 1.74/1.87 (op(e3, e0) = op(e3, op(e1, e3))),
% 1.74/1.87 inference(symmetry,[status(thm)],[11627])).
% 1.74/1.87 tff(11629,plain,
% 1.74/1.87 (e1 = op(e3, e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11506])).
% 1.74/1.87 tff(11630,plain,
% 1.74/1.87 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.74/1.87 inference(transitivity,[status(thm)],[11629, 11628, 11626, 11624, 10079])).
% 1.74/1.87 tff(11631,plain,
% 1.74/1.87 ($false),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[5879, 11630, 11621, 2813])).
% 1.74/1.87 tff(11632,plain,((op(e1, e3) = e1) | (~(op(e3, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.87 tff(11633,plain,
% 1.74/1.87 (op(e2, e0) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[11632, 10610, 1304, 76, 2812, 1291, 75, 84])).
% 1.74/1.87 tff(11634,plain,
% 1.74/1.87 ((op(e2, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11633])).
% 1.74/1.87 tff(11635,plain,
% 1.74/1.87 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11634, 6411])).
% 1.74/1.87 tff(11636,plain,
% 1.74/1.87 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11635])).
% 1.74/1.87 tff(11637,plain,
% 1.74/1.87 (~(op(e3, e0) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[747, 11636])).
% 1.74/1.87 tff(11638,plain,
% 1.74/1.87 ((op(e3, e3) = e3) <=> (e2 = e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[2812])).
% 1.74/1.87 tff(11639,plain,
% 1.74/1.87 ((e2 = e3) <=> (op(e3, e3) = e3)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11638])).
% 1.74/1.87 tff(11640,plain,
% 1.74/1.87 ((~(e2 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11639])).
% 1.74/1.87 tff(11641,plain,
% 1.74/1.87 (~(op(e3, e3) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1321, 11640])).
% 1.74/1.87 tff(11642,plain,
% 1.74/1.87 (op(e0, e3) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[151, 10610, 9667, 76])).
% 1.74/1.87 tff(11643,plain,
% 1.74/1.87 ((op(e2, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.87 tff(11644,plain,
% 1.74/1.87 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11643, 6411])).
% 1.74/1.87 tff(11645,plain,
% 1.74/1.87 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11644])).
% 1.74/1.87 tff(11646,plain,
% 1.74/1.87 (~(op(e3, e0) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[747, 11645])).
% 1.74/1.87 tff(11647,plain,
% 1.74/1.87 (op(e1, e0) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[247, 1080, 1291, 75])).
% 1.74/1.87 tff(11648,plain,
% 1.74/1.87 (e3 = op(e1, e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11647])).
% 1.74/1.87 tff(11649,plain,
% 1.74/1.87 (op(e2, e3) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[480, 1080, 468, 11546])).
% 1.74/1.87 tff(11650,plain,
% 1.74/1.87 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11649])).
% 1.74/1.87 tff(11651,plain,
% 1.74/1.87 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11650])).
% 1.74/1.87 tff(11652,plain,
% 1.74/1.87 (~(op(e2, e2) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[515, 11651])).
% 1.74/1.87 tff(11653,plain,
% 1.74/1.87 ((op(e1, e3) = op(e1, e0)) <=> (op(e1, e0) = op(e1, e3))),
% 1.74/1.87 inference(commutativity,[status(thm)],[])).
% 1.74/1.87 tff(11654,plain,
% 1.74/1.87 (op(e1, e3) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[104, 1080, 72, 87])).
% 1.74/1.87 tff(11655,plain,
% 1.74/1.87 (e0 = op(e1, e3)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11654])).
% 1.74/1.87 tff(11656,plain,
% 1.74/1.87 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11655])).
% 1.74/1.87 tff(11657,plain,
% 1.74/1.87 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11656])).
% 1.74/1.87 tff(11658,plain,
% 1.74/1.87 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11657])).
% 1.74/1.87 tff(11659,plain,
% 1.74/1.87 (~(op(e1, e2) = e0)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[1850, 11658])).
% 1.74/1.87 tff(11660,plain,
% 1.74/1.87 (op(e0, e2) = e0),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[973, 11659, 17, 85])).
% 1.74/1.87 tff(11661,plain,
% 1.74/1.87 (op(e0, e2) = op(e1, e3)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11660, 11655])).
% 1.74/1.87 tff(11662,plain,
% 1.74/1.87 ((op(e0, e2) = e3) <=> (op(e1, e3) = op(e1, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11661, 11648])).
% 1.74/1.87 tff(11663,plain,
% 1.74/1.87 ((op(e0, e2) = e3) <=> (op(e1, e0) = op(e1, e3))),
% 1.74/1.87 inference(transitivity,[status(thm)],[11662, 11653])).
% 1.74/1.87 tff(11664,plain,
% 1.74/1.87 ((op(e1, e0) = op(e1, e3)) <=> (op(e0, e2) = e3)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11663])).
% 1.74/1.87 tff(11665,plain,
% 1.74/1.87 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e0, e2) = e3))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11664])).
% 1.74/1.87 tff(11666,plain,
% 1.74/1.87 (~(op(e0, e2) = e3)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[110, 11665])).
% 1.74/1.87 tff(11667,plain,
% 1.74/1.87 (op(e3, e2) = e3),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2111, 11666, 11652, 75])).
% 1.74/1.87 tff(11668,plain,
% 1.74/1.87 (op(e3, e2) = op(e1, e0)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11667, 11648])).
% 1.74/1.87 tff(11669,plain,
% 1.74/1.87 ((op(e3, e2) = e1) <=> (op(e1, e0) = e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11668])).
% 1.74/1.87 tff(11670,plain,
% 1.74/1.87 ((op(e1, e0) = e1) <=> (op(e3, e2) = e1)),
% 1.74/1.87 inference(symmetry,[status(thm)],[11669])).
% 1.74/1.87 tff(11671,plain,
% 1.74/1.87 ((~(op(e1, e0) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11670])).
% 1.74/1.87 tff(11672,plain,
% 1.74/1.87 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.87 tff(11673,plain,
% 1.74/1.87 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e1))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11672])).
% 1.74/1.87 tff(11674,plain,
% 1.74/1.87 (~(op(e1, e0) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[756, 11673])).
% 1.74/1.87 tff(11675,plain,
% 1.74/1.87 (~(op(e3, e2) = e1)),
% 1.74/1.87 inference(modus_ponens,[status(thm)],[11674, 11671])).
% 1.74/1.87 tff(11676,plain,
% 1.74/1.87 (op(e3, e1) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[939, 11675, 926, 11646])).
% 1.74/1.87 tff(11677,plain,
% 1.74/1.87 (op(op(e1, e0), e1) = op(e3, e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11647])).
% 1.74/1.87 tff(11678,plain,
% 1.74/1.87 (op(e3, op(e3, e1)) = op(op(e1, e0), e1)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11648, 11676])).
% 1.74/1.87 tff(11679,plain,
% 1.74/1.87 (op(e3, op(e3, e1)) = e1),
% 1.74/1.87 inference(transitivity,[status(thm)],[11678, 11677, 11676])).
% 1.74/1.87 tff(11680,plain,
% 1.74/1.87 (op(e2, op(e1, e0)) = op(e2, e3)),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11647])).
% 1.74/1.87 tff(11681,plain,
% 1.74/1.87 (op(e2, e3) = op(e1, e0)),
% 1.74/1.87 inference(transitivity,[status(thm)],[11649, 11648])).
% 1.74/1.87 tff(11682,plain,
% 1.74/1.87 (op(e2, op(e2, e3)) = op(e2, op(e1, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11681])).
% 1.74/1.87 tff(11683,plain,
% 1.74/1.87 (op(e2, op(e2, e3)) = e3),
% 1.74/1.87 inference(transitivity,[status(thm)],[11682, 11680, 11649])).
% 1.74/1.87 tff(11684,plain,
% 1.74/1.87 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[2344, 11683])).
% 1.74/1.87 tff(11685,plain,
% 1.74/1.87 (op(op(e1, e3), e3) = e1),
% 1.74/1.87 inference(unit_resolution,[status(thm)],[1223, 11654, 19])).
% 1.74/1.87 tff(11686,plain,
% 1.74/1.87 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 1.74/1.87 inference(monotonicity,[status(thm)],[11648])).
% 1.74/1.88 tff(11687,plain,
% 1.74/1.88 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11686])).
% 1.74/1.88 tff(11688,plain,
% 1.74/1.88 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11687])).
% 1.74/1.88 tff(11689,plain,
% 1.74/1.88 (~(op(e0, e0) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[2471, 11688])).
% 1.74/1.88 tff(11690,plain,
% 1.74/1.88 (op(e0, e1) = e3),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1495, 11666, 11546, 11689])).
% 1.74/1.88 tff(11691,plain,
% 1.74/1.88 (op(e0, op(e0, e1)) = op(op(e1, e3), e3)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11655, 11690])).
% 1.74/1.88 tff(11692,plain,
% 1.74/1.88 (op(e0, op(e0, e1)) = e1),
% 1.74/1.88 inference(transitivity,[status(thm)],[11691, 11685])).
% 1.74/1.88 tff(11693,plain,
% 1.74/1.88 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[2449, 11692])).
% 1.74/1.88 tff(11694,plain,
% 1.74/1.88 (op(op(e3, e2), e2) = e3),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[7919, 11667])).
% 1.74/1.88 tff(11695,plain,
% 1.74/1.88 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1339, 11694])).
% 1.74/1.88 tff(11696,plain,
% 1.74/1.88 ((op(op(e2, e0), e2) = e0) <=> (op(e1, e2) = e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[10281])).
% 1.74/1.88 tff(11697,plain,
% 1.74/1.88 ((op(e1, e2) = e0) <=> (op(op(e2, e0), e2) = e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11696])).
% 1.74/1.88 tff(11698,plain,
% 1.74/1.88 ((op(e1, e2) = op(e1, e3)) <=> (op(op(e2, e0), e2) = e0)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11657, 11697])).
% 1.74/1.88 tff(11699,plain,
% 1.74/1.88 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11698])).
% 1.74/1.88 tff(11700,plain,
% 1.74/1.88 (~(op(op(e2, e0), e2) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[1850, 11699])).
% 1.74/1.88 tff(11701,plain,
% 1.74/1.88 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1379, 11700])).
% 1.74/1.88 tff(11702,plain,
% 1.74/1.88 ((op(e2, e0) = e2) <=> (e1 = e2)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.88 tff(11703,plain,
% 1.74/1.88 ((e1 = e2) <=> (op(e2, e0) = e2)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11702])).
% 1.74/1.88 tff(11704,plain,
% 1.74/1.88 ((~(e1 = e2)) <=> (~(op(e2, e0) = e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11703])).
% 1.74/1.88 tff(11705,plain,
% 1.74/1.88 (~(op(e2, e0) = e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[708, 11704])).
% 1.74/1.88 tff(11706,plain,
% 1.74/1.88 ((e2 = e3) <=> (e2 = op(e1, e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11648])).
% 1.74/1.88 tff(11707,plain,
% 1.74/1.88 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11706, 2154])).
% 1.74/1.88 tff(11708,plain,
% 1.74/1.88 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11707])).
% 1.74/1.88 tff(11709,plain,
% 1.74/1.88 (~(op(e1, e0) = e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[1321, 11708])).
% 1.74/1.88 tff(11710,plain,
% 1.74/1.88 (op(e0, e0) = e2),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[589, 11709, 3786, 11705])).
% 1.74/1.88 tff(11711,plain,
% 1.74/1.88 (op(e0, op(e0, e2)) = op(e0, e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11660])).
% 1.74/1.88 tff(11712,plain,
% 1.74/1.88 (op(e0, op(e0, e2)) = e2),
% 1.74/1.88 inference(transitivity,[status(thm)],[11711, 11710])).
% 1.74/1.88 tff(11713,plain,
% 1.74/1.88 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1331, 11712])).
% 1.74/1.88 tff(11714,plain,
% 1.74/1.88 (op(e2, op(e1, e3)) = op(e2, e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11654])).
% 1.74/1.88 tff(11715,plain,
% 1.74/1.88 ((op(e2, e0) = e0) <=> (e1 = e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.88 tff(11716,plain,
% 1.74/1.88 ((op(e2, e0) = e0) <=> (e0 = e1)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11715, 18])).
% 1.74/1.88 tff(11717,plain,
% 1.74/1.88 ((e0 = e1) <=> (op(e2, e0) = e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11716])).
% 1.74/1.88 tff(11718,plain,
% 1.74/1.88 ((~(e0 = e1)) <=> (~(op(e2, e0) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11717])).
% 1.74/1.88 tff(11719,plain,
% 1.74/1.88 (~(op(e2, e0) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[26, 11718])).
% 1.74/1.88 tff(11720,plain,
% 1.74/1.88 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11655])).
% 1.74/1.88 tff(11721,plain,
% 1.74/1.88 ((op(e2, e3) = e0) <=> (op(e1, e3) = op(e2, e3))),
% 1.74/1.88 inference(transitivity,[status(thm)],[11720, 1687])).
% 1.74/1.88 tff(11722,plain,
% 1.74/1.88 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11721])).
% 1.74/1.88 tff(11723,plain,
% 1.74/1.88 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11722])).
% 1.74/1.88 tff(11724,plain,
% 1.74/1.88 (~(op(e2, e3) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[118, 11723])).
% 1.74/1.88 tff(11725,plain,
% 1.74/1.88 (op(e2, e1) = e0),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[2311, 11724, 17, 11719])).
% 1.74/1.88 tff(11726,plain,
% 1.74/1.88 (op(e2, e1) = op(e1, e3)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11725, 11655])).
% 1.74/1.88 tff(11727,plain,
% 1.74/1.88 (op(e2, op(e2, e1)) = op(e2, op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11726])).
% 1.74/1.88 tff(11728,plain,
% 1.74/1.88 (op(e2, op(e2, e1)) = e1),
% 1.74/1.88 inference(transitivity,[status(thm)],[11727, 11714, 767])).
% 1.74/1.88 tff(11729,plain,
% 1.74/1.88 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1355, 11728])).
% 1.74/1.88 tff(11730,plain,
% 1.74/1.88 (op(op(e0, e3), e3) = e0),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[11654, 11576])).
% 1.74/1.88 tff(11731,plain,
% 1.74/1.88 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1361, 11730])).
% 1.74/1.88 tff(11732,plain,
% 1.74/1.88 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e1, e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11648])).
% 1.74/1.88 tff(11733,plain,
% 1.74/1.88 ((op(e3, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 1.74/1.88 inference(transitivity,[status(thm)],[11732, 2294])).
% 1.74/1.88 tff(11734,plain,
% 1.74/1.88 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11733])).
% 1.74/1.88 tff(11735,plain,
% 1.74/1.88 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11734])).
% 1.74/1.88 tff(11736,plain,
% 1.74/1.88 (~(op(e3, e0) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[410, 11735])).
% 1.74/1.88 tff(11737,plain,
% 1.74/1.88 (op(e3, e0) = e0),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[5422, 11736, 11646, 3786])).
% 1.74/1.88 tff(11738,plain,
% 1.74/1.88 (op(op(e1, e0), e0) = op(e3, e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11647])).
% 1.74/1.88 tff(11739,plain,
% 1.74/1.88 (op(e3, op(e1, e3)) = op(op(e1, e0), e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11648, 11654])).
% 1.74/1.88 tff(11740,plain,
% 1.74/1.88 (op(e3, e0) = op(e1, e3)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11737, 11655])).
% 1.74/1.88 tff(11741,plain,
% 1.74/1.88 (op(e3, op(e3, e0)) = op(e3, op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11740])).
% 1.74/1.88 tff(11742,plain,
% 1.74/1.88 (op(e3, op(e3, e0)) = e0),
% 1.74/1.88 inference(transitivity,[status(thm)],[11741, 11739, 11738, 11737])).
% 1.74/1.88 tff(11743,plain,
% 1.74/1.88 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1345, 11742])).
% 1.74/1.88 tff(11744,plain,
% 1.74/1.88 (op(e1, op(e1, e0)) = op(e1, e3)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11647])).
% 1.74/1.88 tff(11745,plain,
% 1.74/1.88 (op(e1, op(e1, e0)) = e0),
% 1.74/1.88 inference(transitivity,[status(thm)],[11744, 11654])).
% 1.74/1.88 tff(11746,plain,
% 1.74/1.88 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1836, 11745])).
% 1.74/1.88 tff(11747,plain,
% 1.74/1.88 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11710])).
% 1.74/1.88 tff(11748,plain,
% 1.74/1.88 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11747, 4838])).
% 1.74/1.88 tff(11749,plain,
% 1.74/1.88 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11748])).
% 1.74/1.88 tff(11750,plain,
% 1.74/1.88 (~(op(e0, e1) = e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[811, 11749])).
% 1.74/1.88 tff(11751,plain,
% 1.74/1.88 ((op(e2, e1) = e2) <=> (op(e1, e3) = e2)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11726])).
% 1.74/1.88 tff(11752,plain,
% 1.74/1.88 ((op(e1, e3) = e2) <=> (op(e2, e1) = e2)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11751])).
% 1.74/1.88 tff(11753,plain,
% 1.74/1.88 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e1) = e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11752])).
% 1.74/1.88 tff(11754,plain,
% 1.74/1.88 (~(op(e2, e1) = e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[72, 11753])).
% 1.74/1.88 tff(11755,plain,
% 1.74/1.88 (op(e1, e1) = e2),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1993, 11754, 82, 11750])).
% 1.74/1.88 tff(11756,plain,
% 1.74/1.88 ((op(e2, e0) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.88 tff(11757,plain,
% 1.74/1.88 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11756, 316])).
% 1.74/1.88 tff(11758,plain,
% 1.74/1.88 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11757])).
% 1.74/1.88 tff(11759,plain,
% 1.74/1.88 (~(op(e2, e2) = e1)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[2228, 11758])).
% 1.74/1.88 tff(11760,plain,
% 1.74/1.88 (op(e2, e2) = e2),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[524, 11652, 17, 11759])).
% 1.74/1.88 tff(11761,plain,
% 1.74/1.88 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11760])).
% 1.74/1.88 tff(11762,plain,
% 1.74/1.88 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11761])).
% 1.74/1.88 tff(11763,plain,
% 1.74/1.88 (~(op(e1, e2) = e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[1273, 11762])).
% 1.74/1.88 tff(11764,plain,
% 1.74/1.88 (op(e1, e2) = e1),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1859, 11763, 75, 11659])).
% 1.74/1.88 tff(11765,plain,
% 1.74/1.88 (op(e1, op(e1, e2)) = op(e1, e1)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11764])).
% 1.74/1.88 tff(11766,plain,
% 1.74/1.88 (op(e1, op(e1, e2)) = e2),
% 1.74/1.88 inference(transitivity,[status(thm)],[11765, 11755])).
% 1.74/1.88 tff(11767,plain,
% 1.74/1.88 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[2377, 11766])).
% 1.74/1.88 tff(11768,plain,
% 1.74/1.88 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1459, 11767, 11746, 11743, 11731, 1304, 11729, 11713, 11701, 11695, 11693, 11684])).
% 1.74/1.88 tff(11769,plain,
% 1.74/1.88 (~(op(e3, op(e3, e1)) = e1)),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[2594, 11768])).
% 1.74/1.88 tff(11770,plain,
% 1.74/1.88 ($false),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[11769, 11679])).
% 1.74/1.88 tff(11771,plain,((op(e1, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e3, e3) = e1) | (op(e1, e2) = e3) | (op(e3, e1) = e2) | (~(op(e2, e0) = e1)) | (op(e1, e3) = e2) | (op(e2, e2) = e0) | (op(e3, e2) = e0) | (op(e3, e0) = e2) | (~(op(e0, e3) = e1)) | (op(e3, e3) = e3) | (op(e1, e3) = e1) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.88 tff(11772,plain,
% 1.74/1.88 (op(e1, e3) = e3),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[11771, 85, 9667, 75, 9684, 11633, 10589, 11102, 1304, 9955, 11642, 11641, 10610, 1291])).
% 1.74/1.88 tff(11773,plain,
% 1.74/1.88 (e3 = op(e1, e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11772])).
% 1.74/1.88 tff(11774,plain,
% 1.74/1.88 ((e0 = e3) <=> (e0 = op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11773])).
% 1.74/1.88 tff(11775,plain,
% 1.74/1.88 ((e0 = e3) <=> (op(e1, e3) = e0)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11774, 6095])).
% 1.74/1.88 tff(11776,plain,
% 1.74/1.88 ((~(e0 = e3)) <=> (~(op(e1, e3) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11775])).
% 1.74/1.88 tff(11777,plain,
% 1.74/1.88 (~(op(e1, e3) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[181, 11776])).
% 1.74/1.88 tff(11778,plain,
% 1.74/1.88 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11773])).
% 1.74/1.88 tff(11779,plain,
% 1.74/1.88 ((op(e2, e3) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 1.74/1.88 inference(transitivity,[status(thm)],[11778, 1687])).
% 1.74/1.88 tff(11780,plain,
% 1.74/1.88 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11779])).
% 1.74/1.88 tff(11781,plain,
% 1.74/1.88 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11780])).
% 1.74/1.88 tff(11782,plain,
% 1.74/1.88 (~(op(e2, e3) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[118, 11781])).
% 1.74/1.88 tff(11783,plain,
% 1.74/1.88 (op(e2, e3) = e0),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[206, 11782, 9692, 76])).
% 1.74/1.88 tff(11784,plain,
% 1.74/1.88 (e0 = op(e2, e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11783])).
% 1.74/1.88 tff(11785,plain,
% 1.74/1.88 ((op(e2, e0) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11633])).
% 1.74/1.88 tff(11786,plain,
% 1.74/1.88 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11785, 316])).
% 1.74/1.88 tff(11787,plain,
% 1.74/1.88 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11786])).
% 1.74/1.88 tff(11788,plain,
% 1.74/1.88 (~(op(e2, e2) = e1)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[2228, 11787])).
% 1.74/1.88 tff(11789,plain,
% 1.74/1.88 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11642])).
% 1.74/1.88 tff(11790,plain,
% 1.74/1.88 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11789])).
% 1.74/1.88 tff(11791,plain,
% 1.74/1.88 (~(op(e0, e2) = e1)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[918, 11790])).
% 1.74/1.88 tff(11792,plain,
% 1.74/1.88 ((op(e2, e0) = e3) <=> (e1 = e3)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[767])).
% 1.74/1.88 tff(11793,plain,
% 1.74/1.88 ((e1 = e3) <=> (op(e2, e0) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11792])).
% 1.74/1.88 tff(11794,plain,
% 1.74/1.88 ((~(e1 = e3)) <=> (~(op(e2, e0) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11793])).
% 1.74/1.88 tff(11795,plain,
% 1.74/1.88 (~(op(e2, e0) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[303, 11794])).
% 1.74/1.88 tff(11796,plain,
% 1.74/1.88 (e3 = op(e3, e1)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11164])).
% 1.74/1.88 tff(11797,plain,
% 1.74/1.88 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e3, e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11796])).
% 1.74/1.88 tff(11798,plain,
% 1.74/1.88 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11797])).
% 1.74/1.88 tff(11799,plain,
% 1.74/1.88 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11798])).
% 1.74/1.88 tff(11800,plain,
% 1.74/1.88 (~(op(e2, e1) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[402, 11799])).
% 1.74/1.88 tff(11801,plain,
% 1.74/1.88 (op(e2, e2) = e3),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1559, 11800, 11795, 11219])).
% 1.74/1.88 tff(11802,plain,
% 1.74/1.88 (e3 = op(e2, e2)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[11801, 1796])).
% 1.74/1.88 tff(11803,plain,
% 1.74/1.88 (op(e2, e2) = op(e3, e1)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11801, 11796])).
% 1.74/1.88 tff(11804,plain,
% 1.74/1.88 (op(e2, op(e2, e2)) = op(e2, op(e3, e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11803])).
% 1.74/1.88 tff(11805,plain,
% 1.74/1.88 (op(e2, op(e3, e1)) = op(e2, op(e2, e2))),
% 1.74/1.88 inference(symmetry,[status(thm)],[11804])).
% 1.74/1.88 tff(11806,plain,
% 1.74/1.88 (op(e2, op(e3, e1)) = op(e2, op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11166])).
% 1.74/1.88 tff(11807,plain,
% 1.74/1.88 (op(e2, op(e1, e3)) = op(e2, op(e3, e1))),
% 1.74/1.88 inference(symmetry,[status(thm)],[11806])).
% 1.74/1.88 tff(11808,plain,
% 1.74/1.88 (op(e2, e3) = op(e2, op(e1, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11135])).
% 1.74/1.88 tff(11809,plain,
% 1.74/1.88 (e0 = op(e2, op(e2, e2))),
% 1.74/1.88 inference(transitivity,[status(thm)],[252, 11808, 11807, 11805])).
% 1.74/1.88 tff(11810,plain,
% 1.74/1.88 (op(e2, op(e1, e3)) = op(e2, e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11808])).
% 1.74/1.88 tff(11811,plain,
% 1.74/1.88 (op(e2, op(e2, e2)) = e0),
% 1.74/1.88 inference(transitivity,[status(thm)],[11804, 11806, 11810, 251])).
% 1.74/1.88 tff(11812,plain,
% 1.74/1.88 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11199])).
% 1.74/1.88 tff(11813,plain,
% 1.74/1.88 (~(op(e1, e0) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[110, 11812])).
% 1.74/1.88 tff(11814,plain,
% 1.74/1.88 ((op(e3, e3) = e0) <=> (e2 = e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[2812])).
% 1.74/1.88 tff(11815,plain,
% 1.74/1.88 ((op(e3, e3) = e0) <=> (e0 = e2)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11814, 1])).
% 1.74/1.88 tff(11816,plain,
% 1.74/1.88 ((e0 = e2) <=> (op(e3, e3) = e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11815])).
% 1.74/1.88 tff(11817,plain,
% 1.74/1.88 ((~(e0 = e2)) <=> (~(op(e3, e3) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11816])).
% 1.74/1.88 tff(11818,plain,
% 1.74/1.88 (~(op(e3, e3) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[14, 11817])).
% 1.74/1.88 tff(11819,plain,
% 1.74/1.88 (op(e3, e0) = e0),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1916, 11146, 11818, 85])).
% 1.74/1.88 tff(11820,plain,
% 1.74/1.88 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11819])).
% 1.74/1.88 tff(11821,plain,
% 1.74/1.88 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11820])).
% 1.74/1.88 tff(11822,plain,
% 1.74/1.88 (~(op(e1, e0) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[410, 11821])).
% 1.74/1.88 tff(11823,plain,
% 1.74/1.88 (op(e1, e0) = e2),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[728, 11822, 11674, 11813])).
% 1.74/1.88 tff(11824,plain,
% 1.74/1.88 (e2 = op(e1, e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11823])).
% 1.74/1.88 tff(11825,plain,
% 1.74/1.88 (op(e2, op(e2, op(e2, e2))) = op(op(e1, e0), e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11824, 11811])).
% 1.74/1.88 tff(11826,plain,
% 1.74/1.88 (op(op(e1, e0), e0) = op(e2, op(e2, op(e2, e2)))),
% 1.74/1.88 inference(symmetry,[status(thm)],[11825])).
% 1.74/1.88 tff(11827,plain,
% 1.74/1.88 (op(op(e1, e0), e0) = op(e2, op(e2, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11823, 252])).
% 1.74/1.88 tff(11828,plain,
% 1.74/1.88 (op(e2, op(e2, e3)) = op(op(e1, e0), e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11827])).
% 1.74/1.88 tff(11829,plain,
% 1.74/1.88 (op(e2, e0) = op(e2, op(e2, e3))),
% 1.74/1.88 inference(symmetry,[status(thm)],[11212])).
% 1.74/1.88 tff(11830,plain,
% 1.74/1.88 (e1 = op(e2, op(e2, op(e2, e2)))),
% 1.74/1.88 inference(transitivity,[status(thm)],[768, 11829, 11828, 11826])).
% 1.74/1.88 tff(11831,plain,
% 1.74/1.88 ($false),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1810, 11830, 11809, 11802])).
% 1.74/1.88 tff(11832,plain,((op(e3, e2) = e3) | (~(op(e2, e0) = e1)) | (~(op(e2, e3) = e0)) | (~(op(e1, e3) = e3)) | (op(e3, e2) = e0) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.88 tff(11833,plain,
% 1.74/1.88 (op(e3, e2) = e3),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[11832, 11783, 11633, 11772, 85, 2812])).
% 1.74/1.88 tff(11834,plain,
% 1.74/1.88 (op(e3, e2) = op(e1, e3)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11833, 11773])).
% 1.74/1.88 tff(11835,plain,
% 1.74/1.88 ((op(e3, e2) = e1) <=> (op(e1, e3) = e1)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11834])).
% 1.74/1.88 tff(11836,plain,
% 1.74/1.88 ((op(e1, e3) = e1) <=> (op(e3, e2) = e1)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11835])).
% 1.74/1.88 tff(11837,plain,
% 1.74/1.88 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11836])).
% 1.74/1.88 tff(11838,plain,
% 1.74/1.88 (~(op(e3, e2) = e1)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[10610, 11837])).
% 1.74/1.88 tff(11839,plain,
% 1.74/1.88 (op(e1, e2) = e1),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[1613, 11838, 11791, 11788])).
% 1.74/1.88 tff(11840,plain,
% 1.74/1.88 ((op(e1, e2) = e0) <=> (e1 = op(e2, e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11839, 11784])).
% 1.74/1.88 tff(11841,plain,
% 1.74/1.88 ((op(e1, e2) = e0) <=> (op(e2, e3) = e1)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11840, 5574])).
% 1.74/1.88 tff(11842,plain,
% 1.74/1.88 ((op(e2, e3) = e1) <=> (op(e1, e2) = e0)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11841])).
% 1.74/1.88 tff(11843,plain,
% 1.74/1.88 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e2) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11842])).
% 1.74/1.88 tff(11844,plain,
% 1.74/1.88 (~(op(e1, e2) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[76, 11843])).
% 1.74/1.88 tff(11845,plain,
% 1.74/1.88 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11783])).
% 1.74/1.88 tff(11846,plain,
% 1.74/1.88 (op(e3, e0) = op(e3, op(e2, e3))),
% 1.74/1.88 inference(symmetry,[status(thm)],[11845])).
% 1.74/1.88 tff(11847,plain,
% 1.74/1.88 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11846])).
% 1.74/1.88 tff(11848,plain,
% 1.74/1.88 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.74/1.88 inference(symmetry,[status(thm)],[11847])).
% 1.74/1.88 tff(11849,plain,
% 1.74/1.88 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11846, 11833])).
% 1.74/1.88 tff(11850,plain,
% 1.74/1.88 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 1.74/1.88 inference(transitivity,[status(thm)],[11849, 11848])).
% 1.74/1.88 tff(11851,plain,
% 1.74/1.88 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11850])).
% 1.74/1.88 tff(11852,plain,
% 1.74/1.88 (~(op(e3, e0) = e3)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[1133, 11851])).
% 1.74/1.88 tff(11853,plain,
% 1.74/1.88 (op(e3, e0) = e0),
% 1.74/1.88 inference(unit_resolution,[status(thm)],[5422, 11852, 11637, 9955])).
% 1.74/1.88 tff(11854,plain,
% 1.74/1.88 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11853])).
% 1.74/1.88 tff(11855,plain,
% 1.74/1.88 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.74/1.88 inference(monotonicity,[status(thm)],[11854])).
% 1.74/1.88 tff(11856,plain,
% 1.74/1.88 (~(op(e1, e0) = e0)),
% 1.74/1.88 inference(modus_ponens,[status(thm)],[410, 11855])).
% 1.74/1.88 tff(11857,plain,
% 1.74/1.88 ($false),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[1830, 11856, 11844, 84, 11777])).
% 1.74/1.89 tff(11858,plain,((op(e3, e2) = e0) | (op(e1, e1) = e0) | (op(e2, e3) = e1) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.89 tff(11859,plain,
% 1.74/1.89 (op(e3, e2) = e0),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[11858, 1291, 76, 2812, 75, 1304, 84])).
% 1.74/1.89 tff(11860,plain,
% 1.74/1.89 (e0 = op(e3, e2)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11859])).
% 1.74/1.89 tff(11861,plain,
% 1.74/1.89 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11860])).
% 1.74/1.89 tff(11862,plain,
% 1.74/1.89 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11861])).
% 1.74/1.89 tff(11863,plain,
% 1.74/1.89 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11862])).
% 1.74/1.89 tff(11864,plain,
% 1.74/1.89 (~(op(e3, e0) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[1133, 11863])).
% 1.74/1.89 tff(11865,plain,
% 1.74/1.89 (op(e3, e0) = e3),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[5422, 11864, 11637, 9955])).
% 1.74/1.89 tff(11866,plain,
% 1.74/1.89 (op(e3, e0) = op(e3, op(e3, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11860])).
% 1.74/1.89 tff(11867,plain,
% 1.74/1.89 (op(e3, op(e3, e2)) = op(e3, e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11866])).
% 1.74/1.89 tff(11868,plain,
% 1.74/1.89 (op(op(e3, e0), e0) = op(e3, op(e3, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11865, 11860])).
% 1.74/1.89 tff(11869,plain,
% 1.74/1.89 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11860])).
% 1.74/1.89 tff(11870,plain,
% 1.74/1.89 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11869])).
% 1.74/1.89 tff(11871,plain,
% 1.74/1.89 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11870])).
% 1.74/1.89 tff(11872,plain,
% 1.74/1.89 (~(op(e3, e1) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[3429, 11871])).
% 1.74/1.89 tff(11873,plain,
% 1.74/1.89 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11642])).
% 1.74/1.89 tff(11874,plain,
% 1.74/1.89 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11873, 18])).
% 1.74/1.89 tff(11875,plain,
% 1.74/1.89 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11874])).
% 1.74/1.89 tff(11876,plain,
% 1.74/1.89 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11875])).
% 1.74/1.89 tff(11877,plain,
% 1.74/1.89 (~(op(e0, e3) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[26, 11876])).
% 1.74/1.89 tff(11878,plain,
% 1.74/1.89 ((op(e3, op(e3, op(e3, e3))) = e0) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.74/1.89 inference(commutativity,[status(thm)],[])).
% 1.74/1.89 tff(11879,plain,
% 1.74/1.89 (e3 = op(e3, e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11865])).
% 1.74/1.89 tff(11880,plain,
% 1.74/1.89 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11879])).
% 1.74/1.89 tff(11881,plain,
% 1.74/1.89 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11880])).
% 1.74/1.89 tff(11882,plain,
% 1.74/1.89 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11881])).
% 1.74/1.89 tff(11883,plain,
% 1.74/1.89 (~(op(e1, e0) = e3)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[410, 11882])).
% 1.74/1.89 tff(11884,plain,
% 1.74/1.89 (op(e1, e3) = e3),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[247, 11883, 1291, 75])).
% 1.74/1.89 tff(11885,plain,
% 1.74/1.89 (op(e1, e3) = op(e3, op(e3, op(e3, e3)))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11884, 11879, 11866, 10079])).
% 1.74/1.89 tff(11886,plain,
% 1.74/1.89 ((op(e1, e3) = e0) <=> (op(e3, op(e3, op(e3, e3))) = e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11885])).
% 1.74/1.89 tff(11887,plain,
% 1.74/1.89 ((op(e1, e3) = e0) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11886, 11878])).
% 1.74/1.89 tff(11888,plain,
% 1.74/1.89 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e1, e3) = e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11887])).
% 1.74/1.89 tff(11889,plain,
% 1.74/1.89 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e1, e3) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11888])).
% 1.74/1.89 tff(11890,plain,
% 1.74/1.89 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.74/1.89 inference(transitivity,[status(thm)],[6490, 11867])).
% 1.74/1.89 tff(11891,plain,
% 1.74/1.89 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e3, e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11860, 11890])).
% 1.74/1.89 tff(11892,plain,
% 1.74/1.89 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = op(e3, e2))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11891, 1123])).
% 1.74/1.89 tff(11893,plain,
% 1.74/1.89 ((op(e3, e0) = op(e3, e2)) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.74/1.89 inference(symmetry,[status(thm)],[11892])).
% 1.74/1.89 tff(11894,plain,
% 1.74/1.89 ((~(op(e3, e0) = op(e3, e2))) <=> (~(e0 = op(e3, op(e3, op(e3, e3)))))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11893])).
% 1.74/1.89 tff(11895,plain,
% 1.74/1.89 (~(e0 = op(e3, op(e3, op(e3, e3))))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[1133, 11894])).
% 1.74/1.89 tff(11896,plain,
% 1.74/1.89 (~(op(e1, e3) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11895, 11889])).
% 1.74/1.89 tff(11897,plain,
% 1.74/1.89 (op(e2, e3) = e0),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[1098, 11896, 11818, 11877])).
% 1.74/1.89 tff(11898,plain,
% 1.74/1.89 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11897])).
% 1.74/1.89 tff(11899,plain,
% 1.74/1.89 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11898])).
% 1.74/1.89 tff(11900,plain,
% 1.74/1.89 (~(op(e2, e1) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[197, 11899])).
% 1.74/1.89 tff(11901,plain,
% 1.74/1.89 (op(e0, e1) = e0),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[292, 11900, 84, 11872])).
% 1.74/1.89 tff(11902,plain,
% 1.74/1.89 (op(e3, op(e0, e1)) = op(op(e3, e0), e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11879, 11901])).
% 1.74/1.89 tff(11903,plain,
% 1.74/1.89 (op(e3, op(e0, e1)) = e3),
% 1.74/1.89 inference(transitivity,[status(thm)],[11902, 11868, 11867, 11865])).
% 1.74/1.89 tff(11904,plain,
% 1.74/1.89 ((op(e2, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11633])).
% 1.74/1.89 tff(11905,plain,
% 1.74/1.89 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11904, 697])).
% 1.74/1.89 tff(11906,plain,
% 1.74/1.89 ((op(e0, e2) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 1.74/1.89 inference(symmetry,[status(thm)],[11905])).
% 1.74/1.89 tff(11907,plain,
% 1.74/1.89 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e2, e0))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11906, 6337])).
% 1.74/1.89 tff(11908,plain,
% 1.74/1.89 ((~(op(e0, e2) = e1)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11907])).
% 1.74/1.89 tff(11909,plain,
% 1.74/1.89 (~(op(e0, e2) = op(e2, e0))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11791, 11908])).
% 1.74/1.89 tff(11910,plain,
% 1.74/1.89 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[6347, 11909])).
% 1.74/1.89 tff(11911,plain,
% 1.74/1.89 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e2)) = e3)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11866])).
% 1.74/1.89 tff(11912,plain,
% 1.74/1.89 (op(e3, op(e3, e2)) = e3),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11865, 11911])).
% 1.74/1.89 tff(11913,plain,
% 1.74/1.89 (((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)) | (~(op(e3, op(e3, e2)) = e3))),
% 1.74/1.89 inference(tautology,[status(thm)],[])).
% 1.74/1.89 tff(11914,plain,
% 1.74/1.89 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[11913, 11912])).
% 1.74/1.89 tff(11915,plain,
% 1.74/1.89 ((~(op(e0, e2) = e1)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11906])).
% 1.74/1.89 tff(11916,plain,
% 1.74/1.89 (~(op(e2, e0) = op(e0, e2))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11791, 11915])).
% 1.74/1.89 tff(11917,plain,
% 1.74/1.89 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[6358, 11916])).
% 1.74/1.89 tff(11918,plain,
% 1.74/1.89 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11859])).
% 1.74/1.89 tff(11919,plain,
% 1.74/1.89 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11918])).
% 1.74/1.89 tff(11920,plain,
% 1.74/1.89 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11919])).
% 1.74/1.89 tff(11921,plain,
% 1.74/1.89 (~(op(e3, e2) = e1)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[26, 11920])).
% 1.74/1.89 tff(11922,plain,
% 1.74/1.89 (op(e3, e1) = e1),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[939, 11921, 9667, 11637])).
% 1.74/1.89 tff(11923,plain,
% 1.74/1.89 ((op(e3, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11922])).
% 1.74/1.89 tff(11924,plain,
% 1.74/1.89 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11923, 28])).
% 1.74/1.89 tff(11925,plain,
% 1.74/1.89 ((op(e1, e3) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.74/1.89 inference(symmetry,[status(thm)],[11924])).
% 1.74/1.89 tff(11926,plain,
% 1.74/1.89 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11925])).
% 1.74/1.89 tff(11927,plain,
% 1.74/1.89 (~(op(e3, e1) = op(e1, e3))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[10610, 11926])).
% 1.74/1.89 tff(11928,plain,
% 1.74/1.89 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[6362, 11927])).
% 1.74/1.89 tff(11929,plain,
% 1.74/1.89 (op(e3, op(e2, e3)) = op(op(e3, e0), e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11879, 11897])).
% 1.74/1.89 tff(11930,plain,
% 1.74/1.89 (op(e3, op(e2, e3)) = e3),
% 1.74/1.89 inference(transitivity,[status(thm)],[11929, 11868, 11867, 11865])).
% 1.74/1.89 tff(11931,plain,
% 1.74/1.89 (((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)) | (~(op(e3, op(e2, e3)) = e3))),
% 1.74/1.89 inference(tautology,[status(thm)],[])).
% 1.74/1.89 tff(11932,plain,
% 1.74/1.89 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[11931, 11930])).
% 1.74/1.89 tff(11933,plain,
% 1.74/1.89 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e3, e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11860])).
% 1.74/1.89 tff(11934,plain,
% 1.74/1.89 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11933])).
% 1.74/1.89 tff(11935,plain,
% 1.74/1.89 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11934])).
% 1.74/1.89 tff(11936,plain,
% 1.74/1.89 (~(op(e1, e2) = e0)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[2292, 11935])).
% 1.74/1.89 tff(11937,plain,
% 1.74/1.89 (op(e1, e0) = e0),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[1830, 11896, 84, 11936])).
% 1.74/1.89 tff(11938,plain,
% 1.74/1.89 (op(e3, op(e1, e0)) = op(op(e3, e0), e0)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11879, 11937])).
% 1.74/1.89 tff(11939,plain,
% 1.74/1.89 (op(e3, op(e1, e0)) = e3),
% 1.74/1.89 inference(transitivity,[status(thm)],[11938, 11868, 11867, 11865])).
% 1.74/1.89 tff(11940,plain,
% 1.74/1.89 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[9792, 11939])).
% 1.74/1.89 tff(11941,plain,
% 1.74/1.89 ((op(e1, op(e3, e3)) = e1) <=> (op(e1, e2) = e1)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[7120])).
% 1.74/1.89 tff(11942,plain,
% 1.74/1.89 ((op(e1, e2) = e1) <=> (op(e1, op(e3, e3)) = e1)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11941])).
% 1.74/1.89 tff(11943,plain,
% 1.74/1.89 (op(e1, e2) = e1),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[1613, 11921, 11791, 11788])).
% 1.74/1.89 tff(11944,plain,
% 1.74/1.89 (op(e1, op(e3, e3)) = e1),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11943, 11942])).
% 1.74/1.89 tff(11945,plain,
% 1.74/1.89 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[5685, 11944])).
% 1.74/1.89 tff(11946,plain,
% 1.74/1.89 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11943])).
% 1.74/1.89 tff(11947,plain,
% 1.74/1.89 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 1.74/1.89 inference(symmetry,[status(thm)],[11946])).
% 1.74/1.89 tff(11948,plain,
% 1.74/1.89 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11947])).
% 1.74/1.89 tff(11949,plain,
% 1.74/1.89 ((op(e2, e0) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11633])).
% 1.74/1.89 tff(11950,plain,
% 1.74/1.89 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11949, 2355])).
% 1.74/1.89 tff(11951,plain,
% 1.74/1.89 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11950])).
% 1.74/1.89 tff(11952,plain,
% 1.74/1.89 (~(op(e2, e1) = e1)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[1966, 11951])).
% 1.74/1.89 tff(11953,plain,
% 1.74/1.89 (~(op(e2, e1) = op(e1, e2))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11952, 11948])).
% 1.74/1.89 tff(11954,plain,
% 1.74/1.89 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[557, 11953])).
% 1.74/1.89 tff(11955,plain,
% 1.74/1.89 (e1 = op(e0, e3)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11642])).
% 1.74/1.89 tff(11956,plain,
% 1.74/1.89 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11955])).
% 1.74/1.89 tff(11957,plain,
% 1.74/1.89 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11635, 11956, 453])).
% 1.74/1.89 tff(11958,plain,
% 1.74/1.89 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11957])).
% 1.74/1.89 tff(11959,plain,
% 1.74/1.89 (~(op(e0, e3) = op(e3, e0))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[747, 11958])).
% 1.74/1.89 tff(11960,plain,
% 1.74/1.89 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[496, 11959])).
% 1.74/1.89 tff(11961,plain,
% 1.74/1.89 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11922])).
% 1.74/1.89 tff(11962,plain,
% 1.74/1.89 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11961])).
% 1.74/1.89 tff(11963,plain,
% 1.74/1.89 (~(op(e1, e1) = e1)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[945, 11962])).
% 1.74/1.89 tff(11964,plain,
% 1.74/1.89 (op(e1, e1) = e2),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[630, 11963, 84, 1291])).
% 1.74/1.89 tff(11965,plain,
% 1.74/1.89 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11964])).
% 1.74/1.89 tff(11966,plain,
% 1.74/1.89 (e2 = op(e1, e1)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11964])).
% 1.74/1.89 tff(11967,plain,
% 1.74/1.89 ((op(e2, e0) = e2) <=> (e1 = e2)),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11633])).
% 1.74/1.89 tff(11968,plain,
% 1.74/1.89 ((e1 = e2) <=> (op(e2, e0) = e2)),
% 1.74/1.89 inference(symmetry,[status(thm)],[11967])).
% 1.74/1.89 tff(11969,plain,
% 1.74/1.89 ((~(e1 = e2)) <=> (~(op(e2, e0) = e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11968])).
% 1.74/1.89 tff(11970,plain,
% 1.74/1.89 (~(op(e2, e0) = e2)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[708, 11969])).
% 1.74/1.89 tff(11971,plain,
% 1.74/1.89 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11964])).
% 1.74/1.89 tff(11972,plain,
% 1.74/1.89 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11971, 1960])).
% 1.74/1.89 tff(11973,plain,
% 1.74/1.89 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11972])).
% 1.74/1.89 tff(11974,plain,
% 1.74/1.89 (~(op(e2, e1) = e2)),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[225, 11973])).
% 1.74/1.89 tff(11975,plain,
% 1.74/1.89 (op(e2, e2) = e2),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[2088, 11974, 9692, 11970])).
% 1.74/1.89 tff(11976,plain,
% 1.74/1.89 (op(e2, e2) = op(e1, e1)),
% 1.74/1.89 inference(transitivity,[status(thm)],[11975, 11966])).
% 1.74/1.89 tff(11977,plain,
% 1.74/1.89 (op(e1, op(e2, e2)) = op(e1, op(e1, e1))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11976])).
% 1.74/1.89 tff(11978,plain,
% 1.74/1.89 (op(e1, op(e2, e2)) = e1),
% 1.74/1.89 inference(transitivity,[status(thm)],[11977, 11965, 11943])).
% 1.74/1.89 tff(11979,plain,
% 1.74/1.89 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.74/1.89 inference(unit_resolution,[status(thm)],[6714, 11978])).
% 1.74/1.89 tff(11980,plain,
% 1.74/1.89 ((op(e2, e1) = e1) <=> (op(e1, e2) = op(e2, e1))),
% 1.74/1.89 inference(transitivity,[status(thm)],[11947, 531])).
% 1.74/1.89 tff(11981,plain,
% 1.74/1.89 ((~(op(e2, e1) = e1)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.74/1.89 inference(monotonicity,[status(thm)],[11980])).
% 1.74/1.89 tff(11982,plain,
% 1.74/1.89 (~(op(e1, e2) = op(e2, e1))),
% 1.74/1.89 inference(modus_ponens,[status(thm)],[11952, 11981])).
% 1.74/1.89 tff(11983,plain,
% 1.74/1.89 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[539, 11982])).
% 1.74/1.90 tff(11984,plain,
% 1.74/1.90 ((op(e1, e3) = e1) <=> (op(e1, e3) = op(e3, e1))),
% 1.74/1.90 inference(transitivity,[status(thm)],[11925, 6290])).
% 1.74/1.90 tff(11985,plain,
% 1.74/1.90 ((~(op(e1, e3) = e1)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[11984])).
% 1.74/1.90 tff(11986,plain,
% 1.74/1.90 (~(op(e1, e3) = op(e3, e1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[10610, 11985])).
% 1.74/1.90 tff(11987,plain,
% 1.74/1.90 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6307, 11986])).
% 1.74/1.90 tff(11988,plain,
% 1.74/1.90 (op(e1, op(e1, e1)) = e1),
% 1.74/1.90 inference(transitivity,[status(thm)],[11965, 11943])).
% 1.74/1.90 tff(11989,plain,
% 1.74/1.90 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5678, 11988])).
% 1.74/1.90 tff(11990,plain,
% 1.74/1.90 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e1, e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[11966])).
% 1.74/1.90 tff(11991,plain,
% 1.74/1.90 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 1.74/1.90 inference(symmetry,[status(thm)],[11990])).
% 1.74/1.90 tff(11992,plain,
% 1.74/1.90 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[11991])).
% 1.74/1.90 tff(11993,plain,
% 1.74/1.90 (~(op(e1, e0) = e2)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[737, 11992])).
% 1.74/1.90 tff(11994,plain,
% 1.74/1.90 (op(e0, e0) = e2),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[589, 11993, 9955, 11970])).
% 1.74/1.90 tff(11995,plain,
% 1.74/1.90 (op(e0, e0) = op(e1, e1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[11994, 11966])).
% 1.74/1.90 tff(11996,plain,
% 1.74/1.90 (op(e1, op(e0, e0)) = op(e1, op(e1, e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[11995])).
% 1.74/1.90 tff(11997,plain,
% 1.74/1.90 (op(e1, op(e0, e0)) = e1),
% 1.74/1.90 inference(transitivity,[status(thm)],[11996, 11965, 11943])).
% 1.74/1.90 tff(11998,plain,
% 1.74/1.90 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6717, 11997])).
% 1.74/1.90 tff(11999,plain,
% 1.74/1.90 (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5367, 11998, 11989, 11987, 11983, 11979, 11960, 11954, 11945, 11940, 11932, 11928, 11917, 11914, 11910])).
% 1.74/1.90 tff(12000,plain,
% 1.74/1.90 (((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)) | (~(op(e3, op(e0, e1)) = e3))),
% 1.74/1.90 inference(tautology,[status(thm)],[])).
% 1.74/1.90 tff(12001,plain,
% 1.74/1.90 (~(op(e3, op(e0, e1)) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[12000, 11999])).
% 1.74/1.90 tff(12002,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[12001, 11903])).
% 1.74/1.90 tff(12003,plain,((op(e1, e1) = e3) | (op(e1, e1) = e0) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(12004,plain,
% 1.74/1.90 (op(e1, e1) = e3),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[12003, 84, 2812, 75, 76, 1304])).
% 1.74/1.90 tff(12005,plain,
% 1.74/1.90 ((op(e1, e1) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12004])).
% 1.74/1.90 tff(12006,plain,
% 1.74/1.90 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12005, 3230])).
% 1.74/1.90 tff(12007,plain,
% 1.74/1.90 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12006])).
% 1.74/1.90 tff(12008,plain,
% 1.74/1.90 (~(op(e1, e3) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[619, 12007])).
% 1.74/1.90 tff(12009,plain,
% 1.74/1.90 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12004])).
% 1.74/1.90 tff(12010,plain,
% 1.74/1.90 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12009])).
% 1.74/1.90 tff(12011,plain,
% 1.74/1.90 (~(op(e0, e1) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[792, 12010])).
% 1.74/1.90 tff(12012,plain,
% 1.74/1.90 ((op(e3, e3) = e1) <=> (e2 = e1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2812])).
% 1.74/1.90 tff(12013,plain,
% 1.74/1.90 ((op(e3, e3) = e1) <=> (e1 = e2)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12012, 69])).
% 1.74/1.90 tff(12014,plain,
% 1.74/1.90 ((e1 = e2) <=> (op(e3, e3) = e1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12013])).
% 1.74/1.90 tff(12015,plain,
% 1.74/1.90 ((~(e1 = e2)) <=> (~(op(e3, e3) = e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12014])).
% 1.74/1.90 tff(12016,plain,
% 1.74/1.90 (~(op(e3, e3) = e1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[708, 12015])).
% 1.74/1.90 tff(12017,plain,
% 1.74/1.90 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4960])).
% 1.74/1.90 tff(12018,plain,
% 1.74/1.90 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12017])).
% 1.74/1.90 tff(12019,plain,
% 1.74/1.90 (~(op(e0, e1) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[792, 12018])).
% 1.74/1.90 tff(12020,plain,
% 1.74/1.90 ((op(e1, e1) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4960])).
% 1.74/1.90 tff(12021,plain,
% 1.74/1.90 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12020, 3230])).
% 1.74/1.90 tff(12022,plain,
% 1.74/1.90 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12021])).
% 1.74/1.90 tff(12023,plain,
% 1.74/1.90 (~(op(e1, e3) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[619, 12022])).
% 1.74/1.90 tff(12024,plain,
% 1.74/1.90 (op(e0, e3) = e1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[151, 87, 926, 76])).
% 1.74/1.90 tff(12025,plain,
% 1.74/1.90 (op(e1, e3) = e0),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[104, 87, 72, 1080])).
% 1.74/1.90 tff(12026,plain,
% 1.74/1.90 (e0 = op(e1, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12025])).
% 1.74/1.90 tff(12027,plain,
% 1.74/1.90 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12026])).
% 1.74/1.90 tff(12028,plain,
% 1.74/1.90 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12027])).
% 1.74/1.90 tff(12029,plain,
% 1.74/1.90 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12028])).
% 1.74/1.90 tff(12030,plain,
% 1.74/1.90 (~(op(e1, e2) = e0)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1850, 12029])).
% 1.74/1.90 tff(12031,plain,
% 1.74/1.90 (op(e0, e2) = e0),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[973, 12030, 17, 85])).
% 1.74/1.90 tff(12032,plain,
% 1.74/1.90 (op(e0, e2) = op(e1, e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12031, 12026])).
% 1.74/1.90 tff(12033,plain,
% 1.74/1.90 ((op(e0, e2) = e3) <=> (op(e1, e3) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12032])).
% 1.74/1.90 tff(12034,plain,
% 1.74/1.90 ((op(e1, e3) = e3) <=> (op(e0, e2) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12033])).
% 1.74/1.90 tff(12035,plain,
% 1.74/1.90 ((~(op(e1, e3) = e3)) <=> (~(op(e0, e2) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12034])).
% 1.74/1.90 tff(12036,plain,
% 1.74/1.90 (~(op(e0, e2) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1080, 12035])).
% 1.74/1.90 tff(12037,plain,
% 1.74/1.90 (e1 = op(e0, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12024])).
% 1.74/1.90 tff(12038,plain,
% 1.74/1.90 (op(e0, e1) = op(e0, op(e0, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12037])).
% 1.74/1.90 tff(12039,plain,
% 1.74/1.90 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12038])).
% 1.74/1.90 tff(12040,plain,
% 1.74/1.90 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12039])).
% 1.74/1.90 tff(12041,plain,
% 1.74/1.90 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12038, 12031])).
% 1.74/1.90 tff(12042,plain,
% 1.74/1.90 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12041, 12040])).
% 1.74/1.90 tff(12043,plain,
% 1.74/1.90 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12042])).
% 1.74/1.90 tff(12044,plain,
% 1.74/1.90 (~(op(e0, e1) = e0)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2102, 12043])).
% 1.74/1.90 tff(12045,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5000, 12044, 12036, 2527, 12024])).
% 1.74/1.90 tff(12046,plain,((op(e1, e3) = e1) | (op(e0, e1) = e3) | (op(e1, e3) = e3) | (op(e2, e2) = e0) | (op(e3, e2) = e0) | (op(e1, e3) = e2) | (op(e3, e3) = e1) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(12047,plain,
% 1.74/1.90 (op(e1, e3) = e1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[12046, 85, 12023, 17, 12019, 10589, 12016, 76])).
% 1.74/1.90 tff(12048,plain,
% 1.74/1.90 (e1 = op(e1, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12047])).
% 1.74/1.90 tff(12049,plain,
% 1.74/1.90 ((e0 = e1) <=> (e0 = op(e1, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12048])).
% 1.74/1.90 tff(12050,plain,
% 1.74/1.90 ((e0 = e1) <=> (op(e1, e3) = e0)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12049, 6095])).
% 1.74/1.90 tff(12051,plain,
% 1.74/1.90 ((~(e0 = e1)) <=> (~(op(e1, e3) = e0))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12050])).
% 1.74/1.90 tff(12052,plain,
% 1.74/1.90 (~(op(e1, e3) = e0)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[26, 12051])).
% 1.74/1.90 tff(12053,plain,
% 1.74/1.90 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12048])).
% 1.74/1.90 tff(12054,plain,
% 1.74/1.90 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12053])).
% 1.74/1.90 tff(12055,plain,
% 1.74/1.90 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12054])).
% 1.74/1.90 tff(12056,plain,
% 1.74/1.90 (~(op(e0, e3) = e1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[64, 12055])).
% 1.74/1.90 tff(12057,plain,
% 1.74/1.90 (op(e1, e3) = e2),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[10335, 124, 79, 80, 76, 121])).
% 1.74/1.90 tff(12058,plain,
% 1.74/1.90 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12057])).
% 1.74/1.90 tff(12059,plain,
% 1.74/1.90 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12058, 120])).
% 1.74/1.90 tff(12060,plain,
% 1.74/1.90 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12059])).
% 1.74/1.90 tff(12061,plain,
% 1.74/1.90 (~(op(e2, e3) = e2)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[118, 12060])).
% 1.74/1.90 tff(12062,plain,
% 1.74/1.90 (op(e2, e3) = e0),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[206, 12061, 76, 124])).
% 1.74/1.90 tff(12063,plain,
% 1.74/1.90 (op(e2, op(e2, e3)) = op(e2, e0)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12062])).
% 1.74/1.90 tff(12064,plain,
% 1.74/1.90 (op(e2, e0) = op(e2, op(e2, e3))),
% 1.74/1.90 inference(symmetry,[status(thm)],[12063])).
% 1.74/1.90 tff(12065,plain,
% 1.74/1.90 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12064])).
% 1.74/1.90 tff(12066,plain,
% 1.74/1.90 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12065])).
% 1.74/1.90 tff(12067,plain,
% 1.74/1.90 (e0 = op(e2, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12062])).
% 1.74/1.90 tff(12068,plain,
% 1.74/1.90 (op(e0, e3) = op(op(e2, e3), e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12067])).
% 1.74/1.90 tff(12069,plain,
% 1.74/1.90 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12057])).
% 1.74/1.90 tff(12070,plain,
% 1.74/1.90 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12069])).
% 1.74/1.90 tff(12071,plain,
% 1.74/1.90 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12070])).
% 1.74/1.90 tff(12072,plain,
% 1.74/1.90 (~(op(e1, e3) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1321, 12071])).
% 1.74/1.90 tff(12073,plain,
% 1.74/1.90 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12057])).
% 1.74/1.90 tff(12074,plain,
% 1.74/1.90 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12073, 69])).
% 1.74/1.90 tff(12075,plain,
% 1.74/1.90 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12074])).
% 1.74/1.90 tff(12076,plain,
% 1.74/1.90 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12075])).
% 1.74/1.90 tff(12077,plain,
% 1.74/1.90 (~(op(e1, e3) = e1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[708, 12076])).
% 1.74/1.90 tff(12078,plain,
% 1.74/1.90 (op(e3, e3) = e1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[151, 12077, 121, 76])).
% 1.74/1.90 tff(12079,plain,
% 1.74/1.90 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12078])).
% 1.74/1.90 tff(12080,plain,
% 1.74/1.90 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12079])).
% 1.74/1.90 tff(12081,plain,
% 1.74/1.90 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12080])).
% 1.74/1.90 tff(12082,plain,
% 1.74/1.90 (~(op(e3, e3) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[303, 12081])).
% 1.74/1.90 tff(12083,plain,
% 1.74/1.90 (op(e0, e3) = e3),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[480, 12082, 124, 12072])).
% 1.74/1.90 tff(12084,plain,
% 1.74/1.90 (e3 = op(e0, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12083])).
% 1.74/1.90 tff(12085,plain,
% 1.74/1.90 (op(e3, op(e2, e3)) = op(e3, e0)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12062])).
% 1.74/1.90 tff(12086,plain,
% 1.74/1.90 (op(e3, e0) = op(e3, op(e2, e3))),
% 1.74/1.90 inference(symmetry,[status(thm)],[12085])).
% 1.74/1.90 tff(12087,plain,
% 1.74/1.90 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12086])).
% 1.74/1.90 tff(12088,plain,
% 1.74/1.90 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12087])).
% 1.74/1.90 tff(12089,plain,
% 1.74/1.90 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12085, 12084])).
% 1.74/1.90 tff(12090,plain,
% 1.74/1.90 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12089])).
% 1.74/1.90 tff(12091,plain,
% 1.74/1.90 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12090, 12088])).
% 1.74/1.90 tff(12092,plain,
% 1.74/1.90 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12091])).
% 1.74/1.90 tff(12093,plain,
% 1.74/1.90 (op(e2, op(e0, e3)) = op(e2, e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12083])).
% 1.74/1.90 tff(12094,plain,
% 1.74/1.90 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12093])).
% 1.74/1.90 tff(12095,plain,
% 1.74/1.90 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12094])).
% 1.74/1.90 tff(12096,plain,
% 1.74/1.90 ((~(op(e2, e3) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12095])).
% 1.74/1.90 tff(12097,plain,
% 1.74/1.90 (~(op(e2, op(e0, e3)) = e2)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[12061, 12096])).
% 1.74/1.90 tff(12098,plain,
% 1.74/1.90 (op(op(e2, e3), e3) = op(e0, e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12068])).
% 1.74/1.90 tff(12099,plain,
% 1.74/1.90 (op(e0, op(e0, e3)) = op(op(e2, e3), e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12067, 12083])).
% 1.74/1.90 tff(12100,plain,
% 1.74/1.90 (op(e0, op(e0, e3)) = op(e0, e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12099, 12098])).
% 1.74/1.90 tff(12101,plain,
% 1.74/1.90 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12100, 12067])).
% 1.74/1.90 tff(12102,plain,
% 1.74/1.90 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12101])).
% 1.74/1.90 tff(12103,plain,
% 1.74/1.90 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12102])).
% 1.74/1.90 tff(12104,plain,
% 1.74/1.90 (~(op(e0, op(e0, e3)) = e0)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[964, 12103])).
% 1.74/1.90 tff(12105,plain,
% 1.74/1.90 (op(e3, op(e0, e3)) = op(e3, e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12083])).
% 1.74/1.90 tff(12106,plain,
% 1.74/1.90 (op(e3, op(e0, e3)) = e1),
% 1.74/1.90 inference(transitivity,[status(thm)],[12105, 12078])).
% 1.74/1.90 tff(12107,plain,
% 1.74/1.90 ((op(e3, op(e0, e3)) = e3) <=> (e1 = op(e0, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12106, 12084])).
% 1.74/1.90 tff(12108,plain,
% 1.74/1.90 ((op(e3, op(e0, e3)) = e3) <=> (op(e0, e3) = e1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12107, 10225])).
% 1.74/1.90 tff(12109,plain,
% 1.74/1.90 ((op(e0, e3) = e1) <=> (op(e3, op(e0, e3)) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12108])).
% 1.74/1.90 tff(12110,plain,
% 1.74/1.90 ((~(op(e0, e3) = e1)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12109])).
% 1.74/1.90 tff(12111,plain,
% 1.74/1.90 (~(op(e3, op(e0, e3)) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[121, 12110])).
% 1.74/1.90 tff(12112,plain,
% 1.74/1.90 (op(e1, op(e0, e3)) = op(e1, e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12083])).
% 1.74/1.90 tff(12113,plain,
% 1.74/1.90 (op(e1, op(e0, e3)) = e2),
% 1.74/1.90 inference(transitivity,[status(thm)],[12112, 12057])).
% 1.74/1.90 tff(12114,plain,
% 1.74/1.90 ((op(e1, op(e0, e3)) = e1) <=> (e2 = e1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12113])).
% 1.74/1.90 tff(12115,plain,
% 1.74/1.90 ((op(e1, op(e0, e3)) = e1) <=> (e1 = e2)),
% 1.74/1.90 inference(transitivity,[status(thm)],[12114, 69])).
% 1.74/1.90 tff(12116,plain,
% 1.74/1.90 ((e1 = e2) <=> (op(e1, op(e0, e3)) = e1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12115])).
% 1.74/1.90 tff(12117,plain,
% 1.74/1.90 ((~(e1 = e2)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12116])).
% 1.74/1.90 tff(12118,plain,
% 1.74/1.90 (~(op(e1, op(e0, e3)) = e1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[708, 12117])).
% 1.74/1.90 tff(12119,plain,
% 1.74/1.90 (~(op(e3, e0) = op(e0, e3))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4654, 12118, 121, 12111, 12104, 12097])).
% 1.74/1.90 tff(12120,plain,
% 1.74/1.90 (~(op(e3, e0) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[12119, 12092])).
% 1.74/1.90 tff(12121,plain,
% 1.74/1.90 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12084])).
% 1.74/1.90 tff(12122,plain,
% 1.74/1.90 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12121])).
% 1.74/1.90 tff(12123,plain,
% 1.74/1.90 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12122])).
% 1.74/1.90 tff(12124,plain,
% 1.74/1.90 (~(op(e0, e0) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[3414, 12123])).
% 1.74/1.90 tff(12125,plain,
% 1.74/1.90 ((op(op(e2, e3), e3) = e2) <=> (op(e0, e3) = e2)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12098])).
% 1.74/1.90 tff(12126,plain,
% 1.74/1.90 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12125])).
% 1.74/1.90 tff(12127,plain,
% 1.74/1.90 ((~(op(e0, e3) = e2)) <=> (~(op(op(e2, e3), e3) = e2))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12126])).
% 1.74/1.90 tff(12128,plain,
% 1.74/1.90 (~(op(op(e2, e3), e3) = e2)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[79, 12127])).
% 1.74/1.90 tff(12129,assumption,(~(op(op(e2, e3), e3) = e2)), introduced(assumption)).
% 1.74/1.90 tff(12130,plain,
% 1.74/1.90 (op(op(e1, e3), e1) = op(e2, e1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[264])).
% 1.74/1.90 tff(12131,plain,
% 1.74/1.90 ((op(op(e1, e3), e1) = e3) <=> (op(e2, e1) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12130])).
% 1.74/1.90 tff(12132,plain,
% 1.74/1.90 ((~(op(op(e1, e3), e1) = e3)) <=> (~(op(e2, e1) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12131])).
% 1.74/1.90 tff(12133,plain,
% 1.74/1.90 ((op(op(e1, e3), e3) = e1) <=> (op(e2, e3) = e1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[322])).
% 1.74/1.90 tff(12134,plain,
% 1.74/1.90 ((op(e2, e3) = e1) <=> (op(op(e1, e3), e3) = e1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12133])).
% 1.74/1.90 tff(12135,plain,
% 1.74/1.90 ((~(op(e2, e3) = e1)) <=> (~(op(op(e1, e3), e3) = e1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12134])).
% 1.74/1.90 tff(12136,plain,
% 1.74/1.90 (~(op(op(e1, e3), e3) = e1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[76, 12135])).
% 1.74/1.90 tff(12137,plain,
% 1.74/1.90 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e2) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6670])).
% 1.74/1.90 tff(12138,plain,
% 1.74/1.90 ((op(e1, e2) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12137])).
% 1.74/1.90 tff(12139,plain,
% 1.74/1.90 ((~(op(e1, e2) = e3)) <=> (~(op(e1, op(e1, e3)) = e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12138])).
% 1.74/1.90 tff(12140,plain,
% 1.74/1.90 (~(op(e1, op(e1, e3)) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[75, 12139])).
% 1.74/1.90 tff(12141,plain,
% 1.74/1.90 ((~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.74/1.90 inference(tautology,[status(thm)],[])).
% 1.74/1.90 tff(12142,plain,
% 1.74/1.90 (~(op(op(e1, e3), e1) = e3)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[12141, 12140, 1304, 12136])).
% 1.74/1.90 tff(12143,plain,
% 1.74/1.90 (~(op(e2, e1) = e3)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[12142, 12132])).
% 1.74/1.90 tff(12144,plain,
% 1.74/1.90 (op(e3, e3) = e1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[151, 6651, 121, 76])).
% 1.74/1.90 tff(12145,plain,
% 1.74/1.90 ((e2 = op(op(e2, e3), e3)) <=> (op(op(e2, e3), e3) = e2)),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(12146,plain,
% 1.74/1.90 (op(e0, e3) = op(op(e2, e3), e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[252])).
% 1.74/1.90 tff(12147,plain,
% 1.74/1.90 (e3 = op(op(e2, e3), e3)),
% 1.74/1.90 inference(transitivity,[status(thm)],[1870, 12146])).
% 1.74/1.90 tff(12148,plain,
% 1.74/1.90 (op(e3, e0) = op(e3, op(e2, e3))),
% 1.74/1.90 inference(symmetry,[status(thm)],[10439])).
% 1.74/1.90 tff(12149,plain,
% 1.74/1.90 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[12148])).
% 1.74/1.90 tff(12150,plain,
% 1.74/1.90 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 1.74/1.90 inference(symmetry,[status(thm)],[12149])).
% 1.74/1.90 tff(12151,plain,
% 1.74/1.90 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[10439, 1870])).
% 1.74/1.90 tff(12152,plain,
% 1.74/1.90 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, op(e2, e3)) = e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12151])).
% 1.74/1.91 tff(12153,plain,
% 1.74/1.91 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12152, 12150])).
% 1.74/1.91 tff(12154,plain,
% 1.74/1.91 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12153])).
% 1.74/1.91 tff(12155,plain,
% 1.74/1.91 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[9765])).
% 1.74/1.91 tff(12156,plain,
% 1.74/1.91 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12155])).
% 1.74/1.91 tff(12157,plain,
% 1.74/1.91 ((~(op(e2, e3) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12156])).
% 1.74/1.91 tff(12158,plain,
% 1.74/1.91 (~(op(e2, op(e0, e3)) = e2)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6598, 12157])).
% 1.74/1.91 tff(12159,plain,
% 1.74/1.91 (op(op(e2, e3), e3) = op(e0, e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12146])).
% 1.74/1.91 tff(12160,plain,
% 1.74/1.91 (op(e0, op(e0, e3)) = op(op(e2, e3), e3)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[252, 1869])).
% 1.74/1.91 tff(12161,plain,
% 1.74/1.91 (op(e0, op(e0, e3)) = op(e0, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12160, 12159])).
% 1.74/1.91 tff(12162,plain,
% 1.74/1.91 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12161, 252])).
% 1.74/1.91 tff(12163,plain,
% 1.74/1.91 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12162])).
% 1.74/1.91 tff(12164,plain,
% 1.74/1.91 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12163])).
% 1.74/1.91 tff(12165,plain,
% 1.74/1.91 (~(op(e0, op(e0, e3)) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[964, 12164])).
% 1.74/1.91 tff(12166,plain,
% 1.74/1.91 (op(e3, op(e0, e3)) = op(e3, e3)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1869])).
% 1.74/1.91 tff(12167,plain,
% 1.74/1.91 (op(e3, op(e0, e3)) = e1),
% 1.74/1.91 inference(transitivity,[status(thm)],[12166, 12144])).
% 1.74/1.91 tff(12168,plain,
% 1.74/1.91 ((op(e3, op(e0, e3)) = e3) <=> (e1 = op(e0, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12167, 1870])).
% 1.74/1.91 tff(12169,plain,
% 1.74/1.91 ((op(e3, op(e0, e3)) = e3) <=> (op(e0, e3) = e1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12168, 10225])).
% 1.74/1.91 tff(12170,plain,
% 1.74/1.91 ((op(e0, e3) = e1) <=> (op(e3, op(e0, e3)) = e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12169])).
% 1.74/1.91 tff(12171,plain,
% 1.74/1.91 ((~(op(e0, e3) = e1)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12170])).
% 1.74/1.91 tff(12172,plain,
% 1.74/1.91 (~(op(e3, op(e0, e3)) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[121, 12171])).
% 1.74/1.91 tff(12173,plain,
% 1.74/1.91 (op(e1, op(e0, e3)) = e2),
% 1.74/1.91 inference(transitivity,[status(thm)],[9798, 264])).
% 1.74/1.91 tff(12174,plain,
% 1.74/1.91 ((op(e1, op(e0, e3)) = e1) <=> (e2 = e1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12173])).
% 1.74/1.91 tff(12175,plain,
% 1.74/1.91 ((op(e1, op(e0, e3)) = e1) <=> (e1 = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12174, 69])).
% 1.74/1.91 tff(12176,plain,
% 1.74/1.91 ((e1 = e2) <=> (op(e1, op(e0, e3)) = e1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12175])).
% 1.74/1.91 tff(12177,plain,
% 1.74/1.91 ((~(e1 = e2)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12176])).
% 1.74/1.91 tff(12178,plain,
% 1.74/1.91 (~(op(e1, op(e0, e3)) = e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[708, 12177])).
% 1.74/1.91 tff(12179,plain,
% 1.74/1.91 (~(op(e3, e0) = op(e0, e3))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4654, 12178, 121, 12172, 12165, 12158])).
% 1.74/1.91 tff(12180,plain,
% 1.74/1.91 (~(op(e3, e0) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12179, 12154])).
% 1.74/1.91 tff(12181,plain,
% 1.74/1.91 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12144])).
% 1.74/1.91 tff(12182,plain,
% 1.74/1.91 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12181])).
% 1.74/1.91 tff(12183,plain,
% 1.74/1.91 (~(op(e3, e0) = e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[157, 12182])).
% 1.74/1.91 tff(12184,plain,
% 1.74/1.91 (op(e3, e0) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5422, 3786, 12183, 12180])).
% 1.74/1.91 tff(12185,plain,
% 1.74/1.91 ((op(e3, e0) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12184])).
% 1.74/1.91 tff(12186,plain,
% 1.74/1.91 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12185, 5470])).
% 1.74/1.91 tff(12187,plain,
% 1.74/1.91 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12186])).
% 1.74/1.91 tff(12188,plain,
% 1.74/1.91 (~(op(e3, e1) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[580, 12187])).
% 1.74/1.91 tff(12189,plain,
% 1.74/1.91 (op(e0, e1) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[292, 12188, 2559, 84])).
% 1.74/1.91 tff(12190,plain,
% 1.74/1.91 (op(e0, e1) = op(e2, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12189, 252])).
% 1.74/1.91 tff(12191,plain,
% 1.74/1.91 ((op(e0, e1) = e2) <=> (op(e2, e3) = e2)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12190])).
% 1.74/1.91 tff(12192,plain,
% 1.74/1.91 ((op(e2, e3) = e2) <=> (op(e0, e1) = e2)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12191])).
% 1.74/1.91 tff(12193,plain,
% 1.74/1.91 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e1) = e2))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12192])).
% 1.74/1.91 tff(12194,plain,
% 1.74/1.91 (~(op(e0, e1) = e2)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6598, 12193])).
% 1.74/1.91 tff(12195,plain,
% 1.74/1.91 ((op(e3, e2) = e3) <=> (e2 = op(op(e2, e3), e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7516, 12147])).
% 1.74/1.91 tff(12196,plain,
% 1.74/1.91 ((op(e3, e2) = e3) <=> (op(op(e2, e3), e3) = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12195, 12145])).
% 1.74/1.91 tff(12197,plain,
% 1.74/1.91 ((op(op(e2, e3), e3) = e2) <=> (op(e3, e2) = e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12196])).
% 1.74/1.91 tff(12198,plain,
% 1.74/1.91 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e3, e2) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12197])).
% 1.74/1.91 tff(12199,plain,
% 1.74/1.91 (~(op(e3, e2) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12129, 12198])).
% 1.74/1.91 tff(12200,plain,
% 1.74/1.91 (op(e2, e2) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2111, 12199, 75, 9688])).
% 1.74/1.91 tff(12201,plain,
% 1.74/1.91 (op(e2, e2) = op(e0, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12200, 1870])).
% 1.74/1.91 tff(12202,plain,
% 1.74/1.91 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12201])).
% 1.74/1.91 tff(12203,plain,
% 1.74/1.91 (op(e2, op(e2, e2)) = op(e2, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12202, 9765])).
% 1.74/1.91 tff(12204,plain,
% 1.74/1.91 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12203])).
% 1.74/1.91 tff(12205,plain,
% 1.74/1.91 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12204, 1942])).
% 1.74/1.91 tff(12206,plain,
% 1.74/1.91 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (e1 = op(e2, e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12205])).
% 1.74/1.91 tff(12207,plain,
% 1.74/1.91 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12206, 16])).
% 1.74/1.91 tff(12208,plain,
% 1.74/1.91 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, op(e2, e2))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[12207])).
% 1.74/1.91 tff(12209,plain,
% 1.74/1.91 (op(e2, e1) = e2),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1993, 82, 5828, 68])).
% 1.74/1.91 tff(12210,plain,
% 1.74/1.91 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12209])).
% 1.74/1.91 tff(12211,plain,
% 1.74/1.91 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12210, 69])).
% 1.74/1.91 tff(12212,plain,
% 1.74/1.91 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12211])).
% 1.74/1.91 tff(12213,plain,
% 1.74/1.91 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12212])).
% 1.74/1.91 tff(12214,plain,
% 1.74/1.91 (~(op(e2, e1) = e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[708, 12213])).
% 1.74/1.91 tff(12215,plain,
% 1.74/1.91 ((op(e2, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12201])).
% 1.74/1.91 tff(12216,plain,
% 1.74/1.91 ((op(e0, e3) = e1) <=> (op(e2, e2) = e1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12215])).
% 1.74/1.91 tff(12217,plain,
% 1.74/1.91 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e2) = e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12216])).
% 1.74/1.91 tff(12218,plain,
% 1.74/1.91 (~(op(e2, e2) = e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[121, 12217])).
% 1.74/1.91 tff(12219,plain,
% 1.74/1.91 (op(e2, e0) = e1),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[345, 12218, 76, 12214])).
% 1.74/1.91 tff(12220,plain,
% 1.74/1.91 (e1 = op(e2, op(e2, op(e2, e2)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12219, 12208])).
% 1.74/1.91 tff(12221,plain,
% 1.74/1.91 (e3 = op(e2, e2)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12200, 1796])).
% 1.74/1.91 tff(12222,plain,
% 1.74/1.91 (op(e2, op(e0, e3)) = op(e2, op(e2, e2))),
% 1.74/1.91 inference(symmetry,[status(thm)],[12202])).
% 1.74/1.91 tff(12223,plain,
% 1.74/1.91 (e0 = op(e2, op(e2, e2))),
% 1.74/1.91 inference(transitivity,[status(thm)],[252, 10034, 12222])).
% 1.74/1.91 tff(12224,plain,
% 1.74/1.91 (~(e1 = op(e2, op(e2, op(e2, e2))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1810, 12223, 12221])).
% 1.74/1.91 tff(12225,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12224, 12220])).
% 1.74/1.91 tff(12226,plain,((op(e3, e1) = e2) | (~(op(e0, e3) = e3)) | (~(op(e2, e3) = e0)) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e1, e2) = e3) | (op(op(e2, e3), e3) = e2) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e2) | (op(e3, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(12227,plain,
% 1.74/1.91 (op(e3, e1) = e2),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12226, 12194, 251, 76, 121, 75, 12129, 1869, 741, 4442, 3786])).
% 1.74/1.91 tff(12228,plain,
% 1.74/1.91 ((op(e3, e1) = e3) <=> (e2 = op(op(e2, e3), e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12227, 12147])).
% 1.74/1.91 tff(12229,plain,
% 1.74/1.91 ((op(e3, e1) = e3) <=> (op(op(e2, e3), e3) = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12228, 12145])).
% 1.74/1.91 tff(12230,plain,
% 1.74/1.91 ((op(op(e2, e3), e3) = e2) <=> (op(e3, e1) = e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12229])).
% 1.74/1.91 tff(12231,plain,
% 1.74/1.91 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e3, e1) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12230])).
% 1.74/1.91 tff(12232,plain,
% 1.74/1.91 (~(op(e3, e1) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12129, 12231])).
% 1.74/1.91 tff(12233,plain,
% 1.74/1.91 (op(e1, e1) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1730, 12232, 9934, 3271])).
% 1.74/1.91 tff(12234,plain,
% 1.74/1.91 (e3 = op(e1, e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12233, 1740])).
% 1.74/1.91 tff(12235,plain,
% 1.74/1.91 (op(e1, e1) = op(e0, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12233, 1870])).
% 1.74/1.91 tff(12236,plain,
% 1.74/1.91 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12235])).
% 1.74/1.91 tff(12237,plain,
% 1.74/1.91 (op(e1, op(e0, e3)) = op(e1, op(e1, e1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[12236])).
% 1.74/1.91 tff(12238,plain,
% 1.74/1.91 (op(e1, e3) = op(e1, op(e0, e3))),
% 1.74/1.91 inference(symmetry,[status(thm)],[9798])).
% 1.74/1.91 tff(12239,plain,
% 1.74/1.91 (e2 = op(e1, op(e1, e1))),
% 1.74/1.91 inference(transitivity,[status(thm)],[265, 12238, 12237])).
% 1.74/1.91 tff(12240,plain,
% 1.74/1.91 (op(e1, op(e1, e1)) = e2),
% 1.74/1.91 inference(transitivity,[status(thm)],[12236, 9798, 264])).
% 1.74/1.91 tff(12241,plain,
% 1.74/1.91 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12240])).
% 1.74/1.91 tff(12242,plain,
% 1.74/1.91 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[12241])).
% 1.74/1.91 tff(12243,plain,
% 1.74/1.91 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12184])).
% 1.74/1.91 tff(12244,plain,
% 1.74/1.91 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12243])).
% 1.74/1.91 tff(12245,plain,
% 1.74/1.91 (~(op(e1, e0) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[410, 12244])).
% 1.74/1.91 tff(12246,plain,
% 1.74/1.91 (op(e1, e2) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1830, 12245, 80, 84])).
% 1.74/1.91 tff(12247,plain,
% 1.74/1.91 (e0 = op(e1, e2)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12246])).
% 1.74/1.91 tff(12248,plain,
% 1.74/1.91 (e0 = op(e1, op(e1, op(e1, e1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[12247, 12242])).
% 1.74/1.91 tff(12249,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1753, 12248, 12239, 12234])).
% 1.74/1.91 tff(12250,plain,((op(e3, e0) = e2) | (~(op(e1, e3) = e2)) | (~(op(e0, e3) = e3)) | (op(e2, e1) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(e2, e3) = e0)) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e1, e2) = e3) | (op(e2, e1) = e0) | (op(e1, e1) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(12251,plain,
% 1.74/1.91 (op(e3, e0) = e2),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12250, 84, 1869, 3271, 12129, 251, 76, 121, 75, 2559, 264, 80])).
% 1.74/1.91 tff(12252,plain,
% 1.74/1.91 ((op(e3, e0) = e0) <=> (e2 = op(e2, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[9332, 252])).
% 1.74/1.91 tff(12253,plain,
% 1.74/1.91 ((op(e3, e0) = e0) <=> (op(e2, e3) = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12252, 120])).
% 1.74/1.91 tff(12254,plain,
% 1.74/1.91 ((op(e2, e3) = e2) <=> (op(e3, e0) = e0)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12253])).
% 1.74/1.91 tff(12255,plain,
% 1.74/1.91 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e0) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12254])).
% 1.74/1.91 tff(12256,plain,
% 1.74/1.91 (~(op(e3, e0) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4382, 12255])).
% 1.74/1.91 tff(12257,plain,
% 1.74/1.91 (op(e3, e1) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1916, 12256, 10415, 85])).
% 1.74/1.91 tff(12258,plain,
% 1.74/1.91 (e0 = op(e3, op(e3, e3))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12257, 8736])).
% 1.74/1.91 tff(12259,plain,
% 1.74/1.91 (op(e3, op(e3, e1)) = op(e3, op(e3, op(e3, e3)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8729])).
% 1.74/1.91 tff(12260,plain,
% 1.74/1.91 (op(e3, op(e3, e1)) = op(op(e0, e3), e0)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1870, 12257])).
% 1.74/1.91 tff(12261,plain,
% 1.74/1.91 (op(op(e0, e3), e0) = op(e3, op(e3, e1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[12260])).
% 1.74/1.91 tff(12262,plain,
% 1.74/1.91 (op(op(e0, e3), e0) = op(e3, op(e2, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1869, 252])).
% 1.74/1.91 tff(12263,plain,
% 1.74/1.91 (op(e3, op(e2, e3)) = op(op(e0, e3), e0)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12262])).
% 1.74/1.91 tff(12264,plain,
% 1.74/1.91 (e2 = op(e3, op(e3, op(e3, e3)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[9333, 12148, 12263, 12261, 12259])).
% 1.74/1.91 tff(12265,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5397, 12264, 12258, 6771])).
% 1.74/1.91 tff(12266,plain,((~(op(e3, e0) = e2)) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e3)) | (~(op(e3, e3) = e1)) | (op(e3, e2) = e0) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(12267,plain,
% 1.74/1.91 (op(e3, e2) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12266, 12251, 1869, 12144, 251, 6598])).
% 1.74/1.91 tff(12268,plain,
% 1.74/1.91 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12267])).
% 1.74/1.91 tff(12269,plain,
% 1.74/1.91 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12268])).
% 1.74/1.91 tff(12270,plain,
% 1.74/1.91 (~(op(e3, e1) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[3429, 12269])).
% 1.74/1.91 tff(12271,plain,
% 1.74/1.91 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12144])).
% 1.74/1.91 tff(12272,plain,
% 1.74/1.91 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12271])).
% 1.74/1.91 tff(12273,plain,
% 1.74/1.91 (~(op(e3, e1) = e1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[437, 12272])).
% 1.74/1.91 tff(12274,plain,
% 1.74/1.91 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12251])).
% 1.74/1.91 tff(12275,plain,
% 1.74/1.91 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12274, 637])).
% 1.74/1.91 tff(12276,plain,
% 1.74/1.91 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12275])).
% 1.74/1.91 tff(12277,plain,
% 1.74/1.91 (~(op(e3, e1) = e2)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[580, 12276])).
% 1.74/1.91 tff(12278,plain,
% 1.74/1.91 (op(e3, e1) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[446, 12277, 12273, 12270])).
% 1.74/1.91 tff(12279,plain,
% 1.74/1.91 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12278])).
% 1.74/1.91 tff(12280,plain,
% 1.74/1.91 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12279])).
% 1.74/1.91 tff(12281,plain,
% 1.74/1.91 (~(op(e1, e1) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[945, 12280])).
% 1.74/1.91 tff(12282,plain,
% 1.74/1.91 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12267])).
% 1.74/1.91 tff(12283,plain,
% 1.74/1.91 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12282])).
% 1.74/1.91 tff(12284,plain,
% 1.74/1.91 (~(op(e1, e2) = e0)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2292, 12283])).
% 1.74/1.91 tff(12285,plain,
% 1.74/1.91 (op(e1, e0) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1830, 12284, 80, 84])).
% 1.74/1.91 tff(12286,plain,
% 1.74/1.91 (op(e1, e0) = op(e2, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12285, 252])).
% 1.74/1.91 tff(12287,plain,
% 1.74/1.91 ((op(e1, e0) = e3) <=> (op(e2, e3) = op(e0, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12286, 1870])).
% 1.74/1.91 tff(12288,plain,
% 1.74/1.91 ((op(e1, e0) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 1.74/1.91 inference(transitivity,[status(thm)],[12287, 925])).
% 1.74/1.91 tff(12289,plain,
% 1.74/1.91 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e0) = e3)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12288])).
% 1.74/1.91 tff(12290,plain,
% 1.74/1.91 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e0) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12289])).
% 1.74/1.91 tff(12291,plain,
% 1.74/1.91 (~(op(e1, e0) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[964, 12290])).
% 1.74/1.91 tff(12292,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[247, 12291, 12281, 6613, 75])).
% 1.74/1.91 tff(12293,plain,((op(e1, e1) = e0) | (op(e1, e2) = e3) | (~(op(e0, e3) = e3)) | (~(op(e2, e3) = e0)) | (op(e1, e3) = e0) | (op(e2, e1) = e3) | (op(op(e2, e3), e3) = e2) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e2, e1) = e0) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(12294,plain,
% 1.74/1.91 (op(e1, e1) = e0),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12293, 75, 1869, 251, 80, 12143, 12129, 76, 121, 2559, 264])).
% 1.74/1.91 tff(12295,plain,
% 1.74/1.91 (~(op(e1, e0) = e3)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[278, 12294, 264, 251])).
% 1.74/1.91 tff(12296,plain,
% 1.74/1.91 (op(e1, e1) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[247, 12295, 6613, 75])).
% 1.74/1.91 tff(12297,plain,
% 1.74/1.91 (e3 = op(e1, e1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12296])).
% 1.74/1.91 tff(12298,plain,
% 1.74/1.91 (op(e0, e3) = op(e2, e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[1869, 12297, 12294, 252])).
% 1.74/1.91 tff(12299,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[964, 12298])).
% 1.74/1.91 tff(12300,plain,((op(e1, e2) = e3) | (~(op(e2, e3) = e0)) | (~(op(e0, e3) = e3)) | (~(op(e1, e3) = e2)) | (op(e1, e3) = e0) | (op(op(e2, e3), e3) = e2) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e2, e1) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(12301,plain,
% 1.74/1.91 (op(e1, e2) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[12300, 12062, 12083, 12057, 80, 12128, 76, 121, 7791, 5425])).
% 1.74/1.91 tff(12302,plain,
% 1.74/1.91 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12301])).
% 1.74/1.91 tff(12303,plain,
% 1.74/1.91 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12302])).
% 1.74/1.91 tff(12304,plain,
% 1.74/1.91 (~(op(e1, e0) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1312, 12303])).
% 1.74/1.91 tff(12305,plain,
% 1.74/1.91 (op(e2, e0) = e3),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2713, 12304, 12124, 12120])).
% 1.74/1.91 tff(12306,plain,
% 1.74/1.91 (op(e2, op(e2, e3)) = op(op(e2, e3), e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12063, 12305, 12084, 12068])).
% 1.74/1.91 tff(12307,plain,
% 1.74/1.91 ((op(e2, op(e2, e3)) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12306])).
% 1.74/1.91 tff(12308,plain,
% 1.74/1.91 ((op(op(e2, e3), e3) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12307])).
% 1.74/1.91 tff(12309,plain,
% 1.74/1.91 ((op(op(e2, e3), e3) = e2) <=> (op(e2, e0) = e2)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12308, 12066])).
% 1.74/1.91 tff(12310,plain,
% 1.74/1.91 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12309])).
% 1.74/1.91 tff(12311,plain,
% 1.74/1.91 (~(op(e2, e0) = e2)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[12128, 12310])).
% 1.74/1.91 tff(12312,plain,
% 1.74/1.91 ((op(e1, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12301])).
% 1.74/1.91 tff(12313,plain,
% 1.74/1.91 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.74/1.91 inference(transitivity,[status(thm)],[12312, 502])).
% 1.74/1.91 tff(12314,plain,
% 1.74/1.91 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12313])).
% 1.74/1.91 tff(12315,plain,
% 1.74/1.91 (~(op(e2, e2) = e3)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1273, 12314])).
% 1.74/1.91 tff(12316,plain,
% 1.74/1.91 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12067])).
% 1.74/1.91 tff(12317,plain,
% 1.74/1.91 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e0)),
% 1.74/1.91 inference(symmetry,[status(thm)],[12316])).
% 1.74/1.91 tff(12318,plain,
% 1.74/1.91 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e0))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[12317])).
% 1.74/1.91 tff(12319,plain,
% 1.74/1.91 (~(op(e2, e2) = e0)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[515, 12318])).
% 1.74/1.92 tff(12320,plain,
% 1.74/1.92 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12078])).
% 1.74/1.92 tff(12321,plain,
% 1.74/1.92 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12320])).
% 1.74/1.92 tff(12322,plain,
% 1.74/1.92 (~(op(e3, e2) = e1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1888, 12321])).
% 1.74/1.92 tff(12323,plain,
% 1.74/1.92 (op(e1, e2) = op(e0, e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12301, 12084])).
% 1.74/1.92 tff(12324,plain,
% 1.74/1.92 ((op(e1, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12323])).
% 1.74/1.92 tff(12325,plain,
% 1.74/1.92 ((op(e0, e3) = e1) <=> (op(e1, e2) = e1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12324])).
% 1.74/1.92 tff(12326,plain,
% 1.74/1.92 ((~(op(e0, e3) = e1)) <=> (~(op(e1, e2) = e1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12325])).
% 1.74/1.92 tff(12327,plain,
% 1.74/1.92 (~(op(e1, e2) = e1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[121, 12326])).
% 1.74/1.92 tff(12328,plain,
% 1.74/1.92 ((op(e1, e2) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12323, 12067])).
% 1.74/1.92 tff(12329,plain,
% 1.74/1.92 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e2) = e0)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12328])).
% 1.74/1.92 tff(12330,plain,
% 1.74/1.92 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e2) = e0))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12329])).
% 1.74/1.92 tff(12331,plain,
% 1.74/1.92 (~(op(e1, e2) = e0)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[964, 12330])).
% 1.74/1.92 tff(12332,plain,
% 1.74/1.92 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12301])).
% 1.74/1.92 tff(12333,plain,
% 1.74/1.92 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12332])).
% 1.74/1.92 tff(12334,plain,
% 1.74/1.92 (~(op(e1, e1) = e3)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1604, 12333])).
% 1.74/1.92 tff(12335,plain,
% 1.74/1.92 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12057])).
% 1.74/1.92 tff(12336,plain,
% 1.74/1.92 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12335])).
% 1.74/1.92 tff(12337,plain,
% 1.74/1.92 (~(op(e1, e1) = e2)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[619, 12336])).
% 1.74/1.92 tff(12338,plain,
% 1.74/1.92 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12078])).
% 1.74/1.92 tff(12339,plain,
% 1.74/1.92 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12338])).
% 1.74/1.92 tff(12340,plain,
% 1.74/1.92 (~(op(e3, e0) = e1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[157, 12339])).
% 1.74/1.92 tff(12341,plain,
% 1.74/1.92 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12301])).
% 1.74/1.92 tff(12342,plain,
% 1.74/1.92 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12341, 3423])).
% 1.74/1.92 tff(12343,plain,
% 1.74/1.92 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12342])).
% 1.74/1.92 tff(12344,plain,
% 1.74/1.92 (~(op(e3, e2) = e3)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2292, 12343])).
% 1.74/1.92 tff(12345,plain,
% 1.74/1.92 (op(e3, e1) = e3),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6055, 12344, 12083, 12119])).
% 1.74/1.92 tff(12346,plain,
% 1.74/1.92 (op(e3, e1) = op(e0, e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12345, 12084])).
% 1.74/1.92 tff(12347,plain,
% 1.74/1.92 ((op(e3, e1) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12346, 12067])).
% 1.74/1.92 tff(12348,plain,
% 1.74/1.92 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e1) = e0)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12347])).
% 1.74/1.92 tff(12349,plain,
% 1.74/1.92 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e0))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12348])).
% 1.74/1.92 tff(12350,plain,
% 1.74/1.92 (~(op(e3, e1) = e0)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[964, 12349])).
% 1.74/1.92 tff(12351,plain,
% 1.74/1.92 ((op(e3, e3) = e0) <=> (e1 = e0)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12078])).
% 1.74/1.92 tff(12352,plain,
% 1.74/1.92 ((op(e3, e3) = e0) <=> (e0 = e1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12351, 18])).
% 1.74/1.92 tff(12353,plain,
% 1.74/1.92 ((e0 = e1) <=> (op(e3, e3) = e0)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12352])).
% 1.74/1.92 tff(12354,plain,
% 1.74/1.92 ((~(e0 = e1)) <=> (~(op(e3, e3) = e0))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12353])).
% 1.74/1.92 tff(12355,plain,
% 1.74/1.92 (~(op(e3, e3) = e0)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[26, 12354])).
% 1.74/1.92 tff(12356,plain,
% 1.74/1.92 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12345])).
% 1.74/1.92 tff(12357,plain,
% 1.74/1.92 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12356])).
% 1.74/1.92 tff(12358,plain,
% 1.74/1.92 (~(op(e2, e1) = e3)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[402, 12357])).
% 1.74/1.92 tff(12359,plain,
% 1.74/1.92 (op(e2, e0) = op(e0, e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12305, 12084])).
% 1.74/1.92 tff(12360,plain,
% 1.74/1.92 ((op(e2, e0) = e1) <=> (op(e0, e3) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12359])).
% 1.74/1.92 tff(12361,plain,
% 1.74/1.92 ((op(e0, e3) = e1) <=> (op(e2, e0) = e1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12360])).
% 1.74/1.92 tff(12362,plain,
% 1.74/1.92 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12361])).
% 1.74/1.92 tff(12363,plain,
% 1.74/1.92 (~(op(e2, e0) = e1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[121, 12362])).
% 1.74/1.92 tff(12364,plain,
% 1.74/1.92 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12323])).
% 1.74/1.92 tff(12365,plain,
% 1.74/1.92 (op(e1, op(e1, e2)) = e2),
% 1.74/1.92 inference(transitivity,[status(thm)],[12364, 12112, 12057])).
% 1.74/1.92 tff(12366,plain,
% 1.74/1.92 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2377, 12365])).
% 1.74/1.92 tff(12367,plain,
% 1.74/1.92 (op(e3, op(e3, e1)) = op(e3, e3)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12345])).
% 1.74/1.92 tff(12368,plain,
% 1.74/1.92 (op(e3, op(e3, e1)) = e1),
% 1.74/1.92 inference(transitivity,[status(thm)],[12367, 12078])).
% 1.74/1.92 tff(12369,plain,
% 1.74/1.92 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2594, 12368])).
% 1.74/1.92 tff(12370,plain,
% 1.74/1.92 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12359])).
% 1.74/1.92 tff(12371,plain,
% 1.74/1.92 (op(e2, op(e2, e0)) = e0),
% 1.74/1.92 inference(transitivity,[status(thm)],[12370, 12093, 12062])).
% 1.74/1.92 tff(12372,plain,
% 1.74/1.92 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2653, 12371])).
% 1.74/1.92 tff(12373,plain,
% 1.74/1.92 (op(e0, e1) = e0),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[292, 84, 2559, 183])).
% 1.74/1.92 tff(12374,plain,
% 1.74/1.92 (op(e0, e1) = op(e2, e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12373, 252])).
% 1.74/1.92 tff(12375,plain,
% 1.74/1.92 ((op(e0, e1) = e2) <=> (op(e2, e3) = e2)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12374])).
% 1.74/1.92 tff(12376,plain,
% 1.74/1.92 ((op(e2, e3) = e2) <=> (op(e0, e1) = e2)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12375])).
% 1.74/1.92 tff(12377,plain,
% 1.74/1.92 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e1) = e2))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12376])).
% 1.74/1.92 tff(12378,plain,
% 1.74/1.92 (~(op(e0, e1) = e2)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4382, 12377])).
% 1.74/1.92 tff(12379,plain,
% 1.74/1.92 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[257])).
% 1.74/1.92 tff(12380,plain,
% 1.74/1.92 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e0) = e1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12379])).
% 1.74/1.92 tff(12381,plain,
% 1.74/1.92 (op(e1, op(e2, e3)) = op(e2, e3)),
% 1.74/1.92 inference(transitivity,[status(thm)],[256, 3352, 252])).
% 1.74/1.92 tff(12382,plain,
% 1.74/1.92 ((op(e1, op(e2, e3)) = e1) <=> (op(e2, e3) = e1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12381])).
% 1.74/1.92 tff(12383,plain,
% 1.74/1.92 ((op(e2, e3) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[12382])).
% 1.74/1.92 tff(12384,plain,
% 1.74/1.92 ((op(e2, e3) = e1) <=> (op(e1, e0) = e1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[12383, 12380])).
% 1.74/1.92 tff(12385,plain,
% 1.74/1.92 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e0) = e1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12384])).
% 1.74/1.92 tff(12386,plain,
% 1.74/1.92 (~(op(e1, e0) = e1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[76, 12385])).
% 1.74/1.92 tff(12387,plain,
% 1.74/1.92 (op(e0, e0) = e1),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1480, 12386, 1349, 931])).
% 1.74/1.92 tff(12388,plain,
% 1.74/1.92 ((op(e0, e0) = e2) <=> (e1 = e2)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[12387])).
% 1.74/1.92 tff(12389,plain,
% 1.74/1.92 ((e1 = e2) <=> (op(e0, e0) = e2)),
% 1.82/1.92 inference(symmetry,[status(thm)],[12388])).
% 1.82/1.92 tff(12390,plain,
% 1.82/1.92 ((~(e1 = e2)) <=> (~(op(e0, e0) = e2))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12389])).
% 1.82/1.92 tff(12391,plain,
% 1.82/1.92 (~(op(e0, e0) = e2)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[708, 12390])).
% 1.82/1.92 tff(12392,plain,
% 1.82/1.92 (op(e0, e2) = e2),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[3652, 12391, 79, 12378])).
% 1.82/1.92 tff(12393,plain,
% 1.82/1.92 (op(e0, op(e0, e2)) = op(op(e2, e3), e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[252, 12392])).
% 1.82/1.92 tff(12394,plain,
% 1.82/1.92 (op(e0, op(e0, e2)) = e2),
% 1.82/1.92 inference(transitivity,[status(thm)],[12393, 5088, 12392])).
% 1.82/1.92 tff(12395,plain,
% 1.82/1.92 (op(e1, e1) = e1),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[630, 84, 68, 1291])).
% 1.82/1.92 tff(12396,plain,
% 1.82/1.92 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12395])).
% 1.82/1.92 tff(12397,plain,
% 1.82/1.92 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 1.82/1.92 inference(transitivity,[status(thm)],[12396, 2355])).
% 1.82/1.92 tff(12398,plain,
% 1.82/1.92 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12397])).
% 1.82/1.92 tff(12399,plain,
% 1.82/1.92 (~(op(e2, e1) = e1)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[225, 12398])).
% 1.82/1.92 tff(12400,plain,
% 1.82/1.92 (op(e2, e2) = e1),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[345, 12399, 76, 1349])).
% 1.82/1.92 tff(12401,plain,
% 1.82/1.92 (op(e2, e1) = e2),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[2367, 12399, 2559, 3271])).
% 1.82/1.92 tff(12402,plain,
% 1.82/1.92 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12401])).
% 1.82/1.92 tff(12403,plain,
% 1.82/1.92 (op(e2, op(e2, e1)) = e1),
% 1.82/1.92 inference(transitivity,[status(thm)],[12402, 12400])).
% 1.82/1.92 tff(12404,plain,
% 1.82/1.92 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1355, 12403])).
% 1.82/1.92 tff(12405,plain,
% 1.82/1.92 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12373])).
% 1.82/1.92 tff(12406,plain,
% 1.82/1.92 (op(op(e0, e1), e1) = e0),
% 1.82/1.92 inference(transitivity,[status(thm)],[12405, 12373])).
% 1.82/1.92 tff(12407,plain,
% 1.82/1.92 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[2650, 12406])).
% 1.82/1.92 tff(12408,plain,
% 1.82/1.92 (op(e3, e0) = e2),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[5422, 10005, 931, 2410])).
% 1.82/1.92 tff(12409,plain,
% 1.82/1.92 (op(e3, e2) = e0),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1916, 10005, 656, 183])).
% 1.82/1.92 tff(12410,plain,
% 1.82/1.92 (op(e3, op(e3, e2)) = op(op(e0, e3), e0)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[1870, 12409])).
% 1.82/1.92 tff(12411,plain,
% 1.82/1.92 (op(e3, op(e3, e2)) = e2),
% 1.82/1.92 inference(transitivity,[status(thm)],[12410, 12262, 10439, 12408])).
% 1.82/1.92 tff(12412,plain,
% 1.82/1.92 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1904, 12411])).
% 1.82/1.92 tff(12413,plain,
% 1.82/1.92 (op(e3, op(e3, e0)) = op(e3, e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12408])).
% 1.82/1.92 tff(12414,plain,
% 1.82/1.92 (op(e3, op(e3, e0)) = e0),
% 1.82/1.92 inference(transitivity,[status(thm)],[12413, 12409])).
% 1.82/1.92 tff(12415,plain,
% 1.82/1.92 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1345, 12414])).
% 1.82/1.92 tff(12416,plain,
% 1.82/1.92 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1459, 12415, 2421, 1275, 3342, 1304, 3356, 12412, 1358, 12407, 12404, 9764])).
% 1.82/1.92 tff(12417,plain,
% 1.82/1.92 (~(op(e0, op(e0, e2)) = e2)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[1331, 12416])).
% 1.82/1.92 tff(12418,plain,
% 1.82/1.92 ($false),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[12417, 12394])).
% 1.82/1.92 tff(12419,plain,((op(e1, e1) = e0) | (~(op(e2, e3) = e0)) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (op(e0, e3) = e2) | (~(op(e0, e3) = e3)) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e2, e1) = e0) | (op(e2, e1) = e3) | (op(e3, e3) = e0) | (op(e3, e1) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e3) | (op(e2, e3) = e2) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e1, e3) = e0) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.92 tff(12420,plain,
% 1.82/1.92 (op(e1, e1) = e0),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[12419, 12062, 12372, 12369, 5469, 5425, 12366, 79, 12083, 76, 12363, 7791, 12358, 12355, 12350, 12340, 12120, 12061, 12337, 12334, 80, 12331])).
% 1.82/1.92 tff(12421,plain,
% 1.82/1.92 (op(e1, e1) = op(e2, e3)),
% 1.82/1.92 inference(transitivity,[status(thm)],[12420, 12067])).
% 1.82/1.92 tff(12422,plain,
% 1.82/1.92 ((op(e1, e1) = e1) <=> (op(e2, e3) = e1)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12421])).
% 1.82/1.92 tff(12423,plain,
% 1.82/1.92 ((op(e2, e3) = e1) <=> (op(e1, e1) = e1)),
% 1.82/1.92 inference(symmetry,[status(thm)],[12422])).
% 1.82/1.92 tff(12424,plain,
% 1.82/1.92 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e1) = e1))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12423])).
% 1.82/1.92 tff(12425,plain,
% 1.82/1.92 (~(op(e1, e1) = e1)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[76, 12424])).
% 1.82/1.92 tff(12426,plain,
% 1.82/1.92 (op(e1, e0) = e1),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[954, 12425, 12077, 12327])).
% 1.82/1.92 tff(12427,plain,
% 1.82/1.92 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12359])).
% 1.82/1.92 tff(12428,plain,
% 1.82/1.92 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.82/1.92 inference(transitivity,[status(thm)],[12427, 7797])).
% 1.82/1.92 tff(12429,plain,
% 1.82/1.92 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.82/1.92 inference(symmetry,[status(thm)],[12428])).
% 1.82/1.92 tff(12430,plain,
% 1.82/1.92 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 1.82/1.92 inference(transitivity,[status(thm)],[12429, 6337])).
% 1.82/1.92 tff(12431,plain,
% 1.82/1.92 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12430])).
% 1.82/1.92 tff(12432,plain,
% 1.82/1.92 (~(op(e0, e2) = op(e2, e0))),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[918, 12431])).
% 1.82/1.92 tff(12433,plain,
% 1.82/1.92 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[6347, 12432])).
% 1.82/1.92 tff(12434,plain,
% 1.82/1.92 (op(e1, op(e2, e3)) = op(e1, e0)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12062])).
% 1.82/1.92 tff(12435,plain,
% 1.82/1.92 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12057])).
% 1.82/1.92 tff(12436,plain,
% 1.82/1.92 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12435])).
% 1.82/1.92 tff(12437,plain,
% 1.82/1.92 (~(op(e1, e0) = e2)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[110, 12436])).
% 1.82/1.92 tff(12438,plain,
% 1.82/1.92 ((op(e1, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12057])).
% 1.82/1.92 tff(12439,plain,
% 1.82/1.92 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 1.82/1.92 inference(transitivity,[status(thm)],[12438, 565])).
% 1.82/1.92 tff(12440,plain,
% 1.82/1.92 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12439])).
% 1.82/1.92 tff(12441,plain,
% 1.82/1.92 (~(op(e3, e3) = e2)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[571, 12440])).
% 1.82/1.92 tff(12442,plain,
% 1.82/1.92 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12420])).
% 1.82/1.92 tff(12443,plain,
% 1.82/1.92 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12442])).
% 1.82/1.92 tff(12444,plain,
% 1.82/1.92 (~(op(e0, e1) = e0)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[792, 12443])).
% 1.82/1.92 tff(12445,plain,
% 1.82/1.92 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12084])).
% 1.82/1.92 tff(12446,plain,
% 1.82/1.92 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 1.82/1.92 inference(symmetry,[status(thm)],[12445])).
% 1.82/1.92 tff(12447,plain,
% 1.82/1.92 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12446])).
% 1.82/1.92 tff(12448,plain,
% 1.82/1.92 (~(op(e0, e1) = e3)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[818, 12447])).
% 1.82/1.92 tff(12449,plain,
% 1.82/1.92 (op(e3, e1) = op(op(e2, e3), e3)),
% 1.82/1.92 inference(transitivity,[status(thm)],[12345, 12084, 12068])).
% 1.82/1.92 tff(12450,plain,
% 1.82/1.92 ((op(e3, e1) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12449])).
% 1.82/1.92 tff(12451,plain,
% 1.82/1.92 ((op(op(e2, e3), e3) = e2) <=> (op(e3, e1) = e2)),
% 1.82/1.92 inference(symmetry,[status(thm)],[12450])).
% 1.82/1.92 tff(12452,plain,
% 1.82/1.92 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e3, e1) = e2))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12451])).
% 1.82/1.92 tff(12453,plain,
% 1.82/1.92 (~(op(e3, e1) = e2)),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[12128, 12452])).
% 1.82/1.92 tff(12454,plain,
% 1.82/1.92 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12429])).
% 1.82/1.92 tff(12455,plain,
% 1.82/1.92 (~(op(e2, e0) = op(e0, e2))),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[918, 12454])).
% 1.82/1.92 tff(12456,plain,
% 1.82/1.92 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[6358, 12455])).
% 1.82/1.92 tff(12457,plain,
% 1.82/1.92 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12057])).
% 1.82/1.92 tff(12458,plain,
% 1.82/1.92 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 1.82/1.92 inference(symmetry,[status(thm)],[12457])).
% 1.82/1.92 tff(12459,plain,
% 1.82/1.92 ((op(op(e2, e3), e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 1.82/1.92 inference(transitivity,[status(thm)],[12451, 12458])).
% 1.82/1.92 tff(12460,plain,
% 1.82/1.92 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12459])).
% 1.82/1.92 tff(12461,plain,
% 1.82/1.92 (~(op(e3, e1) = op(e1, e3))),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[12128, 12460])).
% 1.82/1.92 tff(12462,plain,
% 1.82/1.92 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[6362, 12461])).
% 1.82/1.92 tff(12463,plain,
% 1.82/1.92 (op(e1, e0) = op(e1, op(e2, e3))),
% 1.82/1.92 inference(symmetry,[status(thm)],[12434])).
% 1.82/1.92 tff(12464,plain,
% 1.82/1.92 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12463])).
% 1.82/1.92 tff(12465,plain,
% 1.82/1.92 (op(e1, op(e2, e3)) = e1),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[12426, 12464])).
% 1.82/1.92 tff(12466,plain,
% 1.82/1.92 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[10724, 12465])).
% 1.82/1.92 tff(12467,plain,
% 1.82/1.92 ((op(op(e2, e3), e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 1.82/1.92 inference(transitivity,[status(thm)],[12451, 12458, 6290])).
% 1.82/1.92 tff(12468,plain,
% 1.82/1.92 ((~(op(op(e2, e3), e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12467])).
% 1.82/1.92 tff(12469,plain,
% 1.82/1.92 (~(op(e1, e3) = op(e3, e1))),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[12128, 12468])).
% 1.82/1.92 tff(12470,plain,
% 1.82/1.92 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[6307, 12469])).
% 1.82/1.92 tff(12471,plain,
% 1.82/1.92 (op(e3, op(e1, e0)) = op(e3, e1)),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12426])).
% 1.82/1.92 tff(12472,plain,
% 1.82/1.92 (op(e3, op(e1, e0)) = e3),
% 1.82/1.92 inference(transitivity,[status(thm)],[12471, 12345])).
% 1.82/1.92 tff(12473,plain,
% 1.82/1.92 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[9792, 12472])).
% 1.82/1.92 tff(12474,plain,
% 1.82/1.92 (~(op(e0, e3) = op(e3, e0))),
% 1.82/1.92 inference(modus_ponens,[status(thm)],[12119, 454])).
% 1.82/1.92 tff(12475,plain,
% 1.82/1.92 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.82/1.92 inference(unit_resolution,[status(thm)],[496, 12474])).
% 1.82/1.92 tff(12476,plain,
% 1.82/1.92 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 1.82/1.92 inference(monotonicity,[status(thm)],[12421])).
% 1.82/1.92 tff(12477,plain,
% 1.82/1.92 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12476])).
% 1.82/1.93 tff(12478,plain,
% 1.82/1.93 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12477])).
% 1.82/1.93 tff(12479,plain,
% 1.82/1.93 ((op(e1, e0) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12464, 12478])).
% 1.82/1.93 tff(12480,plain,
% 1.82/1.93 (op(e1, op(e1, e1)) = e1),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[12426, 12479])).
% 1.82/1.93 tff(12481,plain,
% 1.82/1.93 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[5678, 12480])).
% 1.82/1.93 tff(12482,plain,
% 1.82/1.93 (op(e3, op(e3, e3)) = op(e3, e1)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12078])).
% 1.82/1.93 tff(12483,plain,
% 1.82/1.93 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12482])).
% 1.82/1.93 tff(12484,plain,
% 1.82/1.93 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12483])).
% 1.82/1.93 tff(12485,plain,
% 1.82/1.93 (op(e3, op(e3, e3)) = e3),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[12345, 12484])).
% 1.82/1.93 tff(12486,plain,
% 1.82/1.93 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[6277, 12485])).
% 1.82/1.93 tff(12487,plain,
% 1.82/1.93 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e3)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12301])).
% 1.82/1.93 tff(12488,plain,
% 1.82/1.93 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 1.82/1.93 inference(symmetry,[status(thm)],[12487])).
% 1.82/1.93 tff(12489,plain,
% 1.82/1.93 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = op(e1, e2))),
% 1.82/1.93 inference(transitivity,[status(thm)],[12356, 12488])).
% 1.82/1.93 tff(12490,plain,
% 1.82/1.93 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12489])).
% 1.82/1.93 tff(12491,plain,
% 1.82/1.93 (~(op(e2, e1) = op(e1, e2))),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[402, 12490])).
% 1.82/1.93 tff(12492,plain,
% 1.82/1.93 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[557, 12491])).
% 1.82/1.93 tff(12493,plain,
% 1.82/1.93 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e2) = op(e2, e1))),
% 1.82/1.93 inference(transitivity,[status(thm)],[12356, 12488, 531])).
% 1.82/1.93 tff(12494,plain,
% 1.82/1.93 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12493])).
% 1.82/1.93 tff(12495,plain,
% 1.82/1.93 (~(op(e1, e2) = op(e2, e1))),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[402, 12494])).
% 1.82/1.93 tff(12496,plain,
% 1.82/1.93 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[539, 12495])).
% 1.82/1.93 tff(12497,plain,
% 1.82/1.93 (op(e3, e0) = e0),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[5422, 3786, 931, 2410])).
% 1.82/1.93 tff(12498,plain,
% 1.82/1.93 (op(e3, e0) = op(e2, e3)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12497, 252])).
% 1.82/1.93 tff(12499,plain,
% 1.82/1.93 ((op(e3, e0) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12498])).
% 1.82/1.93 tff(12500,plain,
% 1.82/1.93 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 1.82/1.93 inference(transitivity,[status(thm)],[12499, 394])).
% 1.82/1.93 tff(12501,plain,
% 1.82/1.93 ((op(e3, e0) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.82/1.93 inference(transitivity,[status(thm)],[12500, 395])).
% 1.82/1.93 tff(12502,plain,
% 1.82/1.93 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12501])).
% 1.82/1.93 tff(12503,plain,
% 1.82/1.93 (~(op(e2, e3) = op(e3, e2))),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[1133, 12502])).
% 1.82/1.93 tff(12504,plain,
% 1.82/1.93 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[430, 12503])).
% 1.82/1.93 tff(12505,plain,
% 1.82/1.93 (op(e0, e0) = e2),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[589, 3786, 6687, 982])).
% 1.82/1.93 tff(12506,plain,
% 1.82/1.93 ((op(e0, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12505])).
% 1.82/1.93 tff(12507,plain,
% 1.82/1.93 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12506, 4838])).
% 1.82/1.93 tff(12508,plain,
% 1.82/1.93 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e2))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12507])).
% 1.82/1.93 tff(12509,plain,
% 1.82/1.93 (~(op(e0, e1) = e2)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[811, 12508])).
% 1.82/1.93 tff(12510,plain,
% 1.82/1.93 (op(e2, e1) = e2),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[1993, 12509, 82, 68])).
% 1.82/1.93 tff(12511,plain,
% 1.82/1.93 (op(e3, e2) = e2),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[2015, 3786, 126, 82])).
% 1.82/1.93 tff(12512,plain,
% 1.82/1.93 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12511])).
% 1.82/1.93 tff(12513,plain,
% 1.82/1.93 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12512])).
% 1.82/1.93 tff(12514,plain,
% 1.82/1.93 (~(op(e2, e2) = e2)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[1546, 12513])).
% 1.82/1.93 tff(12515,plain,
% 1.82/1.93 (op(e2, e2) = e1),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[524, 12514, 1951, 2431])).
% 1.82/1.93 tff(12516,plain,
% 1.82/1.93 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12515])).
% 1.82/1.93 tff(12517,plain,
% 1.82/1.93 (op(e2, op(e2, e2)) = e2),
% 1.82/1.93 inference(transitivity,[status(thm)],[12516, 12510])).
% 1.82/1.93 tff(12518,plain,
% 1.82/1.93 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[528, 12517])).
% 1.82/1.93 tff(12519,plain,
% 1.82/1.93 (op(e0, op(e0, e0)) = op(op(e2, e3), e2)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[252, 12505])).
% 1.82/1.93 tff(12520,plain,
% 1.82/1.93 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12519, 5088])).
% 1.82/1.93 tff(12521,plain,
% 1.82/1.93 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e2) = e0)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12520])).
% 1.82/1.93 tff(12522,plain,
% 1.82/1.93 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12521])).
% 1.82/1.93 tff(12523,plain,
% 1.82/1.93 ((op(e0, e3) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[252])).
% 1.82/1.93 tff(12524,plain,
% 1.82/1.93 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e0)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12523])).
% 1.82/1.93 tff(12525,plain,
% 1.82/1.93 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e0))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12524])).
% 1.82/1.93 tff(12526,plain,
% 1.82/1.93 (~(op(e0, e3) = e0)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[964, 12525])).
% 1.82/1.93 tff(12527,plain,
% 1.82/1.93 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e0)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12497])).
% 1.82/1.93 tff(12528,plain,
% 1.82/1.93 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e0))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12527])).
% 1.82/1.93 tff(12529,plain,
% 1.82/1.93 (~(op(e0, e0) = e0)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[6384, 12528])).
% 1.82/1.93 tff(12530,plain,
% 1.82/1.93 (op(e0, e2) = e0),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[3976, 12529, 12526, 3849])).
% 1.82/1.93 tff(12531,plain,
% 1.82/1.93 (op(e0, op(e0, e0)) = e0),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[12530, 12522])).
% 1.82/1.93 tff(12532,plain,
% 1.82/1.93 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[5598, 12531])).
% 1.82/1.93 tff(12533,plain,
% 1.82/1.93 (op(e0, e1) = e1),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[829, 12509, 2527, 3849])).
% 1.82/1.93 tff(12534,plain,
% 1.82/1.93 (op(e2, op(e0, e1)) = op(e2, e1)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12533])).
% 1.82/1.93 tff(12535,plain,
% 1.82/1.93 (op(e2, op(e0, e1)) = e2),
% 1.82/1.93 inference(transitivity,[status(thm)],[12534, 12510])).
% 1.82/1.93 tff(12536,plain,
% 1.82/1.93 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[9902, 12535])).
% 1.82/1.93 tff(12537,plain,
% 1.82/1.93 ($false),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[5367, 12536, 12532, 5673, 5680, 6688, 6689, 5670, 5681, 5669, 12518, 5671, 5511, 5674, 12504, 9846])).
% 1.82/1.93 tff(12538,plain,((op(e3, e0) = e2) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e2, e3) = e0)) | (op(e2, e2) = e3) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e3) | (op(e0, e1) = e0) | (op(e3, e3) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e1) | (op(e3, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.93 tff(12539,plain,
% 1.82/1.93 (op(e3, e0) = e2),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[12538, 12496, 12492, 12486, 12481, 12475, 12473, 12470, 12466, 12462, 12456, 12433, 12062, 12315, 12453, 12337, 12448, 12444, 12441, 12437, 12311, 12340, 12120])).
% 1.82/1.93 tff(12540,plain,
% 1.82/1.93 (op(e3, e2) = e0),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[12266, 12539, 12083, 12078, 12062, 12061])).
% 1.82/1.93 tff(12541,plain,
% 1.82/1.93 (op(e3, e2) = op(e2, e3)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12540, 12067])).
% 1.82/1.93 tff(12542,plain,
% 1.82/1.93 (op(e1, op(e3, e2)) = op(e1, op(e2, e3))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12541])).
% 1.82/1.93 tff(12543,plain,
% 1.82/1.93 (op(e1, op(e3, e2)) = e1),
% 1.82/1.93 inference(transitivity,[status(thm)],[12542, 12434, 12426])).
% 1.82/1.93 tff(12544,plain,
% 1.82/1.93 (((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)) | (~(op(e1, op(e3, e2)) = e1))),
% 1.82/1.93 inference(tautology,[status(thm)],[])).
% 1.82/1.93 tff(12545,plain,
% 1.82/1.93 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.82/1.93 inference(unit_resolution,[status(thm)],[12544, 12543])).
% 1.82/1.93 tff(12546,plain,
% 1.82/1.93 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12420])).
% 1.82/1.93 tff(12547,plain,
% 1.82/1.93 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12546])).
% 1.82/1.93 tff(12548,plain,
% 1.82/1.93 (~(op(e1, e0) = e0)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[737, 12547])).
% 1.82/1.93 tff(12549,plain,
% 1.82/1.93 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e3))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12067])).
% 1.82/1.93 tff(12550,plain,
% 1.82/1.93 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e0)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12549])).
% 1.82/1.93 tff(12551,plain,
% 1.82/1.93 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e0))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12550])).
% 1.82/1.93 tff(12552,plain,
% 1.82/1.93 (~(op(e2, e0) = e0)),
% 1.82/1.93 inference(modus_ponens,[status(thm)],[989, 12551])).
% 1.82/1.93 tff(12553,plain,
% 1.82/1.93 ((op(e3, e0) = e0) <=> (e2 = op(e2, e3))),
% 1.82/1.93 inference(monotonicity,[status(thm)],[12539, 12067])).
% 1.82/1.93 tff(12554,plain,
% 1.82/1.93 ((op(e3, e0) = e0) <=> (op(e2, e3) = e2)),
% 1.82/1.93 inference(transitivity,[status(thm)],[12553, 120])).
% 1.82/1.93 tff(12555,plain,
% 1.82/1.93 ((op(e2, e3) = e2) <=> (op(e3, e0) = e0)),
% 1.82/1.93 inference(symmetry,[status(thm)],[12554])).
% 1.82/1.93 tff(12556,plain,
% 1.82/1.93 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e0) = e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12555])).
% 1.82/1.94 tff(12557,plain,
% 1.82/1.94 (~(op(e3, e0) = e0)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[12061, 12556])).
% 1.82/1.94 tff(12558,plain,
% 1.82/1.94 (op(e0, e0) = e0),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5651, 12557, 12552, 12548])).
% 1.82/1.94 tff(12559,plain,
% 1.82/1.94 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12558])).
% 1.82/1.94 tff(12560,plain,
% 1.82/1.94 (op(e0, op(e0, e0)) = e0),
% 1.82/1.94 inference(transitivity,[status(thm)],[12559, 12558])).
% 1.82/1.94 tff(12561,plain,
% 1.82/1.94 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5598, 12560])).
% 1.82/1.94 tff(12562,plain,
% 1.82/1.94 (op(e2, e2) = e2),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[524, 1348, 17, 2431])).
% 1.82/1.94 tff(12563,plain,
% 1.82/1.94 (op(e2, op(e2, e2)) = op(e2, e2)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12562])).
% 1.82/1.94 tff(12564,plain,
% 1.82/1.94 (op(e2, op(e2, e2)) = e2),
% 1.82/1.94 inference(transitivity,[status(thm)],[12563, 12562])).
% 1.82/1.94 tff(12565,plain,
% 1.82/1.94 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[528, 12564])).
% 1.82/1.94 tff(12566,plain,
% 1.82/1.94 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e1, e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[5903])).
% 1.82/1.94 tff(12567,plain,
% 1.82/1.94 ((op(e0, e1) = e1) <=> (op(e1, e0) = op(e0, e1))),
% 1.82/1.94 inference(transitivity,[status(thm)],[12566, 595])).
% 1.82/1.94 tff(12568,plain,
% 1.82/1.94 (op(e0, e2) = e1),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[1613, 1348, 4515, 930])).
% 1.82/1.94 tff(12569,plain,
% 1.82/1.94 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12568])).
% 1.82/1.94 tff(12570,plain,
% 1.82/1.94 ((op(e0, e1) = op(e0, e2)) <=> (op(e1, e0) = op(e0, e1))),
% 1.82/1.94 inference(transitivity,[status(thm)],[12569, 12567])).
% 1.82/1.94 tff(12571,plain,
% 1.82/1.94 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12570])).
% 1.82/1.94 tff(12572,plain,
% 1.82/1.94 (~(op(e1, e0) = op(e0, e1))),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[2102, 12571])).
% 1.82/1.94 tff(12573,plain,
% 1.82/1.94 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[613, 12572])).
% 1.82/1.94 tff(12574,plain,
% 1.82/1.94 ($false),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5367, 12573, 12565, 5673, 5680, 6688, 6689, 5670, 5681, 5669, 5667, 5671, 5511, 5674, 5668, 9846])).
% 1.82/1.94 tff(12575,plain,((op(e2, e2) = e1) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e1, e0) = e1)) | (op(e1, e2) = e1) | (op(e3, e2) = e1) | (op(e2, e2) = e0) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.94 tff(12576,plain,
% 1.82/1.94 (op(e2, e2) = e1),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[12575, 12496, 12492, 12486, 12481, 12475, 12473, 12470, 12561, 12466, 12462, 12456, 12545, 12433, 12426, 12327, 12322, 12319, 12315])).
% 1.82/1.94 tff(12577,plain,
% 1.82/1.94 ((op(e2, e2) = e2) <=> (e1 = e2)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12576])).
% 1.82/1.94 tff(12578,plain,
% 1.82/1.94 ((e1 = e2) <=> (op(e2, e2) = e2)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12577])).
% 1.82/1.94 tff(12579,plain,
% 1.82/1.94 ((~(e1 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12578])).
% 1.82/1.94 tff(12580,plain,
% 1.82/1.94 (~(op(e2, e2) = e2)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[708, 12579])).
% 1.82/1.94 tff(12581,plain,
% 1.82/1.94 (op(e2, e1) = e2),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[2088, 12580, 12061, 12311])).
% 1.82/1.94 tff(12582,plain,
% 1.82/1.94 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12426])).
% 1.82/1.94 tff(12583,plain,
% 1.82/1.94 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12582])).
% 1.82/1.94 tff(12584,plain,
% 1.82/1.94 (~(op(e0, e0) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[2471, 12583])).
% 1.82/1.94 tff(12585,plain,
% 1.82/1.94 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12576])).
% 1.82/1.94 tff(12586,plain,
% 1.82/1.94 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12585])).
% 1.82/1.94 tff(12587,plain,
% 1.82/1.94 (~(op(e0, e2) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[2736, 12586])).
% 1.82/1.94 tff(12588,plain,
% 1.82/1.94 (op(e0, e1) = e1),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[384, 12587, 121, 12584])).
% 1.82/1.94 tff(12589,plain,
% 1.82/1.94 (op(e2, op(e0, e1)) = op(e2, e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12588])).
% 1.82/1.94 tff(12590,plain,
% 1.82/1.94 (op(e2, op(e0, e1)) = e2),
% 1.82/1.94 inference(transitivity,[status(thm)],[12589, 12581])).
% 1.82/1.94 tff(12591,plain,
% 1.82/1.94 (op(e3, op(e2, e2)) = op(e3, e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12576])).
% 1.82/1.94 tff(12592,plain,
% 1.82/1.94 (op(e3, op(e2, e2)) = e3),
% 1.82/1.94 inference(transitivity,[status(thm)],[12591, 12345])).
% 1.82/1.94 tff(12593,plain,
% 1.82/1.94 (((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)) | (~(op(e3, op(e2, e2)) = e3))),
% 1.82/1.94 inference(tautology,[status(thm)],[])).
% 1.82/1.94 tff(12594,plain,
% 1.82/1.94 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[12593, 12592])).
% 1.82/1.94 tff(12595,plain,
% 1.82/1.94 (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5367, 12594, 12496, 12492, 12486, 12481, 12475, 12473, 12470, 12561, 12466, 12462, 12456, 12545, 12433])).
% 1.82/1.94 tff(12596,plain,
% 1.82/1.94 (~(op(e2, op(e0, e1)) = e2)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[9902, 12595])).
% 1.82/1.94 tff(12597,plain,
% 1.82/1.94 ($false),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[12596, 12590])).
% 1.82/1.94 tff(12598,plain,((op(e2, e3) = e3) | (op(e0, e3) = e1) | (op(e2, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.94 tff(12599,plain,
% 1.82/1.94 (op(e2, e3) = e3),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[12598, 12056, 76, 10592, 12052])).
% 1.82/1.94 tff(12600,plain,
% 1.82/1.94 ((op(e2, e3) = e0) <=> (e3 = e0)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12599])).
% 1.82/1.94 tff(12601,plain,
% 1.82/1.94 ((op(e2, e3) = e0) <=> (e0 = e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12600, 159])).
% 1.82/1.94 tff(12602,plain,
% 1.82/1.94 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12601])).
% 1.82/1.94 tff(12603,plain,
% 1.82/1.94 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12602])).
% 1.82/1.94 tff(12604,plain,
% 1.82/1.94 (~(op(e2, e3) = e0)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[181, 12603])).
% 1.82/1.94 tff(12605,plain,
% 1.82/1.94 (~(op(e2, e1) = e0)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[7365, 12056, 10592, 9696, 12052])).
% 1.82/1.94 tff(12606,plain,
% 1.82/1.94 (op(op(e1, e3), e1) = op(e1, e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12047])).
% 1.82/1.94 tff(12607,plain,
% 1.82/1.94 (op(op(e1, e3), e1) = e3),
% 1.82/1.94 inference(transitivity,[status(thm)],[12606, 4960])).
% 1.82/1.94 tff(12608,plain,
% 1.82/1.94 (op(e0, e3) = e0),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[1105, 12604, 9696, 12056, 12607, 10592])).
% 1.82/1.94 tff(12609,plain,
% 1.82/1.94 (op(e0, e1) = op(e0, op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12048])).
% 1.82/1.94 tff(12610,plain,
% 1.82/1.94 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12609])).
% 1.82/1.94 tff(12611,plain,
% 1.82/1.94 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e1) = e0)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12610])).
% 1.82/1.94 tff(12612,plain,
% 1.82/1.94 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e3)) = e0)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12609, 12608])).
% 1.82/1.94 tff(12613,plain,
% 1.82/1.94 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12612, 12611])).
% 1.82/1.94 tff(12614,plain,
% 1.82/1.94 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12613])).
% 1.82/1.94 tff(12615,plain,
% 1.82/1.94 (~(op(e0, e1) = e0)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[818, 12614])).
% 1.82/1.94 tff(12616,plain,
% 1.82/1.94 (op(e3, e1) = e0),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[292, 12615, 84, 12605])).
% 1.82/1.94 tff(12617,plain,
% 1.82/1.94 (op(e3, e2) = e3),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[10084, 12616, 2812])).
% 1.82/1.94 tff(12618,plain,
% 1.82/1.94 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12599])).
% 1.82/1.94 tff(12619,plain,
% 1.82/1.94 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12618])).
% 1.82/1.94 tff(12620,plain,
% 1.82/1.94 (~(op(e2, e2) = e3)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[515, 12619])).
% 1.82/1.94 tff(12621,plain,
% 1.82/1.94 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[4960])).
% 1.82/1.94 tff(12622,plain,
% 1.82/1.94 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12621])).
% 1.82/1.94 tff(12623,plain,
% 1.82/1.94 (~(op(e1, e0) = e3)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[737, 12622])).
% 1.82/1.94 tff(12624,plain,
% 1.82/1.94 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12048])).
% 1.82/1.94 tff(12625,plain,
% 1.82/1.94 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12624])).
% 1.82/1.94 tff(12626,plain,
% 1.82/1.94 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12625])).
% 1.82/1.94 tff(12627,plain,
% 1.82/1.94 (~(op(e1, e0) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[110, 12626])).
% 1.82/1.94 tff(12628,plain,
% 1.82/1.94 (op(e2, e0) = e0),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[2311, 12604, 17, 12605])).
% 1.82/1.94 tff(12629,plain,
% 1.82/1.94 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12628])).
% 1.82/1.94 tff(12630,plain,
% 1.82/1.94 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12629])).
% 1.82/1.94 tff(12631,plain,
% 1.82/1.94 (~(op(e1, e0) = e0)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[756, 12630])).
% 1.82/1.94 tff(12632,plain,
% 1.82/1.94 (op(e1, e0) = e2),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[728, 12631, 12627, 12623])).
% 1.82/1.94 tff(12633,plain,
% 1.82/1.94 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12632])).
% 1.82/1.94 tff(12634,plain,
% 1.82/1.94 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12633])).
% 1.82/1.94 tff(12635,plain,
% 1.82/1.94 (~(op(e0, e0) = e2)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[2471, 12634])).
% 1.82/1.94 tff(12636,plain,
% 1.82/1.94 (op(e2, op(e2, e3)) = op(e2, e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12599])).
% 1.82/1.94 tff(12637,plain,
% 1.82/1.94 (op(e2, op(e2, e3)) = e3),
% 1.82/1.94 inference(transitivity,[status(thm)],[12636, 12599])).
% 1.82/1.94 tff(12638,plain,
% 1.82/1.94 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[2344, 12637])).
% 1.82/1.94 tff(12639,plain,
% 1.82/1.94 (e0 = op(e0, e3)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12608])).
% 1.82/1.94 tff(12640,plain,
% 1.82/1.94 (op(e3, e1) = op(e0, e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12616, 12639])).
% 1.82/1.94 tff(12641,plain,
% 1.82/1.94 ((op(e3, e1) = op(e1, e3)) <=> (op(e0, e3) = op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12640])).
% 1.82/1.94 tff(12642,plain,
% 1.82/1.94 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e1) = op(e1, e3))),
% 1.82/1.94 inference(symmetry,[status(thm)],[12641])).
% 1.82/1.94 tff(12643,plain,
% 1.82/1.94 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = op(e3, e1))),
% 1.82/1.94 inference(transitivity,[status(thm)],[12642, 6290])).
% 1.82/1.94 tff(12644,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12643])).
% 1.82/1.94 tff(12645,plain,
% 1.82/1.94 (~(op(e1, e3) = op(e3, e1))),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[64, 12644])).
% 1.82/1.94 tff(12646,plain,
% 1.82/1.94 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[6307, 12645])).
% 1.82/1.94 tff(12647,plain,
% 1.82/1.94 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5468, 12056, 10592])).
% 1.82/1.94 tff(12648,plain,
% 1.82/1.94 (op(op(e0, e3), e3) = e0),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5461, 12608])).
% 1.82/1.94 tff(12649,plain,
% 1.82/1.94 (op(op(e3, e1), e3) = op(op(e0, e3), e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12640])).
% 1.82/1.94 tff(12650,plain,
% 1.82/1.94 (op(op(e3, e1), e3) = op(e0, e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12649, 12648, 12639])).
% 1.82/1.94 tff(12651,plain,
% 1.82/1.94 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12650, 12048])).
% 1.82/1.94 tff(12652,plain,
% 1.82/1.94 ((op(e0, e3) = op(e1, e3)) <=> (op(op(e3, e1), e3) = e1)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12651])).
% 1.82/1.94 tff(12653,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12652])).
% 1.82/1.94 tff(12654,plain,
% 1.82/1.94 (~(op(op(e3, e1), e3) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[64, 12653])).
% 1.82/1.94 tff(12655,plain,
% 1.82/1.94 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[1050, 12654])).
% 1.82/1.94 tff(12656,plain,
% 1.82/1.94 (op(e2, e0) = op(e0, e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12628, 12639])).
% 1.82/1.94 tff(12657,plain,
% 1.82/1.94 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12656])).
% 1.82/1.94 tff(12658,plain,
% 1.82/1.94 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 1.82/1.94 inference(transitivity,[status(thm)],[12657, 452])).
% 1.82/1.94 tff(12659,plain,
% 1.82/1.94 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.82/1.94 inference(transitivity,[status(thm)],[12658, 453])).
% 1.82/1.94 tff(12660,plain,
% 1.82/1.94 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12659])).
% 1.82/1.94 tff(12661,plain,
% 1.82/1.94 (~(op(e0, e3) = op(e3, e0))),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[747, 12660])).
% 1.82/1.94 tff(12662,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[496, 12661])).
% 1.82/1.94 tff(12663,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12642])).
% 1.82/1.94 tff(12664,plain,
% 1.82/1.94 (~(op(e3, e1) = op(e1, e3))),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[64, 12663])).
% 1.82/1.94 tff(12665,plain,
% 1.82/1.94 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[6362, 12664])).
% 1.82/1.94 tff(12666,plain,
% 1.82/1.94 (op(op(e1, e3), e3) = e1),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[137, 12047])).
% 1.82/1.94 tff(12667,plain,
% 1.82/1.94 (op(e1, op(e2, e3)) = op(op(e1, e3), e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12048, 12599])).
% 1.82/1.94 tff(12668,plain,
% 1.82/1.94 (op(e1, op(e2, e3)) = e1),
% 1.82/1.94 inference(transitivity,[status(thm)],[12667, 12666])).
% 1.82/1.94 tff(12669,plain,
% 1.82/1.94 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[10724, 12668])).
% 1.82/1.94 tff(12670,plain,
% 1.82/1.94 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[4960])).
% 1.82/1.94 tff(12671,plain,
% 1.82/1.94 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e3) = e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12670])).
% 1.82/1.94 tff(12672,plain,
% 1.82/1.94 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12671])).
% 1.82/1.94 tff(12673,plain,
% 1.82/1.94 (op(e1, op(e1, e1)) = e1),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[12047, 12672])).
% 1.82/1.94 tff(12674,plain,
% 1.82/1.94 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5678, 12673])).
% 1.82/1.94 tff(12675,plain,
% 1.82/1.94 (op(e3, op(e1, e3)) = op(e3, e1)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12047])).
% 1.82/1.94 tff(12676,plain,
% 1.82/1.94 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12048])).
% 1.82/1.94 tff(12677,plain,
% 1.82/1.94 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12676])).
% 1.82/1.94 tff(12678,plain,
% 1.82/1.94 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12642, 12677])).
% 1.82/1.94 tff(12679,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e1) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12678])).
% 1.82/1.94 tff(12680,plain,
% 1.82/1.94 (~(op(e3, e1) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[64, 12679])).
% 1.82/1.94 tff(12681,plain,
% 1.82/1.94 ((op(e3, e2) = e1) <=> (e3 = op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12617, 12048])).
% 1.82/1.94 tff(12682,plain,
% 1.82/1.94 ((op(e3, e2) = e1) <=> (op(e1, e3) = e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12681, 3230])).
% 1.82/1.94 tff(12683,plain,
% 1.82/1.94 ((op(e1, e3) = e3) <=> (op(e3, e2) = e1)),
% 1.82/1.94 inference(symmetry,[status(thm)],[12682])).
% 1.82/1.94 tff(12684,plain,
% 1.82/1.94 ((~(op(e1, e3) = e3)) <=> (~(op(e3, e2) = e1))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12683])).
% 1.82/1.94 tff(12685,plain,
% 1.82/1.94 (~(op(e3, e2) = e1)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[12023, 12684])).
% 1.82/1.94 tff(12686,plain,
% 1.82/1.94 (op(e3, e0) = e1),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[939, 12685, 12016, 12680])).
% 1.82/1.94 tff(12687,plain,
% 1.82/1.94 (op(e3, e0) = op(e1, e3)),
% 1.82/1.94 inference(transitivity,[status(thm)],[12686, 12048])).
% 1.82/1.94 tff(12688,plain,
% 1.82/1.94 (op(e3, op(e3, e0)) = op(e3, op(e1, e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12687])).
% 1.82/1.94 tff(12689,plain,
% 1.82/1.94 (op(e3, op(e3, e0)) = e0),
% 1.82/1.94 inference(transitivity,[status(thm)],[12688, 12675, 12616])).
% 1.82/1.94 tff(12690,plain,
% 1.82/1.94 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[1345, 12689])).
% 1.82/1.94 tff(12691,plain,
% 1.82/1.94 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12599])).
% 1.82/1.94 tff(12692,plain,
% 1.82/1.94 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12691])).
% 1.82/1.94 tff(12693,plain,
% 1.82/1.94 (~(op(e0, e3) = e3)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[964, 12692])).
% 1.82/1.94 tff(12694,plain,
% 1.82/1.94 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12617])).
% 1.82/1.94 tff(12695,plain,
% 1.82/1.94 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12694])).
% 1.82/1.94 tff(12696,plain,
% 1.82/1.94 (~(op(e0, e2) = e3)),
% 1.82/1.94 inference(modus_ponens,[status(thm)],[1467, 12695])).
% 1.82/1.94 tff(12697,plain,
% 1.82/1.94 (op(e0, e0) = e3),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[1495, 12696, 12019, 12693])).
% 1.82/1.94 tff(12698,plain,
% 1.82/1.94 (op(e0, op(e0, e0)) = op(op(e0, e3), e3)),
% 1.82/1.94 inference(monotonicity,[status(thm)],[12639, 12697])).
% 1.82/1.94 tff(12699,plain,
% 1.82/1.94 (op(e0, op(e0, e0)) = e0),
% 1.82/1.94 inference(transitivity,[status(thm)],[12698, 12648])).
% 1.82/1.94 tff(12700,plain,
% 1.82/1.94 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.82/1.94 inference(unit_resolution,[status(thm)],[5598, 12699])).
% 1.82/1.94 tff(12701,plain,
% 1.82/1.94 ((e0 = op(e0, op(e3, e3))) <=> (op(e0, op(e3, e3)) = e0)),
% 1.82/1.94 inference(commutativity,[status(thm)],[])).
% 1.82/1.95 tff(12702,plain,
% 1.82/1.95 (op(e0, op(e3, e3)) = op(e0, e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[2812])).
% 1.82/1.95 tff(12703,plain,
% 1.82/1.95 (op(e0, e2) = op(e0, op(e3, e3))),
% 1.82/1.95 inference(symmetry,[status(thm)],[12702])).
% 1.82/1.95 tff(12704,plain,
% 1.82/1.95 (op(e2, e0) = e0),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[2311, 17, 2559, 1063])).
% 1.82/1.95 tff(12705,plain,
% 1.82/1.95 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, op(e3, e3)))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12704, 12703])).
% 1.82/1.95 tff(12706,plain,
% 1.82/1.95 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, op(e3, e3)) = e0)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12705, 12701])).
% 1.82/1.95 tff(12707,plain,
% 1.82/1.95 ((op(e0, op(e3, e3)) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 1.82/1.95 inference(symmetry,[status(thm)],[12706])).
% 1.82/1.95 tff(12708,plain,
% 1.82/1.95 ((op(e0, op(e3, e3)) = e0) <=> (op(e0, e2) = op(e2, e0))),
% 1.82/1.95 inference(transitivity,[status(thm)],[12707, 6337])).
% 1.82/1.95 tff(12709,plain,
% 1.82/1.95 ((~(op(e0, op(e3, e3)) = e0)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12708])).
% 1.82/1.95 tff(12710,plain,
% 1.82/1.95 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, op(e3, e3)) = e0)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12703, 771])).
% 1.82/1.95 tff(12711,plain,
% 1.82/1.95 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, op(e3, e3)) = e0))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12710])).
% 1.82/1.95 tff(12712,plain,
% 1.82/1.95 (~(op(e0, op(e3, e3)) = e0)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[918, 12711])).
% 1.82/1.95 tff(12713,plain,
% 1.82/1.95 (~(op(e0, e2) = op(e2, e0))),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[12712, 12709])).
% 1.82/1.95 tff(12714,plain,
% 1.82/1.95 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[6347, 12713])).
% 1.82/1.95 tff(12715,plain,
% 1.82/1.95 (op(e0, op(e3, e2)) = op(op(e0, e3), e3)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[772, 856])).
% 1.82/1.95 tff(12716,plain,
% 1.82/1.95 (op(e0, op(e3, e2)) = e0),
% 1.82/1.95 inference(transitivity,[status(thm)],[12715, 8782])).
% 1.82/1.95 tff(12717,plain,
% 1.82/1.95 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[10702, 12716])).
% 1.82/1.95 tff(12718,plain,
% 1.82/1.95 ((~(op(e0, op(e3, e3)) = e0)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12707])).
% 1.82/1.95 tff(12719,plain,
% 1.82/1.95 (~(op(e2, e0) = op(e0, e2))),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[12712, 12718])).
% 1.82/1.95 tff(12720,plain,
% 1.82/1.95 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[6358, 12719])).
% 1.82/1.95 tff(12721,assumption,(~(op(e0, e0) = e2)), introduced(assumption)).
% 1.82/1.95 tff(12722,plain,
% 1.82/1.95 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[981])).
% 1.82/1.95 tff(12723,plain,
% 1.82/1.95 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12722])).
% 1.82/1.95 tff(12724,plain,
% 1.82/1.95 (op(e2, op(e0, e3)) = op(e0, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[980, 12704, 772])).
% 1.82/1.95 tff(12725,plain,
% 1.82/1.95 ((op(e2, op(e0, e3)) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12724, 2834])).
% 1.82/1.95 tff(12726,plain,
% 1.82/1.95 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, op(e0, e3)) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12725])).
% 1.82/1.95 tff(12727,plain,
% 1.82/1.95 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e0) = e2)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12726, 12723])).
% 1.82/1.95 tff(12728,plain,
% 1.82/1.95 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e0) = e2))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12727])).
% 1.82/1.95 tff(12729,plain,
% 1.82/1.95 (~(op(e2, e0) = e2)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[1077, 12728])).
% 1.82/1.95 tff(12730,plain,
% 1.82/1.95 (op(e1, e0) = e2),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[589, 12729, 3786, 12721])).
% 1.82/1.95 tff(12731,plain,
% 1.82/1.95 (op(e1, e0) = op(e3, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12730, 2834])).
% 1.82/1.95 tff(12732,plain,
% 1.82/1.95 (op(e3, op(e1, e0)) = op(e3, op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12731])).
% 1.82/1.95 tff(12733,plain,
% 1.82/1.95 (op(e3, op(e1, e0)) = e3),
% 1.82/1.95 inference(transitivity,[status(thm)],[12732, 2814, 856])).
% 1.82/1.95 tff(12734,plain,
% 1.82/1.95 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[9792, 12733])).
% 1.82/1.95 tff(12735,plain,
% 1.82/1.95 (op(e3, op(e3, e3)) = e3),
% 1.82/1.95 inference(transitivity,[status(thm)],[2814, 856])).
% 1.82/1.95 tff(12736,plain,
% 1.82/1.95 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[6277, 12735])).
% 1.82/1.95 tff(12737,plain,
% 1.82/1.95 (op(e1, e2) = e0),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[973, 17, 919, 85])).
% 1.82/1.95 tff(12738,plain,
% 1.82/1.95 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e0)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12737])).
% 1.82/1.95 tff(12739,plain,
% 1.82/1.95 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 1.82/1.95 inference(symmetry,[status(thm)],[12738])).
% 1.82/1.95 tff(12740,plain,
% 1.82/1.95 ((op(e2, e1) = e0) <=> (op(e1, e2) = op(e2, e1))),
% 1.82/1.95 inference(transitivity,[status(thm)],[12739, 531])).
% 1.82/1.95 tff(12741,plain,
% 1.82/1.95 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12740])).
% 1.82/1.95 tff(12742,plain,
% 1.82/1.95 (~(op(e1, e2) = op(e2, e1))),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[2559, 12741])).
% 1.82/1.95 tff(12743,plain,
% 1.82/1.95 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[539, 12742])).
% 1.82/1.95 tff(12744,plain,
% 1.82/1.95 ((~(op(e2, e1) = e0)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12739])).
% 1.82/1.95 tff(12745,plain,
% 1.82/1.95 (~(op(e2, e1) = op(e1, e2))),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[2559, 12744])).
% 1.82/1.95 tff(12746,plain,
% 1.82/1.95 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[557, 12745])).
% 1.82/1.95 tff(12747,plain,
% 1.82/1.95 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[856])).
% 1.82/1.95 tff(12748,plain,
% 1.82/1.95 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12747, 128])).
% 1.82/1.95 tff(12749,plain,
% 1.82/1.95 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12748])).
% 1.82/1.95 tff(12750,plain,
% 1.82/1.95 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12749])).
% 1.82/1.95 tff(12751,plain,
% 1.82/1.95 (~(op(e3, e2) = e1)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[303, 12750])).
% 1.82/1.95 tff(12752,plain,
% 1.82/1.95 (op(e2, e0) = op(e0, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12704, 772])).
% 1.82/1.95 tff(12753,plain,
% 1.82/1.95 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12752])).
% 1.82/1.95 tff(12754,plain,
% 1.82/1.95 (op(e2, op(e2, e0)) = e0),
% 1.82/1.95 inference(transitivity,[status(thm)],[12753, 980, 12704])).
% 1.82/1.95 tff(12755,plain,
% 1.82/1.95 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[2653, 12754])).
% 1.82/1.95 tff(12756,plain,
% 1.82/1.95 (op(e1, e2) = op(e0, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12737, 772])).
% 1.82/1.95 tff(12757,plain,
% 1.82/1.95 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12756])).
% 1.82/1.95 tff(12758,plain,
% 1.82/1.95 (op(e1, op(e1, e2)) = op(e1, e0)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12757, 2179])).
% 1.82/1.95 tff(12759,plain,
% 1.82/1.95 ((op(e1, op(e1, e2)) = e2) <=> (op(e1, e0) = e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12758])).
% 1.82/1.95 tff(12760,plain,
% 1.82/1.95 ((op(e1, e0) = e2) <=> (op(e1, op(e1, e2)) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12759])).
% 1.82/1.95 tff(12761,plain,
% 1.82/1.95 (op(e1, op(e1, e2)) = e2),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[12730, 12760])).
% 1.82/1.95 tff(12762,plain,
% 1.82/1.95 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[2377, 12761])).
% 1.82/1.95 tff(12763,plain,
% 1.82/1.95 (op(e1, op(e1, e0)) = op(e1, op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12731])).
% 1.82/1.95 tff(12764,plain,
% 1.82/1.95 (op(e1, op(e1, e0)) = e0),
% 1.82/1.95 inference(transitivity,[status(thm)],[12763, 7120, 12737])).
% 1.82/1.95 tff(12765,plain,
% 1.82/1.95 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1836, 12764])).
% 1.82/1.95 tff(12766,plain,
% 1.82/1.95 (op(e1, e2) = op(e1, op(e3, e3))),
% 1.82/1.95 inference(symmetry,[status(thm)],[7120])).
% 1.82/1.95 tff(12767,plain,
% 1.82/1.95 ((op(e1, e2) = e1) <=> (op(e1, op(e3, e3)) = e1)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12766])).
% 1.82/1.95 tff(12768,plain,
% 1.82/1.95 ((op(e1, op(e3, e3)) = e1) <=> (op(e1, e2) = e1)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12767])).
% 1.82/1.95 tff(12769,plain,
% 1.82/1.95 ((op(e1, op(e3, e3)) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[7120, 3710])).
% 1.82/1.95 tff(12770,plain,
% 1.82/1.95 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, op(e3, e3)) = e1)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12769])).
% 1.82/1.95 tff(12771,plain,
% 1.82/1.95 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12770, 12768])).
% 1.82/1.95 tff(12772,plain,
% 1.82/1.95 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12771])).
% 1.82/1.95 tff(12773,plain,
% 1.82/1.95 (~(op(e1, e2) = e1)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[1850, 12772])).
% 1.82/1.95 tff(12774,plain,
% 1.82/1.95 (op(e0, e2) = e1),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1613, 1348, 12773, 930])).
% 1.82/1.95 tff(12775,plain,
% 1.82/1.95 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12562])).
% 1.82/1.95 tff(12776,plain,
% 1.82/1.95 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12775])).
% 1.82/1.95 tff(12777,plain,
% 1.82/1.95 (~(op(e0, e2) = e2)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[2736, 12776])).
% 1.82/1.95 tff(12778,plain,
% 1.82/1.95 (op(e0, e1) = e2),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[3652, 12777, 79, 12721])).
% 1.82/1.95 tff(12779,plain,
% 1.82/1.95 (op(e0, e1) = op(e3, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12778, 2834])).
% 1.82/1.95 tff(12780,plain,
% 1.82/1.95 (op(e0, op(e0, e1)) = op(e0, op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12779])).
% 1.82/1.95 tff(12781,plain,
% 1.82/1.95 (op(e0, op(e0, e1)) = e1),
% 1.82/1.95 inference(transitivity,[status(thm)],[12780, 12702, 12774])).
% 1.82/1.95 tff(12782,plain,
% 1.82/1.95 (op(op(e0, e2), e2) = op(e1, op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12774, 2834])).
% 1.82/1.95 tff(12783,plain,
% 1.82/1.95 (op(op(e0, e2), e2) = e0),
% 1.82/1.95 inference(transitivity,[status(thm)],[12782, 7120, 6900])).
% 1.82/1.95 tff(12784,plain,
% 1.82/1.95 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1956, 12783])).
% 1.82/1.95 tff(12785,plain,
% 1.82/1.95 (op(e2, e1) = e1),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[345, 1348, 76, 1349])).
% 1.82/1.95 tff(12786,plain,
% 1.82/1.95 (op(e2, e1) = op(e1, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12785, 3710])).
% 1.82/1.95 tff(12787,plain,
% 1.82/1.95 (op(e2, op(e2, e1)) = op(e2, op(e1, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12786])).
% 1.82/1.95 tff(12788,plain,
% 1.82/1.95 (op(e2, op(e2, e1)) = e1),
% 1.82/1.95 inference(transitivity,[status(thm)],[12787, 3796, 12785])).
% 1.82/1.95 tff(12789,plain,
% 1.82/1.95 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1355, 12788])).
% 1.82/1.95 tff(12790,plain,
% 1.82/1.95 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1459, 12789, 12784, 1275, 3342, 1304, 1357, 3341, 1358, 1926, 2421, 1347])).
% 1.82/1.95 tff(12791,plain,
% 1.82/1.95 (~(op(e0, op(e0, e1)) = e1)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[2449, 12790])).
% 1.82/1.95 tff(12792,plain,
% 1.82/1.95 ($false),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[12791, 12781])).
% 1.82/1.95 tff(12793,plain,((op(e2, e2) = e1) | (~(op(e3, e3) = e2)) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e0, e3) = e2) | (op(e0, e0) = e2) | (~(op(e1, e3) = e1)) | (~(op(e1, e2) = e0)) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e3, e2) = e1) | (op(e2, e2) = e0) | (op(e2, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.95 tff(12794,plain,
% 1.82/1.95 (op(e2, e2) = e1),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[12793, 12765, 1275, 3342, 1304, 2812, 9773, 12762, 1926, 12755, 1347, 79, 12721, 132, 12737, 76, 1349, 12751, 17, 2431])).
% 1.82/1.95 tff(12795,plain,
% 1.82/1.95 (op(e2, e2) = op(e1, e3)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12794, 3710])).
% 1.82/1.95 tff(12796,plain,
% 1.82/1.95 (op(e2, op(e2, e2)) = op(e2, op(e1, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12795])).
% 1.82/1.95 tff(12797,plain,
% 1.82/1.95 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12796])).
% 1.82/1.95 tff(12798,plain,
% 1.82/1.95 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12797])).
% 1.82/1.95 tff(12799,plain,
% 1.82/1.95 ((op(e2, e1) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 1.82/1.95 inference(transitivity,[status(thm)],[3885, 12798])).
% 1.82/1.95 tff(12800,plain,
% 1.82/1.95 ((op(e2, e2) = e2) <=> (op(e1, e3) = op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12795, 2834])).
% 1.82/1.95 tff(12801,plain,
% 1.82/1.95 ((op(e1, e3) = op(e3, e3)) <=> (op(e2, e2) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12800])).
% 1.82/1.95 tff(12802,plain,
% 1.82/1.95 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e2, e2) = e2))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12801])).
% 1.82/1.95 tff(12803,plain,
% 1.82/1.95 (~(op(e2, e2) = e2)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[571, 12802])).
% 1.82/1.95 tff(12804,plain,
% 1.82/1.95 (op(e2, e1) = e2),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[2088, 12803, 4382, 12729])).
% 1.82/1.95 tff(12805,plain,
% 1.82/1.95 (op(e2, op(e2, e2)) = e2),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[12804, 12799])).
% 1.82/1.95 tff(12806,plain,
% 1.82/1.95 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[528, 12805])).
% 1.82/1.95 tff(12807,plain,
% 1.82/1.95 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12730])).
% 1.82/1.95 tff(12808,plain,
% 1.82/1.95 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.82/1.95 inference(transitivity,[status(thm)],[12807, 4838])).
% 1.82/1.95 tff(12809,plain,
% 1.82/1.95 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.82/1.95 inference(symmetry,[status(thm)],[12808])).
% 1.82/1.95 tff(12810,plain,
% 1.82/1.95 ((op(e1, e2) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12756, 2834])).
% 1.82/1.95 tff(12811,plain,
% 1.82/1.95 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e2) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12810])).
% 1.82/1.95 tff(12812,plain,
% 1.82/1.95 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e2) = e2))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12811])).
% 1.82/1.95 tff(12813,plain,
% 1.82/1.95 (~(op(e1, e2) = e2)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[1077, 12812])).
% 1.82/1.95 tff(12814,plain,
% 1.82/1.95 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e3))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[2834])).
% 1.82/1.95 tff(12815,plain,
% 1.82/1.95 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e2)),
% 1.82/1.95 inference(symmetry,[status(thm)],[12814])).
% 1.82/1.95 tff(12816,plain,
% 1.82/1.95 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e2))),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12815])).
% 1.82/1.95 tff(12817,plain,
% 1.82/1.95 (~(op(e3, e2) = e2)),
% 1.82/1.95 inference(modus_ponens,[status(thm)],[1888, 12816])).
% 1.82/1.95 tff(12818,plain,
% 1.82/1.95 (op(e0, e2) = e2),
% 1.82/1.95 inference(unit_resolution,[status(thm)],[1151, 12803, 12817, 12813])).
% 1.82/1.95 tff(12819,plain,
% 1.82/1.95 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 1.82/1.95 inference(monotonicity,[status(thm)],[12818])).
% 1.82/1.95 tff(12820,plain,
% 1.82/1.95 ((op(e0, e1) = op(e0, e2)) <=> (op(e1, e0) = op(e0, e1))),
% 1.82/1.95 inference(transitivity,[status(thm)],[12819, 12809])).
% 1.82/1.95 tff(12821,plain,
% 1.82/1.95 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12820])).
% 1.82/1.96 tff(12822,plain,
% 1.82/1.96 (~(op(e1, e0) = op(e0, e1))),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[2102, 12821])).
% 1.82/1.96 tff(12823,plain,
% 1.82/1.96 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[613, 12822])).
% 1.82/1.96 tff(12824,plain,
% 1.82/1.96 ($false),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[5367, 12823, 12806, 12746, 12743, 12736, 6689, 5670, 12734, 5669, 5667, 5671, 5511, 12720, 12717, 12714])).
% 1.82/1.96 tff(12825,plain,((op(e2, e2) = e0) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~(op(e1, e3) = e1)) | (op(e2, e3) = e2) | (~(op(e3, e3) = e2)) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e0, e3) = e2) | (op(e0, e0) = e2) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e2, e2) = e3) | (~(op(e3, e2) = e3)) | (~(op(e0, e3) = e0)) | (op(e3, e0) = e2) | (op(e2, e1) = e0) | (op(e3, e2) = e0) | (op(e2, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.96 tff(12826,plain,
% 1.82/1.96 ($false),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[12825, 12700, 12690, 17, 12047, 12674, 12669, 12665, 12662, 9692, 2812, 12655, 12647, 1304, 12646, 12638, 10592, 12635, 76, 1349, 12620, 12617, 12608, 9955, 12605, 85, 12604])).
% 1.82/1.96 tff(12827,plain,((op(e3, e2) = e0) | (op(e2, e2) = e0) | (~(op(e3, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e3) = e1) | (op(e2, e0) = e1) | (op(e1, e1) = e0) | (~(op(e1, e1) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.96 tff(12828,plain,
% 1.82/1.96 (op(e3, e2) = e0),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[12827, 1349, 2812, 1304, 76, 11102, 84, 12004])).
% 1.82/1.96 tff(12829,plain,
% 1.82/1.96 (e0 = op(e3, e2)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12828])).
% 1.82/1.96 tff(12830,plain,
% 1.82/1.96 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12829])).
% 1.82/1.96 tff(12831,plain,
% 1.82/1.96 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12830])).
% 1.82/1.96 tff(12832,plain,
% 1.82/1.96 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12831])).
% 1.82/1.96 tff(12833,plain,
% 1.82/1.96 (~(op(e1, e2) = e0)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[2292, 12832])).
% 1.82/1.96 tff(12834,plain,
% 1.82/1.96 ((op(e1, e1) = e1) <=> (e3 = e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.96 tff(12835,plain,
% 1.82/1.96 ((op(e1, e1) = e1) <=> (e1 = e3)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12834, 128])).
% 1.82/1.96 tff(12836,plain,
% 1.82/1.96 ((e1 = e3) <=> (op(e1, e1) = e1)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12835])).
% 1.82/1.96 tff(12837,plain,
% 1.82/1.96 ((~(e1 = e3)) <=> (~(op(e1, e1) = e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12836])).
% 1.82/1.96 tff(12838,plain,
% 1.82/1.96 (~(op(e1, e1) = e1)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[303, 12837])).
% 1.82/1.96 tff(12839,plain,
% 1.82/1.96 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.96 tff(12840,plain,
% 1.82/1.96 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12839, 396])).
% 1.82/1.96 tff(12841,plain,
% 1.82/1.96 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12840])).
% 1.82/1.96 tff(12842,plain,
% 1.82/1.96 (~(op(e3, e1) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[945, 12841])).
% 1.82/1.96 tff(12843,plain,
% 1.82/1.96 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12829])).
% 1.82/1.96 tff(12844,plain,
% 1.82/1.96 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12843])).
% 1.82/1.96 tff(12845,plain,
% 1.82/1.96 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12844])).
% 1.82/1.96 tff(12846,plain,
% 1.82/1.96 (~(op(e3, e1) = e0)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[3429, 12845])).
% 1.82/1.96 tff(12847,plain,
% 1.82/1.96 (op(e3, e1) = e1),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[446, 12846, 12842, 9684])).
% 1.82/1.96 tff(12848,plain,
% 1.82/1.96 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12847])).
% 1.82/1.96 tff(12849,plain,
% 1.82/1.96 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12848])).
% 1.82/1.96 tff(12850,plain,
% 1.82/1.96 (~(op(e2, e1) = e1)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[402, 12849])).
% 1.82/1.96 tff(12851,plain,
% 1.82/1.96 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.96 tff(12852,plain,
% 1.82/1.96 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12851, 1262])).
% 1.82/1.96 tff(12853,plain,
% 1.82/1.96 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12852])).
% 1.82/1.96 tff(12854,plain,
% 1.82/1.96 (~(op(e2, e1) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[225, 12853])).
% 1.82/1.96 tff(12855,plain,
% 1.82/1.96 (op(e2, e2) = e1),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[345, 12850, 76, 1349])).
% 1.82/1.96 tff(12856,plain,
% 1.82/1.96 ((op(e3, e2) = e3) <=> (e0 = e3)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12828])).
% 1.82/1.96 tff(12857,plain,
% 1.82/1.96 ((e0 = e3) <=> (op(e3, e2) = e3)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12856])).
% 1.82/1.96 tff(12858,plain,
% 1.82/1.96 ((~(e0 = e3)) <=> (~(op(e3, e2) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12857])).
% 1.82/1.96 tff(12859,plain,
% 1.82/1.96 (~(op(e3, e2) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[181, 12858])).
% 1.82/1.96 tff(12860,plain,
% 1.82/1.96 (op(e3, e0) = e3),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[422, 12859, 11641, 12842])).
% 1.82/1.96 tff(12861,plain,
% 1.82/1.96 (op(e3, e0) = op(e3, op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12829])).
% 1.82/1.96 tff(12862,plain,
% 1.82/1.96 (e3 = op(e3, e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12860])).
% 1.82/1.96 tff(12863,plain,
% 1.82/1.96 (e3 = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12862, 12861, 10079])).
% 1.82/1.96 tff(12864,plain,
% 1.82/1.96 ((op(e2, e2) = e3) <=> (e1 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12855, 12863])).
% 1.82/1.96 tff(12865,plain,
% 1.82/1.96 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e2) = e3)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12864])).
% 1.82/1.96 tff(12866,plain,
% 1.82/1.96 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e2, e2) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12865])).
% 1.82/1.96 tff(12867,plain,
% 1.82/1.96 (e0 = op(e3, op(e3, e3))),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[12828, 6497])).
% 1.82/1.96 tff(12868,plain,
% 1.82/1.96 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[5879, 12867, 2813])).
% 1.82/1.96 tff(12869,plain,
% 1.82/1.96 (~(op(e2, e2) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[12868, 12866])).
% 1.82/1.96 tff(12870,plain,
% 1.82/1.96 (op(e0, e2) = e3),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2111, 12869, 12859, 75])).
% 1.82/1.96 tff(12871,plain,
% 1.82/1.96 ((op(e1, e1) = e2) <=> (e3 = e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.96 tff(12872,plain,
% 1.82/1.96 ((op(e1, e1) = e2) <=> (e2 = e3)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12871, 1314])).
% 1.82/1.96 tff(12873,plain,
% 1.82/1.96 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12872])).
% 1.82/1.96 tff(12874,plain,
% 1.82/1.96 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12873])).
% 1.82/1.96 tff(12875,plain,
% 1.82/1.96 (~(op(e1, e1) = e2)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[1321, 12874])).
% 1.82/1.96 tff(12876,plain,
% 1.82/1.96 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12855])).
% 1.82/1.96 tff(12877,plain,
% 1.82/1.96 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12876])).
% 1.82/1.96 tff(12878,plain,
% 1.82/1.96 (~(op(e1, e2) = e1)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[1273, 12877])).
% 1.82/1.96 tff(12879,plain,
% 1.82/1.96 (op(e1, e2) = e2),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1859, 12878, 75, 12833])).
% 1.82/1.96 tff(12880,plain,
% 1.82/1.96 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12879])).
% 1.82/1.96 tff(12881,plain,
% 1.82/1.96 (op(e1, op(e1, e2)) = e2),
% 1.82/1.96 inference(transitivity,[status(thm)],[12880, 12879])).
% 1.82/1.96 tff(12882,plain,
% 1.82/1.96 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2377, 12881])).
% 1.82/1.96 tff(12883,plain,
% 1.82/1.96 (op(e3, op(e3, e1)) = op(e3, e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12847])).
% 1.82/1.96 tff(12884,plain,
% 1.82/1.96 (op(e3, op(e3, e1)) = e1),
% 1.82/1.96 inference(transitivity,[status(thm)],[12883, 12847])).
% 1.82/1.96 tff(12885,plain,
% 1.82/1.96 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2594, 12884])).
% 1.82/1.96 tff(12886,assumption,(op(e3, e0) = e3), introduced(assumption)).
% 1.82/1.96 tff(12887,plain,
% 1.82/1.96 (e3 = op(e3, e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12886])).
% 1.82/1.96 tff(12888,plain,
% 1.82/1.96 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12887])).
% 1.82/1.96 tff(12889,plain,
% 1.82/1.96 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12888])).
% 1.82/1.96 tff(12890,plain,
% 1.82/1.96 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12889])).
% 1.82/1.96 tff(12891,plain,
% 1.82/1.96 (~(op(e2, e0) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[747, 12890])).
% 1.82/1.96 tff(12892,plain,
% 1.82/1.96 (op(e3, e0) = op(e3, op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[6784])).
% 1.82/1.96 tff(12893,plain,
% 1.82/1.96 (e3 = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12887, 12892, 10079])).
% 1.82/1.96 tff(12894,plain,
% 1.82/1.96 ((op(e2, e2) = e3) <=> (e1 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[307, 12893])).
% 1.82/1.96 tff(12895,plain,
% 1.82/1.96 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e2) = e3)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12894])).
% 1.82/1.96 tff(12896,plain,
% 1.82/1.96 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e2, e2) = e3))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12895])).
% 1.82/1.96 tff(12897,plain,
% 1.82/1.96 (~(op(e2, e2) = e3)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[11123, 12896])).
% 1.82/1.96 tff(12898,plain,
% 1.82/1.96 (op(e2, e3) = e3),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1559, 12897, 3271, 12891])).
% 1.82/1.96 tff(12899,plain,
% 1.82/1.96 (op(e2, op(e3, e0)) = op(e2, e3)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12886])).
% 1.82/1.96 tff(12900,plain,
% 1.82/1.96 (op(e2, e3) = op(e3, e0)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12898, 12887])).
% 1.82/1.96 tff(12901,plain,
% 1.82/1.96 (op(e2, op(e2, e3)) = op(e2, op(e3, e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12900])).
% 1.82/1.96 tff(12902,plain,
% 1.82/1.96 (op(e2, op(e2, e3)) = e3),
% 1.82/1.96 inference(transitivity,[status(thm)],[12901, 12899, 12898])).
% 1.82/1.96 tff(12903,plain,
% 1.82/1.96 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2344, 12902])).
% 1.82/1.96 tff(12904,plain,
% 1.82/1.96 (op(op(e3, e2), e2) = op(e0, e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[5819])).
% 1.82/1.96 tff(12905,plain,
% 1.82/1.96 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[6784])).
% 1.82/1.96 tff(12906,plain,
% 1.82/1.96 ((op(e2, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12905, 394])).
% 1.82/1.96 tff(12907,plain,
% 1.82/1.96 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12906])).
% 1.82/1.96 tff(12908,plain,
% 1.82/1.96 (op(e2, e3) = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12898, 12887, 12892, 10079])).
% 1.82/1.96 tff(12909,plain,
% 1.82/1.96 ((op(e3, e2) = op(e2, e3)) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[5819, 12908])).
% 1.82/1.96 tff(12910,plain,
% 1.82/1.96 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e2, e3))),
% 1.82/1.96 inference(symmetry,[status(thm)],[12909])).
% 1.82/1.96 tff(12911,plain,
% 1.82/1.96 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e3) = e0)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12910, 12907])).
% 1.82/1.96 tff(12912,plain,
% 1.82/1.96 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e2, e3) = e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12911])).
% 1.82/1.96 tff(12913,plain,
% 1.82/1.96 (op(e3, e0) = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12892, 10079])).
% 1.82/1.96 tff(12914,plain,
% 1.82/1.96 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, op(e3, op(e3, e3))) = e0)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12913, 5819])).
% 1.82/1.96 tff(12915,plain,
% 1.82/1.96 ((op(e3, e0) = op(e3, e2)) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(transitivity,[status(thm)],[12914, 11878])).
% 1.82/1.96 tff(12916,plain,
% 1.82/1.96 ((~(op(e3, e0) = op(e3, e2))) <=> (~(e0 = op(e3, op(e3, op(e3, e3)))))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12915])).
% 1.82/1.96 tff(12917,plain,
% 1.82/1.96 (~(e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[1133, 12916])).
% 1.82/1.96 tff(12918,plain,
% 1.82/1.96 (~(op(e2, e3) = e0)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[12917, 12912])).
% 1.82/1.96 tff(12919,plain,
% 1.82/1.96 ((op(op(e3, e2), e3) = e2) <=> (op(e0, e3) = e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[6603])).
% 1.82/1.96 tff(12920,plain,
% 1.82/1.96 ((op(e0, e3) = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12919])).
% 1.82/1.96 tff(12921,plain,
% 1.82/1.96 ((~(op(e0, e3) = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12920])).
% 1.82/1.96 tff(12922,plain,
% 1.82/1.96 (~(op(op(e3, e2), e3) = e2)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[10592, 12921])).
% 1.82/1.96 tff(12923,plain,
% 1.82/1.96 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2408, 12922])).
% 1.82/1.96 tff(12924,plain,
% 1.82/1.96 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[307])).
% 1.82/1.96 tff(12925,plain,
% 1.82/1.96 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12924])).
% 1.82/1.96 tff(12926,plain,
% 1.82/1.96 (~(op(e1, e2) = e1)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[1273, 12925])).
% 1.82/1.96 tff(12927,plain,
% 1.82/1.96 (op(e1, e0) = e1),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[954, 87, 1266, 12926])).
% 1.82/1.96 tff(12928,plain,
% 1.82/1.96 (op(e1, op(e3, e2)) = op(e1, e0)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[5819])).
% 1.82/1.96 tff(12929,plain,
% 1.82/1.96 (op(op(e1, e0), e0) = op(e1, op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12927, 6784])).
% 1.82/1.96 tff(12930,plain,
% 1.82/1.96 (op(op(e1, e0), e0) = e1),
% 1.82/1.96 inference(transitivity,[status(thm)],[12929, 12928, 12927])).
% 1.82/1.96 tff(12931,plain,
% 1.82/1.96 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[3015, 12930])).
% 1.82/1.96 tff(12932,plain,
% 1.82/1.96 (op(op(e0, e2), e2) = op(e3, e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[7826])).
% 1.82/1.96 tff(12933,plain,
% 1.82/1.96 (op(op(e0, e2), e2) = e0),
% 1.82/1.96 inference(transitivity,[status(thm)],[12932, 5819])).
% 1.82/1.96 tff(12934,plain,
% 1.82/1.96 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1956, 12933])).
% 1.82/1.96 tff(12935,plain,
% 1.82/1.96 (op(e3, op(e3, e2)) = op(e3, e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12892])).
% 1.82/1.96 tff(12936,plain,
% 1.82/1.96 (op(op(e3, e0), e0) = op(e3, op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12886, 6784])).
% 1.82/1.96 tff(12937,plain,
% 1.82/1.96 (op(op(e3, e0), e0) = e3),
% 1.82/1.96 inference(transitivity,[status(thm)],[12936, 12935, 12886])).
% 1.82/1.96 tff(12938,plain,
% 1.82/1.96 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[4026, 12937])).
% 1.82/1.96 tff(12939,plain,
% 1.82/1.96 (op(e1, e3) = e0),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[104, 87, 10589, 1080])).
% 1.82/1.96 tff(12940,plain,
% 1.82/1.96 (op(e1, op(e3, e0)) = op(e1, e3)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12886])).
% 1.82/1.96 tff(12941,plain,
% 1.82/1.96 (op(op(e0, e3), e3) = op(e1, op(e3, e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[11107, 12887])).
% 1.82/1.96 tff(12942,plain,
% 1.82/1.96 (op(op(e0, e3), e3) = e0),
% 1.82/1.96 inference(transitivity,[status(thm)],[12941, 12940, 12939])).
% 1.82/1.96 tff(12943,plain,
% 1.82/1.96 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1361, 12942])).
% 1.82/1.96 tff(12944,plain,
% 1.82/1.96 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[6784])).
% 1.82/1.96 tff(12945,plain,
% 1.82/1.96 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 1.82/1.96 inference(symmetry,[status(thm)],[12944])).
% 1.82/1.96 tff(12946,plain,
% 1.82/1.96 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12945])).
% 1.82/1.96 tff(12947,plain,
% 1.82/1.96 (~(op(e3, e1) = e0)),
% 1.82/1.96 inference(modus_ponens,[status(thm)],[3429, 12946])).
% 1.82/1.96 tff(12948,plain,
% 1.82/1.96 (op(e0, e1) = e0),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[292, 2559, 84, 12947])).
% 1.82/1.96 tff(12949,plain,
% 1.82/1.96 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12948])).
% 1.82/1.96 tff(12950,plain,
% 1.82/1.96 (op(op(e0, e1), e1) = e0),
% 1.82/1.96 inference(transitivity,[status(thm)],[12949, 12948])).
% 1.82/1.96 tff(12951,plain,
% 1.82/1.96 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2650, 12950])).
% 1.82/1.96 tff(12952,plain,
% 1.82/1.96 (op(e2, e1) = e2),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2367, 2559, 3271, 4530])).
% 1.82/1.96 tff(12953,plain,
% 1.82/1.96 (op(e2, op(e2, e1)) = op(e2, e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12952])).
% 1.82/1.96 tff(12954,plain,
% 1.82/1.96 (op(e2, op(e2, e1)) = e1),
% 1.82/1.96 inference(transitivity,[status(thm)],[12953, 307])).
% 1.82/1.96 tff(12955,plain,
% 1.82/1.96 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1355, 12954])).
% 1.82/1.96 tff(12956,plain,
% 1.82/1.96 (op(e2, e0) = e0),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2311, 2559, 17, 1063])).
% 1.82/1.96 tff(12957,plain,
% 1.82/1.96 (op(e2, op(e3, e2)) = op(e2, e0)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[5819])).
% 1.82/1.96 tff(12958,plain,
% 1.82/1.96 (op(e2, e0) = op(e3, e2)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12956, 6784])).
% 1.82/1.96 tff(12959,plain,
% 1.82/1.96 (op(e2, op(e2, e0)) = op(e2, op(e3, e2))),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12958])).
% 1.82/1.96 tff(12960,plain,
% 1.82/1.96 (op(e2, op(e2, e0)) = e0),
% 1.82/1.96 inference(transitivity,[status(thm)],[12959, 12957, 12956])).
% 1.82/1.96 tff(12961,plain,
% 1.82/1.96 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[2653, 12960])).
% 1.82/1.96 tff(12962,plain,
% 1.82/1.96 ($false),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[1459, 12961, 12955, 1363, 1926, 3342, 1304, 1275, 1358, 1357, 3341, 12951, 1347])).
% 1.82/1.96 tff(12963,plain,((op(e2, e1) = e0) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e3, e2) = e0)) | (~(op(e2, e2) = e1)) | (op(e2, e2) = e0) | (op(e2, e3) = e0) | (op(e2, e1) = e3) | (op(e2, e1) = e1) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.96 tff(12964,plain,
% 1.82/1.96 (op(e2, e1) = e0),
% 1.82/1.96 inference(unit_resolution,[status(thm)],[12963, 12943, 12938, 12934, 1304, 1275, 1358, 12931, 12923, 12903, 5819, 307, 17, 12918, 3271, 4530, 84])).
% 1.82/1.96 tff(12965,plain,
% 1.82/1.96 (op(e2, e1) = op(e3, e2)),
% 1.82/1.96 inference(transitivity,[status(thm)],[12964, 6784])).
% 1.82/1.96 tff(12966,plain,
% 1.82/1.96 (op(op(e2, e1), e2) = op(op(e3, e2), e2)),
% 1.82/1.96 inference(monotonicity,[status(thm)],[12965])).
% 1.82/1.97 tff(12967,plain,
% 1.82/1.97 (op(op(e2, e1), e2) = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[12966, 12904, 7826, 12887, 12892, 10079])).
% 1.82/1.97 tff(12968,plain,
% 1.82/1.97 ((op(op(e2, e1), e2) = e1) <=> (op(e3, op(e3, op(e3, e3))) = e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12967])).
% 1.82/1.97 tff(12969,plain,
% 1.82/1.97 ((op(op(e2, e1), e2) = e1) <=> (e1 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.97 inference(transitivity,[status(thm)],[12968, 3065])).
% 1.82/1.97 tff(12970,plain,
% 1.82/1.97 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(op(e2, e1), e2) = e1)),
% 1.82/1.97 inference(symmetry,[status(thm)],[12969])).
% 1.82/1.97 tff(12971,plain,
% 1.82/1.97 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(op(e2, e1), e2) = e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12970])).
% 1.82/1.97 tff(12972,plain,
% 1.82/1.97 (~(op(op(e2, e1), e2) = e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[11123, 12971])).
% 1.82/1.97 tff(12973,plain,
% 1.82/1.97 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[5808, 12972])).
% 1.82/1.97 tff(12974,plain,
% 1.82/1.97 ((op(e2, e1) = e2) <=> (op(e3, e2) = e2)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12965])).
% 1.82/1.97 tff(12975,plain,
% 1.82/1.97 ((op(e3, e2) = e2) <=> (op(e2, e1) = e2)),
% 1.82/1.97 inference(symmetry,[status(thm)],[12974])).
% 1.82/1.97 tff(12976,plain,
% 1.82/1.97 ((~(op(e3, e2) = e2)) <=> (~(op(e2, e1) = e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12975])).
% 1.82/1.97 tff(12977,plain,
% 1.82/1.97 (~(op(e2, e1) = e2)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[9699, 12976])).
% 1.82/1.97 tff(12978,plain,
% 1.82/1.97 (op(e0, e1) = e2),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1993, 12977, 9684, 68])).
% 1.82/1.97 tff(12979,plain,
% 1.82/1.97 (op(op(e0, e1), e1) = op(e2, e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12978])).
% 1.82/1.97 tff(12980,plain,
% 1.82/1.97 (op(op(e0, e1), e1) = e0),
% 1.82/1.97 inference(transitivity,[status(thm)],[12979, 12964])).
% 1.82/1.97 tff(12981,plain,
% 1.82/1.97 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[2650, 12980])).
% 1.82/1.97 tff(12982,plain,
% 1.82/1.97 ((op(e2, e2) = e2) <=> (e1 = e2)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[307])).
% 1.82/1.97 tff(12983,plain,
% 1.82/1.97 ((e1 = e2) <=> (op(e2, e2) = e2)),
% 1.82/1.97 inference(symmetry,[status(thm)],[12982])).
% 1.82/1.97 tff(12984,plain,
% 1.82/1.97 ((~(e1 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12983])).
% 1.82/1.97 tff(12985,plain,
% 1.82/1.97 (~(op(e2, e2) = e2)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[708, 12984])).
% 1.82/1.97 tff(12986,plain,
% 1.82/1.97 (op(e2, e0) = e2),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[2088, 12977, 9692, 12985])).
% 1.82/1.97 tff(12987,plain,
% 1.82/1.97 (op(op(e2, e0), e0) = op(e2, op(e3, e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12986, 6784])).
% 1.82/1.97 tff(12988,plain,
% 1.82/1.97 (op(op(e2, e0), e0) = e2),
% 1.82/1.97 inference(transitivity,[status(thm)],[12987, 12957, 12986])).
% 1.82/1.97 tff(12989,plain,
% 1.82/1.97 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1945, 12988])).
% 1.82/1.97 tff(12990,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1459, 12989, 12981, 12934, 12938, 12943, 1304, 1275, 1358, 12931, 12923, 12973, 12903])).
% 1.82/1.97 tff(12991,plain,((op(e1, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~(op(e3, e2) = e0)) | (op(e1, e1) = e2) | (~(op(e0, e2) = e3)) | (~(op(e3, e0) = e3)) | (~(op(e3, e3) = e2)) | (~(op(e2, e2) = e1)) | (op(e2, e2) = e0) | (op(e2, e1) = e3) | (op(e2, e1) = e1) | (op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e3) = e3) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(12992,plain,
% 1.82/1.97 (op(e1, e3) = e1),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[12991, 12885, 1304, 12882, 12828, 12875, 12870, 12860, 2812, 12855, 11102, 12854, 12850, 84, 12838, 12008, 76])).
% 1.82/1.97 tff(12993,plain,
% 1.82/1.97 ((op(e1, e3) = e0) <=> (e1 = op(e3, e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12992, 12829])).
% 1.82/1.97 tff(12994,plain,
% 1.82/1.97 ((op(e1, e3) = e0) <=> (op(e3, e2) = e1)),
% 1.82/1.97 inference(transitivity,[status(thm)],[12993, 7171])).
% 1.82/1.97 tff(12995,plain,
% 1.82/1.97 ((op(e3, e2) = e1) <=> (op(e1, e3) = e0)),
% 1.82/1.97 inference(symmetry,[status(thm)],[12994])).
% 1.82/1.97 tff(12996,plain,
% 1.82/1.97 ((~(op(e3, e2) = e1)) <=> (~(op(e1, e3) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12995])).
% 1.82/1.97 tff(12997,plain,
% 1.82/1.97 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12829])).
% 1.82/1.97 tff(12998,plain,
% 1.82/1.97 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12997])).
% 1.82/1.97 tff(12999,plain,
% 1.82/1.97 (~(op(e3, e2) = e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[26, 12998])).
% 1.82/1.97 tff(13000,plain,
% 1.82/1.97 (~(op(e1, e3) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[12999, 12996])).
% 1.82/1.97 tff(13001,plain,
% 1.82/1.97 (op(e1, e0) = e0),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1830, 13000, 84, 12833])).
% 1.82/1.97 tff(13002,plain,
% 1.82/1.97 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13001])).
% 1.82/1.97 tff(13003,plain,
% 1.82/1.97 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13002, 4499])).
% 1.82/1.97 tff(13004,plain,
% 1.82/1.97 ((op(e2, e0) = e0) <=> (op(e1, e0) = op(e2, e0))),
% 1.82/1.97 inference(symmetry,[status(thm)],[13003])).
% 1.82/1.97 tff(13005,plain,
% 1.82/1.97 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12829])).
% 1.82/1.97 tff(13006,plain,
% 1.82/1.97 ((op(e2, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 1.82/1.97 inference(transitivity,[status(thm)],[13005, 394])).
% 1.82/1.97 tff(13007,plain,
% 1.82/1.97 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13006])).
% 1.82/1.97 tff(13008,plain,
% 1.82/1.97 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e3, e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12862])).
% 1.82/1.97 tff(13009,plain,
% 1.82/1.97 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13008])).
% 1.82/1.97 tff(13010,plain,
% 1.82/1.97 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13009])).
% 1.82/1.97 tff(13011,plain,
% 1.82/1.97 (~(op(e2, e0) = e3)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[747, 13010])).
% 1.82/1.97 tff(13012,plain,
% 1.82/1.97 (op(e2, e3) = e3),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[1559, 12869, 12854, 13011])).
% 1.82/1.97 tff(13013,plain,
% 1.82/1.97 (op(e2, e3) = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[13012, 12862, 12861, 10079])).
% 1.82/1.97 tff(13014,plain,
% 1.82/1.97 ((op(e3, e2) = op(e2, e3)) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12828, 13013])).
% 1.82/1.97 tff(13015,plain,
% 1.82/1.97 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e2, e3))),
% 1.82/1.97 inference(symmetry,[status(thm)],[13014])).
% 1.82/1.97 tff(13016,plain,
% 1.82/1.97 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e3) = e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13015, 13007])).
% 1.82/1.97 tff(13017,plain,
% 1.82/1.97 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e2, e3) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13016])).
% 1.82/1.97 tff(13018,plain,
% 1.82/1.97 (op(e3, e0) = op(e3, op(e3, op(e3, e3)))),
% 1.82/1.97 inference(transitivity,[status(thm)],[12861, 10079])).
% 1.82/1.97 tff(13019,plain,
% 1.82/1.97 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, op(e3, op(e3, e3))) = e0)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13018, 12828])).
% 1.82/1.97 tff(13020,plain,
% 1.82/1.97 ((op(e3, e0) = op(e3, e2)) <=> (e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.97 inference(transitivity,[status(thm)],[13019, 11878])).
% 1.82/1.97 tff(13021,plain,
% 1.82/1.97 ((~(op(e3, e0) = op(e3, e2))) <=> (~(e0 = op(e3, op(e3, op(e3, e3)))))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13020])).
% 1.82/1.97 tff(13022,plain,
% 1.82/1.97 (~(e0 = op(e3, op(e3, op(e3, e3))))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[1133, 13021])).
% 1.82/1.97 tff(13023,plain,
% 1.82/1.97 (~(op(e2, e3) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[13022, 13017])).
% 1.82/1.97 tff(13024,plain,
% 1.82/1.97 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12992])).
% 1.82/1.97 tff(13025,plain,
% 1.82/1.97 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13024])).
% 1.82/1.97 tff(13026,plain,
% 1.82/1.97 (~(op(e0, e3) = e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[64, 13025])).
% 1.82/1.97 tff(13027,plain,
% 1.82/1.97 (~(op(e2, e1) = e0)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[6988, 13000, 11818, 12011, 13026, 10592])).
% 1.82/1.97 tff(13028,plain,
% 1.82/1.97 (op(e2, e0) = e0),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[2311, 13027, 11102, 13023])).
% 1.82/1.97 tff(13029,plain,
% 1.82/1.97 (op(e1, e0) = op(e2, e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[13028, 13004])).
% 1.82/1.97 tff(13030,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[756, 13029])).
% 1.82/1.97 tff(13031,plain,((op(e2, e0) = e1) | (op(e1, e1) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e3) = e2)) | (op(e2, e3) = e1) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(13032,plain,
% 1.82/1.97 (op(e2, e0) = e1),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[13031, 84, 1304, 2812, 76, 75])).
% 1.82/1.97 tff(13033,plain,
% 1.82/1.97 ((op(e2, e0) = e0) <=> (e1 = e0)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13032])).
% 1.82/1.97 tff(13034,plain,
% 1.82/1.97 ((op(e2, e0) = e0) <=> (e0 = e1)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13033, 18])).
% 1.82/1.97 tff(13035,plain,
% 1.82/1.97 ((e0 = e1) <=> (op(e2, e0) = e0)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13034])).
% 1.82/1.97 tff(13036,plain,
% 1.82/1.97 ((~(e0 = e1)) <=> (~(op(e2, e0) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13035])).
% 1.82/1.97 tff(13037,plain,
% 1.82/1.97 (~(op(e2, e0) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[26, 13036])).
% 1.82/1.97 tff(13038,plain,
% 1.82/1.97 ((op(e1, e3) = e0) <=> (e1 = e0)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[132])).
% 1.82/1.97 tff(13039,plain,
% 1.82/1.97 ((op(e1, e3) = e0) <=> (e0 = e1)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13038, 18])).
% 1.82/1.97 tff(13040,plain,
% 1.82/1.97 ((e0 = e1) <=> (op(e1, e3) = e0)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13039])).
% 1.82/1.97 tff(13041,plain,
% 1.82/1.97 ((~(e0 = e1)) <=> (~(op(e1, e3) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13040])).
% 1.82/1.97 tff(13042,plain,
% 1.82/1.97 (~(op(e1, e3) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[26, 13041])).
% 1.82/1.97 tff(13043,plain,
% 1.82/1.97 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[132])).
% 1.82/1.97 tff(13044,plain,
% 1.82/1.97 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13043])).
% 1.82/1.97 tff(13045,plain,
% 1.82/1.97 (~(op(e0, e3) = e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[64, 13044])).
% 1.82/1.97 tff(13046,plain,
% 1.82/1.97 (op(e2, e3) = e3),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[12598, 13045, 76, 79, 13042])).
% 1.82/1.97 tff(13047,plain,
% 1.82/1.97 (~(op(e2, e1) = e0)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[6988, 13042, 656, 2527, 13045, 79])).
% 1.82/1.97 tff(13048,plain,
% 1.82/1.97 (op(e2, e3) = e0),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[2311, 13047, 17, 983])).
% 1.82/1.97 tff(13049,plain,
% 1.82/1.97 (e0 = op(e2, e3)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13048])).
% 1.82/1.97 tff(13050,plain,
% 1.82/1.97 (e0 = e3),
% 1.82/1.97 inference(transitivity,[status(thm)],[13049, 13046])).
% 1.82/1.97 tff(13051,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[181, 13050])).
% 1.82/1.97 tff(13052,plain,((~(op(e1, e3) = e1)) | (op(e2, e2) = e0) | (op(e2, e0) = e0) | (op(e2, e3) = e1) | (op(e0, e3) = e2) | (op(e3, e3) = e0) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(13053,plain,
% 1.82/1.97 (~(op(e1, e3) = e1)),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[13052, 13037, 11102, 76, 10592, 11818, 12011])).
% 1.82/1.97 tff(13054,plain,
% 1.82/1.97 (op(e1, e3) = e0),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[104, 13053, 10589, 12008])).
% 1.82/1.97 tff(13055,plain,
% 1.82/1.97 (op(e1, op(e1, e3)) = op(e1, e0)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13054])).
% 1.82/1.97 tff(13056,plain,
% 1.82/1.97 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.97 tff(13057,plain,
% 1.82/1.97 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13056])).
% 1.82/1.97 tff(13058,plain,
% 1.82/1.97 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13057, 13055])).
% 1.82/1.97 tff(13059,plain,
% 1.82/1.97 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13058])).
% 1.82/1.97 tff(13060,plain,
% 1.82/1.97 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13059, 2154])).
% 1.82/1.97 tff(13061,plain,
% 1.82/1.97 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13060])).
% 1.82/1.97 tff(13062,plain,
% 1.82/1.97 (e3 = op(e1, e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[12004, 1740])).
% 1.82/1.97 tff(13063,plain,
% 1.82/1.97 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13056])).
% 1.82/1.97 tff(13064,plain,
% 1.82/1.97 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e3) = e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13063, 6095])).
% 1.82/1.97 tff(13065,plain,
% 1.82/1.97 ((op(e1, e3) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 1.82/1.97 inference(symmetry,[status(thm)],[13064])).
% 1.82/1.97 tff(13066,plain,
% 1.82/1.97 (e0 = op(e1, op(e1, e1))),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[13054, 13065])).
% 1.82/1.97 tff(13067,plain,
% 1.82/1.97 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[3009, 13066, 13062])).
% 1.82/1.97 tff(13068,plain,
% 1.82/1.97 (~(op(e1, e0) = e2)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[13067, 13061])).
% 1.82/1.97 tff(13069,plain,
% 1.82/1.97 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[12004])).
% 1.82/1.97 tff(13070,plain,
% 1.82/1.97 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13069])).
% 1.82/1.97 tff(13071,plain,
% 1.82/1.97 (~(op(e1, e0) = e3)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[737, 13070])).
% 1.82/1.97 tff(13072,plain,
% 1.82/1.97 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e1)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13032])).
% 1.82/1.97 tff(13073,plain,
% 1.82/1.97 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13072])).
% 1.82/1.97 tff(13074,plain,
% 1.82/1.97 (~(op(e1, e0) = e1)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[756, 13073])).
% 1.82/1.97 tff(13075,plain,
% 1.82/1.97 (e0 = op(e1, e3)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13054])).
% 1.82/1.97 tff(13076,plain,
% 1.82/1.97 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e1, e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13075])).
% 1.82/1.97 tff(13077,plain,
% 1.82/1.97 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e0)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13076])).
% 1.82/1.97 tff(13078,plain,
% 1.82/1.97 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13077])).
% 1.82/1.97 tff(13079,plain,
% 1.82/1.97 (~(op(e1, e0) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[110, 13078])).
% 1.82/1.97 tff(13080,plain,
% 1.82/1.97 (op(e1, e0) = e2),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[728, 13079, 13074, 13071])).
% 1.82/1.97 tff(13081,plain,
% 1.82/1.97 ($false),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[13080, 13068])).
% 1.82/1.97 tff(13082,plain,((op(e1, e1) = e0) | (op(e2, e3) = e1) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.97 tff(13083,plain,
% 1.82/1.97 (op(e1, e1) = e0),
% 1.82/1.97 inference(unit_resolution,[status(thm)],[13082, 76, 1304, 2812, 75])).
% 1.82/1.97 tff(13084,plain,
% 1.82/1.97 (e0 = op(e1, e1)),
% 1.82/1.97 inference(symmetry,[status(thm)],[13083])).
% 1.82/1.97 tff(13085,plain,
% 1.82/1.97 ((e0 = e3) <=> (op(e1, e1) = e3)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13084])).
% 1.82/1.97 tff(13086,plain,
% 1.82/1.97 ((~(e0 = e3)) <=> (~(op(e1, e1) = e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13085])).
% 1.82/1.97 tff(13087,plain,
% 1.82/1.97 (~(op(e1, e1) = e3)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[181, 13086])).
% 1.82/1.97 tff(13088,plain,
% 1.82/1.97 ((op(e1, e1) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13083])).
% 1.82/1.97 tff(13089,plain,
% 1.82/1.97 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13088, 6095])).
% 1.82/1.97 tff(13090,plain,
% 1.82/1.97 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13089])).
% 1.82/1.97 tff(13091,plain,
% 1.82/1.97 (~(op(e1, e3) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[619, 13090])).
% 1.82/1.97 tff(13092,plain,
% 1.82/1.97 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13083])).
% 1.82/1.97 tff(13093,plain,
% 1.82/1.97 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13092])).
% 1.82/1.97 tff(13094,plain,
% 1.82/1.97 (~(op(e1, e0) = e0)),
% 1.82/1.97 inference(modus_ponens,[status(thm)],[737, 13093])).
% 1.82/1.97 tff(13095,plain,
% 1.82/1.97 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 1.82/1.97 inference(monotonicity,[status(thm)],[13083])).
% 1.82/1.97 tff(13096,plain,
% 1.82/1.97 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 1.82/1.97 inference(transitivity,[status(thm)],[13095, 83])).
% 1.88/1.97 tff(13097,plain,
% 1.88/1.97 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13096])).
% 1.88/1.97 tff(13098,plain,
% 1.88/1.97 (~(op(e2, e1) = e0)),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[225, 13097])).
% 1.88/1.97 tff(13099,plain,
% 1.88/1.97 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13083])).
% 1.88/1.97 tff(13100,plain,
% 1.88/1.97 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.88/1.97 inference(transitivity,[status(thm)],[13099, 5470])).
% 1.88/1.97 tff(13101,plain,
% 1.88/1.97 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13100])).
% 1.88/1.97 tff(13102,plain,
% 1.88/1.97 (~(op(e3, e1) = e0)),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[945, 13101])).
% 1.88/1.97 tff(13103,plain,
% 1.88/1.97 (op(e1, e3) = e1),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[104, 1080, 10589, 80])).
% 1.88/1.97 tff(13104,plain,
% 1.88/1.97 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13103])).
% 1.88/1.97 tff(13105,plain,
% 1.88/1.97 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13104])).
% 1.88/1.97 tff(13106,plain,
% 1.88/1.97 (~(op(e0, e3) = e1)),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[64, 13105])).
% 1.88/1.97 tff(13107,plain,
% 1.88/1.97 (op(e2, e3) = e3),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[12598, 13106, 76, 10592, 80])).
% 1.88/1.97 tff(13108,plain,
% 1.88/1.97 (op(e2, e3) = op(e1, e0)),
% 1.88/1.97 inference(transitivity,[status(thm)],[13107, 11648])).
% 1.88/1.97 tff(13109,plain,
% 1.88/1.97 ((op(e2, e3) = e0) <=> (op(e1, e0) = e0)),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13108])).
% 1.88/1.97 tff(13110,plain,
% 1.88/1.97 ((op(e1, e0) = e0) <=> (op(e2, e3) = e0)),
% 1.88/1.97 inference(symmetry,[status(thm)],[13109])).
% 1.88/1.97 tff(13111,plain,
% 1.88/1.97 ((~(op(e1, e0) = e0)) <=> (~(op(e2, e3) = e0))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13110])).
% 1.88/1.97 tff(13112,plain,
% 1.88/1.97 (~(op(e2, e3) = e0)),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[2167, 13111])).
% 1.88/1.97 tff(13113,plain,
% 1.88/1.97 (op(e2, e0) = e0),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[2311, 13112, 17, 2559])).
% 1.88/1.97 tff(13114,plain,
% 1.88/1.97 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13113])).
% 1.88/1.97 tff(13115,plain,
% 1.88/1.97 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.88/1.97 inference(transitivity,[status(thm)],[13114, 8115])).
% 1.88/1.97 tff(13116,plain,
% 1.88/1.97 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13115])).
% 1.88/1.97 tff(13117,plain,
% 1.88/1.97 (~(op(e3, e0) = e0)),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[747, 13116])).
% 1.88/1.97 tff(13118,plain,
% 1.88/1.97 (op(e3, e2) = e0),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[1916, 13117, 9696, 183])).
% 1.88/1.97 tff(13119,plain,
% 1.88/1.97 (e0 = op(e3, op(e3, e3))),
% 1.88/1.97 inference(modus_ponens,[status(thm)],[13118, 6497])).
% 1.88/1.97 tff(13120,plain,
% 1.88/1.97 (op(e3, op(e3, e2)) = op(op(e1, e0), e0)),
% 1.88/1.97 inference(monotonicity,[status(thm)],[11648, 13118])).
% 1.88/1.97 tff(13121,plain,
% 1.88/1.97 (op(op(e1, e0), e0) = op(e3, op(e3, e2))),
% 1.88/1.97 inference(symmetry,[status(thm)],[13120])).
% 1.88/1.97 tff(13122,plain,
% 1.88/1.97 (op(e3, e0) = op(op(e1, e0), e0)),
% 1.88/1.97 inference(symmetry,[status(thm)],[11738])).
% 1.88/1.97 tff(13123,plain,
% 1.88/1.97 (op(e3, e0) = e1),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[5422, 13117, 11736, 9955])).
% 1.88/1.97 tff(13124,plain,
% 1.88/1.97 (e1 = op(e3, e0)),
% 1.88/1.97 inference(symmetry,[status(thm)],[13123])).
% 1.88/1.97 tff(13125,plain,
% 1.88/1.97 (e1 = op(e3, op(e3, op(e3, e3)))),
% 1.88/1.97 inference(transitivity,[status(thm)],[13124, 13122, 13121, 10079])).
% 1.88/1.97 tff(13126,plain,
% 1.88/1.97 ($false),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[5879, 13125, 13119, 2813])).
% 1.88/1.97 tff(13127,plain,((op(e1, e3) = e3) | (~(op(e3, e3) = e2)) | (op(e3, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e1) = e0) | (op(e1, e0) = e0) | (op(e2, e3) = e1) | (op(e1, e3) = e0) | (op(e1, e1) = e3) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.88/1.97 tff(13128,plain,
% 1.88/1.97 (op(e1, e3) = e3),
% 1.88/1.97 inference(unit_resolution,[status(thm)],[13127, 13102, 2812, 11102, 13098, 13094, 76, 13091, 13087, 75])).
% 1.88/1.97 tff(13129,plain,
% 1.88/1.97 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 1.88/1.97 inference(monotonicity,[status(thm)],[13128])).
% 1.88/1.97 tff(13130,plain,
% 1.88/1.97 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 1.88/1.97 inference(transitivity,[status(thm)],[13129, 112])).
% 1.88/1.98 tff(13131,plain,
% 1.88/1.98 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13130])).
% 1.88/1.98 tff(13132,plain,
% 1.88/1.98 (~(op(e2, e3) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[118, 13131])).
% 1.88/1.98 tff(13133,plain,
% 1.88/1.98 (op(e2, e3) = e0),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[206, 13132, 9692, 76])).
% 1.88/1.98 tff(13134,plain,
% 1.88/1.98 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13128])).
% 1.88/1.98 tff(13135,plain,
% 1.88/1.98 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13134, 128])).
% 1.88/1.98 tff(13136,plain,
% 1.88/1.98 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13135])).
% 1.88/1.98 tff(13137,plain,
% 1.88/1.98 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13136])).
% 1.88/1.98 tff(13138,plain,
% 1.88/1.98 (~(op(e1, e3) = e1)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[303, 13137])).
% 1.88/1.98 tff(13139,plain,
% 1.88/1.98 (op(e0, e3) = e1),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[151, 13138, 9667, 76])).
% 1.88/1.98 tff(13140,plain,
% 1.88/1.98 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13141,plain,
% 1.88/1.98 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13140, 67])).
% 1.88/1.98 tff(13142,plain,
% 1.88/1.98 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13141])).
% 1.88/1.98 tff(13143,plain,
% 1.88/1.98 (~(op(e1, e2) = e0)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[1604, 13142])).
% 1.88/1.98 tff(13144,plain,
% 1.88/1.98 (op(e0, e2) = e0),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[973, 85, 17, 13143])).
% 1.88/1.98 tff(13145,plain,
% 1.88/1.98 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13144])).
% 1.88/1.98 tff(13146,plain,
% 1.88/1.98 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 1.88/1.98 inference(symmetry,[status(thm)],[13145])).
% 1.88/1.98 tff(13147,plain,
% 1.88/1.98 ((op(e2, e0) = e0) <=> (op(e0, e2) = op(e2, e0))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13146, 6337])).
% 1.88/1.98 tff(13148,plain,
% 1.88/1.98 ((~(op(e2, e0) = e0)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13147])).
% 1.88/1.98 tff(13149,plain,
% 1.88/1.98 (~(op(e0, e2) = op(e2, e0))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[10091, 13148])).
% 1.88/1.98 tff(13150,plain,
% 1.88/1.98 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[6347, 13149])).
% 1.88/1.98 tff(13151,plain,
% 1.88/1.98 ((~(op(e2, e0) = e0)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13146])).
% 1.88/1.98 tff(13152,plain,
% 1.88/1.98 (~(op(e2, e0) = op(e0, e2))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[10091, 13151])).
% 1.88/1.98 tff(13153,plain,
% 1.88/1.98 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[6358, 13152])).
% 1.88/1.98 tff(13154,plain,
% 1.88/1.98 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[164])).
% 1.88/1.98 tff(13155,plain,
% 1.88/1.98 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 1.88/1.98 inference(symmetry,[status(thm)],[13154])).
% 1.88/1.98 tff(13156,plain,
% 1.88/1.98 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13157,plain,
% 1.88/1.98 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13156])).
% 1.88/1.98 tff(13158,plain,
% 1.88/1.98 (~(op(e0, e1) = e0)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[792, 13157])).
% 1.88/1.98 tff(13159,plain,
% 1.88/1.98 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13144])).
% 1.88/1.98 tff(13160,plain,
% 1.88/1.98 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13159])).
% 1.88/1.98 tff(13161,plain,
% 1.88/1.98 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13160])).
% 1.88/1.98 tff(13162,plain,
% 1.88/1.98 (~(op(e0, e2) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[181, 13161])).
% 1.88/1.98 tff(13163,plain,
% 1.88/1.98 (op(e0, e1) = e3),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5000, 13162, 13158, 19])).
% 1.88/1.98 tff(13164,plain,
% 1.88/1.98 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13163])).
% 1.88/1.98 tff(13165,plain,
% 1.88/1.98 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13164, 396])).
% 1.88/1.98 tff(13166,plain,
% 1.88/1.98 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13165, 13155])).
% 1.88/1.98 tff(13167,plain,
% 1.88/1.98 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13166])).
% 1.88/1.98 tff(13168,plain,
% 1.88/1.98 (~(op(e3, e1) = op(e1, e3))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[3046, 13167])).
% 1.88/1.98 tff(13169,plain,
% 1.88/1.98 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[6362, 13168])).
% 1.88/1.98 tff(13170,plain,
% 1.88/1.98 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13163])).
% 1.88/1.98 tff(13171,plain,
% 1.88/1.98 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 1.88/1.98 inference(symmetry,[status(thm)],[13170])).
% 1.88/1.98 tff(13172,plain,
% 1.88/1.98 ((op(e1, e0) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13171, 596])).
% 1.88/1.98 tff(13173,plain,
% 1.88/1.98 ((~(op(e1, e0) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13172])).
% 1.88/1.98 tff(13174,plain,
% 1.88/1.98 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[164])).
% 1.88/1.98 tff(13175,plain,
% 1.88/1.98 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13174])).
% 1.88/1.98 tff(13176,plain,
% 1.88/1.98 (~(op(e1, e0) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[110, 13175])).
% 1.88/1.98 tff(13177,plain,
% 1.88/1.98 (~(op(e0, e1) = op(e1, e0))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13176, 13173])).
% 1.88/1.98 tff(13178,plain,
% 1.88/1.98 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[609, 13177])).
% 1.88/1.98 tff(13179,plain,
% 1.88/1.98 ((op(e0, op(e3, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[12702])).
% 1.88/1.98 tff(13180,plain,
% 1.88/1.98 ((op(e0, e2) = e0) <=> (op(e0, op(e3, e3)) = e0)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13179])).
% 1.88/1.98 tff(13181,plain,
% 1.88/1.98 (op(e0, op(e3, e3)) = e0),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13144, 13180])).
% 1.88/1.98 tff(13182,plain,
% 1.88/1.98 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[392, 13181])).
% 1.88/1.98 tff(13183,plain,
% 1.88/1.98 ((op(e0, e2) = e2) <=> (e0 = e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13144])).
% 1.88/1.98 tff(13184,plain,
% 1.88/1.98 ((e0 = e2) <=> (op(e0, e2) = e2)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13183])).
% 1.88/1.98 tff(13185,plain,
% 1.88/1.98 ((~(e0 = e2)) <=> (~(op(e0, e2) = e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13184])).
% 1.88/1.98 tff(13186,plain,
% 1.88/1.98 (~(op(e0, e2) = e2)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[14, 13185])).
% 1.88/1.98 tff(13187,plain,
% 1.88/1.98 ((op(e1, e1) = e2) <=> (e0 = e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13188,plain,
% 1.88/1.98 ((e0 = e2) <=> (op(e1, e1) = e2)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13187])).
% 1.88/1.98 tff(13189,plain,
% 1.88/1.98 ((~(e0 = e2)) <=> (~(op(e1, e1) = e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13188])).
% 1.88/1.98 tff(13190,plain,
% 1.88/1.98 (~(op(e1, e1) = e2)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[14, 13189])).
% 1.88/1.98 tff(13191,plain,
% 1.88/1.98 ((op(e0, e1) = e2) <=> (e3 = e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13163])).
% 1.88/1.98 tff(13192,plain,
% 1.88/1.98 ((op(e0, e1) = e2) <=> (e2 = e3)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13191, 1314])).
% 1.88/1.98 tff(13193,plain,
% 1.88/1.98 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13192])).
% 1.88/1.98 tff(13194,plain,
% 1.88/1.98 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13193])).
% 1.88/1.98 tff(13195,plain,
% 1.88/1.98 (~(op(e0, e1) = e2)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[1321, 13194])).
% 1.88/1.98 tff(13196,plain,
% 1.88/1.98 (op(e2, e1) = e2),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[1993, 13195, 9684, 13190])).
% 1.88/1.98 tff(13197,plain,
% 1.88/1.98 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13196])).
% 1.88/1.98 tff(13198,plain,
% 1.88/1.98 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13197, 81])).
% 1.88/1.98 tff(13199,plain,
% 1.88/1.98 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13198])).
% 1.88/1.98 tff(13200,plain,
% 1.88/1.98 (~(op(e2, e2) = e2)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[508, 13199])).
% 1.88/1.98 tff(13201,plain,
% 1.88/1.98 (op(e1, e2) = e2),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[1151, 13200, 9699, 13186])).
% 1.88/1.98 tff(13202,plain,
% 1.88/1.98 (op(e0, op(e1, e2)) = op(e0, e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13201])).
% 1.88/1.98 tff(13203,plain,
% 1.88/1.98 (op(e0, op(e1, e2)) = e0),
% 1.88/1.98 inference(transitivity,[status(thm)],[13202, 13144])).
% 1.88/1.98 tff(13204,plain,
% 1.88/1.98 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[6398, 13203])).
% 1.88/1.98 tff(13205,plain,
% 1.88/1.98 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13206,plain,
% 1.88/1.98 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13205, 5470])).
% 1.88/1.98 tff(13207,plain,
% 1.88/1.98 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13206])).
% 1.88/1.98 tff(13208,plain,
% 1.88/1.98 (~(op(e3, e1) = e0)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[945, 13207])).
% 1.88/1.98 tff(13209,plain,
% 1.88/1.98 (op(e3, e0) = e0),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[1916, 85, 9696, 13208])).
% 1.88/1.98 tff(13210,plain,
% 1.88/1.98 ((op(e3, e0) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13209])).
% 1.88/1.98 tff(13211,plain,
% 1.88/1.98 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13210, 1079])).
% 1.88/1.98 tff(13212,plain,
% 1.88/1.98 ((op(e0, e3) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/1.98 inference(symmetry,[status(thm)],[13211])).
% 1.88/1.98 tff(13213,plain,
% 1.88/1.98 ((op(e0, e3) = e0) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13212, 453])).
% 1.88/1.98 tff(13214,plain,
% 1.88/1.98 ((~(op(e0, e3) = e0)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13213])).
% 1.88/1.98 tff(13215,plain,
% 1.88/1.98 (~(op(e0, e3) = op(e3, e0))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[4725, 13214])).
% 1.88/1.98 tff(13216,plain,
% 1.88/1.98 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[496, 13215])).
% 1.88/1.98 tff(13217,plain,
% 1.88/1.98 (op(e0, e0) = e2),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[3652, 13195, 10592, 13186])).
% 1.88/1.98 tff(13218,plain,
% 1.88/1.98 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13217])).
% 1.88/1.98 tff(13219,plain,
% 1.88/1.98 (op(e0, op(e0, e0)) = e0),
% 1.88/1.98 inference(transitivity,[status(thm)],[13218, 13144])).
% 1.88/1.98 tff(13220,plain,
% 1.88/1.98 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5598, 13219])).
% 1.88/1.98 tff(13221,plain,
% 1.88/1.98 (op(e0, op(e2, e1)) = op(e0, e2)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13196])).
% 1.88/1.98 tff(13222,plain,
% 1.88/1.98 (op(e0, op(e2, e1)) = e0),
% 1.88/1.98 inference(transitivity,[status(thm)],[13221, 13144])).
% 1.88/1.98 tff(13223,plain,
% 1.88/1.98 (((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)) | (~(op(e0, op(e2, e1)) = e0))),
% 1.88/1.98 inference(tautology,[status(thm)],[])).
% 1.88/1.98 tff(13224,plain,
% 1.88/1.98 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[13223, 13222])).
% 1.88/1.98 tff(13225,plain,
% 1.88/1.98 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13165, 13155, 6290])).
% 1.88/1.98 tff(13226,plain,
% 1.88/1.98 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13225])).
% 1.88/1.98 tff(13227,plain,
% 1.88/1.98 (~(op(e1, e3) = op(e3, e1))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[3046, 13226])).
% 1.88/1.98 tff(13228,plain,
% 1.88/1.98 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[6307, 13227])).
% 1.88/1.98 tff(13229,plain,
% 1.88/1.98 ((~(op(e1, e0) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13171])).
% 1.88/1.98 tff(13230,plain,
% 1.88/1.98 (~(op(e1, e0) = op(e0, e1))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13176, 13229])).
% 1.88/1.98 tff(13231,plain,
% 1.88/1.98 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[613, 13230])).
% 1.88/1.98 tff(13232,plain,
% 1.88/1.98 (op(e1, op(e1, e1)) = op(e1, e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13233,plain,
% 1.88/1.98 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e0) = e1)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13232])).
% 1.88/1.98 tff(13234,plain,
% 1.88/1.98 ((op(e1, e0) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13233])).
% 1.88/1.98 tff(13235,plain,
% 1.88/1.98 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[249])).
% 1.88/1.98 tff(13236,plain,
% 1.88/1.98 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13235])).
% 1.88/1.98 tff(13237,plain,
% 1.88/1.98 (~(op(e1, e0) = e0)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[737, 13236])).
% 1.88/1.98 tff(13238,plain,
% 1.88/1.98 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13217])).
% 1.88/1.98 tff(13239,plain,
% 1.88/1.98 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13238, 2154])).
% 1.88/1.98 tff(13240,plain,
% 1.88/1.98 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13239])).
% 1.88/1.98 tff(13241,plain,
% 1.88/1.98 (~(op(e1, e0) = e2)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[2471, 13240])).
% 1.88/1.98 tff(13242,plain,
% 1.88/1.98 (op(e1, e0) = e1),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[728, 13241, 13237, 13176])).
% 1.88/1.98 tff(13243,plain,
% 1.88/1.98 (op(e1, op(e1, e1)) = e1),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13242, 13234])).
% 1.88/1.98 tff(13244,plain,
% 1.88/1.98 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5678, 13243])).
% 1.88/1.98 tff(13245,plain,
% 1.88/1.98 ((op(e3, e0) = e3) <=> (e0 = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13209])).
% 1.88/1.98 tff(13246,plain,
% 1.88/1.98 ((e0 = e3) <=> (op(e3, e0) = e3)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13245])).
% 1.88/1.98 tff(13247,plain,
% 1.88/1.98 ((~(e0 = e3)) <=> (~(op(e3, e0) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13246])).
% 1.88/1.98 tff(13248,plain,
% 1.88/1.98 (~(op(e3, e0) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[181, 13247])).
% 1.88/1.98 tff(13249,plain,
% 1.88/1.98 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13165])).
% 1.88/1.98 tff(13250,plain,
% 1.88/1.98 (~(op(e3, e1) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[3046, 13249])).
% 1.88/1.98 tff(13251,plain,
% 1.88/1.98 (op(e3, e2) = e3),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[422, 13250, 11641, 13248])).
% 1.88/1.98 tff(13252,plain,
% 1.88/1.98 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13251])).
% 1.88/1.98 tff(13253,plain,
% 1.88/1.98 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13252])).
% 1.88/1.98 tff(13254,plain,
% 1.88/1.98 (~(op(e2, e2) = e3)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[1546, 13253])).
% 1.88/1.98 tff(13255,plain,
% 1.88/1.98 (op(e2, e2) = e1),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[524, 13254, 17, 13200])).
% 1.88/1.98 tff(13256,plain,
% 1.88/1.98 (op(e2, e2) = op(e0, e3)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13255, 4681])).
% 1.88/1.98 tff(13257,plain,
% 1.88/1.98 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13256])).
% 1.88/1.98 tff(13258,plain,
% 1.88/1.98 (op(e2, op(e2, e2)) = e2),
% 1.88/1.98 inference(transitivity,[status(thm)],[13257, 4816, 13196])).
% 1.88/1.98 tff(13259,plain,
% 1.88/1.98 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[528, 13258])).
% 1.88/1.98 tff(13260,plain,
% 1.88/1.98 ($false),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5367, 13259, 13244, 13231, 13228, 13224, 13220, 13216, 13204, 13182, 13178, 11412, 13169, 13153, 11403, 13150])).
% 1.88/1.98 tff(13261,plain,((op(e3, e2) = e0) | (~(op(e0, e3) = e1)) | (~(op(e1, e1) = e0)) | (op(e2, e2) = e0) | (~(op(e1, e3) = e3)) | (~(op(e3, e3) = e2)) | (~(op(e2, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.98 tff(13262,plain,
% 1.88/1.98 (op(e3, e2) = e0),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[13261, 13139, 13083, 11102, 13128, 2812, 13133])).
% 1.88/1.98 tff(13263,plain,
% 1.88/1.98 (op(e3, op(e3, e2)) = op(e3, e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13262])).
% 1.88/1.98 tff(13264,plain,
% 1.88/1.98 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.88/1.98 inference(transitivity,[status(thm)],[6490, 13263])).
% 1.88/1.98 tff(13265,plain,
% 1.88/1.98 (e1 = op(e0, e3)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13139])).
% 1.88/1.98 tff(13266,plain,
% 1.88/1.98 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13265, 13264])).
% 1.88/1.98 tff(13267,plain,
% 1.88/1.98 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/1.98 inference(transitivity,[status(thm)],[13266, 452])).
% 1.88/1.98 tff(13268,plain,
% 1.88/1.98 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = op(e0, e3)))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13267])).
% 1.88/1.98 tff(13269,plain,
% 1.88/1.98 (e0 = op(e3, op(e3, e3))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13262, 6497])).
% 1.88/1.98 tff(13270,plain,
% 1.88/1.98 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5879, 13269, 2813])).
% 1.88/1.98 tff(13271,plain,
% 1.88/1.98 (~(op(e3, e0) = op(e0, e3))),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13270, 13268])).
% 1.88/1.98 tff(13272,plain,
% 1.88/1.98 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e0)),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13262])).
% 1.88/1.98 tff(13273,plain,
% 1.88/1.98 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e0))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13272])).
% 1.88/1.98 tff(13274,plain,
% 1.88/1.98 (~(op(e3, e0) = e0)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[1133, 13273])).
% 1.88/1.98 tff(13275,plain,
% 1.88/1.98 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13265])).
% 1.88/1.98 tff(13276,plain,
% 1.88/1.98 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e1)),
% 1.88/1.98 inference(symmetry,[status(thm)],[13275])).
% 1.88/1.98 tff(13277,plain,
% 1.88/1.98 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13267, 13276])).
% 1.88/1.98 tff(13278,plain,
% 1.88/1.98 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13277])).
% 1.88/1.98 tff(13279,plain,
% 1.88/1.98 (~(op(e3, e0) = e1)),
% 1.88/1.98 inference(modus_ponens,[status(thm)],[13270, 13278])).
% 1.88/1.98 tff(13280,plain,
% 1.88/1.98 (op(e3, e0) = e3),
% 1.88/1.98 inference(unit_resolution,[status(thm)],[5422, 13279, 13274, 9955])).
% 1.88/1.98 tff(13281,plain,
% 1.88/1.98 (op(e2, e2) = op(e0, e3)),
% 1.88/1.98 inference(transitivity,[status(thm)],[307, 4681])).
% 1.88/1.98 tff(13282,plain,
% 1.88/1.98 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 1.88/1.98 inference(monotonicity,[status(thm)],[13281])).
% 1.88/1.98 tff(13283,plain,
% 1.88/1.98 (op(e2, op(e2, e2)) = op(e2, e1)),
% 1.88/1.98 inference(transitivity,[status(thm)],[13282, 4816])).
% 1.88/1.99 tff(13284,plain,
% 1.88/1.99 ((e3 = op(e2, op(e2, e2))) <=> (e3 = op(e2, e1))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13283])).
% 1.88/1.99 tff(13285,plain,
% 1.88/1.99 ((e3 = op(e2, op(e2, e2))) <=> (op(e2, e1) = e3)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13284, 1262])).
% 1.88/1.99 tff(13286,plain,
% 1.88/1.99 ((op(e2, e1) = e3) <=> (e3 = op(e2, op(e2, e2)))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13285])).
% 1.88/1.99 tff(13287,plain,
% 1.88/1.99 ((op(e2, e2) = e3) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13281, 12887])).
% 1.88/1.99 tff(13288,plain,
% 1.88/1.99 ((op(e2, e2) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13287, 452])).
% 1.88/1.99 tff(13289,plain,
% 1.88/1.99 ((op(e3, e0) = op(e0, e3)) <=> (op(e2, e2) = e3)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13288])).
% 1.88/1.99 tff(13290,plain,
% 1.88/1.99 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e2, e2) = e3))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13289])).
% 1.88/1.99 tff(13291,plain,
% 1.88/1.99 (~(op(e2, e2) = e3)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[5528, 13290])).
% 1.88/1.99 tff(13292,plain,
% 1.88/1.99 (op(e2, e1) = e3),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[1559, 13291, 124, 12891])).
% 1.88/1.99 tff(13293,plain,
% 1.88/1.99 (e3 = op(e2, op(e2, e2))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13292, 13286])).
% 1.88/1.99 tff(13294,plain,
% 1.88/1.99 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e1))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13283])).
% 1.88/1.99 tff(13295,plain,
% 1.88/1.99 (op(e2, op(e2, e1)) = op(e2, op(e2, op(e2, e2)))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13294])).
% 1.88/1.99 tff(13296,plain,
% 1.88/1.99 (op(e2, e1) = op(e3, e0)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13292, 12887])).
% 1.88/1.99 tff(13297,plain,
% 1.88/1.99 (op(e2, op(e2, e1)) = op(e2, op(e3, e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13296])).
% 1.88/1.99 tff(13298,plain,
% 1.88/1.99 (op(e2, op(e3, e0)) = op(e2, op(e2, e1))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13297])).
% 1.88/1.99 tff(13299,plain,
% 1.88/1.99 (op(e2, e3) = op(e2, op(e3, e0))),
% 1.88/1.99 inference(symmetry,[status(thm)],[12899])).
% 1.88/1.99 tff(13300,plain,
% 1.88/1.99 (e0 = op(e2, op(e2, op(e2, e2)))),
% 1.88/1.99 inference(transitivity,[status(thm)],[252, 13299, 13298, 13295])).
% 1.88/1.99 tff(13301,plain,
% 1.88/1.99 ($false),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[334, 13300, 13293, 318])).
% 1.88/1.99 tff(13302,plain,((~(op(e2, e2) = e1)) | (~(op(e2, e3) = e0)) | (~(op(e3, e0) = e3)) | (~(op(e0, e3) = e1)) | (op(e2, e3) = e3) | (op(e3, e0) = op(e0, e3))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.99 tff(13303,plain,
% 1.88/1.99 (~(op(e2, e2) = e1)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[13302, 13133, 13280, 13139, 13132, 13271])).
% 1.88/1.99 tff(13304,plain,
% 1.88/1.99 ((op(e1, e1) = e2) <=> (e0 = e2)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13083])).
% 1.88/1.99 tff(13305,plain,
% 1.88/1.99 ((e0 = e2) <=> (op(e1, e1) = e2)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13304])).
% 1.88/1.99 tff(13306,plain,
% 1.88/1.99 ((~(e0 = e2)) <=> (~(op(e1, e1) = e2))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13305])).
% 1.88/1.99 tff(13307,plain,
% 1.88/1.99 (~(op(e1, e1) = e2)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[14, 13306])).
% 1.88/1.99 tff(13308,plain,
% 1.88/1.99 ((op(e3, e2) = e1) <=> (e0 = op(e0, e3))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13262, 13265])).
% 1.88/1.99 tff(13309,plain,
% 1.88/1.99 ((op(e3, e2) = e1) <=> (op(e0, e3) = e0)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13308, 1079])).
% 1.88/1.99 tff(13310,plain,
% 1.88/1.99 ((op(e0, e3) = e0) <=> (op(e3, e2) = e1)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13309])).
% 1.88/1.99 tff(13311,plain,
% 1.88/1.99 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e2) = e1))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13310])).
% 1.88/1.99 tff(13312,plain,
% 1.88/1.99 ((e0 = e1) <=> (e0 = op(e0, e3))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13265])).
% 1.88/1.99 tff(13313,plain,
% 1.88/1.99 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13312, 1079])).
% 1.88/1.99 tff(13314,plain,
% 1.88/1.99 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13313])).
% 1.88/1.99 tff(13315,plain,
% 1.88/1.99 (~(op(e0, e3) = e0)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[26, 13314])).
% 1.88/1.99 tff(13316,plain,
% 1.88/1.99 (~(op(e3, e2) = e1)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13315, 13311])).
% 1.88/1.99 tff(13317,plain,
% 1.88/1.99 (op(e3, e1) = e1),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[939, 13279, 9667, 13316])).
% 1.88/1.99 tff(13318,plain,
% 1.88/1.99 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e1)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13317])).
% 1.88/1.99 tff(13319,plain,
% 1.88/1.99 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e1))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13318])).
% 1.88/1.99 tff(13320,plain,
% 1.88/1.99 (~(op(e2, e1) = e1)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[402, 13319])).
% 1.88/1.99 tff(13321,plain,
% 1.88/1.99 (op(e2, e0) = e1),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[345, 13303, 76, 13320])).
% 1.88/1.99 tff(13322,plain,
% 1.88/1.99 (op(e2, e0) = op(e0, e3)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13321, 13265])).
% 1.88/1.99 tff(13323,plain,
% 1.88/1.99 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13322])).
% 1.88/1.99 tff(13324,plain,
% 1.88/1.99 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13323, 7797])).
% 1.88/1.99 tff(13325,plain,
% 1.88/1.99 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13324])).
% 1.88/1.99 tff(13326,plain,
% 1.88/1.99 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13325, 6337])).
% 1.88/1.99 tff(13327,plain,
% 1.88/1.99 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13326])).
% 1.88/1.99 tff(13328,plain,
% 1.88/1.99 (~(op(e0, e2) = op(e2, e0))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[918, 13327])).
% 1.88/1.99 tff(13329,plain,
% 1.88/1.99 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[6347, 13328])).
% 1.88/1.99 tff(13330,plain,
% 1.88/1.99 (op(e0, op(e3, e2)) = op(e0, e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13262])).
% 1.88/1.99 tff(13331,plain,
% 1.88/1.99 ((op(e0, op(e3, e2)) = e0) <=> (op(e0, e0) = e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13330])).
% 1.88/1.99 tff(13332,plain,
% 1.88/1.99 ((op(e0, e0) = e0) <=> (op(e0, op(e3, e2)) = e0)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13331])).
% 1.88/1.99 tff(13333,plain,
% 1.88/1.99 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13083])).
% 1.88/1.99 tff(13334,plain,
% 1.88/1.99 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13333])).
% 1.88/1.99 tff(13335,plain,
% 1.88/1.99 (~(op(e0, e1) = e0)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[792, 13334])).
% 1.88/1.99 tff(13336,plain,
% 1.88/1.99 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13262])).
% 1.88/1.99 tff(13337,plain,
% 1.88/1.99 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13336])).
% 1.88/1.99 tff(13338,plain,
% 1.88/1.99 (~(op(e0, e2) = e0)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[1467, 13337])).
% 1.88/1.99 tff(13339,plain,
% 1.88/1.99 (op(e0, e0) = e0),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[3976, 13338, 13335, 13315])).
% 1.88/1.99 tff(13340,plain,
% 1.88/1.99 (op(e0, op(e3, e2)) = e0),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13339, 13332])).
% 1.88/1.99 tff(13341,plain,
% 1.88/1.99 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[10702, 13340])).
% 1.88/1.99 tff(13342,plain,
% 1.88/1.99 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13325])).
% 1.88/1.99 tff(13343,plain,
% 1.88/1.99 (~(op(e2, e0) = op(e0, e2))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[918, 13342])).
% 1.88/1.99 tff(13344,plain,
% 1.88/1.99 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[6358, 13343])).
% 1.88/1.99 tff(13345,plain,
% 1.88/1.99 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13128])).
% 1.88/1.99 tff(13346,plain,
% 1.88/1.99 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13345])).
% 1.88/1.99 tff(13347,plain,
% 1.88/1.99 (e3 = op(e3, e0)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13280])).
% 1.88/1.99 tff(13348,plain,
% 1.88/1.99 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e3, e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13347])).
% 1.88/1.99 tff(13349,plain,
% 1.88/1.99 ((op(e3, e1) = e3) <=> (op(e3, e0) = op(e3, e1))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13348, 881])).
% 1.88/1.99 tff(13350,plain,
% 1.88/1.99 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13349])).
% 1.88/1.99 tff(13351,plain,
% 1.88/1.99 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13350, 13346])).
% 1.88/1.99 tff(13352,plain,
% 1.88/1.99 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13351])).
% 1.88/1.99 tff(13353,plain,
% 1.88/1.99 (~(op(e3, e1) = op(e1, e3))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[580, 13352])).
% 1.88/1.99 tff(13354,plain,
% 1.88/1.99 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[6362, 13353])).
% 1.88/1.99 tff(13355,plain,
% 1.88/1.99 (op(e0, op(e2, e3)) = op(e0, e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13133])).
% 1.88/1.99 tff(13356,plain,
% 1.88/1.99 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e0) = e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13355])).
% 1.88/1.99 tff(13357,plain,
% 1.88/1.99 ((op(e0, e0) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13356])).
% 1.88/1.99 tff(13358,plain,
% 1.88/1.99 (op(e0, op(e2, e3)) = e0),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13339, 13357])).
% 1.88/1.99 tff(13359,plain,
% 1.88/1.99 (((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)) | (~(op(e0, op(e2, e3)) = e0))),
% 1.88/1.99 inference(tautology,[status(thm)],[])).
% 1.88/1.99 tff(13360,plain,
% 1.88/1.99 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[13359, 13358])).
% 1.88/1.99 tff(13361,plain,
% 1.88/1.99 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e3))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13265])).
% 1.88/1.99 tff(13362,plain,
% 1.88/1.99 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13361])).
% 1.88/1.99 tff(13363,plain,
% 1.88/1.99 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13362])).
% 1.88/1.99 tff(13364,plain,
% 1.88/1.99 (~(op(e0, e2) = e1)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[918, 13363])).
% 1.88/1.99 tff(13365,plain,
% 1.88/1.99 (op(e1, e2) = e1),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[1613, 13303, 13316, 13364])).
% 1.88/1.99 tff(13366,plain,
% 1.88/1.99 (op(e1, op(e3, e3)) = e1),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13365, 11942])).
% 1.88/1.99 tff(13367,plain,
% 1.88/1.99 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[5685, 13366])).
% 1.88/1.99 tff(13368,plain,
% 1.88/1.99 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13365])).
% 1.88/1.99 tff(13369,plain,
% 1.88/1.99 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 1.88/1.99 inference(symmetry,[status(thm)],[13368])).
% 1.88/1.99 tff(13370,plain,
% 1.88/1.99 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13369])).
% 1.88/1.99 tff(13371,plain,
% 1.88/1.99 (~(op(e2, e1) = op(e1, e2))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13320, 13370])).
% 1.88/1.99 tff(13372,plain,
% 1.88/1.99 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[557, 13371])).
% 1.88/1.99 tff(13373,plain,
% 1.88/1.99 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13267, 453])).
% 1.88/1.99 tff(13374,plain,
% 1.88/1.99 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13373])).
% 1.88/1.99 tff(13375,plain,
% 1.88/1.99 (~(op(e0, e3) = op(e3, e0))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13270, 13374])).
% 1.88/1.99 tff(13376,plain,
% 1.88/1.99 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[496, 13375])).
% 1.88/1.99 tff(13377,plain,
% 1.88/1.99 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13339])).
% 1.88/1.99 tff(13378,plain,
% 1.88/1.99 (op(e0, op(e0, e0)) = e0),
% 1.88/1.99 inference(transitivity,[status(thm)],[13377, 13339])).
% 1.88/1.99 tff(13379,plain,
% 1.88/1.99 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[5598, 13378])).
% 1.88/1.99 tff(13380,plain,
% 1.88/1.99 ((op(e2, e1) = e1) <=> (op(e1, e2) = op(e2, e1))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13369, 531])).
% 1.88/1.99 tff(13381,plain,
% 1.88/1.99 ((~(op(e2, e1) = e1)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13380])).
% 1.88/1.99 tff(13382,plain,
% 1.88/1.99 (~(op(e1, e2) = op(e2, e1))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13320, 13381])).
% 1.88/1.99 tff(13383,plain,
% 1.88/1.99 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[539, 13382])).
% 1.88/1.99 tff(13384,plain,
% 1.88/1.99 ((op(e3, e0) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13350, 13346, 6290])).
% 1.88/1.99 tff(13385,plain,
% 1.88/1.99 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13384])).
% 1.88/1.99 tff(13386,plain,
% 1.88/1.99 (~(op(e1, e3) = op(e3, e1))),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[580, 13385])).
% 1.88/1.99 tff(13387,plain,
% 1.88/1.99 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[6307, 13386])).
% 1.88/1.99 tff(13388,plain,
% 1.88/1.99 (op(e0, op(e1, e1)) = op(e0, e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13083])).
% 1.88/1.99 tff(13389,plain,
% 1.88/1.99 ((op(e0, op(e1, e1)) = e0) <=> (op(e0, e0) = e0)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13388])).
% 1.88/1.99 tff(13390,plain,
% 1.88/1.99 ((op(e0, e0) = e0) <=> (op(e0, op(e1, e1)) = e0)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13389])).
% 1.88/1.99 tff(13391,plain,
% 1.88/1.99 (op(e0, op(e1, e1)) = e0),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[13339, 13390])).
% 1.88/1.99 tff(13392,plain,
% 1.88/1.99 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[635, 13391])).
% 1.88/1.99 tff(13393,plain,
% 1.88/1.99 ((op(e0, e0) = e2) <=> (e0 = e2)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13339])).
% 1.88/1.99 tff(13394,plain,
% 1.88/1.99 ((e0 = e2) <=> (op(e0, e0) = e2)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13393])).
% 1.88/1.99 tff(13395,plain,
% 1.88/1.99 ((~(e0 = e2)) <=> (~(op(e0, e0) = e2))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13394])).
% 1.88/1.99 tff(13396,plain,
% 1.88/1.99 (~(op(e0, e0) = e2)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[14, 13395])).
% 1.88/1.99 tff(13397,plain,
% 1.88/1.99 ((op(e2, e0) = e2) <=> (op(e0, e3) = e2)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13322])).
% 1.88/1.99 tff(13398,plain,
% 1.88/1.99 ((op(e0, e3) = e2) <=> (op(e2, e0) = e2)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13397])).
% 1.88/1.99 tff(13399,plain,
% 1.88/1.99 ((~(op(e0, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13398])).
% 1.88/1.99 tff(13400,plain,
% 1.88/1.99 (~(op(e2, e0) = e2)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[10592, 13399])).
% 1.88/1.99 tff(13401,plain,
% 1.88/1.99 (op(e1, e0) = e2),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[589, 13400, 9955, 13396])).
% 1.88/1.99 tff(13402,plain,
% 1.88/1.99 (op(e2, e1) = op(e2, op(e0, e3))),
% 1.88/1.99 inference(symmetry,[status(thm)],[4816])).
% 1.88/1.99 tff(13403,plain,
% 1.88/1.99 ((op(e2, e1) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13402])).
% 1.88/1.99 tff(13404,plain,
% 1.88/1.99 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e1) = e2)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13403])).
% 1.88/1.99 tff(13405,plain,
% 1.88/1.99 (op(e2, e1) = e3),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[1559, 2431, 124, 12891])).
% 1.88/1.99 tff(13406,plain,
% 1.88/1.99 (op(e2, op(e0, e3)) = op(e3, e0)),
% 1.88/1.99 inference(transitivity,[status(thm)],[4816, 13405, 12887])).
% 1.88/1.99 tff(13407,plain,
% 1.88/1.99 ((op(e2, op(e0, e3)) = e2) <=> (op(e3, e0) = op(e1, e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13406, 975])).
% 1.88/1.99 tff(13408,plain,
% 1.88/1.99 ((op(e2, op(e0, e3)) = e2) <=> (op(e1, e0) = op(e3, e0))),
% 1.88/1.99 inference(transitivity,[status(thm)],[13407, 2294])).
% 1.88/1.99 tff(13409,plain,
% 1.88/1.99 ((op(e1, e0) = op(e3, e0)) <=> (op(e2, op(e0, e3)) = e2)),
% 1.88/1.99 inference(symmetry,[status(thm)],[13408])).
% 1.88/1.99 tff(13410,plain,
% 1.88/1.99 ((op(e1, e0) = op(e3, e0)) <=> (op(e2, e1) = e2)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13409, 13404])).
% 1.88/1.99 tff(13411,plain,
% 1.88/1.99 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e2, e1) = e2))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13410])).
% 1.88/1.99 tff(13412,plain,
% 1.88/1.99 (~(op(e2, e1) = e2)),
% 1.88/1.99 inference(modus_ponens,[status(thm)],[410, 13411])).
% 1.88/1.99 tff(13413,plain,
% 1.88/1.99 (op(e0, e1) = e2),
% 1.88/1.99 inference(unit_resolution,[status(thm)],[1993, 13412, 82, 68])).
% 1.88/1.99 tff(13414,plain,
% 1.88/1.99 (op(e0, e1) = op(e1, e0)),
% 1.88/1.99 inference(transitivity,[status(thm)],[13413, 975])).
% 1.88/1.99 tff(13415,plain,
% 1.88/1.99 (op(e1, op(e0, e1)) = op(e1, op(e1, e0))),
% 1.88/1.99 inference(monotonicity,[status(thm)],[13414])).
% 1.88/1.99 tff(13416,plain,
% 1.88/1.99 (op(e1, op(e0, e1)) = e1),
% 1.88/1.99 inference(transitivity,[status(thm)],[13415, 921, 6683])).
% 1.88/1.99 tff(13417,plain,
% 1.88/1.99 (op(e1, op(e1, e0)) = e1),
% 1.88/1.99 inference(transitivity,[status(thm)],[921, 6683])).
% 1.88/1.99 tff(13418,plain,
% 1.88/1.99 (((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)) | (~(op(e1, op(e1, e0)) = e1))),
% 1.88/2.00 inference(tautology,[status(thm)],[])).
% 1.88/2.00 tff(13419,plain,
% 1.88/2.00 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13418, 13417])).
% 1.88/2.00 tff(13420,plain,
% 1.88/2.00 (op(e2, e2) = e2),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[524, 2431, 17, 1348])).
% 1.88/2.00 tff(13421,plain,
% 1.88/2.00 (op(e2, e2) = op(e1, e0)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13420, 975])).
% 1.88/2.00 tff(13422,plain,
% 1.88/2.00 (op(e1, op(e2, e2)) = op(e1, op(e1, e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13421])).
% 1.88/2.00 tff(13423,plain,
% 1.88/2.00 (op(e1, op(e2, e2)) = e1),
% 1.88/2.00 inference(transitivity,[status(thm)],[13422, 921, 6683])).
% 1.88/2.00 tff(13424,plain,
% 1.88/2.00 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[6714, 13423])).
% 1.88/2.00 tff(13425,plain,
% 1.88/2.00 (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[5367, 13424, 6689, 5669, 5673, 5667, 5670, 5680, 6688, 13419, 5671, 5511, 5674, 5668, 9846])).
% 1.88/2.00 tff(13426,plain,
% 1.88/2.00 (((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)) | (~(op(e1, op(e0, e1)) = e1))),
% 1.88/2.00 inference(tautology,[status(thm)],[])).
% 1.88/2.00 tff(13427,plain,
% 1.88/2.00 (~(op(e1, op(e0, e1)) = e1)),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13426, 13425])).
% 1.88/2.00 tff(13428,plain,
% 1.88/2.00 ($false),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13427, 13416])).
% 1.88/2.00 tff(13429,plain,((op(e2, e2) = e3) | (~(op(e1, e2) = e1)) | (~(op(e1, e0) = e2)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (~(op(e3, e0) = e3)) | (~(op(e0, e3) = e1)) | (op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.00 tff(13430,plain,
% 1.88/2.00 (op(e2, e2) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13429, 13365, 13401, 13392, 13387, 13383, 13379, 13376, 13372, 13367, 13360, 13354, 13344, 13341, 13329, 9684, 13307, 13280, 13139, 11102, 13303, 13132])).
% 1.88/2.00 tff(13431,plain,
% 1.88/2.00 (e3 = op(e2, e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[13430, 1796])).
% 1.88/2.00 tff(13432,plain,
% 1.88/2.00 (op(e2, e2) = op(e3, e0)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13430, 13347])).
% 1.88/2.00 tff(13433,plain,
% 1.88/2.00 (op(e2, op(e2, e2)) = op(e2, op(e3, e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13432])).
% 1.88/2.00 tff(13434,plain,
% 1.88/2.00 (op(e2, op(e3, e0)) = op(e2, op(e2, e2))),
% 1.88/2.00 inference(symmetry,[status(thm)],[13433])).
% 1.88/2.00 tff(13435,plain,
% 1.88/2.00 (op(e2, op(e3, e0)) = op(e2, e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13280])).
% 1.88/2.00 tff(13436,plain,
% 1.88/2.00 (op(e2, e3) = op(e2, op(e3, e0))),
% 1.88/2.00 inference(symmetry,[status(thm)],[13435])).
% 1.88/2.00 tff(13437,plain,
% 1.88/2.00 (e0 = op(e2, e3)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13133])).
% 1.88/2.00 tff(13438,plain,
% 1.88/2.00 (e0 = op(e2, op(e2, e2))),
% 1.88/2.00 inference(transitivity,[status(thm)],[13437, 13436, 13434])).
% 1.88/2.00 tff(13439,plain,
% 1.88/2.00 (op(e2, op(e2, e2)) = e0),
% 1.88/2.00 inference(transitivity,[status(thm)],[13433, 13435, 13133])).
% 1.88/2.00 tff(13440,plain,
% 1.88/2.00 (e2 = op(e1, e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13401])).
% 1.88/2.00 tff(13441,plain,
% 1.88/2.00 (op(e2, op(e2, op(e2, e2))) = op(op(e1, e0), e0)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13440, 13439])).
% 1.88/2.00 tff(13442,plain,
% 1.88/2.00 (op(op(e1, e0), e0) = op(e2, op(e2, op(e2, e2)))),
% 1.88/2.00 inference(symmetry,[status(thm)],[13441])).
% 1.88/2.00 tff(13443,plain,
% 1.88/2.00 (op(op(e1, e0), e0) = op(e2, e0)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13401])).
% 1.88/2.00 tff(13444,plain,
% 1.88/2.00 (op(e2, e0) = op(op(e1, e0), e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13443])).
% 1.88/2.00 tff(13445,plain,
% 1.88/2.00 (e1 = op(e2, e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13321])).
% 1.88/2.00 tff(13446,plain,
% 1.88/2.00 (e1 = op(e2, op(e2, op(e2, e2)))),
% 1.88/2.00 inference(transitivity,[status(thm)],[13445, 13444, 13442])).
% 1.88/2.00 tff(13447,plain,
% 1.88/2.00 ($false),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1810, 13446, 13438, 13431])).
% 1.88/2.00 tff(13448,plain,((op(e2, e3) = e1) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.00 tff(13449,plain,
% 1.88/2.00 (op(e2, e3) = e1),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13448, 1304, 75, 2812])).
% 1.88/2.00 tff(13450,plain,
% 1.88/2.00 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.00 tff(13451,plain,
% 1.88/2.00 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13450])).
% 1.88/2.00 tff(13452,plain,
% 1.88/2.00 (~(op(e0, e3) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[964, 13451])).
% 1.88/2.00 tff(13453,plain,
% 1.88/2.00 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.00 tff(13454,plain,
% 1.88/2.00 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13453])).
% 1.88/2.00 tff(13455,plain,
% 1.88/2.00 (~(op(e1, e3) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[118, 13454])).
% 1.88/2.00 tff(13456,plain,
% 1.88/2.00 (op(e1, e3) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[104, 1080, 10589, 13455])).
% 1.88/2.00 tff(13457,plain,
% 1.88/2.00 (e0 = op(e1, e3)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13456])).
% 1.88/2.00 tff(13458,plain,
% 1.88/2.00 (op(e3, e0) = op(e3, op(e1, e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13457])).
% 1.88/2.00 tff(13459,plain,
% 1.88/2.00 (op(e3, op(e1, e3)) = op(e3, e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13458])).
% 1.88/2.00 tff(13460,plain,
% 1.88/2.00 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13457])).
% 1.88/2.00 tff(13461,plain,
% 1.88/2.00 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13460])).
% 1.88/2.00 tff(13462,plain,
% 1.88/2.00 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13461])).
% 1.88/2.00 tff(13463,plain,
% 1.88/2.00 (~(op(e1, e2) = e0)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1850, 13462])).
% 1.88/2.00 tff(13464,plain,
% 1.88/2.00 (op(e0, e2) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[973, 85, 17, 13463])).
% 1.88/2.00 tff(13465,plain,
% 1.88/2.00 (op(op(e0, e2), e2) = op(e0, e2)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13464])).
% 1.88/2.00 tff(13466,plain,
% 1.88/2.00 (op(op(e0, e2), e2) = e0),
% 1.88/2.00 inference(transitivity,[status(thm)],[13465, 13464])).
% 1.88/2.00 tff(13467,plain,
% 1.88/2.00 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1956, 13466])).
% 1.88/2.00 tff(13468,plain,
% 1.88/2.00 (op(e1, e0) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[247, 1291, 1080, 75])).
% 1.88/2.00 tff(13469,plain,
% 1.88/2.00 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13468])).
% 1.88/2.00 tff(13470,plain,
% 1.88/2.00 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13469, 660])).
% 1.88/2.00 tff(13471,plain,
% 1.88/2.00 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13470])).
% 1.88/2.00 tff(13472,plain,
% 1.88/2.00 (~(op(e2, e0) = e3)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[756, 13471])).
% 1.88/2.00 tff(13473,plain,
% 1.88/2.00 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.00 tff(13474,plain,
% 1.88/2.00 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13473])).
% 1.88/2.00 tff(13475,plain,
% 1.88/2.00 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13474])).
% 1.88/2.00 tff(13476,plain,
% 1.88/2.00 (~(op(e2, e3) = e3)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[303, 13475])).
% 1.88/2.00 tff(13477,plain,
% 1.88/2.00 (op(e0, e2) = op(e1, e3)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13464, 13457])).
% 1.88/2.00 tff(13478,plain,
% 1.88/2.00 ((op(e0, e2) = e2) <=> (op(e1, e3) = e2)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13477])).
% 1.88/2.00 tff(13479,plain,
% 1.88/2.00 ((op(e1, e3) = e2) <=> (op(e0, e2) = e2)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13478])).
% 1.88/2.00 tff(13480,plain,
% 1.88/2.00 ((~(op(e1, e3) = e2)) <=> (~(op(e0, e2) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13479])).
% 1.88/2.00 tff(13481,plain,
% 1.88/2.00 (~(op(e0, e2) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[10589, 13480])).
% 1.88/2.00 tff(13482,plain,
% 1.88/2.00 ((op(e0, e2) = e1) <=> (op(e1, e3) = e1)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13477])).
% 1.88/2.00 tff(13483,plain,
% 1.88/2.00 ((op(e1, e3) = e1) <=> (op(e0, e2) = e1)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13482])).
% 1.88/2.00 tff(13484,plain,
% 1.88/2.00 ((~(op(e1, e3) = e1)) <=> (~(op(e0, e2) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13483])).
% 1.88/2.00 tff(13485,plain,
% 1.88/2.00 (~(op(e0, e2) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[13455, 13484])).
% 1.88/2.00 tff(13486,plain,
% 1.88/2.00 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13464])).
% 1.88/2.00 tff(13487,plain,
% 1.88/2.00 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13486])).
% 1.88/2.00 tff(13488,plain,
% 1.88/2.00 (~(op(e0, e1) = e0)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[2102, 13487])).
% 1.88/2.00 tff(13489,plain,
% 1.88/2.00 ((op(e1, e1) = e0) <=> (op(e1, e1) = op(e1, e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13457])).
% 1.88/2.00 tff(13490,plain,
% 1.88/2.00 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13489])).
% 1.88/2.00 tff(13491,plain,
% 1.88/2.00 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13490])).
% 1.88/2.00 tff(13492,plain,
% 1.88/2.00 (~(op(e1, e1) = e0)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[619, 13491])).
% 1.88/2.00 tff(13493,plain,
% 1.88/2.00 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13468])).
% 1.88/2.00 tff(13494,plain,
% 1.88/2.00 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13493, 1314])).
% 1.88/2.00 tff(13495,plain,
% 1.88/2.00 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13494])).
% 1.88/2.00 tff(13496,plain,
% 1.88/2.00 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13495])).
% 1.88/2.00 tff(13497,plain,
% 1.88/2.00 (~(op(e1, e0) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1321, 13496])).
% 1.88/2.00 tff(13498,plain,
% 1.88/2.00 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[2684])).
% 1.88/2.00 tff(13499,plain,
% 1.88/2.00 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13498])).
% 1.88/2.00 tff(13500,plain,
% 1.88/2.00 (~(op(e2, e2) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[515, 13499])).
% 1.88/2.00 tff(13501,plain,
% 1.88/2.00 (op(e1, e2) = e2),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[2285, 68, 10589, 6687])).
% 1.88/2.00 tff(13502,plain,
% 1.88/2.00 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13501])).
% 1.88/2.00 tff(13503,plain,
% 1.88/2.00 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13502, 81])).
% 1.88/2.00 tff(13504,plain,
% 1.88/2.00 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13503])).
% 1.88/2.00 tff(13505,plain,
% 1.88/2.00 (~(op(e2, e2) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1273, 13504])).
% 1.88/2.00 tff(13506,plain,
% 1.88/2.00 (op(e2, e2) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[524, 13505, 17, 13500])).
% 1.88/2.00 tff(13507,plain,
% 1.88/2.00 (~(op(e2, e1) = e0)),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[6638, 13506, 2684])).
% 1.88/2.00 tff(13508,plain,
% 1.88/2.00 (op(e3, e1) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[292, 13507, 84, 3849])).
% 1.88/2.00 tff(13509,plain,
% 1.88/2.00 (op(e3, e2) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[10084, 13508, 2812])).
% 1.88/2.00 tff(13510,plain,
% 1.88/2.00 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[11306])).
% 1.88/2.00 tff(13511,plain,
% 1.88/2.00 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13510, 5522])).
% 1.88/2.00 tff(13512,plain,
% 1.88/2.00 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13511])).
% 1.88/2.00 tff(13513,plain,
% 1.88/2.00 (~(op(e1, e2) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1604, 13512])).
% 1.88/2.00 tff(13514,plain,
% 1.88/2.00 (op(e3, e2) = e1),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1613, 13513, 13500, 4484])).
% 1.88/2.00 tff(13515,plain,
% 1.88/2.00 (e1 = op(e3, e2)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13514])).
% 1.88/2.00 tff(13516,plain,
% 1.88/2.00 (e1 = e3),
% 1.88/2.00 inference(transitivity,[status(thm)],[13515, 13509])).
% 1.88/2.00 tff(13517,plain,
% 1.88/2.00 ($false),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[303, 13516])).
% 1.88/2.00 tff(13518,plain,((op(e1, e1) = e2) | (~(op(e3, e3) = e2)) | (op(e1, e1) = e0) | (op(e0, e1) = e0) | (~(op(e2, e3) = e1)) | (op(e2, e2) = e0) | (op(e0, e2) = e1) | (op(e1, e0) = e2) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.00 tff(13519,plain,
% 1.88/2.00 (op(e1, e1) = e2),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[13518, 13497, 13492, 13488, 13449, 17, 13485, 2812, 1291])).
% 1.88/2.00 tff(13520,plain,
% 1.88/2.00 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13519])).
% 1.88/2.00 tff(13521,plain,
% 1.88/2.00 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13520, 5762])).
% 1.88/2.00 tff(13522,plain,
% 1.88/2.00 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13521])).
% 1.88/2.00 tff(13523,plain,
% 1.88/2.00 (~(op(e1, e2) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1604, 13522])).
% 1.88/2.00 tff(13524,plain,
% 1.88/2.00 (op(e2, e2) = e2),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1151, 13523, 9699, 13481])).
% 1.88/2.00 tff(13525,plain,
% 1.88/2.00 ((op(e2, e2) = e3) <=> (e2 = e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13524])).
% 1.88/2.00 tff(13526,plain,
% 1.88/2.00 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13525])).
% 1.88/2.00 tff(13527,plain,
% 1.88/2.00 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13526])).
% 1.88/2.00 tff(13528,plain,
% 1.88/2.00 (~(op(e2, e2) = e3)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[1321, 13527])).
% 1.88/2.00 tff(13529,plain,
% 1.88/2.00 (op(e2, e1) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1559, 13528, 13476, 13472])).
% 1.88/2.00 tff(13530,plain,
% 1.88/2.00 (op(e2, op(e2, e1)) = op(e2, e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13529])).
% 1.88/2.00 tff(13531,plain,
% 1.88/2.00 (op(e2, op(e2, e1)) = e1),
% 1.88/2.00 inference(transitivity,[status(thm)],[13530, 13449])).
% 1.88/2.00 tff(13532,plain,
% 1.88/2.00 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1355, 13531])).
% 1.88/2.00 tff(13533,plain,
% 1.88/2.00 (op(e0, e3) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[480, 1080, 11641, 13476])).
% 1.88/2.00 tff(13534,plain,
% 1.88/2.00 (op(e1, e2) = e1),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[9680, 13519, 75, 2812, 13533, 10592, 1080])).
% 1.88/2.00 tff(13535,plain,
% 1.88/2.00 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13534])).
% 1.88/2.00 tff(13536,plain,
% 1.88/2.00 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13535, 7171])).
% 1.88/2.00 tff(13537,plain,
% 1.88/2.00 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13536])).
% 1.88/2.00 tff(13538,plain,
% 1.88/2.00 (~(op(e3, e2) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[2292, 13537])).
% 1.88/2.00 tff(13539,plain,
% 1.88/2.00 (op(e3, e2) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1898, 13538, 85, 9699])).
% 1.88/2.00 tff(13540,plain,
% 1.88/2.00 (op(op(e3, e2), e2) = e3),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[7919, 13539])).
% 1.88/2.00 tff(13541,plain,
% 1.88/2.00 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[1339, 13540])).
% 1.88/2.00 tff(13542,plain,
% 1.88/2.00 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.00 tff(13543,plain,
% 1.88/2.00 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13542])).
% 1.88/2.00 tff(13544,plain,
% 1.88/2.00 (~(op(e2, e0) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[989, 13543])).
% 1.88/2.00 tff(13545,plain,
% 1.88/2.00 (op(e2, op(e1, e3)) = op(e2, e0)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.00 tff(13546,plain,
% 1.88/2.00 (op(e2, e0) = op(e2, op(e1, e3))),
% 1.88/2.00 inference(symmetry,[status(thm)],[13545])).
% 1.88/2.00 tff(13547,plain,
% 1.88/2.00 ((op(e2, e0) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13546])).
% 1.88/2.00 tff(13548,plain,
% 1.88/2.00 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e0) = e2)),
% 1.88/2.00 inference(symmetry,[status(thm)],[13547])).
% 1.88/2.00 tff(13549,plain,
% 1.88/2.00 ((e2 = op(e2, op(e1, e3))) <=> (op(e2, op(e1, e3)) = e2)),
% 1.88/2.00 inference(commutativity,[status(thm)],[])).
% 1.88/2.00 tff(13550,plain,
% 1.88/2.00 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13519])).
% 1.88/2.00 tff(13551,plain,
% 1.88/2.00 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13550])).
% 1.88/2.00 tff(13552,plain,
% 1.88/2.00 (~(op(e0, e1) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[792, 13551])).
% 1.88/2.00 tff(13553,plain,
% 1.88/2.00 (op(e0, e0) = e2),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[3652, 13552, 10592, 13481])).
% 1.88/2.00 tff(13554,plain,
% 1.88/2.00 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, op(e1, e3)))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13553, 13546])).
% 1.88/2.00 tff(13555,plain,
% 1.88/2.00 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, op(e1, e3)) = e2)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13554, 13549])).
% 1.88/2.00 tff(13556,plain,
% 1.88/2.00 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13555, 13548])).
% 1.88/2.00 tff(13557,plain,
% 1.88/2.00 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13556])).
% 1.88/2.00 tff(13558,plain,
% 1.88/2.00 (~(op(e2, e0) = e2)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[359, 13557])).
% 1.88/2.00 tff(13559,plain,
% 1.88/2.00 (op(e2, e0) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[765, 13558, 13544, 13472])).
% 1.88/2.00 tff(13560,plain,
% 1.88/2.00 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13533])).
% 1.88/2.00 tff(13561,plain,
% 1.88/2.00 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13560])).
% 1.88/2.00 tff(13562,plain,
% 1.88/2.00 (~(op(e0, e1) = e3)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[818, 13561])).
% 1.88/2.00 tff(13563,plain,
% 1.88/2.00 (op(e0, e1) = e1),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[829, 13552, 13562, 13488])).
% 1.88/2.00 tff(13564,plain,
% 1.88/2.00 ((op(e0, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13563])).
% 1.88/2.00 tff(13565,plain,
% 1.88/2.00 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.88/2.00 inference(transitivity,[status(thm)],[13564, 7793])).
% 1.88/2.00 tff(13566,plain,
% 1.88/2.00 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13565])).
% 1.88/2.00 tff(13567,plain,
% 1.88/2.00 (~(op(e3, e1) = e1)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[3046, 13566])).
% 1.88/2.00 tff(13568,plain,
% 1.88/2.00 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13539])).
% 1.88/2.00 tff(13569,plain,
% 1.88/2.00 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 1.88/2.00 inference(monotonicity,[status(thm)],[13568])).
% 1.88/2.00 tff(13570,plain,
% 1.88/2.00 (~(op(e3, e1) = e3)),
% 1.88/2.00 inference(modus_ponens,[status(thm)],[3429, 13569])).
% 1.88/2.00 tff(13571,plain,
% 1.88/2.00 (op(e3, e1) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[446, 13570, 13567, 9684])).
% 1.88/2.00 tff(13572,plain,
% 1.88/2.00 (op(e2, op(e2, e0)) = e0),
% 1.88/2.00 inference(unit_resolution,[status(thm)],[4926, 13571, 13456, 13559])).
% 1.88/2.01 tff(13573,plain,
% 1.88/2.01 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2653, 13572])).
% 1.88/2.01 tff(13574,plain,
% 1.88/2.01 (op(op(e1, e3), e1) = op(e0, e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.01 tff(13575,plain,
% 1.88/2.01 (op(e0, op(e0, e1)) = op(op(e1, e3), e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13457, 13563])).
% 1.88/2.01 tff(13576,plain,
% 1.88/2.01 (op(e0, op(e0, e1)) = e1),
% 1.88/2.01 inference(transitivity,[status(thm)],[13575, 13574, 13563])).
% 1.88/2.01 tff(13577,plain,
% 1.88/2.01 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2449, 13576])).
% 1.88/2.01 tff(13578,plain,
% 1.88/2.01 (op(e1, op(e1, e0)) = op(e1, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13468])).
% 1.88/2.01 tff(13579,plain,
% 1.88/2.01 (op(e1, op(e1, e0)) = e0),
% 1.88/2.01 inference(transitivity,[status(thm)],[13578, 13456])).
% 1.88/2.01 tff(13580,plain,
% 1.88/2.01 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1836, 13579])).
% 1.88/2.01 tff(13581,plain,
% 1.88/2.01 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[5468, 13452, 10592])).
% 1.88/2.01 tff(13582,plain,
% 1.88/2.01 (op(e1, op(e1, e2)) = op(e1, e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13534])).
% 1.88/2.01 tff(13583,plain,
% 1.88/2.01 (op(e1, op(e1, e2)) = e2),
% 1.88/2.01 inference(transitivity,[status(thm)],[13582, 13519])).
% 1.88/2.01 tff(13584,plain,
% 1.88/2.01 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2377, 13583])).
% 1.88/2.01 tff(13585,plain,
% 1.88/2.01 (op(op(e2, e3), e2) = op(e1, e2)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.01 tff(13586,plain,
% 1.88/2.01 ((op(op(e2, e3), e2) = e3) <=> (op(e1, e2) = e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13585])).
% 1.88/2.01 tff(13587,plain,
% 1.88/2.01 ((op(e1, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13586])).
% 1.88/2.01 tff(13588,plain,
% 1.88/2.01 ((~(op(e1, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13587])).
% 1.88/2.01 tff(13589,plain,
% 1.88/2.01 (~(op(op(e2, e3), e2) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[75, 13588])).
% 1.88/2.01 tff(13590,plain,
% 1.88/2.01 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1934, 13589])).
% 1.88/2.01 tff(13591,plain,
% 1.88/2.01 (op(e3, e0) = e1),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[939, 13567, 9667, 13538])).
% 1.88/2.01 tff(13592,plain,
% 1.88/2.01 (op(e3, op(e3, e0)) = op(e3, e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13591])).
% 1.88/2.01 tff(13593,plain,
% 1.88/2.01 (op(e3, op(e3, e0)) = e0),
% 1.88/2.01 inference(transitivity,[status(thm)],[13592, 13571])).
% 1.88/2.01 tff(13594,plain,
% 1.88/2.01 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1345, 13593])).
% 1.88/2.01 tff(13595,plain,
% 1.88/2.01 (op(e3, op(e1, e3)) = op(e3, e0)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.01 tff(13596,plain,
% 1.88/2.01 (op(e3, e1) = op(e1, e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13571, 13457])).
% 1.88/2.01 tff(13597,plain,
% 1.88/2.01 (op(e3, op(e3, e1)) = op(e3, op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13596])).
% 1.88/2.01 tff(13598,plain,
% 1.88/2.01 (op(e3, op(e3, e1)) = e1),
% 1.88/2.01 inference(transitivity,[status(thm)],[13597, 13595, 13591])).
% 1.88/2.01 tff(13599,plain,
% 1.88/2.01 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2594, 13598])).
% 1.88/2.01 tff(13600,plain,
% 1.88/2.01 ($false),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1459, 13599, 13594, 13590, 13584, 13581, 1304, 13580, 13577, 13573, 13541, 13532, 13467])).
% 1.88/2.01 tff(13601,plain,((op(e1, e1) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e3, e2) = e0) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (op(e1, e3) = e3) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.01 tff(13602,plain,
% 1.88/2.01 (op(e1, e1) = e3),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[13601, 85, 1304, 75, 2812, 1080, 17])).
% 1.88/2.01 tff(13603,plain,
% 1.88/2.01 ((op(e1, e1) = e2) <=> (e3 = e2)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13602])).
% 1.88/2.01 tff(13604,plain,
% 1.88/2.01 ((op(e1, e1) = e2) <=> (e2 = e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13603, 1314])).
% 1.88/2.01 tff(13605,plain,
% 1.88/2.01 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13604])).
% 1.88/2.01 tff(13606,plain,
% 1.88/2.01 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13605])).
% 1.88/2.01 tff(13607,plain,
% 1.88/2.01 (~(op(e1, e1) = e2)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[1321, 13606])).
% 1.88/2.01 tff(13608,plain,
% 1.88/2.01 (op(e1, op(e1, e3)) = op(e1, e0)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.01 tff(13609,plain,
% 1.88/2.01 (op(e1, op(e1, e1)) = op(e1, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13602])).
% 1.88/2.01 tff(13610,plain,
% 1.88/2.01 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13609])).
% 1.88/2.01 tff(13611,plain,
% 1.88/2.01 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13610, 13608])).
% 1.88/2.01 tff(13612,plain,
% 1.88/2.01 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13611])).
% 1.88/2.01 tff(13613,plain,
% 1.88/2.01 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13612, 2154])).
% 1.88/2.01 tff(13614,plain,
% 1.88/2.01 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13613])).
% 1.88/2.01 tff(13615,plain,
% 1.88/2.01 (e3 = op(e1, e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13602, 1740])).
% 1.88/2.01 tff(13616,plain,
% 1.88/2.01 (op(e1, e3) = op(e1, op(e1, e1))),
% 1.88/2.01 inference(symmetry,[status(thm)],[13609])).
% 1.88/2.01 tff(13617,plain,
% 1.88/2.01 (e0 = op(e1, op(e1, e1))),
% 1.88/2.01 inference(transitivity,[status(thm)],[13457, 13616])).
% 1.88/2.01 tff(13618,plain,
% 1.88/2.01 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[3009, 13617, 13615])).
% 1.88/2.01 tff(13619,plain,
% 1.88/2.01 (~(op(e1, e0) = e2)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13618, 13614])).
% 1.88/2.01 tff(13620,plain,
% 1.88/2.01 (op(e1, e2) = e2),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2285, 13619, 10589, 13607])).
% 1.88/2.01 tff(13621,plain,
% 1.88/2.01 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.01 tff(13622,plain,
% 1.88/2.01 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13621])).
% 1.88/2.01 tff(13623,plain,
% 1.88/2.01 (~(op(e2, e2) = e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[515, 13622])).
% 1.88/2.01 tff(13624,plain,
% 1.88/2.01 (e3 = op(e0, e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13533])).
% 1.88/2.01 tff(13625,plain,
% 1.88/2.01 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13624])).
% 1.88/2.01 tff(13626,plain,
% 1.88/2.01 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13625])).
% 1.88/2.01 tff(13627,plain,
% 1.88/2.01 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13626])).
% 1.88/2.01 tff(13628,plain,
% 1.88/2.01 (op(op(e1, e3), e3) = op(e0, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.01 tff(13629,plain,
% 1.88/2.01 (op(e0, op(e0, e3)) = op(op(e1, e3), e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13457, 13533])).
% 1.88/2.01 tff(13630,plain,
% 1.88/2.01 (op(e0, op(e0, e3)) = e3),
% 1.88/2.01 inference(transitivity,[status(thm)],[13629, 13628, 13533])).
% 1.88/2.01 tff(13631,plain,
% 1.88/2.01 ((op(e0, op(e0, e3)) = e0) <=> (e3 = op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13630, 13457])).
% 1.88/2.01 tff(13632,plain,
% 1.88/2.01 ((op(e0, op(e0, e3)) = e0) <=> (op(e1, e3) = e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13631, 3230])).
% 1.88/2.01 tff(13633,plain,
% 1.88/2.01 ((op(e1, e3) = e3) <=> (op(e0, op(e0, e3)) = e0)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13632])).
% 1.88/2.01 tff(13634,plain,
% 1.88/2.01 ((~(op(e1, e3) = e3)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13633])).
% 1.88/2.01 tff(13635,plain,
% 1.88/2.01 (~(op(e0, op(e0, e3)) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[1080, 13634])).
% 1.88/2.01 tff(13636,plain,
% 1.88/2.01 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.01 tff(13637,plain,
% 1.88/2.01 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13636, 18])).
% 1.88/2.01 tff(13638,plain,
% 1.88/2.01 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13637])).
% 1.88/2.01 tff(13639,plain,
% 1.88/2.01 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13638])).
% 1.88/2.01 tff(13640,plain,
% 1.88/2.01 (~(op(e2, e3) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[26, 13639])).
% 1.88/2.01 tff(13641,plain,
% 1.88/2.01 (~(op(op(e1, e3), e1) = e3)),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1107, 1080, 13476, 13640, 11818, 9667, 11641, 13452])).
% 1.88/2.01 tff(13642,plain,
% 1.88/2.01 (op(e1, op(e0, e3)) = op(e1, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13533])).
% 1.88/2.01 tff(13643,plain,
% 1.88/2.01 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13642])).
% 1.88/2.01 tff(13644,plain,
% 1.88/2.01 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13643])).
% 1.88/2.01 tff(13645,plain,
% 1.88/2.01 ((~(op(e1, e3) = e1)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13644])).
% 1.88/2.01 tff(13646,plain,
% 1.88/2.01 (~(op(e1, op(e0, e3)) = e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13455, 13645])).
% 1.88/2.01 tff(13647,plain,
% 1.88/2.01 (op(e3, op(e0, e3)) = op(e3, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13533])).
% 1.88/2.01 tff(13648,plain,
% 1.88/2.01 (op(e3, op(e0, e3)) = e2),
% 1.88/2.01 inference(transitivity,[status(thm)],[13647, 2812])).
% 1.88/2.01 tff(13649,plain,
% 1.88/2.01 ((op(e3, op(e0, e3)) = e3) <=> (e2 = e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13648])).
% 1.88/2.01 tff(13650,plain,
% 1.88/2.01 ((e2 = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13649])).
% 1.88/2.01 tff(13651,plain,
% 1.88/2.01 ((~(e2 = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13650])).
% 1.88/2.01 tff(13652,plain,
% 1.88/2.01 (~(op(e3, op(e0, e3)) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[1321, 13651])).
% 1.88/2.01 tff(13653,plain,
% 1.88/2.01 (op(e2, op(e0, e3)) = op(e2, e3)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13533])).
% 1.88/2.01 tff(13654,plain,
% 1.88/2.01 (op(e2, op(e0, e3)) = e1),
% 1.88/2.01 inference(transitivity,[status(thm)],[13653, 13449])).
% 1.88/2.01 tff(13655,plain,
% 1.88/2.01 ((op(e2, op(e0, e3)) = e2) <=> (e1 = e2)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13654])).
% 1.88/2.01 tff(13656,plain,
% 1.88/2.01 ((e1 = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13655])).
% 1.88/2.01 tff(13657,plain,
% 1.88/2.01 ((~(e1 = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13656])).
% 1.88/2.01 tff(13658,plain,
% 1.88/2.01 (~(op(e2, op(e0, e3)) = e2)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[708, 13657])).
% 1.88/2.01 tff(13659,plain,
% 1.88/2.01 (~(op(e3, e0) = op(e0, e3))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[3220, 13658, 13452, 13652, 13646, 13641, 13635])).
% 1.88/2.01 tff(13660,plain,
% 1.88/2.01 (~(op(e3, e0) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13659, 13627])).
% 1.88/2.01 tff(13661,plain,
% 1.88/2.01 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13602])).
% 1.88/2.01 tff(13662,plain,
% 1.88/2.01 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13661, 396])).
% 1.88/2.01 tff(13663,plain,
% 1.88/2.01 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13662])).
% 1.88/2.01 tff(13664,plain,
% 1.88/2.01 (~(op(e3, e1) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[945, 13663])).
% 1.88/2.01 tff(13665,plain,
% 1.88/2.01 (op(e3, e2) = e3),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[422, 13664, 11641, 13660])).
% 1.88/2.01 tff(13666,plain,
% 1.88/2.01 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13665])).
% 1.88/2.01 tff(13667,plain,
% 1.88/2.01 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13666, 128])).
% 1.88/2.01 tff(13668,plain,
% 1.88/2.01 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13667])).
% 1.88/2.01 tff(13669,plain,
% 1.88/2.01 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13668])).
% 1.88/2.01 tff(13670,plain,
% 1.88/2.01 (~(op(e3, e2) = e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[303, 13669])).
% 1.88/2.01 tff(13671,plain,
% 1.88/2.01 (op(e1, e2) = e1),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[1613, 13670, 13623, 13485])).
% 1.88/2.01 tff(13672,plain,
% 1.88/2.01 (e1 = op(e1, e2)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13671])).
% 1.88/2.01 tff(13673,plain,
% 1.88/2.01 (e1 = e2),
% 1.88/2.01 inference(transitivity,[status(thm)],[13672, 13620])).
% 1.88/2.01 tff(13674,plain,
% 1.88/2.01 ($false),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[708, 13673])).
% 1.88/2.01 tff(13675,plain,((op(e3, e2) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2)) | (op(e1, e3) = e3) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.01 tff(13676,plain,
% 1.88/2.01 (op(e3, e2) = e0),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[13675, 1080, 75, 2812, 1304, 17])).
% 1.88/2.01 tff(13677,plain,
% 1.88/2.01 (op(e3, e2) = op(e1, e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13676, 13457])).
% 1.88/2.01 tff(13678,plain,
% 1.88/2.01 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13677])).
% 1.88/2.01 tff(13679,plain,
% 1.88/2.01 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.88/2.01 inference(transitivity,[status(thm)],[6490, 13678, 13459])).
% 1.88/2.01 tff(13680,plain,
% 1.88/2.01 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13679])).
% 1.88/2.01 tff(13681,plain,
% 1.88/2.01 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13680, 6411])).
% 1.88/2.01 tff(13682,plain,
% 1.88/2.01 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13681])).
% 1.88/2.01 tff(13683,plain,
% 1.88/2.01 (e0 = op(e3, op(e3, e3))),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13676, 6497])).
% 1.88/2.01 tff(13684,plain,
% 1.88/2.01 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[5879, 13683, 2813])).
% 1.88/2.01 tff(13685,plain,
% 1.88/2.01 (~(op(e3, e0) = e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[13684, 13682])).
% 1.88/2.01 tff(13686,plain,
% 1.88/2.01 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e0)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13676])).
% 1.88/2.01 tff(13687,plain,
% 1.88/2.01 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13686])).
% 1.88/2.01 tff(13688,plain,
% 1.88/2.01 (~(op(e3, e0) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[1133, 13687])).
% 1.88/2.01 tff(13689,plain,
% 1.88/2.01 (op(e3, e0) = e1),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[5422, 13688, 13660, 9955])).
% 1.88/2.01 tff(13690,plain,
% 1.88/2.01 ($false),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[13689, 13685])).
% 1.88/2.01 tff(13691,plain,((op(e1, e3) = e3) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.01 tff(13692,plain,
% 1.88/2.01 (op(e1, e3) = e3),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[13691, 17, 75, 1304, 2812])).
% 1.88/2.01 tff(13693,plain,
% 1.88/2.01 (e3 = op(e1, e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13692])).
% 1.88/2.01 tff(13694,plain,
% 1.88/2.01 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13693])).
% 1.88/2.01 tff(13695,plain,
% 1.88/2.01 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13694])).
% 1.88/2.01 tff(13696,plain,
% 1.88/2.01 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13695])).
% 1.88/2.01 tff(13697,plain,
% 1.88/2.01 (~(op(e0, e3) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[64, 13696])).
% 1.88/2.01 tff(13698,plain,
% 1.88/2.01 (op(e0, e3) = e0),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[687, 13697, 13452, 10592])).
% 1.88/2.01 tff(13699,plain,
% 1.88/2.01 (e0 = op(e0, e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13698])).
% 1.88/2.01 tff(13700,plain,
% 1.88/2.01 ((e0 = e3) <=> (e0 = op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13693])).
% 1.88/2.01 tff(13701,plain,
% 1.88/2.01 ((e0 = e3) <=> (op(e1, e3) = e0)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13700, 6095])).
% 1.88/2.01 tff(13702,plain,
% 1.88/2.01 ((~(e0 = e3)) <=> (~(op(e1, e3) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13701])).
% 1.88/2.01 tff(13703,plain,
% 1.88/2.01 (~(op(e1, e3) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[181, 13702])).
% 1.88/2.01 tff(13704,plain,
% 1.88/2.01 (~(op(e2, e1) = e0)),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[7365, 13703, 10592, 9696, 13452])).
% 1.88/2.01 tff(13705,plain,
% 1.88/2.01 (op(e2, e0) = e0),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[2311, 13704, 13640, 17])).
% 1.88/2.01 tff(13706,plain,
% 1.88/2.01 (op(e2, e0) = op(e0, e3)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13705, 13699])).
% 1.88/2.01 tff(13707,plain,
% 1.88/2.01 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13706])).
% 1.88/2.01 tff(13708,plain,
% 1.88/2.01 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 1.88/2.01 inference(transitivity,[status(thm)],[13707, 7797])).
% 1.88/2.01 tff(13709,plain,
% 1.88/2.01 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 1.88/2.01 inference(symmetry,[status(thm)],[13708])).
% 1.88/2.01 tff(13710,plain,
% 1.88/2.01 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 1.88/2.01 inference(transitivity,[status(thm)],[13709, 6337])).
% 1.88/2.01 tff(13711,plain,
% 1.88/2.01 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13710])).
% 1.88/2.01 tff(13712,plain,
% 1.88/2.01 (~(op(e0, e2) = op(e2, e0))),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[918, 13711])).
% 1.88/2.01 tff(13713,plain,
% 1.88/2.01 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[6347, 13712])).
% 1.88/2.01 tff(13714,plain,
% 1.88/2.01 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.01 tff(13715,plain,
% 1.88/2.01 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.88/2.01 inference(symmetry,[status(thm)],[13714])).
% 1.88/2.01 tff(13716,plain,
% 1.88/2.01 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[2684])).
% 1.88/2.01 tff(13717,plain,
% 1.88/2.01 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13716])).
% 1.88/2.01 tff(13718,plain,
% 1.88/2.01 (~(op(e0, e3) = e1)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[964, 13717])).
% 1.88/2.01 tff(13719,plain,
% 1.88/2.01 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[11135])).
% 1.88/2.01 tff(13720,plain,
% 1.88/2.01 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13719])).
% 1.88/2.01 tff(13721,plain,
% 1.88/2.01 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13720])).
% 1.88/2.01 tff(13722,plain,
% 1.88/2.01 (~(op(e0, e3) = e3)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[64, 13721])).
% 1.88/2.01 tff(13723,plain,
% 1.88/2.01 (op(e0, e3) = e0),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[687, 13722, 13718, 10592])).
% 1.88/2.01 tff(13724,plain,
% 1.88/2.01 (e0 = op(e0, e3)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13723])).
% 1.88/2.01 tff(13725,plain,
% 1.88/2.01 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e0, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13724])).
% 1.88/2.01 tff(13726,plain,
% 1.88/2.01 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13725])).
% 1.88/2.01 tff(13727,plain,
% 1.88/2.01 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13726])).
% 1.88/2.01 tff(13728,plain,
% 1.88/2.01 (~(op(e0, e2) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[918, 13727])).
% 1.88/2.01 tff(13729,plain,
% 1.88/2.01 (op(e1, e2) = e0),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[973, 85, 17, 13728])).
% 1.88/2.01 tff(13730,plain,
% 1.88/2.01 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13724])).
% 1.88/2.01 tff(13731,plain,
% 1.88/2.01 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13730])).
% 1.88/2.01 tff(13732,plain,
% 1.88/2.01 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 1.88/2.01 inference(monotonicity,[status(thm)],[2684])).
% 1.88/2.01 tff(13733,plain,
% 1.88/2.01 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13732, 18])).
% 1.88/2.01 tff(13734,plain,
% 1.88/2.01 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 1.88/2.01 inference(symmetry,[status(thm)],[13733])).
% 1.88/2.01 tff(13735,plain,
% 1.88/2.01 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13734])).
% 1.88/2.01 tff(13736,plain,
% 1.88/2.01 (~(op(e2, e3) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[26, 13735])).
% 1.88/2.01 tff(13737,plain,
% 1.88/2.01 ((e0 = e3) <=> (e0 = op(e1, e3))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[11135])).
% 1.88/2.01 tff(13738,plain,
% 1.88/2.01 ((e0 = e3) <=> (op(e1, e3) = e0)),
% 1.88/2.01 inference(transitivity,[status(thm)],[13737, 6095])).
% 1.88/2.01 tff(13739,plain,
% 1.88/2.01 ((~(e0 = e3)) <=> (~(op(e1, e3) = e0))),
% 1.88/2.01 inference(monotonicity,[status(thm)],[13738])).
% 1.88/2.01 tff(13740,plain,
% 1.88/2.01 (~(op(e1, e3) = e0)),
% 1.88/2.01 inference(modus_ponens,[status(thm)],[181, 13739])).
% 1.88/2.01 tff(13741,plain,
% 1.88/2.01 (~(op(e2, e1) = e0)),
% 1.88/2.01 inference(unit_resolution,[status(thm)],[7365, 13740, 10592, 9696, 13718])).
% 1.88/2.01 tff(13742,plain,
% 1.88/2.01 (op(e2, e0) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[2311, 13741, 13736, 17])).
% 1.88/2.02 tff(13743,plain,
% 1.88/2.02 (op(e2, e0) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13742, 13724])).
% 1.88/2.02 tff(13744,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13743])).
% 1.88/2.02 tff(13745,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.02 inference(transitivity,[status(thm)],[13744, 452])).
% 1.88/2.02 tff(13746,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13745, 13731])).
% 1.88/2.02 tff(13747,plain,
% 1.88/2.02 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13746])).
% 1.88/2.02 tff(13748,plain,
% 1.88/2.02 (~(op(e3, e0) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[747, 13747])).
% 1.88/2.02 tff(13749,plain,
% 1.88/2.02 (op(e3, e1) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1916, 85, 9696, 13748])).
% 1.88/2.02 tff(13750,plain,
% 1.88/2.02 (op(e3, e2) = e3),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[10084, 13749, 2812])).
% 1.88/2.02 tff(13751,plain,
% 1.88/2.02 (op(e3, e2) = op(e1, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13750, 11135])).
% 1.88/2.02 tff(13752,plain,
% 1.88/2.02 ((op(e3, e2) = e1) <=> (op(e1, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13751])).
% 1.88/2.02 tff(13753,plain,
% 1.88/2.02 ((op(e1, e3) = e1) <=> (op(e3, e2) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13752])).
% 1.88/2.02 tff(13754,plain,
% 1.88/2.02 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13753])).
% 1.88/2.02 tff(13755,plain,
% 1.88/2.02 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[2684])).
% 1.88/2.02 tff(13756,plain,
% 1.88/2.02 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13755])).
% 1.88/2.02 tff(13757,plain,
% 1.88/2.02 (~(op(e1, e3) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[118, 13756])).
% 1.88/2.02 tff(13758,plain,
% 1.88/2.02 (~(op(e3, e2) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13757, 13754])).
% 1.88/2.02 tff(13759,plain,
% 1.88/2.02 (op(e1, e2) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13729, 13724])).
% 1.88/2.02 tff(13760,plain,
% 1.88/2.02 ((op(e1, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13759])).
% 1.88/2.02 tff(13761,plain,
% 1.88/2.02 ((op(e0, e3) = e1) <=> (op(e1, e2) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13760])).
% 1.88/2.02 tff(13762,plain,
% 1.88/2.02 ((~(op(e0, e3) = e1)) <=> (~(op(e1, e2) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13761])).
% 1.88/2.02 tff(13763,plain,
% 1.88/2.02 (~(op(e1, e2) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13718, 13762])).
% 1.88/2.02 tff(13764,plain,
% 1.88/2.02 (op(e0, e2) = e1),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1613, 13763, 13500, 13758])).
% 1.88/2.02 tff(13765,plain,
% 1.88/2.02 (op(op(e0, e2), e2) = op(e1, e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13764])).
% 1.88/2.02 tff(13766,plain,
% 1.88/2.02 (op(op(e0, e2), e2) = e0),
% 1.88/2.02 inference(transitivity,[status(thm)],[13765, 13729])).
% 1.88/2.02 tff(13767,plain,
% 1.88/2.02 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1956, 13766])).
% 1.88/2.02 tff(13768,plain,
% 1.88/2.02 ((op(e2, e0) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13743, 11135])).
% 1.88/2.02 tff(13769,plain,
% 1.88/2.02 ((op(e0, e3) = op(e1, e3)) <=> (op(e2, e0) = e3)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13768])).
% 1.88/2.02 tff(13770,plain,
% 1.88/2.02 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e2, e0) = e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13769])).
% 1.88/2.02 tff(13771,plain,
% 1.88/2.02 (~(op(e2, e0) = e3)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[64, 13770])).
% 1.88/2.02 tff(13772,plain,
% 1.88/2.02 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[2684])).
% 1.88/2.02 tff(13773,plain,
% 1.88/2.02 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13772])).
% 1.88/2.02 tff(13774,plain,
% 1.88/2.02 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13773])).
% 1.88/2.02 tff(13775,plain,
% 1.88/2.02 (~(op(e2, e3) = e3)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[303, 13774])).
% 1.88/2.02 tff(13776,plain,
% 1.88/2.02 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13750])).
% 1.88/2.02 tff(13777,plain,
% 1.88/2.02 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13776])).
% 1.88/2.02 tff(13778,plain,
% 1.88/2.02 (~(op(e2, e2) = e3)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[1546, 13777])).
% 1.88/2.02 tff(13779,plain,
% 1.88/2.02 (op(e2, e1) = e3),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1559, 13778, 13775, 13771])).
% 1.88/2.02 tff(13780,plain,
% 1.88/2.02 (op(e2, e1) = op(e1, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13779, 11135])).
% 1.88/2.02 tff(13781,plain,
% 1.88/2.02 (op(e2, op(e2, e1)) = op(e2, op(e1, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13780])).
% 1.88/2.02 tff(13782,plain,
% 1.88/2.02 (op(e2, op(e2, e1)) = e1),
% 1.88/2.02 inference(transitivity,[status(thm)],[13781, 11227, 2684])).
% 1.88/2.02 tff(13783,plain,
% 1.88/2.02 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1355, 13782])).
% 1.88/2.02 tff(13784,plain,
% 1.88/2.02 (op(op(e3, e2), e2) = e3),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[7919, 13750])).
% 1.88/2.02 tff(13785,plain,
% 1.88/2.02 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1339, 13784])).
% 1.88/2.02 tff(13786,plain,
% 1.88/2.02 (op(e2, op(e0, e3)) = op(e2, e0)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13723])).
% 1.88/2.02 tff(13787,plain,
% 1.88/2.02 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13743])).
% 1.88/2.02 tff(13788,plain,
% 1.88/2.02 (op(e2, op(e2, e0)) = e0),
% 1.88/2.02 inference(transitivity,[status(thm)],[13787, 13786, 13742])).
% 1.88/2.02 tff(13789,plain,
% 1.88/2.02 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[2653, 13788])).
% 1.88/2.02 tff(13790,plain,
% 1.88/2.02 (op(e3, e1) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13749, 13724])).
% 1.88/2.02 tff(13791,plain,
% 1.88/2.02 ((op(e3, e1) = e1) <=> (op(e0, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13790])).
% 1.88/2.02 tff(13792,plain,
% 1.88/2.02 ((op(e0, e3) = e1) <=> (op(e3, e1) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13791])).
% 1.88/2.02 tff(13793,plain,
% 1.88/2.02 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e1) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13792])).
% 1.88/2.02 tff(13794,plain,
% 1.88/2.02 (~(op(e3, e1) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13718, 13793])).
% 1.88/2.02 tff(13795,plain,
% 1.88/2.02 (op(e3, e0) = e1),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[939, 13794, 9667, 13758])).
% 1.88/2.02 tff(13796,plain,
% 1.88/2.02 (op(e3, op(e3, e0)) = op(op(e1, e3), e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[11135, 13795])).
% 1.88/2.02 tff(13797,plain,
% 1.88/2.02 (op(e3, op(e3, e0)) = e0),
% 1.88/2.02 inference(transitivity,[status(thm)],[13796, 11165, 13749])).
% 1.88/2.02 tff(13798,plain,
% 1.88/2.02 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1345, 13797])).
% 1.88/2.02 tff(13799,plain,
% 1.88/2.02 (op(op(e1, e2), e2) = op(e0, e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13729])).
% 1.88/2.02 tff(13800,plain,
% 1.88/2.02 ((op(op(e1, e2), e2) = e1) <=> (op(e0, e2) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13799])).
% 1.88/2.02 tff(13801,plain,
% 1.88/2.02 ((op(e0, e2) = e1) <=> (op(op(e1, e2), e2) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13800])).
% 1.88/2.02 tff(13802,plain,
% 1.88/2.02 (op(op(e1, e2), e2) = e1),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13764, 13801])).
% 1.88/2.02 tff(13803,plain,
% 1.88/2.02 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1335, 13802])).
% 1.88/2.02 tff(13804,plain,
% 1.88/2.02 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[5468, 13718, 10592])).
% 1.88/2.02 tff(13805,plain,
% 1.88/2.02 (op(op(e0, e3), e3) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[5461, 13723])).
% 1.88/2.02 tff(13806,plain,
% 1.88/2.02 (op(op(e3, e1), e3) = op(op(e0, e3), e3)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13790])).
% 1.88/2.02 tff(13807,plain,
% 1.88/2.02 (op(op(e3, e1), e3) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13806, 13805, 13724])).
% 1.88/2.02 tff(13808,plain,
% 1.88/2.02 ((op(op(e3, e1), e3) = e1) <=> (op(e0, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13807])).
% 1.88/2.02 tff(13809,plain,
% 1.88/2.02 ((op(e0, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13808])).
% 1.88/2.02 tff(13810,plain,
% 1.88/2.02 ((~(op(e0, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13809])).
% 1.88/2.02 tff(13811,plain,
% 1.88/2.02 (~(op(op(e3, e1), e3) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13718, 13810])).
% 1.88/2.02 tff(13812,plain,
% 1.88/2.02 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1050, 13811])).
% 1.88/2.02 tff(13813,plain,
% 1.88/2.02 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13724])).
% 1.88/2.02 tff(13814,plain,
% 1.88/2.02 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13813])).
% 1.88/2.02 tff(13815,plain,
% 1.88/2.02 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13814])).
% 1.88/2.02 tff(13816,plain,
% 1.88/2.02 (~(op(e0, e1) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[818, 13815])).
% 1.88/2.02 tff(13817,plain,
% 1.88/2.02 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13779])).
% 1.88/2.02 tff(13818,plain,
% 1.88/2.02 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13817])).
% 1.88/2.02 tff(13819,plain,
% 1.88/2.02 (~(op(e0, e1) = e3)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[606, 13818])).
% 1.88/2.02 tff(13820,plain,
% 1.88/2.02 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13764])).
% 1.88/2.02 tff(13821,plain,
% 1.88/2.02 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13820])).
% 1.88/2.02 tff(13822,plain,
% 1.88/2.02 (~(op(e0, e1) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[2102, 13821])).
% 1.88/2.02 tff(13823,plain,
% 1.88/2.02 (op(e0, e1) = e2),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[829, 13822, 13819, 13816])).
% 1.88/2.02 tff(13824,plain,
% 1.88/2.02 (op(e0, op(e0, e1)) = op(e0, e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13823])).
% 1.88/2.02 tff(13825,plain,
% 1.88/2.02 (op(e0, op(e0, e1)) = e1),
% 1.88/2.02 inference(transitivity,[status(thm)],[13824, 13764])).
% 1.88/2.02 tff(13826,plain,
% 1.88/2.02 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[2449, 13825])).
% 1.88/2.02 tff(13827,plain,
% 1.88/2.02 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13742])).
% 1.88/2.02 tff(13828,plain,
% 1.88/2.02 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13827])).
% 1.88/2.02 tff(13829,plain,
% 1.88/2.02 (~(op(e1, e0) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[756, 13828])).
% 1.88/2.02 tff(13830,plain,
% 1.88/2.02 (op(e1, op(e0, e3)) = op(e1, e0)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13723])).
% 1.88/2.02 tff(13831,plain,
% 1.88/2.02 (op(e1, e0) = op(e1, op(e0, e3))),
% 1.88/2.02 inference(symmetry,[status(thm)],[13830])).
% 1.88/2.02 tff(13832,plain,
% 1.88/2.02 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13831])).
% 1.88/2.02 tff(13833,plain,
% 1.88/2.02 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13832])).
% 1.88/2.02 tff(13834,plain,
% 1.88/2.02 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, op(e0, e3)) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13831, 13795])).
% 1.88/2.02 tff(13835,plain,
% 1.88/2.02 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13834, 13833])).
% 1.88/2.02 tff(13836,plain,
% 1.88/2.02 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13835])).
% 1.88/2.02 tff(13837,plain,
% 1.88/2.02 (~(op(e1, e0) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[410, 13836])).
% 1.88/2.02 tff(13838,plain,
% 1.88/2.02 (op(e1, e0) = e2),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[728, 13837, 13829, 11813])).
% 1.88/2.02 tff(13839,plain,
% 1.88/2.02 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13838])).
% 1.88/2.02 tff(13840,plain,
% 1.88/2.02 (op(e1, op(e1, e0)) = e0),
% 1.88/2.02 inference(transitivity,[status(thm)],[13839, 13729])).
% 1.88/2.02 tff(13841,plain,
% 1.88/2.02 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1836, 13840])).
% 1.88/2.02 tff(13842,plain,
% 1.88/2.02 ($false),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1459, 13841, 13826, 1347, 13812, 13804, 1304, 13803, 13798, 13789, 13785, 13783, 13767])).
% 1.88/2.02 tff(13843,plain,((op(e3, e2) = e0) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e2, e3) = e1)) | (~(op(e1, e3) = e3)) | (~(op(e3, e3) = e2)) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.02 tff(13844,plain,
% 1.88/2.02 (op(e3, e2) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[13843, 13692, 1304, 13449, 13590, 2812, 17])).
% 1.88/2.02 tff(13845,plain,
% 1.88/2.02 (op(e3, e2) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13844, 13699])).
% 1.88/2.02 tff(13846,plain,
% 1.88/2.02 ((op(e3, e2) = e1) <=> (op(e0, e3) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13845])).
% 1.88/2.02 tff(13847,plain,
% 1.88/2.02 ((op(e0, e3) = e1) <=> (op(e3, e2) = e1)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13846])).
% 1.88/2.02 tff(13848,plain,
% 1.88/2.02 ((op(e0, e3) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 1.88/2.02 inference(transitivity,[status(thm)],[13847, 13715, 395])).
% 1.88/2.02 tff(13849,plain,
% 1.88/2.02 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13848])).
% 1.88/2.02 tff(13850,plain,
% 1.88/2.02 (~(op(e2, e3) = op(e3, e2))),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13452, 13849])).
% 1.88/2.02 tff(13851,plain,
% 1.88/2.02 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[430, 13850])).
% 1.88/2.02 tff(13852,plain,
% 1.88/2.02 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13709])).
% 1.88/2.02 tff(13853,plain,
% 1.88/2.02 (~(op(e2, e0) = op(e0, e2))),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[918, 13852])).
% 1.88/2.02 tff(13854,plain,
% 1.88/2.02 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[6358, 13853])).
% 1.88/2.02 tff(13855,plain,
% 1.88/2.02 (op(op(e0, e3), e3) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[5461, 13698])).
% 1.88/2.02 tff(13856,plain,
% 1.88/2.02 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13699])).
% 1.88/2.02 tff(13857,plain,
% 1.88/2.02 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13856])).
% 1.88/2.02 tff(13858,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13706])).
% 1.88/2.02 tff(13859,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.02 inference(transitivity,[status(thm)],[13858, 452])).
% 1.88/2.02 tff(13860,plain,
% 1.88/2.02 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13859, 13857])).
% 1.88/2.02 tff(13861,plain,
% 1.88/2.02 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13860])).
% 1.88/2.02 tff(13862,plain,
% 1.88/2.02 (~(op(e3, e0) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[747, 13861])).
% 1.88/2.02 tff(13863,plain,
% 1.88/2.02 (op(e3, e0) = op(e3, op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13699])).
% 1.88/2.02 tff(13864,plain,
% 1.88/2.02 (op(e3, op(e0, e3)) = op(e3, e0)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13863])).
% 1.88/2.02 tff(13865,plain,
% 1.88/2.02 (op(e3, op(e3, e2)) = op(e3, op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13845])).
% 1.88/2.02 tff(13866,plain,
% 1.88/2.02 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.88/2.02 inference(transitivity,[status(thm)],[6490, 13865, 13864])).
% 1.88/2.02 tff(13867,plain,
% 1.88/2.02 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13866])).
% 1.88/2.02 tff(13868,plain,
% 1.88/2.02 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13867, 6411])).
% 1.88/2.02 tff(13869,plain,
% 1.88/2.02 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13868])).
% 1.88/2.02 tff(13870,plain,
% 1.88/2.02 (e0 = op(e3, op(e3, e3))),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13844, 6497])).
% 1.88/2.02 tff(13871,plain,
% 1.88/2.02 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[5879, 13870, 2813])).
% 1.88/2.02 tff(13872,plain,
% 1.88/2.02 (~(op(e3, e0) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13871, 13869])).
% 1.88/2.02 tff(13873,plain,
% 1.88/2.02 (op(e3, e0) = e3),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[5422, 13872, 13862, 9955])).
% 1.88/2.02 tff(13874,plain,
% 1.88/2.02 (op(e0, op(e3, e0)) = op(op(e0, e3), e3)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13699, 13873])).
% 1.88/2.02 tff(13875,plain,
% 1.88/2.02 (e3 = op(e3, e0)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13873])).
% 1.88/2.02 tff(13876,plain,
% 1.88/2.02 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13705])).
% 1.88/2.02 tff(13877,plain,
% 1.88/2.02 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13876])).
% 1.88/2.02 tff(13878,plain,
% 1.88/2.02 (~(op(e1, e0) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[756, 13877])).
% 1.88/2.02 tff(13879,plain,
% 1.88/2.02 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13844])).
% 1.88/2.02 tff(13880,plain,
% 1.88/2.02 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13879])).
% 1.88/2.02 tff(13881,plain,
% 1.88/2.02 (~(op(e1, e2) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[2292, 13880])).
% 1.88/2.02 tff(13882,plain,
% 1.88/2.02 (op(e1, e1) = e0),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[1830, 13881, 13703, 13878])).
% 1.88/2.02 tff(13883,plain,
% 1.88/2.02 (op(e1, e1) = op(e0, e3)),
% 1.88/2.02 inference(transitivity,[status(thm)],[13882, 13699])).
% 1.88/2.02 tff(13884,plain,
% 1.88/2.02 ((op(e1, e1) = e2) <=> (op(e0, e3) = e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13883])).
% 1.88/2.02 tff(13885,plain,
% 1.88/2.02 ((op(e0, e3) = e2) <=> (op(e1, e1) = e2)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13884])).
% 1.88/2.02 tff(13886,plain,
% 1.88/2.02 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e1) = e2))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13885])).
% 1.88/2.02 tff(13887,plain,
% 1.88/2.02 (~(op(e1, e1) = e2)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[10592, 13886])).
% 1.88/2.02 tff(13888,plain,
% 1.88/2.02 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13847])).
% 1.88/2.02 tff(13889,plain,
% 1.88/2.02 (~(op(e3, e2) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13452, 13888])).
% 1.88/2.02 tff(13890,plain,
% 1.88/2.02 ((op(e0, e0) = e0) <=> (op(e0, e0) = op(e0, e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13699])).
% 1.88/2.02 tff(13891,plain,
% 1.88/2.02 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13890])).
% 1.88/2.02 tff(13892,plain,
% 1.88/2.02 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13891])).
% 1.88/2.02 tff(13893,plain,
% 1.88/2.02 (~(op(e0, e0) = e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[3414, 13892])).
% 1.88/2.02 tff(13894,plain,
% 1.88/2.02 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e3, e0))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[12887])).
% 1.88/2.02 tff(13895,plain,
% 1.88/2.02 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 1.88/2.02 inference(symmetry,[status(thm)],[13894])).
% 1.88/2.02 tff(13896,plain,
% 1.88/2.02 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13895])).
% 1.88/2.02 tff(13897,plain,
% 1.88/2.02 (~(op(e0, e0) = e3)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[6384, 13896])).
% 1.88/2.02 tff(13898,plain,
% 1.88/2.02 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[8026])).
% 1.88/2.02 tff(13899,plain,
% 1.88/2.02 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e1))),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13898])).
% 1.88/2.02 tff(13900,plain,
% 1.88/2.02 (~(op(e0, e0) = e1)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[3603, 13899])).
% 1.88/2.02 tff(13901,plain,
% 1.88/2.02 (op(e0, e0) = e2),
% 1.88/2.02 inference(unit_resolution,[status(thm)],[3612, 13900, 13897, 6213])).
% 1.88/2.02 tff(13902,plain,
% 1.88/2.02 (e2 = op(e0, e0)),
% 1.88/2.02 inference(modus_ponens,[status(thm)],[13901, 78])).
% 1.88/2.02 tff(13903,plain,
% 1.88/2.02 (op(e0, op(e0, e0)) = op(e0, e2)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13901])).
% 1.88/2.02 tff(13904,plain,
% 1.88/2.02 (op(e0, e2) = op(e0, op(e0, e0))),
% 1.88/2.02 inference(symmetry,[status(thm)],[13903])).
% 1.88/2.02 tff(13905,plain,
% 1.88/2.02 (e1 = op(e0, e2)),
% 1.88/2.02 inference(symmetry,[status(thm)],[8026])).
% 1.88/2.02 tff(13906,plain,
% 1.88/2.02 (e1 = op(e0, op(e0, e0))),
% 1.88/2.02 inference(transitivity,[status(thm)],[13905, 13904])).
% 1.88/2.02 tff(13907,plain,
% 1.88/2.02 (op(e0, op(e0, e0)) = e1),
% 1.88/2.02 inference(transitivity,[status(thm)],[13903, 8026])).
% 1.88/2.02 tff(13908,plain,
% 1.88/2.02 (op(e0, op(e0, op(e0, e0))) = op(e0, e1)),
% 1.88/2.02 inference(monotonicity,[status(thm)],[13907])).
% 1.88/2.02 tff(13909,plain,
% 1.88/2.02 (op(e0, e1) = op(e0, op(e0, op(e0, e0)))),
% 1.88/2.02 inference(symmetry,[status(thm)],[13908])).
% 1.88/2.02 tff(13910,plain,
% 1.88/2.03 ((op(e0, e2) = e3) <=> (e1 = op(e3, e0))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[8026, 12887])).
% 1.88/2.03 tff(13911,plain,
% 1.88/2.03 ((op(e0, e2) = e3) <=> (op(e3, e0) = e1)),
% 1.88/2.03 inference(transitivity,[status(thm)],[13910, 6411])).
% 1.88/2.03 tff(13912,plain,
% 1.88/2.03 ((op(e3, e0) = e1) <=> (op(e0, e2) = e3)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13911])).
% 1.88/2.03 tff(13913,plain,
% 1.88/2.03 ((~(op(e3, e0) = e1)) <=> (~(op(e0, e2) = e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13912])).
% 1.88/2.03 tff(13914,plain,
% 1.88/2.03 (~(op(e0, e2) = e3)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[931, 13913])).
% 1.88/2.03 tff(13915,plain,
% 1.88/2.03 (op(e0, e1) = e3),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1495, 13914, 661, 13897])).
% 1.88/2.03 tff(13916,plain,
% 1.88/2.03 (e3 = op(e0, e1)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13915])).
% 1.88/2.03 tff(13917,plain,
% 1.88/2.03 (e3 = op(e0, op(e0, op(e0, e0)))),
% 1.88/2.03 inference(transitivity,[status(thm)],[13916, 13909])).
% 1.88/2.03 tff(13918,plain,
% 1.88/2.03 ($false),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[842, 13917, 13906, 13902])).
% 1.88/2.03 tff(13919,plain,((~(op(e0, e2) = e1)) | (op(e0, e0) = e0) | (op(e0, e3) = e3) | (op(e3, e0) = e1) | (~(op(e3, e0) = e3))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.03 tff(13920,plain,
% 1.88/2.03 (~(op(e0, e2) = e1)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[13919, 13893, 13697, 13872, 13873])).
% 1.88/2.03 tff(13921,plain,
% 1.88/2.03 (op(e1, e2) = e1),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1613, 13920, 13623, 13889])).
% 1.88/2.03 tff(13922,plain,
% 1.88/2.03 ((op(e1, e2) = e2) <=> (e1 = e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13921])).
% 1.88/2.03 tff(13923,plain,
% 1.88/2.03 ((e1 = e2) <=> (op(e1, e2) = e2)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13922])).
% 1.88/2.03 tff(13924,plain,
% 1.88/2.03 ((~(e1 = e2)) <=> (~(op(e1, e2) = e2))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13923])).
% 1.88/2.03 tff(13925,plain,
% 1.88/2.03 (~(op(e1, e2) = e2)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[708, 13924])).
% 1.88/2.03 tff(13926,plain,
% 1.88/2.03 (op(e1, e0) = e2),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[2285, 13925, 10589, 13887])).
% 1.88/2.03 tff(13927,plain,
% 1.88/2.03 (op(op(e1, e0), e1) = op(e2, e1)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13926])).
% 1.88/2.03 tff(13928,plain,
% 1.88/2.03 ((op(op(e1, e0), e1) = e0) <=> (op(e2, e1) = e0)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13927])).
% 1.88/2.03 tff(13929,plain,
% 1.88/2.03 ((op(e2, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13928])).
% 1.88/2.03 tff(13930,plain,
% 1.88/2.03 ((~(op(e2, e1) = e0)) <=> (~(op(op(e1, e0), e1) = e0))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13929])).
% 1.88/2.03 tff(13931,plain,
% 1.88/2.03 (~(op(op(e1, e0), e1) = e0)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[13704, 13930])).
% 1.88/2.03 tff(13932,plain,
% 1.88/2.03 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1302, 13931])).
% 1.88/2.03 tff(13933,plain,
% 1.88/2.03 (op(op(e3, e2), e3) = op(op(e0, e3), e3)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13845])).
% 1.88/2.03 tff(13934,plain,
% 1.88/2.03 (op(op(e3, e2), e3) = op(e0, e3)),
% 1.88/2.03 inference(transitivity,[status(thm)],[13933, 13855, 13699])).
% 1.88/2.03 tff(13935,plain,
% 1.88/2.03 ((op(op(e3, e2), e3) = e2) <=> (op(e0, e3) = e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13934])).
% 1.88/2.03 tff(13936,plain,
% 1.88/2.03 ((op(e0, e3) = e2) <=> (op(op(e3, e2), e3) = e2)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13935])).
% 1.88/2.03 tff(13937,plain,
% 1.88/2.03 ((~(op(e0, e3) = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13936])).
% 1.88/2.03 tff(13938,plain,
% 1.88/2.03 (~(op(op(e3, e2), e3) = e2)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[10592, 13937])).
% 1.88/2.03 tff(13939,plain,
% 1.88/2.03 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[2408, 13938])).
% 1.88/2.03 tff(13940,plain,
% 1.88/2.03 (op(op(e1, e2), e2) = op(e1, e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13921])).
% 1.88/2.03 tff(13941,plain,
% 1.88/2.03 (op(op(e1, e2), e2) = e1),
% 1.88/2.03 inference(transitivity,[status(thm)],[13940, 13921])).
% 1.88/2.03 tff(13942,plain,
% 1.88/2.03 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1335, 13941])).
% 1.88/2.03 tff(13943,plain,
% 1.88/2.03 (op(e3, e1) = e1),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[939, 13872, 9667, 13889])).
% 1.88/2.03 tff(13944,plain,
% 1.88/2.03 (op(op(e1, e3), e1) = op(e3, e1)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13692])).
% 1.88/2.03 tff(13945,plain,
% 1.88/2.03 (op(e3, op(e3, e1)) = op(op(e1, e3), e1)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13693, 13943])).
% 1.88/2.03 tff(13946,plain,
% 1.88/2.03 (op(e3, op(e3, e1)) = e1),
% 1.88/2.03 inference(transitivity,[status(thm)],[13945, 13944, 13943])).
% 1.88/2.03 tff(13947,plain,
% 1.88/2.03 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[2594, 13946])).
% 1.88/2.03 tff(13948,plain,
% 1.88/2.03 (op(e3, e2) = op(e0, e3)),
% 1.88/2.03 inference(transitivity,[status(thm)],[5819, 772])).
% 1.88/2.03 tff(13949,plain,
% 1.88/2.03 ((op(e3, e2) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13948, 11135])).
% 1.88/2.03 tff(13950,plain,
% 1.88/2.03 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e2) = e3)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13949])).
% 1.88/2.03 tff(13951,plain,
% 1.88/2.03 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e2) = e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13950])).
% 1.88/2.03 tff(13952,plain,
% 1.88/2.03 (~(op(e3, e2) = e3)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[64, 13951])).
% 1.88/2.03 tff(13953,plain,
% 1.88/2.03 (op(e0, e2) = e3),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[2111, 2431, 13952, 75])).
% 1.88/2.03 tff(13954,plain,
% 1.88/2.03 (op(op(e0, e2), e2) = op(e3, e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13953])).
% 1.88/2.03 tff(13955,plain,
% 1.88/2.03 (op(op(e0, e2), e2) = e0),
% 1.88/2.03 inference(transitivity,[status(thm)],[13954, 5819])).
% 1.88/2.03 tff(13956,plain,
% 1.88/2.03 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1956, 13955])).
% 1.88/2.03 tff(13957,plain,
% 1.88/2.03 (op(e2, e0) = op(e0, e3)),
% 1.88/2.03 inference(transitivity,[status(thm)],[4921, 772])).
% 1.88/2.03 tff(13958,plain,
% 1.88/2.03 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13957])).
% 1.88/2.03 tff(13959,plain,
% 1.88/2.03 (op(e2, op(e2, e0)) = e0),
% 1.88/2.03 inference(transitivity,[status(thm)],[13958, 3841, 4921])).
% 1.88/2.03 tff(13960,plain,
% 1.88/2.03 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[2653, 13959])).
% 1.88/2.03 tff(13961,plain,
% 1.88/2.03 (op(op(e3, e0), e0) = op(e3, op(e0, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[12886, 772])).
% 1.88/2.03 tff(13962,plain,
% 1.88/2.03 (op(op(e3, e0), e0) = e3),
% 1.88/2.03 inference(transitivity,[status(thm)],[13961, 1342, 12886])).
% 1.88/2.03 tff(13963,plain,
% 1.88/2.03 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[4026, 13962])).
% 1.88/2.03 tff(13964,plain,
% 1.88/2.03 ((op(op(e2, e3), e2) = e3) <=> (op(e1, e2) = e3)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[2897])).
% 1.88/2.03 tff(13965,plain,
% 1.88/2.03 ((op(e1, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13964])).
% 1.88/2.03 tff(13966,plain,
% 1.88/2.03 ((~(op(e1, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13965])).
% 1.88/2.03 tff(13967,plain,
% 1.88/2.03 (~(op(op(e2, e3), e2) = e3)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[75, 13966])).
% 1.88/2.03 tff(13968,plain,
% 1.88/2.03 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1934, 13967])).
% 1.88/2.03 tff(13969,plain,
% 1.88/2.03 (op(e3, e0) = op(e1, e3)),
% 1.88/2.03 inference(transitivity,[status(thm)],[12886, 11135])).
% 1.88/2.03 tff(13970,plain,
% 1.88/2.03 (op(e2, op(e3, e0)) = op(e2, op(e1, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13969])).
% 1.88/2.03 tff(13971,plain,
% 1.88/2.03 ((op(e2, e0) = e3) <=> (op(e0, e3) = op(e1, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13957, 11135])).
% 1.88/2.03 tff(13972,plain,
% 1.88/2.03 ((op(e0, e3) = op(e1, e3)) <=> (op(e2, e0) = e3)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13971])).
% 1.88/2.03 tff(13973,plain,
% 1.88/2.03 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e2, e0) = e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13972])).
% 1.88/2.03 tff(13974,plain,
% 1.88/2.03 (~(op(e2, e0) = e3)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[64, 13973])).
% 1.88/2.03 tff(13975,plain,
% 1.88/2.03 (op(e2, e1) = e3),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1559, 2431, 13775, 13974])).
% 1.88/2.03 tff(13976,plain,
% 1.88/2.03 (op(e2, e1) = op(e3, e0)),
% 1.88/2.03 inference(transitivity,[status(thm)],[13975, 12887])).
% 1.88/2.03 tff(13977,plain,
% 1.88/2.03 (op(e2, op(e2, e1)) = op(e2, op(e3, e0))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13976])).
% 1.88/2.03 tff(13978,plain,
% 1.88/2.03 (op(e2, op(e2, e1)) = e1),
% 1.88/2.03 inference(transitivity,[status(thm)],[13977, 13970, 11227, 2684])).
% 1.88/2.03 tff(13979,plain,
% 1.88/2.03 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1355, 13978])).
% 1.88/2.03 tff(13980,plain,
% 1.88/2.03 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1459, 13979, 13968, 1275, 3342, 1304, 1358, 13963, 13960, 3341, 1357, 13956])).
% 1.88/2.03 tff(13981,plain,
% 1.88/2.03 (op(op(e0, e1), e0) = e1),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1461, 13980])).
% 1.88/2.03 tff(13982,plain,
% 1.88/2.03 ((op(e2, e1) = e2) <=> (op(e3, e0) = e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13976])).
% 1.88/2.03 tff(13983,plain,
% 1.88/2.03 ((op(e3, e0) = e2) <=> (op(e2, e1) = e2)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13982])).
% 1.88/2.03 tff(13984,plain,
% 1.88/2.03 ((~(op(e3, e0) = e2)) <=> (~(op(e2, e1) = e2))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13983])).
% 1.88/2.03 tff(13985,plain,
% 1.88/2.03 (~(op(e2, e1) = e2)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[3786, 13984])).
% 1.88/2.03 tff(13986,plain,
% 1.88/2.03 (op(e0, e1) = e2),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[1993, 13985, 82, 68])).
% 1.88/2.03 tff(13987,plain,
% 1.88/2.03 (e2 = op(e0, e1)),
% 1.88/2.03 inference(symmetry,[status(thm)],[13986])).
% 1.88/2.03 tff(13988,plain,
% 1.88/2.03 (op(e2, op(e0, e3)) = op(op(e0, e1), e0)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13987, 771])).
% 1.88/2.03 tff(13989,plain,
% 1.88/2.03 (e0 = op(e2, e0)),
% 1.88/2.03 inference(symmetry,[status(thm)],[4921])).
% 1.88/2.03 tff(13990,plain,
% 1.88/2.03 (op(e0, e3) = e1),
% 1.88/2.03 inference(transitivity,[status(thm)],[771, 13989, 3813, 13988, 13981])).
% 1.88/2.03 tff(13991,plain,
% 1.88/2.03 ($false),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[13718, 13990])).
% 1.88/2.03 tff(13992,plain,((op(e2, e2) = e3) | (~(op(e0, e3) = e0)) | (~(op(e2, e0) = e0)) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (~(op(e3, e2) = e0)) | (~(op(e2, e3) = e1)) | (~(op(e1, e3) = e3)) | (~(op(e3, e0) = e3)) | (op(e3, e0) = e2) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.03 tff(13993,plain,
% 1.88/2.03 (op(e2, e2) = e3),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[13992, 13698, 13705, 13947, 13581, 1304, 13942, 13939, 13932, 9684, 13887, 13844, 13449, 13692, 13873, 9955, 75])).
% 1.88/2.03 tff(13994,plain,
% 1.88/2.03 (op(e2, e2) = op(e3, e0)),
% 1.88/2.03 inference(transitivity,[status(thm)],[13993, 13875])).
% 1.88/2.03 tff(13995,plain,
% 1.88/2.03 (op(e0, op(e2, e2)) = op(e0, op(e3, e0))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13994])).
% 1.88/2.03 tff(13996,plain,
% 1.88/2.03 (op(e0, op(e2, e2)) = e0),
% 1.88/2.03 inference(transitivity,[status(thm)],[13995, 13874, 13855])).
% 1.88/2.03 tff(13997,plain,
% 1.88/2.03 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[5619, 13996])).
% 1.88/2.03 tff(13998,plain,
% 1.88/2.03 ((op(e0, e3) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.88/2.03 inference(transitivity,[status(thm)],[13847, 13715])).
% 1.88/2.03 tff(13999,plain,
% 1.88/2.03 ((~(op(e0, e3) = e1)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13998])).
% 1.88/2.03 tff(14000,plain,
% 1.88/2.03 (~(op(e3, e2) = op(e2, e3))),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[13452, 13999])).
% 1.88/2.03 tff(14001,plain,
% 1.88/2.03 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[500, 14000])).
% 1.88/2.03 tff(14002,plain,
% 1.88/2.03 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13926])).
% 1.88/2.03 tff(14003,plain,
% 1.88/2.03 (op(e1, op(e1, e0)) = e1),
% 1.88/2.03 inference(transitivity,[status(thm)],[14002, 13921])).
% 1.88/2.03 tff(14004,plain,
% 1.88/2.03 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[13418, 14003])).
% 1.88/2.03 tff(14005,plain,
% 1.88/2.03 (op(e1, op(e3, e3)) = e1),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[13921, 11942])).
% 1.88/2.03 tff(14006,plain,
% 1.88/2.03 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[5685, 14005])).
% 1.88/2.03 tff(14007,plain,
% 1.88/2.03 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13921])).
% 1.88/2.03 tff(14008,plain,
% 1.88/2.03 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 1.88/2.03 inference(symmetry,[status(thm)],[14007])).
% 1.88/2.03 tff(14009,plain,
% 1.88/2.03 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[14008])).
% 1.88/2.03 tff(14010,plain,
% 1.88/2.03 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13449])).
% 1.88/2.03 tff(14011,plain,
% 1.88/2.03 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[14010])).
% 1.88/2.03 tff(14012,plain,
% 1.88/2.03 (~(op(e2, e1) = e1)),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[197, 14011])).
% 1.88/2.03 tff(14013,plain,
% 1.88/2.03 (~(op(e2, e1) = op(e1, e2))),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[14012, 14009])).
% 1.88/2.03 tff(14014,plain,
% 1.88/2.03 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[557, 14013])).
% 1.88/2.03 tff(14015,plain,
% 1.88/2.03 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/2.03 inference(transitivity,[status(thm)],[13859, 453])).
% 1.88/2.03 tff(14016,plain,
% 1.88/2.03 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[14015])).
% 1.88/2.03 tff(14017,plain,
% 1.88/2.03 (~(op(e0, e3) = op(e3, e0))),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[747, 14016])).
% 1.88/2.03 tff(14018,plain,
% 1.88/2.03 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[496, 14017])).
% 1.88/2.03 tff(14019,plain,
% 1.88/2.03 ((op(e2, e1) = e1) <=> (op(e1, e2) = op(e2, e1))),
% 1.88/2.03 inference(transitivity,[status(thm)],[14008, 531])).
% 1.88/2.03 tff(14020,plain,
% 1.88/2.03 ((~(op(e2, e1) = e1)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[14019])).
% 1.88/2.03 tff(14021,plain,
% 1.88/2.03 (~(op(e1, e2) = op(e2, e1))),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[14012, 14020])).
% 1.88/2.03 tff(14022,plain,
% 1.88/2.03 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[539, 14021])).
% 1.88/2.03 tff(14023,plain,
% 1.88/2.03 (op(e3, op(e1, e1)) = op(e3, op(e0, e3))),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13883])).
% 1.88/2.03 tff(14024,plain,
% 1.88/2.03 ((op(e3, op(e1, e1)) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[14023])).
% 1.88/2.03 tff(14025,plain,
% 1.88/2.03 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, op(e1, e1)) = e3)),
% 1.88/2.03 inference(symmetry,[status(thm)],[14024])).
% 1.88/2.03 tff(14026,plain,
% 1.88/2.03 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 1.88/2.03 inference(monotonicity,[status(thm)],[13863])).
% 1.88/2.03 tff(14027,plain,
% 1.88/2.03 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e1)) = e3)),
% 1.88/2.03 inference(transitivity,[status(thm)],[14026, 14025])).
% 1.88/2.03 tff(14028,plain,
% 1.88/2.03 (op(e3, op(e1, e1)) = e3),
% 1.88/2.03 inference(modus_ponens,[status(thm)],[13873, 14027])).
% 1.88/2.03 tff(14029,plain,
% 1.88/2.03 (((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)) | (~(op(e3, op(e1, e1)) = e3))),
% 1.88/2.03 inference(tautology,[status(thm)],[])).
% 1.88/2.03 tff(14030,plain,
% 1.88/2.03 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[14029, 14028])).
% 1.88/2.03 tff(14031,plain,
% 1.88/2.03 (~(op(e1, e3) = op(e3, e1))),
% 1.88/2.03 inference(unit_resolution,[status(thm)],[7757, 13872, 9667, 13449, 14000])).
% 1.88/2.04 tff(14032,plain,
% 1.88/2.04 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[6307, 14031])).
% 1.88/2.04 tff(14033,plain,
% 1.88/2.04 (op(e0, e3) = op(e0, op(e1, e3))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13693])).
% 1.88/2.04 tff(14034,plain,
% 1.88/2.04 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14033])).
% 1.88/2.04 tff(14035,plain,
% 1.88/2.04 (op(e0, op(e1, e3)) = e0),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[13698, 14034])).
% 1.88/2.04 tff(14036,plain,
% 1.88/2.04 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[5501, 14035])).
% 1.88/2.04 tff(14037,plain,
% 1.88/2.04 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13943])).
% 1.88/2.04 tff(14038,plain,
% 1.88/2.04 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14037])).
% 1.88/2.04 tff(14039,plain,
% 1.88/2.04 (~(op(e0, e1) = e1)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[3046, 14038])).
% 1.88/2.04 tff(14040,plain,
% 1.88/2.04 (op(e0, e0) = e1),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[384, 13920, 13452, 14039])).
% 1.88/2.04 tff(14041,plain,
% 1.88/2.04 (op(e2, op(e0, e0)) = op(e2, e1)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14040])).
% 1.88/2.04 tff(14042,plain,
% 1.88/2.04 ((op(e2, op(e0, e0)) = e2) <=> (op(e2, e1) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14041])).
% 1.88/2.04 tff(14043,plain,
% 1.88/2.04 ((op(e2, e1) = e2) <=> (op(e2, op(e0, e0)) = e2)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14042])).
% 1.88/2.04 tff(14044,plain,
% 1.88/2.04 ((op(e2, e0) = e2) <=> (op(e0, e3) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13706])).
% 1.88/2.04 tff(14045,plain,
% 1.88/2.04 ((op(e0, e3) = e2) <=> (op(e2, e0) = e2)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14044])).
% 1.88/2.04 tff(14046,plain,
% 1.88/2.04 ((~(op(e0, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14045])).
% 1.88/2.04 tff(14047,plain,
% 1.88/2.04 (~(op(e2, e0) = e2)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[10592, 14046])).
% 1.88/2.04 tff(14048,plain,
% 1.88/2.04 ((op(e2, e2) = e2) <=> (op(e3, e0) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13994])).
% 1.88/2.04 tff(14049,plain,
% 1.88/2.04 ((op(e3, e0) = e2) <=> (op(e2, e2) = e2)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14048])).
% 1.88/2.04 tff(14050,plain,
% 1.88/2.04 ((~(op(e3, e0) = e2)) <=> (~(op(e2, e2) = e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14049])).
% 1.88/2.04 tff(14051,plain,
% 1.88/2.04 (~(op(e2, e2) = e2)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[9955, 14050])).
% 1.88/2.04 tff(14052,plain,
% 1.88/2.04 (op(e2, e1) = e2),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[2088, 14051, 9692, 14047])).
% 1.88/2.04 tff(14053,plain,
% 1.88/2.04 (op(e2, op(e0, e0)) = e2),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[14052, 14043])).
% 1.88/2.04 tff(14054,plain,
% 1.88/2.04 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[593, 14053])).
% 1.88/2.04 tff(14055,plain,
% 1.88/2.04 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13926])).
% 1.88/2.04 tff(14056,plain,
% 1.88/2.04 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14055, 4838])).
% 1.88/2.04 tff(14057,plain,
% 1.88/2.04 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14056])).
% 1.88/2.04 tff(14058,plain,
% 1.88/2.04 (op(e0, e2) = e2),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[1151, 14051, 9699, 13925])).
% 1.88/2.04 tff(14059,plain,
% 1.88/2.04 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14058])).
% 1.88/2.04 tff(14060,plain,
% 1.88/2.04 ((op(e0, e1) = op(e0, e2)) <=> (op(e1, e0) = op(e0, e1))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14059, 14057])).
% 1.88/2.04 tff(14061,plain,
% 1.88/2.04 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14060])).
% 1.88/2.04 tff(14062,plain,
% 1.88/2.04 (~(op(e1, e0) = op(e0, e1))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[2102, 14061])).
% 1.88/2.04 tff(14063,plain,
% 1.88/2.04 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[613, 14062])).
% 1.88/2.04 tff(14064,plain,
% 1.88/2.04 ($false),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[5367, 14063, 14054, 14036, 14032, 14030, 14022, 14018, 14014, 14006, 14004, 14001, 13997, 13854, 13851, 13713])).
% 1.88/2.04 tff(14065,plain,((op(e2, e2) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.04 tff(14066,plain,
% 1.88/2.04 (op(e2, e2) = e0),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[14065, 1304, 75, 2812])).
% 1.88/2.04 tff(14067,plain,
% 1.88/2.04 (e0 = op(e2, e2)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14066])).
% 1.88/2.04 tff(14068,plain,
% 1.88/2.04 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e2, e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14067])).
% 1.88/2.04 tff(14069,plain,
% 1.88/2.04 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e0)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14068])).
% 1.88/2.04 tff(14070,plain,
% 1.88/2.04 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e0))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14069])).
% 1.88/2.04 tff(14071,plain,
% 1.88/2.04 (~(op(e2, e0) = e0)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[2228, 14070])).
% 1.88/2.04 tff(14072,plain,
% 1.88/2.04 (e3 = op(e2, op(e2, e2))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[7736, 10641])).
% 1.88/2.04 tff(14073,plain,
% 1.88/2.04 (op(e2, op(e2, e2)) = e3),
% 1.88/2.04 inference(transitivity,[status(thm)],[9302, 7736])).
% 1.88/2.04 tff(14074,plain,
% 1.88/2.04 (op(e2, op(e2, op(e2, e2))) = op(e2, e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14073])).
% 1.88/2.04 tff(14075,plain,
% 1.88/2.04 (op(e2, e3) = op(e2, op(e2, op(e2, e2)))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14074])).
% 1.88/2.04 tff(14076,plain,
% 1.88/2.04 (e1 = op(e2, op(e2, op(e2, e2)))),
% 1.88/2.04 inference(transitivity,[status(thm)],[2685, 14075])).
% 1.88/2.04 tff(14077,plain,
% 1.88/2.04 ($false),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[1010, 14076, 14072, 9301])).
% 1.88/2.04 tff(14078,plain,((~(op(e2, e0) = e3)) | (~(op(e2, e3) = e1)) | (~(op(e2, e2) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.04 tff(14079,plain,
% 1.88/2.04 (~(op(e2, e0) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[14078, 13449, 14066])).
% 1.88/2.04 tff(14080,plain,
% 1.88/2.04 (op(e2, e0) = e2),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[765, 14079, 13544, 14071])).
% 1.88/2.04 tff(14081,plain,
% 1.88/2.04 (op(e2, op(e2, e2)) = op(e2, e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14066])).
% 1.88/2.04 tff(14082,plain,
% 1.88/2.04 ((op(e2, e0) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14080])).
% 1.88/2.04 tff(14083,plain,
% 1.88/2.04 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14082, 1960])).
% 1.88/2.04 tff(14084,plain,
% 1.88/2.04 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14083])).
% 1.88/2.04 tff(14085,plain,
% 1.88/2.04 (~(op(e2, e1) = e2)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[1966, 14084])).
% 1.88/2.04 tff(14086,plain,
% 1.88/2.04 ((e0 = e3) <=> (op(e2, e2) = e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14067])).
% 1.88/2.04 tff(14087,plain,
% 1.88/2.04 ((~(e0 = e3)) <=> (~(op(e2, e2) = e3))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14086])).
% 1.88/2.04 tff(14088,plain,
% 1.88/2.04 (~(op(e2, e2) = e3)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[181, 14087])).
% 1.88/2.04 tff(14089,plain,
% 1.88/2.04 (op(e2, e1) = e3),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[1559, 14079, 13476, 14088])).
% 1.88/2.04 tff(14090,plain,
% 1.88/2.04 (e3 = op(e2, e1)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14089])).
% 1.88/2.04 tff(14091,plain,
% 1.88/2.04 (op(e0, op(e2, e1)) = op(e0, e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14089])).
% 1.88/2.04 tff(14092,plain,
% 1.88/2.04 (op(e0, e3) = op(e0, op(e2, e1))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14091])).
% 1.88/2.04 tff(14093,plain,
% 1.88/2.04 ((op(e0, e3) = e0) <=> (op(e0, op(e2, e1)) = e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14092])).
% 1.88/2.04 tff(14094,plain,
% 1.88/2.04 ((op(e0, op(e2, e1)) = e0) <=> (op(e0, e3) = e0)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14093])).
% 1.88/2.04 tff(14095,plain,
% 1.88/2.04 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, op(e2, e1)) = e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14092, 13456])).
% 1.88/2.04 tff(14096,plain,
% 1.88/2.04 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14095, 14094])).
% 1.88/2.04 tff(14097,plain,
% 1.88/2.04 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14096])).
% 1.88/2.04 tff(14098,plain,
% 1.88/2.04 (~(op(e0, e3) = e0)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[64, 14097])).
% 1.88/2.04 tff(14099,plain,
% 1.88/2.04 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e2, e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14067])).
% 1.88/2.04 tff(14100,plain,
% 1.88/2.04 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14099])).
% 1.88/2.04 tff(14101,plain,
% 1.88/2.04 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14100])).
% 1.88/2.04 tff(14102,plain,
% 1.88/2.04 (~(op(e0, e2) = e0)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[2736, 14101])).
% 1.88/2.04 tff(14103,plain,
% 1.88/2.04 (op(e1, op(e2, e1)) = op(e1, e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14089])).
% 1.88/2.04 tff(14104,plain,
% 1.88/2.04 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14090])).
% 1.88/2.04 tff(14105,plain,
% 1.88/2.04 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14104])).
% 1.88/2.04 tff(14106,plain,
% 1.88/2.04 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14105])).
% 1.88/2.04 tff(14107,plain,
% 1.88/2.04 (~(op(e1, e1) = e3)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[225, 14106])).
% 1.88/2.04 tff(14108,plain,
% 1.88/2.04 (op(e1, e0) = e3),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[247, 1080, 14107, 75])).
% 1.88/2.04 tff(14109,plain,
% 1.88/2.04 (op(e1, e0) = op(e2, e1)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14108, 14090])).
% 1.88/2.04 tff(14110,plain,
% 1.88/2.04 (op(e1, op(e1, e0)) = op(e1, op(e2, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14109])).
% 1.88/2.04 tff(14111,plain,
% 1.88/2.04 (op(e1, op(e1, e0)) = e0),
% 1.88/2.04 inference(transitivity,[status(thm)],[14110, 14103, 13456])).
% 1.88/2.04 tff(14112,plain,
% 1.88/2.04 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[1836, 14111])).
% 1.88/2.04 tff(14113,plain,
% 1.88/2.04 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13456])).
% 1.88/2.04 tff(14114,plain,
% 1.88/2.04 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14113])).
% 1.88/2.04 tff(14115,plain,
% 1.88/2.04 (~(op(e1, e1) = e0)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[619, 14114])).
% 1.88/2.04 tff(14116,plain,
% 1.88/2.04 (op(e3, op(e2, e0)) = op(e3, e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14080])).
% 1.88/2.04 tff(14117,plain,
% 1.88/2.04 ((op(e3, op(e2, e0)) = e3) <=> (op(e3, e2) = e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14116])).
% 1.88/2.04 tff(14118,plain,
% 1.88/2.04 ((op(e3, e2) = e3) <=> (op(e3, op(e2, e0)) = e3)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14117])).
% 1.88/2.04 tff(14119,plain,
% 1.88/2.04 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[13533])).
% 1.88/2.04 tff(14120,plain,
% 1.88/2.04 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14119])).
% 1.88/2.04 tff(14121,plain,
% 1.88/2.04 (~(op(e0, e2) = e3)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[918, 14120])).
% 1.88/2.04 tff(14122,plain,
% 1.88/2.04 (op(e3, e2) = e3),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[2111, 14121, 14088, 75])).
% 1.88/2.04 tff(14123,plain,
% 1.88/2.04 (op(e3, op(e2, e0)) = e3),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[14122, 14118])).
% 1.88/2.04 tff(14124,plain,
% 1.88/2.04 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[10697, 14123])).
% 1.88/2.04 tff(14125,plain,
% 1.88/2.04 (op(e3, e2) = op(e2, e1)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14122, 14090])).
% 1.88/2.04 tff(14126,plain,
% 1.88/2.04 ((op(e3, e2) = e1) <=> (op(e2, e1) = e1)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14125])).
% 1.88/2.04 tff(14127,plain,
% 1.88/2.04 ((op(e2, e1) = e1) <=> (op(e3, e2) = e1)),
% 1.88/2.04 inference(symmetry,[status(thm)],[14126])).
% 1.88/2.04 tff(14128,plain,
% 1.88/2.04 ((op(e2, e1) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14127, 13715, 395])).
% 1.88/2.04 tff(14129,plain,
% 1.88/2.04 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14128])).
% 1.88/2.04 tff(14130,plain,
% 1.88/2.04 (~(op(e2, e3) = op(e3, e2))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[14012, 14129])).
% 1.88/2.04 tff(14131,plain,
% 1.88/2.04 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[430, 14130])).
% 1.88/2.04 tff(14132,plain,
% 1.88/2.04 ((op(e2, e1) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14127, 13715])).
% 1.88/2.04 tff(14133,plain,
% 1.88/2.04 ((~(op(e2, e1) = e1)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14132])).
% 1.88/2.04 tff(14134,plain,
% 1.88/2.04 (~(op(e3, e2) = op(e2, e3))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[14012, 14133])).
% 1.88/2.04 tff(14135,plain,
% 1.88/2.04 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[500, 14134])).
% 1.88/2.04 tff(14136,plain,
% 1.88/2.04 ((op(e2, e1) = op(e0, e1)) <=> (op(e0, e1) = op(e2, e1))),
% 1.88/2.04 inference(commutativity,[status(thm)],[])).
% 1.88/2.04 tff(14137,plain,
% 1.88/2.04 ((op(e1, e0) = op(e0, e1)) <=> (op(e2, e1) = op(e0, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14109])).
% 1.88/2.04 tff(14138,plain,
% 1.88/2.04 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e2, e1))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14137, 14136])).
% 1.88/2.04 tff(14139,plain,
% 1.88/2.04 ((op(e0, e1) = op(e2, e1)) <=> (op(e1, e0) = op(e0, e1))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14138])).
% 1.88/2.04 tff(14140,plain,
% 1.88/2.04 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = op(e1, e0))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14139, 596])).
% 1.88/2.04 tff(14141,plain,
% 1.88/2.04 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14140])).
% 1.88/2.04 tff(14142,plain,
% 1.88/2.04 (~(op(e0, e1) = op(e1, e0))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[606, 14141])).
% 1.88/2.04 tff(14143,plain,
% 1.88/2.04 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[609, 14142])).
% 1.88/2.04 tff(14144,plain,
% 1.88/2.04 (op(e3, op(e3, e3)) = e3),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[14122, 9701])).
% 1.88/2.04 tff(14145,plain,
% 1.88/2.04 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[6277, 14144])).
% 1.88/2.04 tff(14146,plain,
% 1.88/2.04 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e1))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14090])).
% 1.88/2.04 tff(14147,plain,
% 1.88/2.04 ((op(e1, e2) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14146, 530])).
% 1.88/2.04 tff(14148,plain,
% 1.88/2.04 ((~(op(e1, e2) = e3)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14147])).
% 1.88/2.04 tff(14149,plain,
% 1.88/2.04 (~(op(e2, e1) = op(e1, e2))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[75, 14148])).
% 1.88/2.04 tff(14150,plain,
% 1.88/2.04 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[557, 14149])).
% 1.88/2.04 tff(14151,plain,
% 1.88/2.04 (op(e3, op(e2, e2)) = op(e3, e0)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14066])).
% 1.88/2.04 tff(14152,plain,
% 1.88/2.04 (op(e3, e0) = op(e3, op(e2, e2))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14151])).
% 1.88/2.04 tff(14153,plain,
% 1.88/2.04 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, op(e2, e2)) = e3)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14152, 13533])).
% 1.88/2.04 tff(14154,plain,
% 1.88/2.04 ((op(e3, op(e2, e2)) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14153])).
% 1.88/2.04 tff(14155,plain,
% 1.88/2.04 ((e3 = op(e3, op(e2, e2))) <=> (op(e3, op(e2, e2)) = e3)),
% 1.88/2.04 inference(commutativity,[status(thm)],[])).
% 1.88/2.04 tff(14156,plain,
% 1.88/2.04 ((op(e1, e0) = op(e3, e0)) <=> (e3 = op(e3, op(e2, e2)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14108, 14152])).
% 1.88/2.04 tff(14157,plain,
% 1.88/2.04 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, op(e2, e2)) = e3)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14156, 14155])).
% 1.88/2.04 tff(14158,plain,
% 1.88/2.04 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14157, 14154, 453])).
% 1.88/2.04 tff(14159,plain,
% 1.88/2.04 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14158])).
% 1.88/2.04 tff(14160,plain,
% 1.88/2.04 (~(op(e0, e3) = op(e3, e0))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[410, 14159])).
% 1.88/2.04 tff(14161,plain,
% 1.88/2.04 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[496, 14160])).
% 1.88/2.04 tff(14162,plain,
% 1.88/2.04 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e1))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14147, 531])).
% 1.88/2.04 tff(14163,plain,
% 1.88/2.04 ((~(op(e1, e2) = e3)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14162])).
% 1.88/2.04 tff(14164,plain,
% 1.88/2.04 (~(op(e1, e2) = op(e2, e1))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[75, 14163])).
% 1.88/2.04 tff(14165,plain,
% 1.88/2.04 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[539, 14164])).
% 1.88/2.04 tff(14166,plain,
% 1.88/2.04 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14139])).
% 1.88/2.04 tff(14167,plain,
% 1.88/2.04 (~(op(e1, e0) = op(e0, e1))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[606, 14166])).
% 1.88/2.04 tff(14168,plain,
% 1.88/2.04 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[613, 14167])).
% 1.88/2.04 tff(14169,plain,
% 1.88/2.04 (op(e1, e3) = op(e2, e2)),
% 1.88/2.04 inference(transitivity,[status(thm)],[13456, 14067])).
% 1.88/2.04 tff(14170,plain,
% 1.88/2.04 (op(e2, op(e1, e3)) = op(e2, op(e2, e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14169])).
% 1.88/2.04 tff(14171,plain,
% 1.88/2.04 (op(e2, op(e1, e3)) = e2),
% 1.88/2.04 inference(transitivity,[status(thm)],[14170, 14081, 14080])).
% 1.88/2.04 tff(14172,plain,
% 1.88/2.04 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[9084, 14171])).
% 1.88/2.04 tff(14173,plain,
% 1.88/2.04 ((op(e2, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[1940])).
% 1.88/2.04 tff(14174,plain,
% 1.88/2.04 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 1.88/2.04 inference(transitivity,[status(thm)],[14173, 3491])).
% 1.88/2.04 tff(14175,plain,
% 1.88/2.04 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 1.88/2.04 inference(symmetry,[status(thm)],[14174])).
% 1.88/2.04 tff(14176,plain,
% 1.88/2.04 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[1940])).
% 1.88/2.04 tff(14177,plain,
% 1.88/2.04 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14176])).
% 1.88/2.04 tff(14178,plain,
% 1.88/2.04 (~(op(e1, e0) = e2)),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[756, 14177])).
% 1.88/2.04 tff(14179,plain,
% 1.88/2.04 (op(e1, e2) = e2),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[2285, 68, 72, 14178])).
% 1.88/2.04 tff(14180,plain,
% 1.88/2.04 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14179])).
% 1.88/2.04 tff(14181,plain,
% 1.88/2.04 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 1.88/2.04 inference(transitivity,[status(thm)],[14180, 14175])).
% 1.88/2.04 tff(14182,plain,
% 1.88/2.04 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14181])).
% 1.88/2.04 tff(14183,plain,
% 1.88/2.04 (~(op(e2, e0) = op(e0, e2))),
% 1.88/2.04 inference(modus_ponens,[status(thm)],[6205, 14182])).
% 1.88/2.04 tff(14184,plain,
% 1.88/2.04 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[6358, 14183])).
% 1.88/2.04 tff(14185,plain,
% 1.88/2.04 (op(e1, e1) = e1),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[630, 68, 1291, 84])).
% 1.88/2.04 tff(14186,plain,
% 1.88/2.04 (op(e1, op(e1, e1)) = op(e1, e1)),
% 1.88/2.04 inference(monotonicity,[status(thm)],[14185])).
% 1.88/2.04 tff(14187,plain,
% 1.88/2.04 (op(e1, op(e1, e1)) = e1),
% 1.88/2.04 inference(transitivity,[status(thm)],[14186, 14185])).
% 1.88/2.04 tff(14188,plain,
% 1.88/2.04 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.88/2.04 inference(unit_resolution,[status(thm)],[5678, 14187])).
% 1.88/2.04 tff(14189,plain,
% 1.88/2.04 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e2, e2))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[9326])).
% 1.88/2.05 tff(14190,plain,
% 1.88/2.05 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 1.88/2.05 inference(symmetry,[status(thm)],[14189])).
% 1.88/2.05 tff(14191,plain,
% 1.88/2.05 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14190])).
% 1.88/2.05 tff(14192,plain,
% 1.88/2.05 (~(op(e0, e2) = e0)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[2736, 14191])).
% 1.88/2.05 tff(14193,plain,
% 1.88/2.05 (op(e0, e1) = e2),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[1993, 68, 82, 1967])).
% 1.88/2.05 tff(14194,plain,
% 1.88/2.05 ((op(e0, e1) = e0) <=> (e2 = op(e2, e2))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14193, 9326])).
% 1.88/2.05 tff(14195,plain,
% 1.88/2.05 ((op(e0, e1) = e0) <=> (op(e2, e2) = e2)),
% 1.88/2.05 inference(transitivity,[status(thm)],[14194, 81])).
% 1.88/2.05 tff(14196,plain,
% 1.88/2.05 ((op(e2, e2) = e2) <=> (op(e0, e1) = e0)),
% 1.88/2.05 inference(symmetry,[status(thm)],[14195])).
% 1.88/2.05 tff(14197,plain,
% 1.88/2.05 ((~(op(e2, e2) = e2)) <=> (~(op(e0, e1) = e0))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14196])).
% 1.88/2.05 tff(14198,plain,
% 1.88/2.05 (~(op(e0, e1) = e0)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[10989, 14197])).
% 1.88/2.05 tff(14199,plain,
% 1.88/2.05 (op(e0, e0) = e0),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[3976, 14198, 14192, 1087])).
% 1.88/2.05 tff(14200,plain,
% 1.88/2.05 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14199])).
% 1.88/2.05 tff(14201,plain,
% 1.88/2.05 (op(e0, op(e0, e0)) = e0),
% 1.88/2.05 inference(transitivity,[status(thm)],[14200, 14199])).
% 1.88/2.05 tff(14202,plain,
% 1.88/2.05 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[5598, 14201])).
% 1.88/2.05 tff(14203,plain,
% 1.88/2.05 (op(e3, e1) = e0),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[292, 14198, 10624, 84])).
% 1.88/2.05 tff(14204,plain,
% 1.88/2.05 (op(e0, op(e3, e1)) = op(e0, e0)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14203])).
% 1.88/2.05 tff(14205,plain,
% 1.88/2.05 (op(e0, op(e3, e1)) = e0),
% 1.88/2.05 inference(transitivity,[status(thm)],[14204, 14199])).
% 1.88/2.05 tff(14206,plain,
% 1.88/2.05 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[5610, 14205])).
% 1.88/2.05 tff(14207,plain,
% 1.88/2.05 ($false),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[5367, 14206, 14202, 5511, 14188, 5675, 5673, 5670, 5680, 6688, 5681, 5671, 10764, 14184, 5668, 9846])).
% 1.88/2.05 tff(14208,plain,((op(e1, e1) = e2) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (op(e1, e1) = e0) | (op(e0, e3) = e0) | (~(op(e2, e2) = e0)) | (~(op(e2, e0) = e2)) | (op(e1, e1) = e3) | (op(e3, e1) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.88/2.05 tff(14209,plain,
% 1.88/2.05 (op(e1, e1) = e2),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[14208, 14172, 14168, 14165, 14161, 14150, 14145, 14143, 14135, 14131, 14124, 14115, 14098, 14066, 14080, 14107, 9684, 10589])).
% 1.88/2.05 tff(14210,plain,
% 1.88/2.05 (op(e1, e2) = e1),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[9680, 14209, 75, 2812, 13533, 10592, 1080])).
% 1.88/2.05 tff(14211,plain,
% 1.88/2.05 (op(e1, op(e1, e2)) = op(e1, e1)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14210])).
% 1.88/2.05 tff(14212,plain,
% 1.88/2.05 (op(e1, op(e1, e2)) = e2),
% 1.88/2.05 inference(transitivity,[status(thm)],[14211, 14209])).
% 1.88/2.05 tff(14213,plain,
% 1.88/2.05 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[2377, 14212])).
% 1.88/2.05 tff(14214,plain,
% 1.88/2.05 (op(op(e3, e2), e2) = e3),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[7919, 14122])).
% 1.88/2.05 tff(14215,plain,
% 1.88/2.05 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[1339, 14214])).
% 1.88/2.05 tff(14216,plain,
% 1.88/2.05 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e2))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14067])).
% 1.88/2.05 tff(14217,plain,
% 1.88/2.05 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e0)),
% 1.88/2.05 inference(symmetry,[status(thm)],[14216])).
% 1.88/2.05 tff(14218,plain,
% 1.88/2.05 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e0))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14217])).
% 1.88/2.05 tff(14219,plain,
% 1.88/2.05 (~(op(e2, e1) = e0)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[508, 14218])).
% 1.88/2.05 tff(14220,plain,
% 1.88/2.05 ((op(e3, e1) = op(e2, e1)) <=> (op(e2, e1) = op(e3, e1))),
% 1.88/2.05 inference(commutativity,[status(thm)],[])).
% 1.88/2.05 tff(14221,plain,
% 1.88/2.05 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e2, e1))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14090])).
% 1.88/2.05 tff(14222,plain,
% 1.88/2.05 ((op(e3, e1) = e3) <=> (op(e2, e1) = op(e3, e1))),
% 1.88/2.05 inference(transitivity,[status(thm)],[14221, 14220])).
% 1.88/2.05 tff(14223,plain,
% 1.88/2.05 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 1.88/2.05 inference(symmetry,[status(thm)],[14222])).
% 1.88/2.05 tff(14224,plain,
% 1.88/2.05 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14223])).
% 1.88/2.05 tff(14225,plain,
% 1.88/2.05 (~(op(e3, e1) = e3)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[402, 14224])).
% 1.88/2.05 tff(14226,plain,
% 1.88/2.05 (op(e2, op(e2, e1)) = op(e2, e3)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14089])).
% 1.88/2.05 tff(14227,plain,
% 1.88/2.05 (op(e2, op(e2, e1)) = e1),
% 1.88/2.05 inference(transitivity,[status(thm)],[14226, 13449])).
% 1.88/2.05 tff(14228,plain,
% 1.88/2.05 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[1355, 14227])).
% 1.88/2.05 tff(14229,plain,
% 1.88/2.05 (op(e2, op(e2, e0)) = op(e2, e2)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[1940])).
% 1.88/2.05 tff(14230,plain,
% 1.88/2.05 (op(e2, op(e2, e0)) = e0),
% 1.88/2.05 inference(transitivity,[status(thm)],[14229, 9300])).
% 1.88/2.05 tff(14231,plain,
% 1.88/2.05 ($false),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[4920, 14230])).
% 1.88/2.05 tff(14232,plain,((~(op(e2, e0) = e2)) | (op(e2, op(e2, e0)) = e0) | (~(op(e2, e2) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.88/2.05 tff(14233,plain,
% 1.88/2.05 (op(e2, op(e2, e0)) = e0),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[14232, 14080, 14066])).
% 1.88/2.05 tff(14234,plain,
% 1.88/2.05 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.88/2.05 inference(unit_resolution,[status(thm)],[2653, 14233])).
% 1.88/2.05 tff(14235,plain,
% 1.88/2.05 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e2))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14067])).
% 1.88/2.05 tff(14236,plain,
% 1.88/2.05 ((op(e3, e2) = e0) <=> (op(e2, e2) = op(e3, e2))),
% 1.88/2.05 inference(transitivity,[status(thm)],[14235, 9346])).
% 1.88/2.05 tff(14237,plain,
% 1.88/2.05 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.88/2.05 inference(symmetry,[status(thm)],[14236])).
% 1.88/2.05 tff(14238,plain,
% 1.88/2.05 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14237])).
% 1.88/2.05 tff(14239,plain,
% 1.88/2.05 (~(op(e3, e2) = e0)),
% 1.88/2.05 inference(modus_ponens,[status(thm)],[1546, 14238])).
% 1.88/2.05 tff(14240,plain,
% 1.88/2.05 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14080])).
% 1.88/2.05 tff(14241,plain,
% 1.88/2.05 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.88/2.05 inference(monotonicity,[status(thm)],[14240])).
% 1.95/2.05 tff(14242,plain,
% 1.95/2.05 (~(op(e0, e0) = e2)),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[359, 14241])).
% 1.95/2.05 tff(14243,plain,
% 1.95/2.05 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14209])).
% 1.95/2.05 tff(14244,plain,
% 1.95/2.05 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14243])).
% 1.95/2.05 tff(14245,plain,
% 1.95/2.05 (~(op(e0, e1) = e2)),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[792, 14244])).
% 1.95/2.05 tff(14246,plain,
% 1.95/2.05 (op(e0, e2) = e2),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[3652, 14245, 10592, 14242])).
% 1.95/2.05 tff(14247,plain,
% 1.95/2.05 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14246])).
% 1.95/2.05 tff(14248,plain,
% 1.95/2.05 (op(e0, op(e0, e2)) = e2),
% 1.95/2.05 inference(transitivity,[status(thm)],[14247, 14246])).
% 1.95/2.05 tff(14249,plain,
% 1.95/2.05 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[1331, 14248])).
% 1.95/2.05 tff(14250,plain,
% 1.95/2.05 (op(e3, e1) = e0),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[9838, 14249, 1304, 14239, 14234, 14228, 13533, 14115, 13581, 13590, 14225, 14219, 14215, 9684, 14213, 9696, 14112])).
% 1.95/2.05 tff(14251,plain,
% 1.95/2.05 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14250])).
% 1.95/2.05 tff(14252,plain,
% 1.95/2.05 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14251])).
% 1.95/2.05 tff(14253,plain,
% 1.95/2.05 (~(op(e0, e1) = e0)),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[3046, 14252])).
% 1.95/2.05 tff(14254,plain,
% 1.95/2.05 (op(e0, e0) = e0),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[3976, 14253, 14102, 14098])).
% 1.95/2.05 tff(14255,plain,
% 1.95/2.05 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14254])).
% 1.95/2.05 tff(14256,plain,
% 1.95/2.05 (op(e0, op(e0, e0)) = e0),
% 1.95/2.05 inference(transitivity,[status(thm)],[14255, 14254])).
% 1.95/2.05 tff(14257,plain,
% 1.95/2.05 (op(e1, op(e0, e2)) = op(e1, e2)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14246])).
% 1.95/2.05 tff(14258,plain,
% 1.95/2.05 (op(e1, op(e0, e2)) = e1),
% 1.95/2.05 inference(transitivity,[status(thm)],[14257, 14210])).
% 1.95/2.05 tff(14259,plain,
% 1.95/2.05 (((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)) | (~(op(e1, op(e0, e2)) = e1))),
% 1.95/2.05 inference(tautology,[status(thm)],[])).
% 1.95/2.05 tff(14260,plain,
% 1.95/2.05 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[14259, 14258])).
% 1.95/2.05 tff(14261,plain,
% 1.95/2.05 (op(e2, e0) = op(e2, op(e2, e2))),
% 1.95/2.05 inference(symmetry,[status(thm)],[14081])).
% 1.95/2.05 tff(14262,plain,
% 1.95/2.05 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14261])).
% 1.95/2.05 tff(14263,plain,
% 1.95/2.05 (op(e2, op(e2, e2)) = e2),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[14080, 14262])).
% 1.95/2.05 tff(14264,plain,
% 1.95/2.05 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[528, 14263])).
% 1.95/2.05 tff(14265,plain,
% 1.95/2.05 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14209])).
% 1.95/2.05 tff(14266,plain,
% 1.95/2.05 (op(e1, op(e1, e1)) = e1),
% 1.95/2.05 inference(transitivity,[status(thm)],[14265, 14210])).
% 1.95/2.05 tff(14267,plain,
% 1.95/2.05 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[5678, 14266])).
% 1.95/2.05 tff(14268,plain,
% 1.95/2.05 (op(e3, e1) = op(e2, e2)),
% 1.95/2.05 inference(transitivity,[status(thm)],[14250, 14067])).
% 1.95/2.05 tff(14269,plain,
% 1.95/2.05 (op(e2, op(e3, e1)) = op(e2, op(e2, e2))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14268])).
% 1.95/2.05 tff(14270,plain,
% 1.95/2.05 (op(e2, op(e3, e1)) = e2),
% 1.95/2.05 inference(transitivity,[status(thm)],[14269, 14081, 14080])).
% 1.95/2.05 tff(14271,plain,
% 1.95/2.05 (((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)) | (~(op(e2, op(e3, e1)) = e2))),
% 1.95/2.05 inference(tautology,[status(thm)],[])).
% 1.95/2.05 tff(14272,plain,
% 1.95/2.05 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[14271, 14270])).
% 1.95/2.05 tff(14273,plain,
% 1.95/2.05 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[5367, 14272, 14172, 14267, 14168, 14165, 14161, 14150, 14145, 14143, 14135, 14264, 14260, 14131, 14124])).
% 1.95/2.05 tff(14274,plain,
% 1.95/2.05 (~(op(e0, op(e0, e0)) = e0)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[5598, 14273])).
% 1.95/2.05 tff(14275,plain,
% 1.95/2.05 ($false),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[14274, 14256])).
% 1.95/2.05 tff(14276,plain,((op(e1, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e2) = e3) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.05 tff(14277,plain,
% 1.95/2.05 (op(e1, e3) = e3),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[14276, 1304, 75, 2812])).
% 1.95/2.05 tff(14278,plain,
% 1.95/2.05 (op(e1, e3) = op(e2, e1)),
% 1.95/2.05 inference(transitivity,[status(thm)],[14277, 14090])).
% 1.95/2.05 tff(14279,plain,
% 1.95/2.05 ((op(e1, e3) = e0) <=> (op(e2, e1) = op(e2, e2))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14278, 14067])).
% 1.95/2.05 tff(14280,plain,
% 1.95/2.05 ((op(e2, e1) = op(e2, e2)) <=> (op(e1, e3) = e0)),
% 1.95/2.05 inference(symmetry,[status(thm)],[14279])).
% 1.95/2.05 tff(14281,plain,
% 1.95/2.05 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e1, e3) = e0))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14280])).
% 1.95/2.05 tff(14282,plain,
% 1.95/2.05 (~(op(e1, e3) = e0)),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[508, 14281])).
% 1.95/2.05 tff(14283,plain,
% 1.95/2.05 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e3)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14277])).
% 1.95/2.05 tff(14284,plain,
% 1.95/2.05 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e3))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14283])).
% 1.95/2.05 tff(14285,plain,
% 1.95/2.05 (~(op(e0, e3) = e3)),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[64, 14284])).
% 1.95/2.05 tff(14286,plain,
% 1.95/2.05 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = op(e2, e1))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14278])).
% 1.95/2.05 tff(14287,plain,
% 1.95/2.05 ((op(e3, e1) = op(e1, e3)) <=> (op(e2, e1) = op(e3, e1))),
% 1.95/2.05 inference(transitivity,[status(thm)],[14286, 14220])).
% 1.95/2.05 tff(14288,plain,
% 1.95/2.05 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 1.95/2.05 inference(symmetry,[status(thm)],[14287])).
% 1.95/2.05 tff(14289,plain,
% 1.95/2.05 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 1.95/2.05 inference(transitivity,[status(thm)],[14288, 6290])).
% 1.95/2.05 tff(14290,plain,
% 1.95/2.05 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14289])).
% 1.95/2.05 tff(14291,plain,
% 1.95/2.05 (~(op(e1, e3) = op(e3, e1))),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[402, 14290])).
% 1.95/2.05 tff(14292,plain,
% 1.95/2.05 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[6307, 14291])).
% 1.95/2.05 tff(14293,plain,
% 1.95/2.05 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14288])).
% 1.95/2.05 tff(14294,plain,
% 1.95/2.05 (~(op(e3, e1) = op(e1, e3))),
% 1.95/2.05 inference(modus_ponens,[status(thm)],[402, 14293])).
% 1.95/2.05 tff(14295,plain,
% 1.95/2.05 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[6362, 14294])).
% 1.95/2.05 tff(14296,plain,
% 1.95/2.05 (op(e1, e0) = e0),
% 1.95/2.05 inference(unit_resolution,[status(thm)],[1830, 84, 10671, 80])).
% 1.95/2.05 tff(14297,plain,
% 1.95/2.05 (op(e1, op(e2, e2)) = op(e2, e2)),
% 1.95/2.05 inference(transitivity,[status(thm)],[10853, 14296, 9326])).
% 1.95/2.05 tff(14298,plain,
% 1.95/2.05 ((op(e1, op(e2, e2)) = e1) <=> (op(e2, e2) = e1)),
% 1.95/2.05 inference(monotonicity,[status(thm)],[14297])).
% 1.95/2.05 tff(14299,plain,
% 1.95/2.05 ((op(e2, e2) = e1) <=> (op(e1, op(e2, e2)) = e1)),
% 1.95/2.05 inference(symmetry,[status(thm)],[14298])).
% 1.95/2.05 tff(14300,plain,
% 1.95/2.05 ((op(e2, e2) = e1) <=> (op(e1, e0) = e1)),
% 1.95/2.05 inference(transitivity,[status(thm)],[14299, 10856])).
% 1.95/2.05 tff(14301,plain,
% 1.95/2.05 ((~(op(e2, e2) = e1)) <=> (~(op(e1, e0) = e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14300])).
% 1.95/2.06 tff(14302,plain,
% 1.95/2.06 (~(op(e1, e0) = e1)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[13500, 14301])).
% 1.95/2.06 tff(14303,plain,
% 1.95/2.06 (~(op(e2, e0) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14078, 2684, 9300])).
% 1.95/2.06 tff(14304,plain,
% 1.95/2.06 (op(e2, e1) = e3),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[1559, 14303, 13775, 10888])).
% 1.95/2.06 tff(14305,plain,
% 1.95/2.06 (e3 = op(e2, e1)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14304])).
% 1.95/2.06 tff(14306,plain,
% 1.95/2.06 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14305])).
% 1.95/2.06 tff(14307,plain,
% 1.95/2.06 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14306])).
% 1.95/2.06 tff(14308,plain,
% 1.95/2.06 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14307])).
% 1.95/2.06 tff(14309,plain,
% 1.95/2.06 (~(op(e1, e1) = e3)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[225, 14308])).
% 1.95/2.06 tff(14310,plain,
% 1.95/2.06 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[2684])).
% 1.95/2.06 tff(14311,plain,
% 1.95/2.06 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14310])).
% 1.95/2.06 tff(14312,plain,
% 1.95/2.06 (~(op(e2, e0) = e1)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[989, 14311])).
% 1.95/2.06 tff(14313,plain,
% 1.95/2.06 (op(e2, e0) = e2),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[765, 14303, 14312, 10651])).
% 1.95/2.06 tff(14314,plain,
% 1.95/2.06 (op(e3, op(e2, e0)) = op(e3, e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14313])).
% 1.95/2.06 tff(14315,plain,
% 1.95/2.06 ((op(e3, op(e2, e0)) = e3) <=> (op(e3, e2) = e3)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14314])).
% 1.95/2.06 tff(14316,plain,
% 1.95/2.06 ((op(e3, e2) = e3) <=> (op(e3, op(e2, e0)) = e3)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14315])).
% 1.95/2.06 tff(14317,plain,
% 1.95/2.06 (op(e0, e3) = e0),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[1098, 80, 9696, 13736])).
% 1.95/2.06 tff(14318,plain,
% 1.95/2.06 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14317])).
% 1.95/2.06 tff(14319,plain,
% 1.95/2.06 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14318])).
% 1.95/2.06 tff(14320,plain,
% 1.95/2.06 (~(op(e0, e1) = e0)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[818, 14319])).
% 1.95/2.06 tff(14321,plain,
% 1.95/2.06 (op(e3, e1) = e0),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[292, 84, 10624, 14320])).
% 1.95/2.06 tff(14322,plain,
% 1.95/2.06 (op(e3, e2) = e3),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[10084, 14321, 2812])).
% 1.95/2.06 tff(14323,plain,
% 1.95/2.06 (op(e3, op(e2, e0)) = e3),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14322, 14316])).
% 1.95/2.06 tff(14324,plain,
% 1.95/2.06 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[10697, 14323])).
% 1.95/2.06 tff(14325,plain,
% 1.95/2.06 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.95/2.06 inference(symmetry,[status(thm)],[7752])).
% 1.95/2.06 tff(14326,plain,
% 1.95/2.06 (op(e3, e2) = op(e2, e1)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14322, 14305])).
% 1.95/2.06 tff(14327,plain,
% 1.95/2.06 ((op(e3, e2) = e1) <=> (op(e2, e1) = e1)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14326])).
% 1.95/2.06 tff(14328,plain,
% 1.95/2.06 ((op(e2, e1) = e1) <=> (op(e3, e2) = e1)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14327])).
% 1.95/2.06 tff(14329,plain,
% 1.95/2.06 ((op(e2, e1) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 1.95/2.06 inference(transitivity,[status(thm)],[14328, 14325, 395])).
% 1.95/2.06 tff(14330,plain,
% 1.95/2.06 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14329])).
% 1.95/2.06 tff(14331,plain,
% 1.95/2.06 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[2684])).
% 1.95/2.06 tff(14332,plain,
% 1.95/2.06 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14331])).
% 1.95/2.06 tff(14333,plain,
% 1.95/2.06 (~(op(e2, e1) = e1)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[197, 14332])).
% 1.95/2.06 tff(14334,plain,
% 1.95/2.06 (~(op(e2, e3) = op(e3, e2))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14333, 14330])).
% 1.95/2.06 tff(14335,plain,
% 1.95/2.06 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[430, 14334])).
% 1.95/2.06 tff(14336,plain,
% 1.95/2.06 (op(e0, op(e2, e1)) = op(e0, e3)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14304])).
% 1.95/2.06 tff(14337,plain,
% 1.95/2.06 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e2, e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14305])).
% 1.95/2.06 tff(14338,plain,
% 1.95/2.06 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14337])).
% 1.95/2.06 tff(14339,plain,
% 1.95/2.06 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e3))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14338])).
% 1.95/2.06 tff(14340,plain,
% 1.95/2.06 (~(op(e0, e1) = e3)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[606, 14339])).
% 1.95/2.06 tff(14341,plain,
% 1.95/2.06 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14322])).
% 1.95/2.06 tff(14342,plain,
% 1.95/2.06 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14341])).
% 1.95/2.06 tff(14343,plain,
% 1.95/2.06 (~(op(e0, e2) = e3)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[1467, 14342])).
% 1.95/2.06 tff(14344,plain,
% 1.95/2.06 (op(e0, e0) = e3),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[1495, 14343, 14340, 661])).
% 1.95/2.06 tff(14345,plain,
% 1.95/2.06 (op(e0, e0) = op(e2, e1)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14344, 14305])).
% 1.95/2.06 tff(14346,plain,
% 1.95/2.06 (op(e0, op(e0, e0)) = op(e0, op(e2, e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14345])).
% 1.95/2.06 tff(14347,plain,
% 1.95/2.06 (op(e0, op(e0, e0)) = e0),
% 1.95/2.06 inference(transitivity,[status(thm)],[14346, 14336, 14317])).
% 1.95/2.06 tff(14348,plain,
% 1.95/2.06 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[5598, 14347])).
% 1.95/2.06 tff(14349,plain,
% 1.95/2.06 (op(e2, op(e2, e2)) = e2),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14313, 10762])).
% 1.95/2.06 tff(14350,plain,
% 1.95/2.06 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[528, 14349])).
% 1.95/2.06 tff(14351,plain,
% 1.95/2.06 ((op(e2, e1) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 1.95/2.06 inference(transitivity,[status(thm)],[14328, 14325])).
% 1.95/2.06 tff(14352,plain,
% 1.95/2.06 ((~(op(e2, e1) = e1)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14351])).
% 1.95/2.06 tff(14353,plain,
% 1.95/2.06 (~(op(e3, e2) = op(e2, e3))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14333, 14352])).
% 1.95/2.06 tff(14354,plain,
% 1.95/2.06 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[500, 14353])).
% 1.95/2.06 tff(14355,plain,
% 1.95/2.06 ((op(e1, e0) = op(e0, e1)) <=> (e0 = op(e0, e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14296])).
% 1.95/2.06 tff(14356,plain,
% 1.95/2.06 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e0)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14355, 5637])).
% 1.95/2.06 tff(14357,plain,
% 1.95/2.06 ((op(e0, e1) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 1.95/2.06 inference(symmetry,[status(thm)],[14356])).
% 1.95/2.06 tff(14358,plain,
% 1.95/2.06 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e1, e0))),
% 1.95/2.06 inference(transitivity,[status(thm)],[14357, 596])).
% 1.95/2.06 tff(14359,plain,
% 1.95/2.06 ((~(op(e0, e1) = e0)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14358])).
% 1.95/2.06 tff(14360,plain,
% 1.95/2.06 (~(op(e0, e1) = op(e1, e0))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14320, 14359])).
% 1.95/2.06 tff(14361,plain,
% 1.95/2.06 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[609, 14360])).
% 1.95/2.06 tff(14362,plain,
% 1.95/2.06 (op(e3, op(e3, e3)) = e3),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14322, 9701])).
% 1.95/2.06 tff(14363,plain,
% 1.95/2.06 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[6277, 14362])).
% 1.95/2.06 tff(14364,plain,
% 1.95/2.06 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14317])).
% 1.95/2.06 tff(14365,plain,
% 1.95/2.06 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 1.95/2.06 inference(symmetry,[status(thm)],[14364])).
% 1.95/2.06 tff(14366,plain,
% 1.95/2.06 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14296])).
% 1.95/2.06 tff(14367,plain,
% 1.95/2.06 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14366, 8115])).
% 1.95/2.06 tff(14368,plain,
% 1.95/2.06 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 1.95/2.06 inference(transitivity,[status(thm)],[14367, 14365, 453])).
% 1.95/2.06 tff(14369,plain,
% 1.95/2.06 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14368])).
% 1.95/2.06 tff(14370,plain,
% 1.95/2.06 (~(op(e0, e3) = op(e3, e0))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[410, 14369])).
% 1.95/2.06 tff(14371,plain,
% 1.95/2.06 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[496, 14370])).
% 1.95/2.06 tff(14372,plain,
% 1.95/2.06 ((~(op(e0, e1) = e0)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14357])).
% 1.95/2.06 tff(14373,plain,
% 1.95/2.06 (~(op(e1, e0) = op(e0, e1))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[14320, 14372])).
% 1.95/2.06 tff(14374,plain,
% 1.95/2.06 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[613, 14373])).
% 1.95/2.06 tff(14375,plain,
% 1.95/2.06 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 1.95/2.06 inference(transitivity,[status(thm)],[14180, 10705])).
% 1.95/2.06 tff(14376,plain,
% 1.95/2.06 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14375])).
% 1.95/2.06 tff(14377,plain,
% 1.95/2.06 (~(op(e2, e0) = op(e0, e2))),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[6205, 14376])).
% 1.95/2.06 tff(14378,plain,
% 1.95/2.06 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[6358, 14377])).
% 1.95/2.06 tff(14379,plain,
% 1.95/2.06 ($false),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[5367, 14188, 14378, 5511, 5669, 5675, 5673, 5670, 5680, 6688, 5681, 5671, 5672, 5667, 5668, 9846])).
% 1.95/2.06 tff(14380,plain,((op(e1, e1) = e2) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e2, e0) = e2)) | (op(e1, e1) = e3) | (op(e1, e1) = e0) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.06 tff(14381,plain,
% 1.95/2.06 (op(e1, e1) = e2),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14380, 14374, 5669, 5511, 5673, 14371, 5680, 14363, 14361, 14354, 14350, 14348, 14335, 14324, 14313, 14309, 84, 10589])).
% 1.95/2.06 tff(14382,plain,
% 1.95/2.06 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14381])).
% 1.95/2.06 tff(14383,plain,
% 1.95/2.06 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14382, 69])).
% 1.95/2.06 tff(14384,plain,
% 1.95/2.06 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 1.95/2.06 inference(symmetry,[status(thm)],[14383])).
% 1.95/2.06 tff(14385,plain,
% 1.95/2.06 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14384])).
% 1.95/2.06 tff(14386,plain,
% 1.95/2.06 (~(op(e1, e1) = e1)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[708, 14385])).
% 1.95/2.06 tff(14387,plain,
% 1.95/2.06 (op(e1, e2) = e1),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[954, 14386, 14302, 13757])).
% 1.95/2.06 tff(14388,plain,
% 1.95/2.06 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14313])).
% 1.95/2.06 tff(14389,plain,
% 1.95/2.06 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14388])).
% 1.95/2.06 tff(14390,plain,
% 1.95/2.06 (~(op(e0, e0) = e2)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[359, 14389])).
% 1.95/2.06 tff(14391,plain,
% 1.95/2.06 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14381])).
% 1.95/2.06 tff(14392,plain,
% 1.95/2.06 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14391])).
% 1.95/2.06 tff(14393,plain,
% 1.95/2.06 (~(op(e0, e1) = e2)),
% 1.95/2.06 inference(modus_ponens,[status(thm)],[792, 14392])).
% 1.95/2.06 tff(14394,plain,
% 1.95/2.06 (op(e0, e2) = e2),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[3652, 14393, 10592, 14390])).
% 1.95/2.06 tff(14395,plain,
% 1.95/2.06 (op(e1, op(e0, e2)) = op(e1, e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14394])).
% 1.95/2.06 tff(14396,plain,
% 1.95/2.06 (op(e1, op(e0, e2)) = e1),
% 1.95/2.06 inference(transitivity,[status(thm)],[14395, 14387])).
% 1.95/2.06 tff(14397,plain,
% 1.95/2.06 (op(op(e2, e1), e2) = op(e3, e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14304])).
% 1.95/2.06 tff(14398,plain,
% 1.95/2.06 (op(e3, op(e1, e1)) = op(op(e2, e1), e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14305, 14381])).
% 1.95/2.06 tff(14399,plain,
% 1.95/2.06 (op(e3, op(e1, e1)) = e3),
% 1.95/2.06 inference(transitivity,[status(thm)],[14398, 14397, 14322])).
% 1.95/2.06 tff(14400,plain,
% 1.95/2.06 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14029, 14399])).
% 1.95/2.06 tff(14401,plain,
% 1.95/2.06 (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[5367, 14400, 5511, 5669, 14374, 5673, 14371, 5680, 14363, 14361, 14354, 14350, 14348, 14335, 14324])).
% 1.95/2.06 tff(14402,plain,
% 1.95/2.06 (~(op(e1, op(e0, e2)) = e1)),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14259, 14401])).
% 1.95/2.06 tff(14403,plain,
% 1.95/2.06 ($false),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14402, 14396])).
% 1.95/2.06 tff(14404,plain,((op(e1, e1) = e0) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (op(e0, e3) = e3) | (~(op(e2, e3) = e1)) | (~(op(e2, e2) = e0)) | (~(op(e3, e3) = e2)) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.06 tff(14405,plain,
% 1.95/2.06 (op(e1, e1) = e0),
% 1.95/2.06 inference(unit_resolution,[status(thm)],[14404, 14295, 14292, 14165, 14150, 14285, 13449, 14066, 2812, 14282])).
% 1.95/2.06 tff(14406,plain,
% 1.95/2.06 (op(e1, e1) = op(e2, e2)),
% 1.95/2.06 inference(transitivity,[status(thm)],[14405, 14067])).
% 1.95/2.06 tff(14407,plain,
% 1.95/2.06 ((op(e1, e1) = e2) <=> (op(e2, e2) = e2)),
% 1.95/2.06 inference(monotonicity,[status(thm)],[14406])).
% 1.95/2.07 tff(14408,plain,
% 1.95/2.07 ((op(e2, e2) = e2) <=> (op(e1, e1) = e2)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14407])).
% 1.95/2.07 tff(14409,plain,
% 1.95/2.07 ((~(op(e2, e2) = e2)) <=> (~(op(e1, e1) = e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14408])).
% 1.95/2.07 tff(14410,plain,
% 1.95/2.07 ((op(e2, e2) = e2) <=> (e0 = e2)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14066])).
% 1.95/2.07 tff(14411,plain,
% 1.95/2.07 ((e0 = e2) <=> (op(e2, e2) = e2)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14410])).
% 1.95/2.07 tff(14412,plain,
% 1.95/2.07 ((~(e0 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14411])).
% 1.95/2.07 tff(14413,plain,
% 1.95/2.07 (~(op(e2, e2) = e2)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[14, 14412])).
% 1.95/2.07 tff(14414,plain,
% 1.95/2.07 (~(op(e1, e1) = e2)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[14413, 14409])).
% 1.95/2.07 tff(14415,plain,
% 1.95/2.07 (op(e0, e1) = e2),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1993, 14414, 9684, 14085])).
% 1.95/2.07 tff(14416,plain,
% 1.95/2.07 (op(op(e0, e1), e0) = op(e2, op(e2, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14415, 14067])).
% 1.95/2.07 tff(14417,plain,
% 1.95/2.07 (op(op(e0, e1), e0) = e2),
% 1.95/2.07 inference(transitivity,[status(thm)],[14416, 14081, 14080])).
% 1.95/2.07 tff(14418,plain,
% 1.95/2.07 ((op(op(e0, e1), e0) = e1) <=> (e2 = e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14417])).
% 1.95/2.07 tff(14419,plain,
% 1.95/2.07 ((op(op(e0, e1), e0) = e1) <=> (e1 = e2)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14418, 69])).
% 1.95/2.07 tff(14420,plain,
% 1.95/2.07 ((e1 = e2) <=> (op(op(e0, e1), e0) = e1)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14419])).
% 1.95/2.07 tff(14421,plain,
% 1.95/2.07 ((~(e1 = e2)) <=> (~(op(op(e0, e1), e0) = e1))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14420])).
% 1.95/2.07 tff(14422,plain,
% 1.95/2.07 (~(op(op(e0, e1), e0) = e1)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[708, 14421])).
% 1.95/2.07 tff(14423,plain,
% 1.95/2.07 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1461, 14422])).
% 1.95/2.07 tff(14424,plain,
% 1.95/2.07 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14080])).
% 1.95/2.07 tff(14425,plain,
% 1.95/2.07 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14424])).
% 1.95/2.07 tff(14426,plain,
% 1.95/2.07 (~(op(e1, e0) = e2)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[756, 14425])).
% 1.95/2.07 tff(14427,plain,
% 1.95/2.07 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14277])).
% 1.95/2.07 tff(14428,plain,
% 1.95/2.07 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14427])).
% 1.95/2.07 tff(14429,plain,
% 1.95/2.07 (~(op(e1, e0) = e3)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[110, 14428])).
% 1.95/2.07 tff(14430,plain,
% 1.95/2.07 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14405])).
% 1.95/2.07 tff(14431,plain,
% 1.95/2.07 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14430])).
% 1.95/2.07 tff(14432,plain,
% 1.95/2.07 (~(op(e1, e0) = e0)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[737, 14431])).
% 1.95/2.07 tff(14433,plain,
% 1.95/2.07 (op(e1, e0) = e1),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[728, 14432, 14429, 14426])).
% 1.95/2.07 tff(14434,plain,
% 1.95/2.07 (op(e1, op(e1, e0)) = op(e1, e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14433])).
% 1.95/2.07 tff(14435,plain,
% 1.95/2.07 (op(e1, op(e1, e0)) = e0),
% 1.95/2.07 inference(transitivity,[status(thm)],[14434, 14405])).
% 1.95/2.07 tff(14436,plain,
% 1.95/2.07 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1836, 14435])).
% 1.95/2.07 tff(14437,plain,
% 1.95/2.07 (op(e1, e2) = e2),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[2285, 14414, 10589, 14426])).
% 1.95/2.07 tff(14438,plain,
% 1.95/2.07 (op(e1, op(e1, e2)) = op(e1, e2)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14437])).
% 1.95/2.07 tff(14439,plain,
% 1.95/2.07 (op(e1, op(e1, e2)) = e2),
% 1.95/2.07 inference(transitivity,[status(thm)],[14438, 14437])).
% 1.95/2.07 tff(14440,plain,
% 1.95/2.07 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[2377, 14439])).
% 1.95/2.07 tff(14441,plain,
% 1.95/2.07 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14405])).
% 1.95/2.07 tff(14442,plain,
% 1.95/2.07 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14441, 5470])).
% 1.95/2.07 tff(14443,plain,
% 1.95/2.07 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14442])).
% 1.95/2.07 tff(14444,plain,
% 1.95/2.07 (~(op(e3, e1) = e0)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[945, 14443])).
% 1.95/2.07 tff(14445,plain,
% 1.95/2.07 (op(e3, e1) = e1),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[446, 14444, 14225, 9684])).
% 1.95/2.07 tff(14446,plain,
% 1.95/2.07 (op(op(e2, e1), e1) = op(e3, e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14089])).
% 1.95/2.07 tff(14447,plain,
% 1.95/2.07 (op(e3, op(e3, e1)) = op(op(e2, e1), e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14090, 14445])).
% 1.95/2.07 tff(14448,plain,
% 1.95/2.07 (op(e3, op(e3, e1)) = e1),
% 1.95/2.07 inference(transitivity,[status(thm)],[14447, 14446, 14445])).
% 1.95/2.07 tff(14449,plain,
% 1.95/2.07 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[2594, 14448])).
% 1.95/2.07 tff(14450,plain,
% 1.95/2.07 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14066])).
% 1.95/2.07 tff(14451,plain,
% 1.95/2.07 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14450, 4959])).
% 1.95/2.07 tff(14452,plain,
% 1.95/2.07 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14451])).
% 1.95/2.07 tff(14453,plain,
% 1.95/2.07 (~(op(e3, e2) = e0)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[1546, 14452])).
% 1.95/2.07 tff(14454,plain,
% 1.95/2.07 (op(e3, e0) = e0),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1916, 14444, 9696, 14453])).
% 1.95/2.07 tff(14455,plain,
% 1.95/2.07 (op(e3, e0) = op(e2, e2)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14454, 14067])).
% 1.95/2.07 tff(14456,plain,
% 1.95/2.07 (op(e3, op(e3, e0)) = op(e3, op(e2, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14455])).
% 1.95/2.07 tff(14457,plain,
% 1.95/2.07 (op(e3, op(e3, e0)) = e0),
% 1.95/2.07 inference(transitivity,[status(thm)],[14456, 14151, 14454])).
% 1.95/2.07 tff(14458,plain,
% 1.95/2.07 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1345, 14457])).
% 1.95/2.07 tff(14459,plain,
% 1.95/2.07 ((op(e3, e1) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14445])).
% 1.95/2.07 tff(14460,plain,
% 1.95/2.07 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14459, 7171])).
% 1.95/2.07 tff(14461,plain,
% 1.95/2.07 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14460])).
% 1.95/2.07 tff(14462,plain,
% 1.95/2.07 (~(op(e3, e2) = e1)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[3429, 14461])).
% 1.95/2.07 tff(14463,plain,
% 1.95/2.07 ((op(e1, e2) = e1) <=> (e2 = e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14437])).
% 1.95/2.07 tff(14464,plain,
% 1.95/2.07 ((op(e1, e2) = e1) <=> (e1 = e2)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14463, 69])).
% 1.95/2.07 tff(14465,plain,
% 1.95/2.07 ((e1 = e2) <=> (op(e1, e2) = e1)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14464])).
% 1.95/2.07 tff(14466,plain,
% 1.95/2.07 ((~(e1 = e2)) <=> (~(op(e1, e2) = e1))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14465])).
% 1.95/2.07 tff(14467,plain,
% 1.95/2.07 (~(op(e1, e2) = e1)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[708, 14466])).
% 1.95/2.07 tff(14468,plain,
% 1.95/2.07 (op(e0, e2) = e1),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1613, 14467, 13623, 14462])).
% 1.95/2.07 tff(14469,plain,
% 1.95/2.07 (op(e0, op(e0, e2)) = e2),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[8031, 14468, 14415])).
% 1.95/2.07 tff(14470,plain,
% 1.95/2.07 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1331, 14469])).
% 1.95/2.07 tff(14471,plain,
% 1.95/2.07 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e2)) = e3)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14152])).
% 1.95/2.07 tff(14472,plain,
% 1.95/2.07 ((op(e3, op(e2, e2)) = e3) <=> (op(e3, e0) = e3)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14471])).
% 1.95/2.07 tff(14473,plain,
% 1.95/2.07 ((op(e2, e2) = op(e2, e1)) <=> (op(e2, e1) = op(e2, e2))),
% 1.95/2.07 inference(commutativity,[status(thm)],[])).
% 1.95/2.07 tff(14474,plain,
% 1.95/2.07 (op(e3, op(e2, e2)) = op(e2, e2)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14151, 14454, 14067])).
% 1.95/2.07 tff(14475,plain,
% 1.95/2.07 ((op(e3, op(e2, e2)) = e3) <=> (op(e2, e2) = op(e2, e1))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14474, 14090])).
% 1.95/2.07 tff(14476,plain,
% 1.95/2.07 ((op(e3, op(e2, e2)) = e3) <=> (op(e2, e1) = op(e2, e2))),
% 1.95/2.07 inference(transitivity,[status(thm)],[14475, 14473])).
% 1.95/2.07 tff(14477,plain,
% 1.95/2.07 ((op(e2, e1) = op(e2, e2)) <=> (op(e3, op(e2, e2)) = e3)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14476])).
% 1.95/2.07 tff(14478,plain,
% 1.95/2.07 ((op(e2, e1) = op(e2, e2)) <=> (op(e3, e0) = e3)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14477, 14472])).
% 1.95/2.07 tff(14479,plain,
% 1.95/2.07 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e3, e0) = e3))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14478])).
% 1.95/2.07 tff(14480,plain,
% 1.95/2.07 (~(op(e3, e0) = e3)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[508, 14479])).
% 1.95/2.07 tff(14481,plain,
% 1.95/2.07 (op(e3, e2) = e3),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[422, 14480, 11641, 14225])).
% 1.95/2.07 tff(14482,plain,
% 1.95/2.07 (op(op(e3, e2), e2) = e3),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[7919, 14481])).
% 1.95/2.07 tff(14483,plain,
% 1.95/2.07 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1339, 14482])).
% 1.95/2.07 tff(14484,plain,
% 1.95/2.07 ($false),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[1459, 14483, 14470, 13590, 14228, 13581, 1304, 14458, 14449, 14234, 14440, 14436, 14423])).
% 1.95/2.07 tff(14485,plain,((~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e3) = e2)) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.07 tff(14486,plain,
% 1.95/2.07 (op(e1, e2) = e3),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[14485, 10604, 2812])).
% 1.95/2.07 tff(14487,plain,
% 1.95/2.07 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14486])).
% 1.95/2.07 tff(14488,plain,
% 1.95/2.07 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14487, 3423])).
% 1.95/2.07 tff(14489,plain,
% 1.95/2.07 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14488])).
% 1.95/2.07 tff(14490,plain,
% 1.95/2.07 (~(op(e3, e2) = e3)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[2292, 14489])).
% 1.95/2.07 tff(14491,plain,
% 1.95/2.07 (e3 = op(e1, e2)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14486])).
% 1.95/2.07 tff(14492,plain,
% 1.95/2.07 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e1, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14491])).
% 1.95/2.07 tff(14493,plain,
% 1.95/2.07 ((op(e1, e3) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 1.95/2.07 inference(transitivity,[status(thm)],[14492, 125])).
% 1.95/2.07 tff(14494,plain,
% 1.95/2.07 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14493])).
% 1.95/2.07 tff(14495,plain,
% 1.95/2.07 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14494])).
% 1.95/2.07 tff(14496,plain,
% 1.95/2.07 (~(op(e1, e3) = e3)),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[1850, 14495])).
% 1.95/2.07 tff(14497,plain,
% 1.95/2.07 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14491])).
% 1.95/2.07 tff(14498,plain,
% 1.95/2.07 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14497])).
% 1.95/2.07 tff(14499,plain,
% 1.95/2.07 ((op(e1, op(e1, e2)) = e1) <=> (op(e1, e3) = e1)),
% 1.95/2.07 inference(symmetry,[status(thm)],[14498])).
% 1.95/2.07 tff(14500,plain,
% 1.95/2.07 ((e2 = op(e1, op(e1, e1))) <=> (e2 = op(e1, e0))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[13232])).
% 1.95/2.07 tff(14501,plain,
% 1.95/2.07 ((e2 = op(e1, op(e1, e1))) <=> (op(e1, e0) = e2)),
% 1.95/2.07 inference(transitivity,[status(thm)],[14500, 2154])).
% 1.95/2.07 tff(14502,plain,
% 1.95/2.07 ((op(e1, e0) = e2) <=> (e2 = op(e1, op(e1, e1)))),
% 1.95/2.07 inference(symmetry,[status(thm)],[14501])).
% 1.95/2.07 tff(14503,plain,
% 1.95/2.07 (op(e1, e0) = e2),
% 1.95/2.07 inference(unit_resolution,[status(thm)],[2285, 13190, 72, 9280])).
% 1.95/2.07 tff(14504,plain,
% 1.95/2.07 (e2 = op(e1, op(e1, e1))),
% 1.95/2.07 inference(modus_ponens,[status(thm)],[14503, 14502])).
% 1.95/2.07 tff(14505,plain,
% 1.95/2.07 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e0))),
% 1.95/2.07 inference(monotonicity,[status(thm)],[13232])).
% 1.95/2.07 tff(14506,plain,
% 1.95/2.07 (op(e1, op(e1, e0)) = op(e1, op(e1, op(e1, e1)))),
% 1.95/2.07 inference(symmetry,[status(thm)],[14505])).
% 1.95/2.07 tff(14507,plain,
% 1.95/2.07 (op(e1, op(e1, e0)) = op(e1, e2)),
% 1.95/2.07 inference(monotonicity,[status(thm)],[14503])).
% 1.95/2.07 tff(14508,plain,
% 1.95/2.07 (op(e1, e2) = op(e1, op(e1, e0))),
% 1.95/2.07 inference(symmetry,[status(thm)],[14507])).
% 1.97/2.07 tff(14509,plain,
% 1.97/2.07 (e3 = op(e1, op(e1, op(e1, e1)))),
% 1.97/2.07 inference(transitivity,[status(thm)],[2900, 14508, 14506])).
% 1.97/2.07 tff(14510,plain,
% 1.97/2.07 ($false),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[2198, 14509, 14504, 250])).
% 1.97/2.07 tff(14511,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e2) = e3)) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.07 tff(14512,plain,
% 1.97/2.07 (~(op(e1, e1) = e0)),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[14511, 14486, 10589])).
% 1.97/2.07 tff(14513,plain,
% 1.97/2.07 (~(op(e3, e1) = e0)),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[10084, 14490, 2812])).
% 1.97/2.07 tff(14514,plain,
% 1.97/2.07 ((e0 = e3) <=> (e0 = op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.07 tff(14515,plain,
% 1.97/2.07 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14514, 67])).
% 1.97/2.07 tff(14516,plain,
% 1.97/2.07 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14515])).
% 1.97/2.07 tff(14517,plain,
% 1.97/2.07 (~(op(e1, e2) = e0)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[181, 14516])).
% 1.97/2.07 tff(14518,plain,
% 1.97/2.07 (op(e1, op(e1, e2)) = op(e1, e3)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14497])).
% 1.97/2.07 tff(14519,plain,
% 1.97/2.07 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[10603, 11818, 10592, 10589])).
% 1.97/2.07 tff(14520,plain,
% 1.97/2.07 (op(e1, e2) = e3),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[14485, 14519, 2812])).
% 1.97/2.07 tff(14521,plain,
% 1.97/2.07 (e3 = op(e1, e2)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14520])).
% 1.97/2.07 tff(14522,plain,
% 1.97/2.07 ((e0 = e3) <=> (e0 = op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14521])).
% 1.97/2.07 tff(14523,plain,
% 1.97/2.07 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14522, 67])).
% 1.97/2.07 tff(14524,plain,
% 1.97/2.07 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14523])).
% 1.97/2.07 tff(14525,plain,
% 1.97/2.07 (~(op(e1, e2) = e0)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[181, 14524])).
% 1.97/2.07 tff(14526,plain,
% 1.97/2.07 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14520])).
% 1.97/2.07 tff(14527,plain,
% 1.97/2.07 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14526, 1314])).
% 1.97/2.07 tff(14528,plain,
% 1.97/2.07 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14527])).
% 1.97/2.07 tff(14529,plain,
% 1.97/2.07 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14528])).
% 1.97/2.07 tff(14530,plain,
% 1.97/2.07 (~(op(e1, e2) = e2)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[1321, 14529])).
% 1.97/2.07 tff(14531,plain,
% 1.97/2.07 (op(e1, e0) = e2),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[2285, 68, 10589, 14530])).
% 1.97/2.07 tff(14532,plain,
% 1.97/2.07 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14531])).
% 1.97/2.07 tff(14533,plain,
% 1.97/2.07 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14532, 1])).
% 1.97/2.07 tff(14534,plain,
% 1.97/2.07 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14533])).
% 1.97/2.07 tff(14535,plain,
% 1.97/2.07 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14534])).
% 1.97/2.07 tff(14536,plain,
% 1.97/2.07 (~(op(e1, e0) = e0)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[14, 14535])).
% 1.97/2.07 tff(14537,plain,
% 1.97/2.07 (op(e1, e3) = e0),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[1830, 14536, 14525, 84])).
% 1.97/2.07 tff(14538,plain,
% 1.97/2.07 (e0 = op(e1, e3)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14537])).
% 1.97/2.07 tff(14539,plain,
% 1.97/2.07 (op(e3, e0) = op(e3, op(e1, e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14538])).
% 1.97/2.07 tff(14540,plain,
% 1.97/2.07 (op(e3, op(e1, e3)) = op(e3, e0)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14539])).
% 1.97/2.07 tff(14541,plain,
% 1.97/2.07 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14521])).
% 1.97/2.07 tff(14542,plain,
% 1.97/2.07 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14541])).
% 1.97/2.07 tff(14543,plain,
% 1.97/2.07 ((op(e1, op(e1, e2)) = e1) <=> (op(e1, e3) = e1)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14542])).
% 1.97/2.07 tff(14544,plain,
% 1.97/2.07 ((e1 = op(e1, op(e1, e2))) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.07 inference(commutativity,[status(thm)],[])).
% 1.97/2.07 tff(14545,plain,
% 1.97/2.07 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14521])).
% 1.97/2.07 tff(14546,plain,
% 1.97/2.07 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14545])).
% 1.97/2.07 tff(14547,plain,
% 1.97/2.07 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14546])).
% 1.97/2.07 tff(14548,plain,
% 1.97/2.07 (~(op(e1, e1) = e3)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[1604, 14547])).
% 1.97/2.07 tff(14549,plain,
% 1.97/2.07 (op(e1, e1) = e1),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[630, 68, 14548, 84])).
% 1.97/2.07 tff(14550,plain,
% 1.97/2.07 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, op(e1, e2)))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14549, 14541])).
% 1.97/2.07 tff(14551,plain,
% 1.97/2.07 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14550, 14544])).
% 1.97/2.07 tff(14552,plain,
% 1.97/2.07 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14551, 14543])).
% 1.97/2.07 tff(14553,plain,
% 1.97/2.07 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14552])).
% 1.97/2.07 tff(14554,plain,
% 1.97/2.07 (~(op(e1, e3) = e1)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[619, 14553])).
% 1.97/2.07 tff(14555,plain,
% 1.97/2.07 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14521])).
% 1.97/2.07 tff(14556,plain,
% 1.97/2.07 ((op(e1, e3) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 1.97/2.07 inference(transitivity,[status(thm)],[14555, 125])).
% 1.97/2.07 tff(14557,plain,
% 1.97/2.07 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14556])).
% 1.97/2.07 tff(14558,plain,
% 1.97/2.07 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14557])).
% 1.97/2.07 tff(14559,plain,
% 1.97/2.07 (~(op(e1, e3) = e3)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[1850, 14558])).
% 1.97/2.07 tff(14560,plain,
% 1.97/2.07 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e1, e2))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14521])).
% 1.97/2.07 tff(14561,plain,
% 1.97/2.07 ((op(e3, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 1.97/2.07 inference(transitivity,[status(thm)],[14560, 3635])).
% 1.97/2.07 tff(14562,plain,
% 1.97/2.07 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.97/2.07 inference(symmetry,[status(thm)],[14561])).
% 1.97/2.07 tff(14563,plain,
% 1.97/2.07 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14562])).
% 1.97/2.07 tff(14564,plain,
% 1.97/2.07 (~(op(e3, e2) = e3)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[2292, 14563])).
% 1.97/2.07 tff(14565,plain,
% 1.97/2.07 (~(op(e3, e1) = e0)),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[10084, 14564, 2812])).
% 1.97/2.07 tff(14566,plain,
% 1.97/2.07 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14549])).
% 1.97/2.07 tff(14567,plain,
% 1.97/2.07 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14566, 7793])).
% 1.97/2.07 tff(14568,plain,
% 1.97/2.07 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14567])).
% 1.97/2.07 tff(14569,plain,
% 1.97/2.07 (~(op(e3, e1) = e1)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[945, 14568])).
% 1.97/2.07 tff(14570,plain,
% 1.97/2.07 (op(e3, e1) = e3),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[446, 14569, 14565, 9684])).
% 1.97/2.07 tff(14571,plain,
% 1.97/2.07 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14570])).
% 1.97/2.07 tff(14572,plain,
% 1.97/2.07 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14571])).
% 1.97/2.07 tff(14573,plain,
% 1.97/2.07 (~(op(e0, e1) = e3)),
% 1.97/2.07 inference(modus_ponens,[status(thm)],[3046, 14572])).
% 1.97/2.07 tff(14574,plain,
% 1.97/2.07 (op(e3, e2) = e0),
% 1.97/2.07 inference(unit_resolution,[status(thm)],[12046, 14573, 76, 17, 14559, 10589, 9667, 14554])).
% 1.97/2.07 tff(14575,plain,
% 1.97/2.07 (op(e3, e2) = op(e1, e3)),
% 1.97/2.07 inference(transitivity,[status(thm)],[14574, 14538])).
% 1.97/2.07 tff(14576,plain,
% 1.97/2.07 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14575])).
% 1.97/2.07 tff(14577,plain,
% 1.97/2.07 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.97/2.07 inference(transitivity,[status(thm)],[6490, 14576, 14540])).
% 1.97/2.07 tff(14578,plain,
% 1.97/2.07 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.97/2.07 inference(monotonicity,[status(thm)],[14577])).
% 1.97/2.07 tff(14579,plain,
% 1.97/2.07 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14578, 6411])).
% 1.97/2.08 tff(14580,plain,
% 1.97/2.08 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14579])).
% 1.97/2.08 tff(14581,plain,
% 1.97/2.08 (e0 = op(e3, op(e3, e3))),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14574, 6497])).
% 1.97/2.08 tff(14582,plain,
% 1.97/2.08 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[5879, 14581, 2813])).
% 1.97/2.08 tff(14583,plain,
% 1.97/2.08 (~(op(e3, e0) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14582, 14580])).
% 1.97/2.08 tff(14584,plain,
% 1.97/2.08 (op(e3, e2) = op(e1, op(e1, e2))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14574, 14538, 14541])).
% 1.97/2.08 tff(14585,plain,
% 1.97/2.08 ((op(e3, e2) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14584])).
% 1.97/2.08 tff(14586,plain,
% 1.97/2.08 ((op(e1, op(e1, e2)) = e1) <=> (op(e3, e2) = e1)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14585])).
% 1.97/2.08 tff(14587,plain,
% 1.97/2.08 ((~(op(e1, op(e1, e2)) = e1)) <=> (~(op(e3, e2) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14586])).
% 1.97/2.08 tff(14588,plain,
% 1.97/2.08 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, op(e1, e2)) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14551])).
% 1.97/2.08 tff(14589,plain,
% 1.97/2.08 (~(op(e1, op(e1, e2)) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[619, 14588])).
% 1.97/2.08 tff(14590,plain,
% 1.97/2.08 (~(op(e3, e2) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14589, 14587])).
% 1.97/2.08 tff(14591,plain,
% 1.97/2.08 (op(e3, e0) = e1),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[939, 14590, 9667, 14569])).
% 1.97/2.08 tff(14592,plain,
% 1.97/2.08 ($false),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[14591, 14583])).
% 1.97/2.08 tff(14593,plain,((op(e1, e1) = e2) | (~(op(e3, e3) = e2)) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.08 tff(14594,plain,
% 1.97/2.08 (op(e1, e1) = e2),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[14593, 84, 76, 17, 2812])).
% 1.97/2.08 tff(14595,plain,
% 1.97/2.08 (op(e1, op(e1, e1)) = op(e1, e2)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14594])).
% 1.97/2.08 tff(14596,plain,
% 1.97/2.08 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14595])).
% 1.97/2.08 tff(14597,plain,
% 1.97/2.08 (op(e1, op(e1, op(e1, e1))) = op(e1, e3)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14596, 14518])).
% 1.97/2.08 tff(14598,plain,
% 1.97/2.08 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14597])).
% 1.97/2.08 tff(14599,plain,
% 1.97/2.08 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e3) = e0)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14598, 6095])).
% 1.97/2.08 tff(14600,plain,
% 1.97/2.08 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e3) = e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14599])).
% 1.97/2.08 tff(14601,plain,
% 1.97/2.08 (e2 = op(e1, e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14594, 2254])).
% 1.97/2.08 tff(14602,plain,
% 1.97/2.08 (op(e1, e2) = op(e1, op(e1, e1))),
% 1.97/2.08 inference(symmetry,[status(thm)],[14595])).
% 1.97/2.08 tff(14603,plain,
% 1.97/2.08 (e3 = op(e1, op(e1, e1))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14491, 14602])).
% 1.97/2.08 tff(14604,plain,
% 1.97/2.08 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2920, 14603, 14601])).
% 1.97/2.08 tff(14605,plain,
% 1.97/2.08 (~(op(e1, e3) = e0)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14604, 14600])).
% 1.97/2.08 tff(14606,plain,
% 1.97/2.08 (op(e1, e0) = e0),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[1830, 14605, 14517, 84])).
% 1.97/2.08 tff(14607,plain,
% 1.97/2.08 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14606])).
% 1.97/2.08 tff(14608,plain,
% 1.97/2.08 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14607, 8115])).
% 1.97/2.08 tff(14609,plain,
% 1.97/2.08 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14608])).
% 1.97/2.08 tff(14610,plain,
% 1.97/2.08 (~(op(e3, e0) = e0)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[410, 14609])).
% 1.97/2.08 tff(14611,plain,
% 1.97/2.08 (op(e3, e2) = e0),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[1916, 14610, 9696, 14513])).
% 1.97/2.08 tff(14612,plain,
% 1.97/2.08 (e0 = op(e3, e2)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14611])).
% 1.97/2.08 tff(14613,plain,
% 1.97/2.08 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14606])).
% 1.97/2.08 tff(14614,plain,
% 1.97/2.08 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14613, 4499])).
% 1.97/2.08 tff(14615,plain,
% 1.97/2.08 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14614])).
% 1.97/2.08 tff(14616,plain,
% 1.97/2.08 (~(op(e2, e0) = e0)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[756, 14615])).
% 1.97/2.08 tff(14617,plain,
% 1.97/2.08 (op(e1, e3) = e1),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[104, 14605, 10589, 14496])).
% 1.97/2.08 tff(14618,plain,
% 1.97/2.08 (e1 = op(e1, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14617])).
% 1.97/2.08 tff(14619,plain,
% 1.97/2.08 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e1, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14618])).
% 1.97/2.08 tff(14620,plain,
% 1.97/2.08 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14619])).
% 1.97/2.08 tff(14621,plain,
% 1.97/2.08 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14620])).
% 1.97/2.08 tff(14622,plain,
% 1.97/2.08 (~(op(e0, e3) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[64, 14621])).
% 1.97/2.08 tff(14623,plain,
% 1.97/2.08 (~(op(e2, e1) = e0)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[7630, 14622, 76, 10592, 14605])).
% 1.97/2.08 tff(14624,plain,
% 1.97/2.08 (op(e2, e3) = e0),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2311, 14623, 17, 14616])).
% 1.97/2.08 tff(14625,plain,
% 1.97/2.08 (op(e2, e3) = e3),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[10335, 14622, 10592, 10589, 76, 14605])).
% 1.97/2.08 tff(14626,plain,
% 1.97/2.08 (e3 = op(e2, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14625])).
% 1.97/2.08 tff(14627,plain,
% 1.97/2.08 (op(e1, e2) = op(e3, e2)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14486, 14626, 14624, 14612])).
% 1.97/2.08 tff(14628,plain,
% 1.97/2.08 ($false),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2292, 14627])).
% 1.97/2.08 tff(14629,plain,((op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.08 tff(14630,plain,
% 1.97/2.08 (op(e2, e3) = e1),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[14629, 17, 14512, 2812])).
% 1.97/2.08 tff(14631,plain,
% 1.97/2.08 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14497, 14630])).
% 1.97/2.08 tff(14632,plain,
% 1.97/2.08 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14631, 14499])).
% 1.97/2.08 tff(14633,plain,
% 1.97/2.08 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14632])).
% 1.97/2.08 tff(14634,plain,
% 1.97/2.08 (~(op(e1, e3) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[118, 14633])).
% 1.97/2.08 tff(14635,plain,
% 1.97/2.08 (op(e1, e3) = e0),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[104, 14634, 10589, 14496])).
% 1.97/2.08 tff(14636,plain,
% 1.97/2.08 (op(e3, op(e1, e3)) = op(e3, e0)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14635])).
% 1.97/2.08 tff(14637,plain,
% 1.97/2.08 (e0 = op(e1, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14635])).
% 1.97/2.08 tff(14638,plain,
% 1.97/2.08 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14639,plain,
% 1.97/2.08 ((op(e3, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14638, 3635])).
% 1.97/2.08 tff(14640,plain,
% 1.97/2.08 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14639])).
% 1.97/2.08 tff(14641,plain,
% 1.97/2.08 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14640])).
% 1.97/2.08 tff(14642,plain,
% 1.97/2.08 (~(op(e3, e2) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[2292, 14641])).
% 1.97/2.08 tff(14643,plain,
% 1.97/2.08 (~(op(e3, e1) = e0)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[10084, 14642, 2812])).
% 1.97/2.08 tff(14644,plain,
% 1.97/2.08 ((op(e2, e3) = e3) <=> (e1 = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14630, 14491])).
% 1.97/2.08 tff(14645,plain,
% 1.97/2.08 ((op(e2, e3) = e3) <=> (op(e1, e2) = e1)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14644, 5522])).
% 1.97/2.08 tff(14646,plain,
% 1.97/2.08 ((op(e1, e2) = e1) <=> (op(e2, e3) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14645])).
% 1.97/2.08 tff(14647,plain,
% 1.97/2.08 ((~(op(e1, e2) = e1)) <=> (~(op(e2, e3) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14646])).
% 1.97/2.08 tff(14648,plain,
% 1.97/2.08 ((e1 = e3) <=> (e1 = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14649,plain,
% 1.97/2.08 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14648, 5522])).
% 1.97/2.08 tff(14650,plain,
% 1.97/2.08 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14649])).
% 1.97/2.08 tff(14651,plain,
% 1.97/2.08 (~(op(e1, e2) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[303, 14650])).
% 1.97/2.08 tff(14652,plain,
% 1.97/2.08 (~(op(e2, e3) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14651, 14647])).
% 1.97/2.08 tff(14653,plain,
% 1.97/2.08 (op(e0, e3) = e3),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[480, 14652, 11641, 14496])).
% 1.97/2.08 tff(14654,plain,
% 1.97/2.08 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14655,plain,
% 1.97/2.08 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14654])).
% 1.97/2.08 tff(14656,plain,
% 1.97/2.08 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14655])).
% 1.97/2.08 tff(14657,plain,
% 1.97/2.08 (~(op(e1, e1) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[1604, 14656])).
% 1.97/2.08 tff(14658,plain,
% 1.97/2.08 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14659,plain,
% 1.97/2.08 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14658])).
% 1.97/2.08 tff(14660,plain,
% 1.97/2.08 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14659])).
% 1.97/2.08 tff(14661,plain,
% 1.97/2.08 (~(op(e1, e0) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[1312, 14660])).
% 1.97/2.08 tff(14662,plain,
% 1.97/2.08 (op(e1, e1) = e1),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2924, 14635, 2812, 14661, 14657, 14630, 14653])).
% 1.97/2.08 tff(14663,plain,
% 1.97/2.08 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14662])).
% 1.97/2.08 tff(14664,plain,
% 1.97/2.08 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14663, 7793])).
% 1.97/2.08 tff(14665,plain,
% 1.97/2.08 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14664])).
% 1.97/2.08 tff(14666,plain,
% 1.97/2.08 (~(op(e3, e1) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[945, 14665])).
% 1.97/2.08 tff(14667,plain,
% 1.97/2.08 (op(e3, e1) = e3),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[446, 14666, 14643, 9684])).
% 1.97/2.08 tff(14668,plain,
% 1.97/2.08 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e3)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14653])).
% 1.97/2.08 tff(14669,plain,
% 1.97/2.08 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14668])).
% 1.97/2.08 tff(14670,plain,
% 1.97/2.08 (~(op(e0, e0) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[3414, 14669])).
% 1.97/2.08 tff(14671,plain,
% 1.97/2.08 (e3 = op(e0, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14653])).
% 1.97/2.08 tff(14672,plain,
% 1.97/2.08 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14671])).
% 1.97/2.08 tff(14673,plain,
% 1.97/2.08 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14672])).
% 1.97/2.08 tff(14674,plain,
% 1.97/2.08 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14673])).
% 1.97/2.08 tff(14675,plain,
% 1.97/2.08 (op(e0, op(e1, e2)) = op(e0, e3)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14486])).
% 1.97/2.08 tff(14676,plain,
% 1.97/2.08 (op(e0, e3) = op(e1, e2)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14653, 14491])).
% 1.97/2.08 tff(14677,plain,
% 1.97/2.08 (op(e0, op(e0, e3)) = op(e0, op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14676])).
% 1.97/2.08 tff(14678,plain,
% 1.97/2.08 (op(e0, op(e0, e3)) = op(e1, e2)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14677, 14675, 14653, 14491])).
% 1.97/2.08 tff(14679,plain,
% 1.97/2.08 ((op(e0, op(e0, e3)) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14678, 14637])).
% 1.97/2.08 tff(14680,plain,
% 1.97/2.08 ((op(e1, e2) = op(e1, e3)) <=> (op(e0, op(e0, e3)) = e0)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14679])).
% 1.97/2.08 tff(14681,plain,
% 1.97/2.08 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14680])).
% 1.97/2.08 tff(14682,plain,
% 1.97/2.08 (~(op(e0, op(e0, e3)) = e0)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[1850, 14681])).
% 1.97/2.08 tff(14683,plain,
% 1.97/2.08 (e1 = op(e2, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14630])).
% 1.97/2.08 tff(14684,plain,
% 1.97/2.08 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14683])).
% 1.97/2.08 tff(14685,plain,
% 1.97/2.08 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14684])).
% 1.97/2.08 tff(14686,plain,
% 1.97/2.08 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14685])).
% 1.97/2.08 tff(14687,plain,
% 1.97/2.08 (~(op(e0, e3) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[964, 14686])).
% 1.97/2.08 tff(14688,plain,
% 1.97/2.08 ((e0 = e1) <=> (e0 = op(e2, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14683])).
% 1.97/2.08 tff(14689,plain,
% 1.97/2.08 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14688, 86])).
% 1.97/2.08 tff(14690,plain,
% 1.97/2.08 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14689])).
% 1.97/2.08 tff(14691,plain,
% 1.97/2.08 (~(op(e2, e3) = e0)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[26, 14690])).
% 1.97/2.08 tff(14692,plain,
% 1.97/2.08 (~(op(op(e1, e3), e1) = e3)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[1107, 14652, 14691, 14496, 9696, 12016, 11641, 14687])).
% 1.97/2.08 tff(14693,plain,
% 1.97/2.08 (op(op(e2, e3), e3) = op(e1, op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14630, 14491])).
% 1.97/2.08 tff(14694,plain,
% 1.97/2.08 (op(e1, op(e0, e3)) = op(op(e2, e3), e3)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14683, 14653])).
% 1.97/2.08 tff(14695,plain,
% 1.97/2.08 (op(e1, op(e0, e3)) = op(e1, e3)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14694, 14693, 14518])).
% 1.97/2.08 tff(14696,plain,
% 1.97/2.08 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14695, 14683])).
% 1.97/2.08 tff(14697,plain,
% 1.97/2.08 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, op(e0, e3)) = e1)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14696])).
% 1.97/2.08 tff(14698,plain,
% 1.97/2.08 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, op(e0, e3)) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14697])).
% 1.97/2.08 tff(14699,plain,
% 1.97/2.08 (~(op(e1, op(e0, e3)) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[118, 14698])).
% 1.97/2.08 tff(14700,plain,
% 1.97/2.08 (op(e3, op(e0, e3)) = op(e3, e3)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14653])).
% 1.97/2.08 tff(14701,plain,
% 1.97/2.08 (op(e3, op(e0, e3)) = e2),
% 1.97/2.08 inference(transitivity,[status(thm)],[14700, 2812])).
% 1.97/2.08 tff(14702,plain,
% 1.97/2.08 ((op(e3, op(e0, e3)) = e3) <=> (e2 = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14701, 14491])).
% 1.97/2.08 tff(14703,plain,
% 1.97/2.08 ((op(e3, op(e0, e3)) = e3) <=> (op(e1, e2) = e2)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14702, 5762])).
% 1.97/2.08 tff(14704,plain,
% 1.97/2.08 ((op(e1, e2) = e2) <=> (op(e3, op(e0, e3)) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14703])).
% 1.97/2.08 tff(14705,plain,
% 1.97/2.08 ((~(op(e1, e2) = e2)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14704])).
% 1.97/2.08 tff(14706,plain,
% 1.97/2.08 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14486])).
% 1.97/2.08 tff(14707,plain,
% 1.97/2.08 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14706, 1314])).
% 1.97/2.08 tff(14708,plain,
% 1.97/2.08 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14707])).
% 1.97/2.08 tff(14709,plain,
% 1.97/2.08 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14708])).
% 1.97/2.08 tff(14710,plain,
% 1.97/2.08 (~(op(e1, e2) = e2)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[1321, 14709])).
% 1.97/2.08 tff(14711,plain,
% 1.97/2.08 (~(op(e3, op(e0, e3)) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14710, 14705])).
% 1.97/2.08 tff(14712,plain,
% 1.97/2.08 (op(e2, op(e0, e3)) = op(e2, op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14676])).
% 1.97/2.08 tff(14713,plain,
% 1.97/2.08 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, op(e1, e2)) = e2)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14712])).
% 1.97/2.08 tff(14714,plain,
% 1.97/2.08 ((op(e2, op(e1, e2)) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14713])).
% 1.97/2.08 tff(14715,plain,
% 1.97/2.08 ((~(op(e2, op(e1, e2)) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14714])).
% 1.97/2.08 tff(14716,plain,
% 1.97/2.08 (op(e2, e3) = op(e2, op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14717,plain,
% 1.97/2.08 (op(e2, op(e1, e2)) = op(e2, e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14716])).
% 1.97/2.08 tff(14718,plain,
% 1.97/2.08 ((op(e2, op(e1, e2)) = e2) <=> (op(e2, e3) = e2)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14717])).
% 1.97/2.08 tff(14719,plain,
% 1.97/2.08 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e2)) = e2)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14718])).
% 1.97/2.08 tff(14720,plain,
% 1.97/2.08 ((~(op(e2, e3) = e2)) <=> (~(op(e2, op(e1, e2)) = e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14719])).
% 1.97/2.08 tff(14721,plain,
% 1.97/2.08 (~(op(e2, op(e1, e2)) = e2)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[9692, 14720])).
% 1.97/2.08 tff(14722,plain,
% 1.97/2.08 (~(op(e2, op(e0, e3)) = e2)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14721, 14715])).
% 1.97/2.08 tff(14723,plain,
% 1.97/2.08 (~(op(e3, e0) = op(e0, e3))),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[3220, 14722, 14687, 14711, 14699, 14692, 14682])).
% 1.97/2.08 tff(14724,plain,
% 1.97/2.08 (~(op(e3, e0) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[14723, 14674])).
% 1.97/2.08 tff(14725,plain,
% 1.97/2.08 (op(e2, e0) = e3),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2713, 14724, 14670, 14661])).
% 1.97/2.08 tff(14726,plain,
% 1.97/2.08 (op(e2, e0) = op(e1, e2)),
% 1.97/2.08 inference(transitivity,[status(thm)],[14725, 14491])).
% 1.97/2.08 tff(14727,plain,
% 1.97/2.08 ((op(e2, e0) = op(e0, e2)) <=> (op(e1, e2) = op(e0, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14726])).
% 1.97/2.08 tff(14728,plain,
% 1.97/2.08 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e1, e2))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14727, 8060])).
% 1.97/2.08 tff(14729,plain,
% 1.97/2.08 ((op(e0, e2) = op(e1, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 1.97/2.08 inference(symmetry,[status(thm)],[14728])).
% 1.97/2.08 tff(14730,plain,
% 1.97/2.08 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = op(e2, e0))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14729, 6337])).
% 1.97/2.08 tff(14731,plain,
% 1.97/2.08 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14730])).
% 1.97/2.08 tff(14732,plain,
% 1.97/2.08 (~(op(e0, e2) = op(e2, e0))),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[6205, 14731])).
% 1.97/2.08 tff(14733,plain,
% 1.97/2.08 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[6347, 14732])).
% 1.97/2.08 tff(14734,plain,
% 1.97/2.08 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14729])).
% 1.97/2.08 tff(14735,plain,
% 1.97/2.08 (~(op(e2, e0) = op(e0, e2))),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[6205, 14734])).
% 1.97/2.08 tff(14736,plain,
% 1.97/2.08 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[6358, 14735])).
% 1.97/2.08 tff(14737,plain,
% 1.97/2.08 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e1, e2))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.08 tff(14738,plain,
% 1.97/2.08 ((op(e2, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 1.97/2.08 inference(transitivity,[status(thm)],[14737, 8066])).
% 1.97/2.08 tff(14739,plain,
% 1.97/2.08 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14738])).
% 1.97/2.08 tff(14740,plain,
% 1.97/2.08 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14739])).
% 1.97/2.08 tff(14741,plain,
% 1.97/2.08 (~(op(e2, e2) = e3)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[1273, 14740])).
% 1.97/2.08 tff(14742,plain,
% 1.97/2.08 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e2, e3))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14683])).
% 1.97/2.08 tff(14743,plain,
% 1.97/2.08 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 1.97/2.08 inference(symmetry,[status(thm)],[14742])).
% 1.97/2.08 tff(14744,plain,
% 1.97/2.08 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14743])).
% 1.97/2.08 tff(14745,plain,
% 1.97/2.08 (~(op(e2, e2) = e1)),
% 1.97/2.08 inference(modus_ponens,[status(thm)],[515, 14744])).
% 1.97/2.08 tff(14746,plain,
% 1.97/2.08 (op(e2, e2) = e2),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[524, 14745, 14741, 17])).
% 1.97/2.08 tff(14747,plain,
% 1.97/2.08 (~(op(e1, e1) = e2)),
% 1.97/2.08 inference(unit_resolution,[status(thm)],[2922, 14635, 14486, 2812, 14630, 14653])).
% 1.97/2.08 tff(14748,plain,
% 1.97/2.08 (op(e2, op(e2, e3)) = op(e2, e1)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14630])).
% 1.97/2.08 tff(14749,plain,
% 1.97/2.08 (op(e2, e1) = op(e2, op(e2, e3))),
% 1.97/2.08 inference(symmetry,[status(thm)],[14748])).
% 1.97/2.08 tff(14750,plain,
% 1.97/2.08 ((op(e2, e1) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 1.97/2.08 inference(monotonicity,[status(thm)],[14749])).
% 1.97/2.09 tff(14751,plain,
% 1.97/2.09 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e1) = e2)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14750])).
% 1.97/2.09 tff(14752,plain,
% 1.97/2.09 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, op(e2, e3)) = e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14749, 14746])).
% 1.97/2.09 tff(14753,plain,
% 1.97/2.09 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e2)),
% 1.97/2.09 inference(transitivity,[status(thm)],[14752, 14751])).
% 1.97/2.09 tff(14754,plain,
% 1.97/2.09 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e2))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14753])).
% 1.97/2.09 tff(14755,plain,
% 1.97/2.09 (~(op(e2, e1) = e2)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[508, 14754])).
% 1.97/2.09 tff(14756,plain,
% 1.97/2.09 (op(e0, e1) = e2),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[1993, 14755, 9684, 14747])).
% 1.97/2.09 tff(14757,plain,
% 1.97/2.09 (op(e2, op(e0, e1)) = op(e2, e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14756])).
% 1.97/2.09 tff(14758,plain,
% 1.97/2.09 (op(e2, op(e0, e1)) = e2),
% 1.97/2.09 inference(transitivity,[status(thm)],[14757, 14746])).
% 1.97/2.09 tff(14759,plain,
% 1.97/2.09 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[9902, 14758])).
% 1.97/2.09 tff(14760,plain,
% 1.97/2.09 (op(e1, e0) = e2),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[2285, 14747, 10589, 14710])).
% 1.97/2.09 tff(14761,plain,
% 1.97/2.09 (op(e2, op(e1, e0)) = op(e2, e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14760])).
% 1.97/2.09 tff(14762,plain,
% 1.97/2.09 (op(e2, op(e1, e0)) = e2),
% 1.97/2.09 inference(transitivity,[status(thm)],[14761, 14746])).
% 1.97/2.09 tff(14763,plain,
% 1.97/2.09 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[10735, 14762])).
% 1.97/2.09 tff(14764,plain,
% 1.97/2.09 (~(op(e0, e3) = op(e3, e0))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14723, 454])).
% 1.97/2.09 tff(14765,plain,
% 1.97/2.09 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[496, 14764])).
% 1.97/2.09 tff(14766,plain,
% 1.97/2.09 (op(e2, op(e3, e3)) = op(e2, e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[2812])).
% 1.97/2.09 tff(14767,plain,
% 1.97/2.09 ((op(e2, op(e3, e3)) = e2) <=> (op(e2, e2) = e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14766])).
% 1.97/2.09 tff(14768,plain,
% 1.97/2.09 ((op(e2, e2) = e2) <=> (op(e2, op(e3, e3)) = e2)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14767])).
% 1.97/2.09 tff(14769,plain,
% 1.97/2.09 (op(e2, op(e3, e3)) = e2),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14746, 14768])).
% 1.97/2.09 tff(14770,plain,
% 1.97/2.09 (((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)) | (~(op(e2, op(e3, e3)) = e2))),
% 1.97/2.09 inference(tautology,[status(thm)],[])).
% 1.97/2.09 tff(14771,plain,
% 1.97/2.09 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[14770, 14769])).
% 1.97/2.09 tff(14772,plain,
% 1.97/2.09 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14637])).
% 1.97/2.09 tff(14773,plain,
% 1.97/2.09 ((op(e3, e1) = e0) <=> (op(e1, e3) = op(e3, e1))),
% 1.97/2.09 inference(transitivity,[status(thm)],[14772, 6290])).
% 1.97/2.09 tff(14774,plain,
% 1.97/2.09 ((~(op(e3, e1) = e0)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14773])).
% 1.97/2.09 tff(14775,plain,
% 1.97/2.09 (~(op(e1, e3) = op(e3, e1))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14643, 14774])).
% 1.97/2.09 tff(14776,plain,
% 1.97/2.09 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[6307, 14775])).
% 1.97/2.09 tff(14777,plain,
% 1.97/2.09 ((~(op(e3, e1) = e0)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14772])).
% 1.97/2.09 tff(14778,plain,
% 1.97/2.09 (~(op(e3, e1) = op(e1, e3))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14643, 14777])).
% 1.97/2.09 tff(14779,plain,
% 1.97/2.09 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[6362, 14778])).
% 1.97/2.09 tff(14780,plain,
% 1.97/2.09 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[5523])).
% 1.97/2.09 tff(14781,plain,
% 1.97/2.09 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14780])).
% 1.97/2.09 tff(14782,plain,
% 1.97/2.09 (~(op(e0, e1) = e1)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[792, 14781])).
% 1.97/2.09 tff(14783,plain,
% 1.97/2.09 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[2685])).
% 1.97/2.09 tff(14784,plain,
% 1.97/2.09 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14783])).
% 1.97/2.09 tff(14785,plain,
% 1.97/2.09 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14784])).
% 1.97/2.09 tff(14786,plain,
% 1.97/2.09 (~(op(e0, e3) = e1)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[964, 14785])).
% 1.97/2.09 tff(14787,plain,
% 1.97/2.09 (op(e0, e2) = e0),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[973, 85, 9423, 17])).
% 1.97/2.09 tff(14788,plain,
% 1.97/2.09 (op(e0, e2) = op(e1, e3)),
% 1.97/2.09 inference(transitivity,[status(thm)],[14787, 2909])).
% 1.97/2.09 tff(14789,plain,
% 1.97/2.09 ((op(e0, e2) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14788, 2685])).
% 1.97/2.09 tff(14790,plain,
% 1.97/2.09 ((op(e1, e3) = op(e2, e3)) <=> (op(e0, e2) = e1)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14789])).
% 1.97/2.09 tff(14791,plain,
% 1.97/2.09 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e0, e2) = e1))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14790])).
% 1.97/2.09 tff(14792,plain,
% 1.97/2.09 (~(op(e0, e2) = e1)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[118, 14791])).
% 1.97/2.09 tff(14793,plain,
% 1.97/2.09 (op(e0, e0) = e1),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[384, 14792, 14786, 14782])).
% 1.97/2.09 tff(14794,plain,
% 1.97/2.09 (op(e1, op(e0, e0)) = op(e1, e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14793])).
% 1.97/2.09 tff(14795,plain,
% 1.97/2.09 (op(e1, op(e0, e0)) = e1),
% 1.97/2.09 inference(transitivity,[status(thm)],[14794, 5523])).
% 1.97/2.09 tff(14796,plain,
% 1.97/2.09 (op(e2, e2) = e2),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[524, 6710, 9447, 17])).
% 1.97/2.09 tff(14797,plain,
% 1.97/2.09 (op(e2, op(e2, e2)) = op(e2, e2)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14796])).
% 1.97/2.09 tff(14798,plain,
% 1.97/2.09 (op(e2, op(e2, e2)) = e2),
% 1.97/2.09 inference(transitivity,[status(thm)],[14797, 14796])).
% 1.97/2.09 tff(14799,plain,
% 1.97/2.09 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[528, 14798])).
% 1.97/2.09 tff(14800,plain,
% 1.97/2.09 (op(e1, op(e2, e3)) = op(e1, e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[2684])).
% 1.97/2.09 tff(14801,plain,
% 1.97/2.09 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e1) = e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14800])).
% 1.97/2.09 tff(14802,plain,
% 1.97/2.09 ((op(e1, e1) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14801])).
% 1.97/2.09 tff(14803,plain,
% 1.97/2.09 (op(e1, op(e2, e3)) = e1),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[5523, 14802])).
% 1.97/2.09 tff(14804,plain,
% 1.97/2.09 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[10724, 14803])).
% 1.97/2.09 tff(14805,plain,
% 1.97/2.09 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, op(e2, e3)) = e3)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[6635, 2899])).
% 1.97/2.09 tff(14806,plain,
% 1.97/2.09 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 1.97/2.09 inference(symmetry,[status(thm)],[14805])).
% 1.97/2.09 tff(14807,plain,
% 1.97/2.09 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, op(e2, e3)) = e3)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[6635, 5607])).
% 1.97/2.09 tff(14808,plain,
% 1.97/2.09 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e2) = op(e2, e1))),
% 1.97/2.09 inference(transitivity,[status(thm)],[14807, 14806, 531])).
% 1.97/2.09 tff(14809,plain,
% 1.97/2.09 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14808])).
% 1.97/2.09 tff(14810,plain,
% 1.97/2.09 (~(op(e1, e2) = op(e2, e1))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[402, 14809])).
% 1.97/2.09 tff(14811,plain,
% 1.97/2.09 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[539, 14810])).
% 1.97/2.09 tff(14812,plain,
% 1.97/2.09 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = op(e1, e2))),
% 1.97/2.09 inference(transitivity,[status(thm)],[14807, 14806])).
% 1.97/2.09 tff(14813,plain,
% 1.97/2.09 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14812])).
% 1.97/2.09 tff(14814,plain,
% 1.97/2.09 (~(op(e2, e1) = op(e1, e2))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[402, 14813])).
% 1.97/2.09 tff(14815,plain,
% 1.97/2.09 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[557, 14814])).
% 1.97/2.09 tff(14816,plain,
% 1.97/2.09 (op(e3, op(e2, e3)) = op(op(e1, e2), e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[2900, 2684])).
% 1.97/2.09 tff(14817,plain,
% 1.97/2.09 (op(e3, e2) = e1),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[1898, 85, 9482, 2386])).
% 1.97/2.09 tff(14818,plain,
% 1.97/2.09 (op(e3, e2) = op(e2, e3)),
% 1.97/2.09 inference(transitivity,[status(thm)],[14817, 2685])).
% 1.97/2.09 tff(14819,plain,
% 1.97/2.09 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14818])).
% 1.97/2.09 tff(14820,plain,
% 1.97/2.09 (op(e3, op(e3, e2)) = e3),
% 1.97/2.09 inference(transitivity,[status(thm)],[14819, 14816, 9365, 5607])).
% 1.97/2.09 tff(14821,plain,
% 1.97/2.09 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[11913, 14820])).
% 1.97/2.09 tff(14822,plain,
% 1.97/2.09 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[5367, 14821, 5511, 5669, 5679, 6688, 5670, 14815, 14811, 5681, 14804, 14799, 5675, 5674, 9846])).
% 1.97/2.09 tff(14823,plain,
% 1.97/2.09 (~(op(e1, op(e0, e0)) = e1)),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[6717, 14822])).
% 1.97/2.09 tff(14824,plain,
% 1.97/2.09 ($false),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[14823, 14795])).
% 1.97/2.09 tff(14825,plain,((op(e3, e2) = e0) | (~(op(e1, e1) = e1)) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e3, e1) = e3)) | (~(op(e2, e3) = e1)) | (~(op(e1, e2) = e3)) | (~(op(e1, e3) = e0)) | (op(e3, e2) = e2) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.09 tff(14826,plain,
% 1.97/2.09 (op(e3, e2) = e0),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[14825, 14662, 14779, 14776, 14771, 14765, 14763, 14759, 14736, 14733, 14667, 14630, 14486, 14635, 9699, 17])).
% 1.97/2.09 tff(14827,plain,
% 1.97/2.09 (op(e3, e2) = op(e1, e3)),
% 1.97/2.09 inference(transitivity,[status(thm)],[14826, 14637])).
% 1.97/2.09 tff(14828,plain,
% 1.97/2.09 (op(e3, op(e3, e2)) = op(e3, op(e1, e3))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14827])).
% 1.97/2.09 tff(14829,plain,
% 1.97/2.09 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 1.97/2.09 inference(transitivity,[status(thm)],[6490, 14828, 14636])).
% 1.97/2.09 tff(14830,plain,
% 1.97/2.09 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e0))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14829])).
% 1.97/2.09 tff(14831,plain,
% 1.97/2.09 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e1)),
% 1.97/2.09 inference(transitivity,[status(thm)],[14830, 6411])).
% 1.97/2.09 tff(14832,plain,
% 1.97/2.09 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e1))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14831])).
% 1.97/2.09 tff(14833,plain,
% 1.97/2.09 (e0 = op(e3, op(e3, e3))),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14826, 6497])).
% 1.97/2.09 tff(14834,plain,
% 1.97/2.09 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[5879, 14833, 2813])).
% 1.97/2.09 tff(14835,plain,
% 1.97/2.09 (~(op(e3, e0) = e1)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[14834, 14832])).
% 1.97/2.09 tff(14836,plain,
% 1.97/2.09 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e0)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14826])).
% 1.97/2.09 tff(14837,plain,
% 1.97/2.09 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e0))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14836])).
% 1.97/2.09 tff(14838,plain,
% 1.97/2.09 (~(op(e3, e0) = e0)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[1133, 14837])).
% 1.97/2.09 tff(14839,plain,
% 1.97/2.09 (op(e3, e0) = e1),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[5422, 14838, 14724, 9955])).
% 1.97/2.09 tff(14840,plain,
% 1.97/2.09 ($false),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[14839, 14835])).
% 1.97/2.09 tff(14841,plain,((op(e2, e2) = e0) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.09 tff(14842,plain,
% 1.97/2.09 (op(e2, e2) = e0),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[14841, 2812])).
% 1.97/2.09 tff(14843,plain,
% 1.97/2.09 (e0 = op(e2, e2)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14842])).
% 1.97/2.09 tff(14844,plain,
% 1.97/2.09 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e2))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14843])).
% 1.97/2.09 tff(14845,plain,
% 1.97/2.09 ((op(e3, e2) = e0) <=> (op(e2, e2) = op(e3, e2))),
% 1.97/2.09 inference(transitivity,[status(thm)],[14844, 9346])).
% 1.97/2.09 tff(14846,plain,
% 1.97/2.09 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14845])).
% 1.97/2.09 tff(14847,plain,
% 1.97/2.09 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14846])).
% 1.97/2.09 tff(14848,plain,
% 1.97/2.09 (~(op(e3, e2) = e0)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[1546, 14847])).
% 1.97/2.09 tff(14849,plain,
% 1.97/2.09 (op(e3, e2) = e1),
% 1.97/2.09 inference(unit_resolution,[status(thm)],[1898, 14848, 14490, 9699])).
% 1.97/2.09 tff(14850,plain,
% 1.97/2.09 (e1 = op(e3, e2)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14849])).
% 1.97/2.09 tff(14851,plain,
% 1.97/2.09 (op(e1, op(e1, e2)) = op(e1, e3)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14486])).
% 1.97/2.09 tff(14852,plain,
% 1.97/2.09 (op(e1, e3) = op(e1, op(e1, e2))),
% 1.97/2.09 inference(symmetry,[status(thm)],[14851])).
% 1.97/2.09 tff(14853,plain,
% 1.97/2.09 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14852])).
% 1.97/2.09 tff(14854,plain,
% 1.97/2.09 ((op(e1, op(e1, e2)) = e1) <=> (op(e1, e3) = e1)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14853])).
% 1.97/2.09 tff(14855,plain,
% 1.97/2.09 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e2, e2))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14843])).
% 1.97/2.09 tff(14856,plain,
% 1.97/2.09 ((op(e2, e3) = e0) <=> (op(e2, e2) = op(e2, e3))),
% 1.97/2.09 inference(transitivity,[status(thm)],[14855, 10611])).
% 1.97/2.09 tff(14857,plain,
% 1.97/2.09 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14856])).
% 1.97/2.09 tff(14858,plain,
% 1.97/2.09 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14857])).
% 1.97/2.09 tff(14859,plain,
% 1.97/2.09 (~(op(e2, e3) = e0)),
% 1.97/2.09 inference(modus_ponens,[status(thm)],[515, 14858])).
% 1.97/2.09 tff(14860,plain,
% 1.97/2.09 (op(e0, e3) = op(e0, op(e1, e2))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.09 tff(14861,plain,
% 1.97/2.09 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14860])).
% 1.97/2.09 tff(14862,plain,
% 1.97/2.09 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e3) = e0)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14861])).
% 1.97/2.09 tff(14863,plain,
% 1.97/2.09 ((e0 = op(e0, op(e1, e2))) <=> (op(e0, op(e1, e2)) = e0)),
% 1.97/2.09 inference(commutativity,[status(thm)],[])).
% 1.97/2.09 tff(14864,plain,
% 1.97/2.09 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e2))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14843])).
% 1.97/2.09 tff(14865,plain,
% 1.97/2.09 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e0)),
% 1.97/2.09 inference(symmetry,[status(thm)],[14864])).
% 1.97/2.09 tff(14866,plain,
% 1.97/2.09 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e0))),
% 1.97/2.09 inference(monotonicity,[status(thm)],[14865])).
% 1.97/2.09 tff(14867,plain,
% 1.97/2.09 (~(op(e2, e1) = e0)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[508, 14866])).
% 1.97/2.10 tff(14868,plain,
% 1.97/2.10 (op(e0, e1) = e0),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[292, 14867, 14513, 14512])).
% 1.97/2.10 tff(14869,plain,
% 1.97/2.10 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, op(e1, e2)))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14868, 14860])).
% 1.97/2.10 tff(14870,plain,
% 1.97/2.10 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e1, e2)) = e0)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14869, 14863])).
% 1.97/2.10 tff(14871,plain,
% 1.97/2.10 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14870, 14862])).
% 1.97/2.10 tff(14872,plain,
% 1.97/2.10 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14871])).
% 1.97/2.10 tff(14873,plain,
% 1.97/2.10 (~(op(e0, e3) = e0)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[818, 14872])).
% 1.97/2.10 tff(14874,plain,
% 1.97/2.10 (op(e1, e3) = e0),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1098, 14873, 9696, 14859])).
% 1.97/2.10 tff(14875,plain,
% 1.97/2.10 (op(e1, op(e1, e2)) = op(e2, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14851, 14874, 14843])).
% 1.97/2.10 tff(14876,plain,
% 1.97/2.10 ((op(e1, op(e1, e2)) = e1) <=> (op(e2, e2) = op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14875, 14850])).
% 1.97/2.10 tff(14877,plain,
% 1.97/2.10 ((op(e2, e2) = op(e3, e2)) <=> (op(e1, op(e1, e2)) = e1)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14876])).
% 1.97/2.10 tff(14878,plain,
% 1.97/2.10 ((op(e2, e2) = op(e3, e2)) <=> (op(e1, e3) = e1)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14877, 14854])).
% 1.97/2.10 tff(14879,plain,
% 1.97/2.10 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e1, e3) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14878])).
% 1.97/2.10 tff(14880,plain,
% 1.97/2.10 (~(op(e1, e3) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[1546, 14879])).
% 1.97/2.10 tff(14881,plain,
% 1.97/2.10 (op(e0, e1) = op(e2, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14868, 14843])).
% 1.97/2.10 tff(14882,plain,
% 1.97/2.10 ((op(e0, e1) = e2) <=> (op(e2, e2) = e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14881])).
% 1.97/2.10 tff(14883,plain,
% 1.97/2.10 ((op(e2, e2) = e2) <=> (op(e0, e1) = e2)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14882])).
% 1.97/2.10 tff(14884,plain,
% 1.97/2.10 ((~(op(e2, e2) = e2)) <=> (~(op(e0, e1) = e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14883])).
% 1.97/2.10 tff(14885,plain,
% 1.97/2.10 ((op(e2, e2) = e2) <=> (e0 = e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14842])).
% 1.97/2.10 tff(14886,plain,
% 1.97/2.10 ((e0 = e2) <=> (op(e2, e2) = e2)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14885])).
% 1.97/2.10 tff(14887,plain,
% 1.97/2.10 ((~(e0 = e2)) <=> (~(op(e2, e2) = e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14886])).
% 1.97/2.10 tff(14888,plain,
% 1.97/2.10 (~(op(e2, e2) = e2)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[14, 14887])).
% 1.97/2.10 tff(14889,plain,
% 1.97/2.10 (~(op(e0, e1) = e2)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[14888, 14884])).
% 1.97/2.10 tff(14890,plain,
% 1.97/2.10 (op(op(e0, e1), e1) = op(e0, e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14868])).
% 1.97/2.10 tff(14891,plain,
% 1.97/2.10 (op(op(e0, e1), e1) = e0),
% 1.97/2.10 inference(transitivity,[status(thm)],[14890, 14868])).
% 1.97/2.10 tff(14892,plain,
% 1.97/2.10 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2650, 14891])).
% 1.97/2.10 tff(14893,plain,
% 1.97/2.10 (op(e1, op(e1, e1)) = op(op(e3, e2), e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[9309, 2891])).
% 1.97/2.10 tff(14894,plain,
% 1.97/2.10 (op(op(e3, e2), e2) = op(e1, op(e1, e1))),
% 1.97/2.10 inference(symmetry,[status(thm)],[14893])).
% 1.97/2.10 tff(14895,plain,
% 1.97/2.10 (op(op(e3, e2), e2) = op(e1, e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[5978])).
% 1.97/2.10 tff(14896,plain,
% 1.97/2.10 (op(e1, e2) = op(op(e3, e2), e2)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14895])).
% 1.97/2.10 tff(14897,plain,
% 1.97/2.10 (e3 = op(e1, op(e1, e1))),
% 1.97/2.10 inference(transitivity,[status(thm)],[2900, 14896, 14894])).
% 1.97/2.10 tff(14898,plain,
% 1.97/2.10 (op(e1, op(e1, e1)) = e3),
% 1.97/2.10 inference(transitivity,[status(thm)],[14893, 14895, 2899])).
% 1.97/2.10 tff(14899,plain,
% 1.97/2.10 (op(e1, op(e1, op(e1, e1))) = op(op(e3, e2), e3)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[9309, 14898])).
% 1.97/2.10 tff(14900,plain,
% 1.97/2.10 (op(op(e3, e2), e3) = op(e1, op(e1, op(e1, e1)))),
% 1.97/2.10 inference(symmetry,[status(thm)],[14899])).
% 1.97/2.10 tff(14901,plain,
% 1.97/2.10 (op(op(e3, e2), e3) = op(e1, op(e1, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[5978, 2900])).
% 1.97/2.10 tff(14902,plain,
% 1.97/2.10 (op(e1, op(e1, e2)) = op(op(e3, e2), e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14901])).
% 1.97/2.10 tff(14903,plain,
% 1.97/2.10 (e0 = op(e1, op(e1, op(e1, e1)))),
% 1.97/2.10 inference(transitivity,[status(thm)],[2909, 9274, 14902, 14900])).
% 1.97/2.10 tff(14904,plain,
% 1.97/2.10 ($false),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2920, 14903, 14897, 2902])).
% 1.97/2.10 tff(14905,plain,((~(op(e1, e1) = e2)) | (~(op(e1, e3) = e0)) | (~(op(e1, e2) = e3)) | (~(op(e3, e2) = e1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.10 tff(14906,plain,
% 1.97/2.10 (~(op(e1, e1) = e2)),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14905, 14874, 14486, 14849])).
% 1.97/2.10 tff(14907,plain,
% 1.97/2.10 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14850])).
% 1.97/2.10 tff(14908,plain,
% 1.97/2.10 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e1)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14907])).
% 1.97/2.10 tff(14909,plain,
% 1.97/2.10 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14908])).
% 1.97/2.10 tff(14910,plain,
% 1.97/2.10 (~(op(e3, e1) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[3429, 14909])).
% 1.97/2.10 tff(14911,plain,
% 1.97/2.10 (op(e3, e1) = e3),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[446, 14910, 14513, 9684])).
% 1.97/2.10 tff(14912,plain,
% 1.97/2.10 (op(op(e1, e2), e1) = op(e3, e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14486])).
% 1.97/2.10 tff(14913,plain,
% 1.97/2.10 (op(e3, op(e3, e2)) = op(op(e1, e2), e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14491, 14849])).
% 1.97/2.10 tff(14914,plain,
% 1.97/2.10 (op(op(e3, e1), e1) = op(e3, op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14911, 14850])).
% 1.97/2.10 tff(14915,plain,
% 1.97/2.10 (op(op(e3, e1), e1) = e3),
% 1.97/2.10 inference(transitivity,[status(thm)],[14914, 14913, 14912, 14911])).
% 1.97/2.10 tff(14916,plain,
% 1.97/2.10 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2416, 14915])).
% 1.97/2.10 tff(14917,plain,
% 1.97/2.10 (op(e3, e0) = e0),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1916, 14848, 9696, 14513])).
% 1.97/2.10 tff(14918,plain,
% 1.97/2.10 (op(e3, op(e2, e2)) = op(e3, e0)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14842])).
% 1.97/2.10 tff(14919,plain,
% 1.97/2.10 (op(e3, e0) = op(e2, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14917, 14843])).
% 1.97/2.10 tff(14920,plain,
% 1.97/2.10 (op(e3, op(e3, e0)) = op(e3, op(e2, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14919])).
% 1.97/2.10 tff(14921,plain,
% 1.97/2.10 (op(e3, op(e3, e0)) = e0),
% 1.97/2.10 inference(transitivity,[status(thm)],[14920, 14918, 14917])).
% 1.97/2.10 tff(14922,plain,
% 1.97/2.10 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1345, 14921])).
% 1.97/2.10 tff(14923,plain,
% 1.97/2.10 (op(e2, e3) = e3),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[206, 76, 4382, 10616])).
% 1.97/2.10 tff(14924,plain,
% 1.97/2.10 (op(e2, e3) = op(e1, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14923, 2900])).
% 1.97/2.10 tff(14925,plain,
% 1.97/2.10 (op(e2, op(e2, e3)) = op(e2, op(e1, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14924])).
% 1.97/2.10 tff(14926,plain,
% 1.97/2.10 (op(e2, op(e2, e3)) = e3),
% 1.97/2.10 inference(transitivity,[status(thm)],[14925, 9377, 14923])).
% 1.97/2.10 tff(14927,plain,
% 1.97/2.10 (op(e3, e2) = e1),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1898, 10630, 10204, 2386])).
% 1.97/2.10 tff(14928,plain,
% 1.97/2.10 (op(e0, e3) = e1),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[151, 76, 926, 87])).
% 1.97/2.10 tff(14929,plain,
% 1.97/2.10 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e1) = e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[5085])).
% 1.97/2.10 tff(14930,plain,
% 1.97/2.10 ((~(op(e0, op(e0, e3)) = e3)) <=> (~(op(e0, e1) = e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14929])).
% 1.97/2.10 tff(14931,plain,
% 1.97/2.10 (~(op(e0, e1) = e3)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[5466, 14930])).
% 1.97/2.10 tff(14932,plain,
% 1.97/2.10 (op(op(e0, e3), e0) = e3),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2635, 5457])).
% 1.97/2.10 tff(14933,plain,
% 1.97/2.10 (op(e1, e0) = e3),
% 1.97/2.10 inference(transitivity,[status(thm)],[4728, 14932])).
% 1.97/2.10 tff(14934,plain,
% 1.97/2.10 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14933])).
% 1.97/2.10 tff(14935,plain,
% 1.97/2.10 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14934])).
% 1.97/2.10 tff(14936,plain,
% 1.97/2.10 (~(op(e0, e0) = e3)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[2471, 14935])).
% 1.97/2.10 tff(14937,plain,
% 1.97/2.10 ($false),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1495, 14936, 14931, 4699, 4412])).
% 1.97/2.10 tff(14938,plain,(((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))) | (op(e0, e2) = e3) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.10 tff(14939,plain,
% 1.97/2.10 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14938, 14928, 9246])).
% 1.97/2.10 tff(14940,plain,
% 1.97/2.10 (op(op(e3, e2), e2) = op(e1, e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14927])).
% 1.97/2.10 tff(14941,plain,
% 1.97/2.10 (op(op(e3, e2), e2) = e3),
% 1.97/2.10 inference(transitivity,[status(thm)],[14940, 2899])).
% 1.97/2.10 tff(14942,plain,
% 1.97/2.10 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1339, 14941])).
% 1.97/2.10 tff(14943,plain,
% 1.97/2.10 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14928])).
% 1.97/2.10 tff(14944,plain,
% 1.97/2.10 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14943])).
% 1.97/2.10 tff(14945,plain,
% 1.97/2.10 (~(op(e0, e0) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[3414, 14944])).
% 1.97/2.10 tff(14946,plain,
% 1.97/2.10 (op(e1, e0) = e2),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2285, 68, 72, 3785])).
% 1.97/2.10 tff(14947,plain,
% 1.97/2.10 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[9309])).
% 1.97/2.10 tff(14948,plain,
% 1.97/2.10 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14947])).
% 1.97/2.10 tff(14949,plain,
% 1.97/2.10 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14948])).
% 1.97/2.10 tff(14950,plain,
% 1.97/2.10 (~(op(e3, e0) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[1133, 14949])).
% 1.97/2.10 tff(14951,plain,
% 1.97/2.10 (op(e1, op(e2, e2)) = e2),
% 1.97/2.10 inference(transitivity,[status(thm)],[10853, 14946])).
% 1.97/2.10 tff(14952,plain,
% 1.97/2.10 ((op(e1, op(e2, e2)) = e1) <=> (e2 = op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14951, 9309])).
% 1.97/2.10 tff(14953,plain,
% 1.97/2.10 ((op(e1, op(e2, e2)) = e1) <=> (op(e3, e2) = e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14952, 2234])).
% 1.97/2.10 tff(14954,plain,
% 1.97/2.10 ((op(e3, e2) = e2) <=> (op(e1, op(e2, e2)) = e1)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14953])).
% 1.97/2.10 tff(14955,plain,
% 1.97/2.10 ((op(e3, e2) = e2) <=> (op(e1, e0) = e1)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14954, 10856])).
% 1.97/2.10 tff(14956,plain,
% 1.97/2.10 ((~(op(e3, e2) = e2)) <=> (~(op(e1, e0) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14955])).
% 1.97/2.10 tff(14957,plain,
% 1.97/2.10 (~(op(e1, e0) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[2386, 14956])).
% 1.97/2.10 tff(14958,plain,
% 1.97/2.10 (op(e2, e0) = e1),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1480, 14957, 14950, 2379])).
% 1.97/2.10 tff(14959,plain,
% 1.97/2.10 (op(op(e2, e0), e0) = op(e1, op(e2, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14958, 9326])).
% 1.97/2.10 tff(14960,plain,
% 1.97/2.10 (op(op(e2, e0), e0) = e2),
% 1.97/2.10 inference(transitivity,[status(thm)],[14959, 10853, 14946])).
% 1.97/2.10 tff(14961,plain,
% 1.97/2.10 (op(e2, e1) = e2),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1993, 68, 82, 5828])).
% 1.97/2.10 tff(14962,plain,
% 1.97/2.10 (op(e2, op(e3, e2)) = op(e2, e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[5978])).
% 1.97/2.10 tff(14963,plain,
% 1.97/2.10 (op(op(e1, e0), e1) = op(e2, op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14946, 9309])).
% 1.97/2.10 tff(14964,plain,
% 1.97/2.10 (op(op(e1, e0), e1) = e2),
% 1.97/2.10 inference(transitivity,[status(thm)],[14963, 14962, 14961])).
% 1.97/2.10 tff(14965,plain,
% 1.97/2.10 ((op(op(e1, e0), e1) = e0) <=> (e2 = op(e2, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14964, 9326])).
% 1.97/2.10 tff(14966,plain,
% 1.97/2.10 ((op(op(e1, e0), e1) = e0) <=> (op(e2, e2) = e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14965, 81])).
% 1.97/2.10 tff(14967,plain,
% 1.97/2.10 ((op(e2, e2) = e2) <=> (op(op(e1, e0), e1) = e0)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14966])).
% 1.97/2.10 tff(14968,plain,
% 1.97/2.10 ((~(op(e2, e2) = e2)) <=> (~(op(op(e1, e0), e1) = e0))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14967])).
% 1.97/2.10 tff(14969,plain,
% 1.97/2.10 (~(op(op(e1, e0), e1) = e0)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[10989, 14968])).
% 1.97/2.10 tff(14970,plain,
% 1.97/2.10 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1302, 14969])).
% 1.97/2.10 tff(14971,plain,
% 1.97/2.10 (op(e0, e2) = e2),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1151, 10989, 2386, 3785])).
% 1.97/2.10 tff(14972,plain,
% 1.97/2.10 (op(e0, op(e0, e2)) = op(e0, e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14971])).
% 1.97/2.10 tff(14973,plain,
% 1.97/2.10 (op(e0, op(e0, e2)) = e2),
% 1.97/2.10 inference(transitivity,[status(thm)],[14972, 14971])).
% 1.97/2.10 tff(14974,plain,
% 1.97/2.10 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1331, 14973])).
% 1.97/2.10 tff(14975,plain,
% 1.97/2.10 (op(op(e2, e1), e1) = op(e2, op(e3, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14961, 9309])).
% 1.97/2.10 tff(14976,plain,
% 1.97/2.10 (op(op(e2, e1), e1) = e2),
% 1.97/2.10 inference(transitivity,[status(thm)],[14975, 14962, 14961])).
% 1.97/2.10 tff(14977,plain,
% 1.97/2.10 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2371, 14976])).
% 1.97/2.10 tff(14978,plain,
% 1.97/2.10 (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1459, 14977, 14974, 3341, 3342, 1304, 1926, 1275, 1347, 1358, 14970, 4549])).
% 1.97/2.10 tff(14979,plain,
% 1.97/2.10 (~(op(op(e2, e0), e0) = e2)),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1945, 14978])).
% 1.97/2.10 tff(14980,plain,
% 1.97/2.10 ($false),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14979, 14960])).
% 1.97/2.10 tff(14981,plain,((op(e1, e1) = e2) | (~(op(e2, e2) = e0)) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (op(e0, e0) = e1) | (~(op(e3, e2) = e1)) | (op(e3, e2) = e2) | (op(e3, e1) = e2) | (op(e0, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.10 tff(14982,plain,
% 1.97/2.10 (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14981, 14945, 14942, 9300, 1304, 1926, 1275, 68, 9370, 4549, 14939, 14927, 2386, 82, 5828, 72, 9280])).
% 1.97/2.10 tff(14983,plain,
% 1.97/2.10 ($false),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2344, 14982, 14926])).
% 1.97/2.10 tff(14984,plain,((op(e2, e3) = e1) | (~(op(e2, e2) = e0)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (op(e1, e1) = e2) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (op(e3, e2) = e2) | (op(e3, e1) = e2) | (op(e0, e1) = e2) | (op(e1, e3) = e2) | (~(op(e1, e2) = e3)) | (op(e2, e3) = e2) | (op(e3, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.10 tff(14985,plain,
% 1.97/2.10 (op(e2, e3) = e1),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14984, 14842, 10604, 14922, 14916, 14906, 14892, 9699, 9684, 14889, 10589, 14486, 9692, 12016, 14880])).
% 1.97/2.10 tff(14986,plain,
% 1.97/2.10 ((op(e1, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14486])).
% 1.97/2.10 tff(14987,plain,
% 1.97/2.10 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14986, 502])).
% 1.97/2.10 tff(14988,plain,
% 1.97/2.10 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14987])).
% 1.97/2.10 tff(14989,plain,
% 1.97/2.10 (~(op(e2, e2) = e3)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[1273, 14988])).
% 1.97/2.10 tff(14990,plain,
% 1.97/2.10 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14491])).
% 1.97/2.10 tff(14991,plain,
% 1.97/2.10 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14990])).
% 1.97/2.10 tff(14992,plain,
% 1.97/2.10 (op(e3, e1) = op(e1, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14911, 14491])).
% 1.97/2.10 tff(14993,plain,
% 1.97/2.10 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = op(e1, e2))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14992])).
% 1.97/2.10 tff(14994,plain,
% 1.97/2.10 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14993, 14991])).
% 1.97/2.10 tff(14995,plain,
% 1.97/2.10 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[14994])).
% 1.97/2.10 tff(14996,plain,
% 1.97/2.10 (~(op(e2, e1) = e3)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[402, 14995])).
% 1.97/2.10 tff(14997,plain,
% 1.97/2.10 (~(op(e2, e0) = e3)),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[14078, 14985, 14842])).
% 1.97/2.10 tff(14998,plain,
% 1.97/2.10 (op(e2, e3) = e3),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1559, 14997, 14996, 14989])).
% 1.97/2.10 tff(14999,plain,
% 1.97/2.10 (e3 = op(e2, e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[14998])).
% 1.97/2.10 tff(15000,plain,
% 1.97/2.10 (op(e1, e2) = op(e3, e2)),
% 1.97/2.10 inference(transitivity,[status(thm)],[14486, 14999, 14985, 14850])).
% 1.97/2.10 tff(15001,plain,
% 1.97/2.10 ($false),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2292, 15000])).
% 1.97/2.10 tff(15002,plain,(~(op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.10 tff(15003,plain,
% 1.97/2.10 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2)),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[2786, 15002])).
% 1.97/2.10 tff(15004,plain,
% 1.97/2.10 (op(e2, e3) = e2),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[15003, 10586, 72])).
% 1.97/2.10 tff(15005,plain,
% 1.97/2.10 (e2 = op(e2, e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[15004])).
% 1.97/2.10 tff(15006,plain,
% 1.97/2.10 ((e0 = e2) <=> (e0 = op(e2, e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15005])).
% 1.97/2.10 tff(15007,plain,
% 1.97/2.10 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 1.97/2.10 inference(transitivity,[status(thm)],[15006, 86])).
% 1.97/2.10 tff(15008,plain,
% 1.97/2.10 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15007])).
% 1.97/2.10 tff(15009,plain,
% 1.97/2.10 (~(op(e2, e3) = e0)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[14, 15008])).
% 1.97/2.10 tff(15010,plain,
% 1.97/2.10 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[105])).
% 1.97/2.10 tff(15011,plain,
% 1.97/2.10 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 1.97/2.10 inference(transitivity,[status(thm)],[15010, 666])).
% 1.97/2.10 tff(15012,plain,
% 1.97/2.10 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15011])).
% 1.97/2.10 tff(15013,plain,
% 1.97/2.10 (~(op(e3, e3) = e3)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[571, 15012])).
% 1.97/2.10 tff(15014,plain,
% 1.97/2.10 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.10 tff(15015,plain,
% 1.97/2.10 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 1.97/2.10 inference(transitivity,[status(thm)],[15014, 657])).
% 1.97/2.10 tff(15016,plain,
% 1.97/2.10 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15015])).
% 1.97/2.10 tff(15017,plain,
% 1.97/2.10 (~(op(e3, e3) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[1077, 15016])).
% 1.97/2.10 tff(15018,plain,
% 1.97/2.10 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e3)),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[1071, 15002])).
% 1.97/2.10 tff(15019,plain,
% 1.97/2.10 (op(e3, e3) = e0),
% 1.97/2.10 inference(unit_resolution,[status(thm)],[15018, 15017, 15013])).
% 1.97/2.10 tff(15020,plain,
% 1.97/2.10 (e0 = op(e3, e3)),
% 1.97/2.10 inference(symmetry,[status(thm)],[15019])).
% 1.97/2.10 tff(15021,plain,
% 1.97/2.10 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.10 tff(15022,plain,
% 1.97/2.10 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15021])).
% 1.97/2.10 tff(15023,plain,
% 1.97/2.10 (~(op(e0, e0) = e1)),
% 1.97/2.10 inference(modus_ponens,[status(thm)],[3414, 15022])).
% 1.97/2.10 tff(15024,plain,
% 1.97/2.10 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 1.97/2.10 inference(monotonicity,[status(thm)],[15004])).
% 1.97/2.10 tff(15025,plain,
% 1.97/2.11 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15024])).
% 1.97/2.11 tff(15026,plain,
% 1.97/2.11 (~(op(e2, e1) = e2)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[197, 15025])).
% 1.97/2.11 tff(15027,plain,
% 1.97/2.11 (op(e0, e1) = op(e2, e3)),
% 1.97/2.11 inference(transitivity,[status(thm)],[3492, 3797])).
% 1.97/2.11 tff(15028,plain,
% 1.97/2.11 ((op(e0, e1) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15027, 4451])).
% 1.97/2.11 tff(15029,plain,
% 1.97/2.11 ((op(e2, e3) = op(e3, e3)) <=> (op(e0, e1) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15028])).
% 1.97/2.11 tff(15030,plain,
% 1.97/2.11 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e0, e1) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15029])).
% 1.97/2.11 tff(15031,plain,
% 1.97/2.11 (~(op(e0, e1) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[368, 15030])).
% 1.97/2.11 tff(15032,plain,
% 1.97/2.11 ((op(e0, e1) = e3) <=> (op(e2, e3) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15027])).
% 1.97/2.11 tff(15033,plain,
% 1.97/2.11 ((op(e2, e3) = e3) <=> (op(e0, e1) = e3)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15032])).
% 1.97/2.11 tff(15034,plain,
% 1.97/2.11 ((~(op(e2, e3) = e3)) <=> (~(op(e0, e1) = e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15033])).
% 1.97/2.11 tff(15035,plain,
% 1.97/2.11 (~(op(e0, e1) = e3)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[124, 15034])).
% 1.97/2.11 tff(15036,plain,
% 1.97/2.11 (op(e0, e2) = e3),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[5000, 15035, 19, 15031])).
% 1.97/2.11 tff(15037,plain,
% 1.97/2.11 ((op(e0, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15036])).
% 1.97/2.11 tff(15038,plain,
% 1.97/2.11 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15037, 502])).
% 1.97/2.11 tff(15039,plain,
% 1.97/2.11 ((op(e2, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 1.97/2.11 inference(symmetry,[status(thm)],[15038])).
% 1.97/2.11 tff(15040,plain,
% 1.97/2.11 (op(e2, e1) = e0),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[292, 15031, 4476, 84])).
% 1.97/2.11 tff(15041,plain,
% 1.97/2.11 (op(e2, e2) = e3),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[7007, 15040, 124, 3853])).
% 1.97/2.11 tff(15042,plain,
% 1.97/2.11 (op(e0, e2) = op(e2, e2)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15041, 15039])).
% 1.97/2.11 tff(15043,plain,
% 1.97/2.11 ($false),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2736, 15042])).
% 1.97/2.11 tff(15044,plain,((~(op(e0, e1) = e2)) | (op(e2, e3) = e3) | (~(op(e0, e3) = e1)) | (op(e1, e1) = e0) | (~(op(e2, e3) = e2)) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.11 tff(15045,plain,
% 1.97/2.11 (~(op(e0, e1) = e2)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[15044, 119, 10582, 84, 15004, 15019])).
% 1.97/2.11 tff(15046,plain,
% 1.97/2.11 (op(e3, e1) = e2),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[1993, 15045, 68, 15026])).
% 1.97/2.11 tff(15047,plain,
% 1.97/2.11 (~(op(e3, e0) = e1)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[8647, 15046, 15019])).
% 1.97/2.11 tff(15048,plain,
% 1.97/2.11 (op(e2, e0) = e1),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[1480, 15047, 15023, 10367])).
% 1.97/2.11 tff(15049,plain,
% 1.97/2.11 ((op(e2, e0) = e0) <=> (e1 = op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15048, 15020])).
% 1.97/2.11 tff(15050,plain,
% 1.97/2.11 ((op(e2, e0) = e0) <=> (op(e3, e3) = e1)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15049, 657])).
% 1.97/2.11 tff(15051,plain,
% 1.97/2.11 ((op(e3, e3) = e1) <=> (op(e2, e0) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15050])).
% 1.97/2.11 tff(15052,plain,
% 1.97/2.11 ((~(op(e3, e3) = e1)) <=> (~(op(e2, e0) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15051])).
% 1.97/2.11 tff(15053,plain,
% 1.97/2.11 (~(op(e2, e0) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15017, 15052])).
% 1.97/2.11 tff(15054,plain,
% 1.97/2.11 (op(e2, e1) = e0),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2311, 15053, 17, 15009])).
% 1.97/2.11 tff(15055,plain,
% 1.97/2.11 (e0 = op(e2, e1)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15054])).
% 1.97/2.11 tff(15056,plain,
% 1.97/2.11 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e2, e1))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15055])).
% 1.97/2.11 tff(15057,plain,
% 1.97/2.11 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15056])).
% 1.97/2.11 tff(15058,plain,
% 1.97/2.11 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15057])).
% 1.97/2.11 tff(15059,plain,
% 1.97/2.11 (~(op(e0, e1) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[606, 15058])).
% 1.97/2.11 tff(15060,plain,
% 1.97/2.11 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.11 tff(15061,plain,
% 1.97/2.11 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15060, 18])).
% 1.97/2.11 tff(15062,plain,
% 1.97/2.11 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15061])).
% 1.97/2.11 tff(15063,plain,
% 1.97/2.11 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15062])).
% 1.97/2.11 tff(15064,plain,
% 1.97/2.11 (~(op(e0, e3) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[26, 15063])).
% 1.97/2.11 tff(15065,plain,
% 1.97/2.11 (op(e0, op(e2, e3)) = op(e0, e2)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15004])).
% 1.97/2.11 tff(15066,plain,
% 1.97/2.11 (op(e0, e2) = op(e0, op(e2, e3))),
% 1.97/2.11 inference(symmetry,[status(thm)],[15065])).
% 1.97/2.11 tff(15067,plain,
% 1.97/2.11 ((op(e0, e2) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15066])).
% 1.97/2.11 tff(15068,plain,
% 1.97/2.11 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e2) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15067])).
% 1.97/2.11 tff(15069,plain,
% 1.97/2.11 (op(e2, op(e3, e3)) = op(e2, e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15019])).
% 1.97/2.11 tff(15070,plain,
% 1.97/2.11 (op(e2, e1) = op(e3, e3)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15054, 15020])).
% 1.97/2.11 tff(15071,plain,
% 1.97/2.11 (op(e2, op(e2, e1)) = op(e2, op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15070])).
% 1.97/2.11 tff(15072,plain,
% 1.97/2.11 (op(e2, op(e2, e1)) = e1),
% 1.97/2.11 inference(transitivity,[status(thm)],[15071, 15069, 15048])).
% 1.97/2.11 tff(15073,plain,
% 1.97/2.11 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[1355, 15072])).
% 1.97/2.11 tff(15074,plain,
% 1.97/2.11 (op(e2, op(e2, e0)) = op(e2, e1)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15048])).
% 1.97/2.11 tff(15075,plain,
% 1.97/2.11 ((op(e2, op(e2, e0)) = e0) <=> (op(e2, e1) = e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15074])).
% 1.97/2.11 tff(15076,plain,
% 1.97/2.11 ((op(e2, e1) = e0) <=> (op(e2, op(e2, e0)) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15075])).
% 1.97/2.11 tff(15077,plain,
% 1.97/2.11 (op(e2, op(e2, e0)) = e0),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15054, 15076])).
% 1.97/2.11 tff(15078,plain,
% 1.97/2.11 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2653, 15077])).
% 1.97/2.11 tff(15079,plain,
% 1.97/2.11 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[10357])).
% 1.97/2.11 tff(15080,plain,
% 1.97/2.11 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15079, 5522])).
% 1.97/2.11 tff(15081,plain,
% 1.97/2.11 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15080])).
% 1.97/2.11 tff(15082,plain,
% 1.97/2.11 (~(op(e1, e2) = e1)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[1604, 15081])).
% 1.97/2.11 tff(15083,plain,
% 1.97/2.11 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15020])).
% 1.97/2.11 tff(15084,plain,
% 1.97/2.11 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15083])).
% 1.97/2.11 tff(15085,plain,
% 1.97/2.11 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15084])).
% 1.97/2.11 tff(15086,plain,
% 1.97/2.11 (~(op(e3, e0) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[157, 15085])).
% 1.97/2.11 tff(15087,plain,
% 1.97/2.11 (op(e3, op(e3, e3)) = op(e3, e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15019])).
% 1.97/2.11 tff(15088,plain,
% 1.97/2.11 (op(e3, e0) = op(e3, op(e3, e3))),
% 1.97/2.11 inference(symmetry,[status(thm)],[15087])).
% 1.97/2.11 tff(15089,plain,
% 1.97/2.11 ((op(e3, e0) = e2) <=> (op(e3, op(e3, e3)) = e2)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15088])).
% 1.97/2.11 tff(15090,plain,
% 1.97/2.11 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15089, 1974])).
% 1.97/2.11 tff(15091,plain,
% 1.97/2.11 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15090])).
% 1.97/2.11 tff(15092,plain,
% 1.97/2.11 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, op(e3, e3)) = e2)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15088, 15046])).
% 1.97/2.11 tff(15093,plain,
% 1.97/2.11 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, op(e3, e3)))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15092, 1974])).
% 1.97/2.11 tff(15094,plain,
% 1.97/2.11 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15093, 15091])).
% 1.97/2.11 tff(15095,plain,
% 1.97/2.11 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15094])).
% 1.97/2.11 tff(15096,plain,
% 1.97/2.11 (~(op(e3, e0) = e2)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[580, 15095])).
% 1.97/2.11 tff(15097,plain,
% 1.97/2.11 (op(e3, e0) = e3),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[5422, 15096, 15086, 15047])).
% 1.97/2.11 tff(15098,plain,
% 1.97/2.11 (op(op(e3, e0), e0) = op(e3, op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15097, 15020])).
% 1.97/2.11 tff(15099,plain,
% 1.97/2.11 (op(op(e3, e0), e0) = e3),
% 1.97/2.11 inference(transitivity,[status(thm)],[15098, 15087, 15097])).
% 1.97/2.11 tff(15100,plain,
% 1.97/2.11 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[4026, 15099])).
% 1.97/2.11 tff(15101,plain,
% 1.97/2.11 (op(e3, e2) = e1),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[939, 15047, 15017, 10361])).
% 1.97/2.11 tff(15102,plain,
% 1.97/2.11 (op(e3, op(e3, e2)) = op(e3, e1)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15101])).
% 1.97/2.11 tff(15103,plain,
% 1.97/2.11 (op(e3, op(e3, e2)) = e2),
% 1.97/2.11 inference(transitivity,[status(thm)],[15102, 15046])).
% 1.97/2.11 tff(15104,plain,
% 1.97/2.11 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[1904, 15103])).
% 1.97/2.11 tff(15105,plain,
% 1.97/2.11 (op(e3, op(e2, e3)) = op(e3, e2)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15004])).
% 1.97/2.11 tff(15106,plain,
% 1.97/2.11 (op(e3, e1) = op(e2, e3)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15046, 15005])).
% 1.97/2.11 tff(15107,plain,
% 1.97/2.11 (op(e3, op(e3, e1)) = op(e3, op(e2, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15106])).
% 1.97/2.11 tff(15108,plain,
% 1.97/2.11 (op(e3, op(e3, e1)) = e1),
% 1.97/2.11 inference(transitivity,[status(thm)],[15107, 15105, 15101])).
% 1.97/2.11 tff(15109,plain,
% 1.97/2.11 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2594, 15108])).
% 1.97/2.11 tff(15110,plain,
% 1.97/2.11 (op(op(e0, e3), e0) = op(e1, e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.11 tff(15111,plain,
% 1.97/2.11 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15110])).
% 1.97/2.11 tff(15112,plain,
% 1.97/2.11 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15111])).
% 1.97/2.11 tff(15113,plain,
% 1.97/2.11 ((~(op(e1, e0) = e3)) <=> (~(op(op(e0, e3), e0) = e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15112])).
% 1.97/2.11 tff(15114,plain,
% 1.97/2.11 (~(op(op(e0, e3), e0) = e3)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[111, 15113])).
% 1.97/2.11 tff(15115,plain,
% 1.97/2.11 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2635, 15114])).
% 1.97/2.11 tff(15116,plain,
% 1.97/2.11 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15097])).
% 1.97/2.11 tff(15117,plain,
% 1.97/2.11 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15116])).
% 1.97/2.11 tff(15118,plain,
% 1.97/2.11 (~(op(e0, e0) = e3)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[6384, 15117])).
% 1.97/2.11 tff(15119,plain,
% 1.97/2.11 ((op(e2, e2) = e2) <=> (op(e2, e2) = op(e2, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15005])).
% 1.97/2.11 tff(15120,plain,
% 1.97/2.11 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15119])).
% 1.97/2.11 tff(15121,plain,
% 1.97/2.11 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15120])).
% 1.97/2.11 tff(15122,plain,
% 1.97/2.11 (~(op(e2, e2) = e2)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[515, 15121])).
% 1.97/2.11 tff(15123,plain,
% 1.97/2.11 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15101])).
% 1.97/2.11 tff(15124,plain,
% 1.97/2.11 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15123])).
% 1.97/2.11 tff(15125,plain,
% 1.97/2.11 (~(op(e2, e2) = e1)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[1546, 15124])).
% 1.97/2.11 tff(15126,plain,
% 1.97/2.11 (op(e2, e2) = e3),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[524, 15125, 17, 15122])).
% 1.97/2.11 tff(15127,plain,
% 1.97/2.11 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15126])).
% 1.97/2.11 tff(15128,plain,
% 1.97/2.11 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15127])).
% 1.97/2.11 tff(15129,plain,
% 1.97/2.11 (~(op(e0, e2) = e3)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[2736, 15128])).
% 1.97/2.11 tff(15130,plain,
% 1.97/2.11 (op(e0, e1) = e3),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[1495, 15129, 10364, 15118])).
% 1.97/2.11 tff(15131,plain,
% 1.97/2.11 (op(e0, op(e0, e1)) = op(e0, e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15130])).
% 1.97/2.11 tff(15132,plain,
% 1.97/2.11 (op(e0, op(e0, e1)) = e1),
% 1.97/2.11 inference(transitivity,[status(thm)],[15131, 10582])).
% 1.97/2.11 tff(15133,plain,
% 1.97/2.11 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[2449, 15132])).
% 1.97/2.11 tff(15134,plain,
% 1.97/2.11 (op(e1, e2) = e0),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[7608, 15133, 17, 84, 10369, 15004, 15115, 15109, 15104, 15100, 75, 15082, 15078, 85, 80, 15073])).
% 1.97/2.11 tff(15135,plain,
% 1.97/2.11 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, op(e2, e3)) = e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15066, 15134])).
% 1.97/2.11 tff(15136,plain,
% 1.97/2.11 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e0)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15135, 15068])).
% 1.97/2.11 tff(15137,plain,
% 1.97/2.11 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e0))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15136])).
% 1.97/2.11 tff(15138,plain,
% 1.97/2.11 (~(op(e0, e2) = e0)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[6205, 15137])).
% 1.97/2.11 tff(15139,plain,
% 1.97/2.11 (op(e0, e0) = e0),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[3976, 15138, 15064, 15059])).
% 1.97/2.11 tff(15140,plain,
% 1.97/2.11 (op(e0, op(e0, e0)) = op(e0, e0)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15139])).
% 1.97/2.11 tff(15141,plain,
% 1.97/2.11 (op(e0, op(e0, e0)) = e0),
% 1.97/2.11 inference(transitivity,[status(thm)],[15140, 15139])).
% 1.97/2.11 tff(15142,plain,
% 1.97/2.11 ((op(e2, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15048])).
% 1.97/2.11 tff(15143,plain,
% 1.97/2.11 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15142, 697])).
% 1.97/2.11 tff(15144,plain,
% 1.97/2.11 ((op(e0, e2) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 1.97/2.11 inference(symmetry,[status(thm)],[15143])).
% 1.97/2.11 tff(15145,plain,
% 1.97/2.11 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e2, e0))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15144, 6337])).
% 1.97/2.11 tff(15146,plain,
% 1.97/2.11 ((~(op(e0, e2) = e1)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15145])).
% 1.97/2.11 tff(15147,plain,
% 1.97/2.11 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.11 tff(15148,plain,
% 1.97/2.11 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15147])).
% 1.97/2.11 tff(15149,plain,
% 1.97/2.11 (~(op(e0, e2) = e1)),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[918, 15148])).
% 1.97/2.11 tff(15150,plain,
% 1.97/2.11 (~(op(e0, e2) = op(e2, e0))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15149, 15146])).
% 1.97/2.11 tff(15151,plain,
% 1.97/2.11 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[6347, 15150])).
% 1.97/2.11 tff(15152,plain,
% 1.97/2.11 ((~(op(e0, e2) = e1)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15144])).
% 1.97/2.11 tff(15153,plain,
% 1.97/2.11 (~(op(e2, e0) = op(e0, e2))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15149, 15152])).
% 1.97/2.11 tff(15154,plain,
% 1.97/2.11 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[6358, 15153])).
% 1.97/2.11 tff(15155,plain,
% 1.97/2.11 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15130])).
% 1.97/2.11 tff(15156,plain,
% 1.97/2.11 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 1.97/2.11 inference(symmetry,[status(thm)],[15155])).
% 1.97/2.11 tff(15157,plain,
% 1.97/2.11 ((~(op(e1, e0) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15156])).
% 1.97/2.11 tff(15158,plain,
% 1.97/2.11 (~(op(e1, e0) = op(e0, e1))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[111, 15157])).
% 1.97/2.11 tff(15159,plain,
% 1.97/2.11 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[613, 15158])).
% 1.97/2.11 tff(15160,plain,
% 1.97/2.11 ((op(e1, e0) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15156, 596])).
% 1.97/2.11 tff(15161,plain,
% 1.97/2.11 ((~(op(e1, e0) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15160])).
% 1.97/2.11 tff(15162,plain,
% 1.97/2.11 (~(op(e0, e1) = op(e1, e0))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[111, 15161])).
% 1.97/2.11 tff(15163,plain,
% 1.97/2.11 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[609, 15162])).
% 1.97/2.11 tff(15164,plain,
% 1.97/2.11 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15106])).
% 1.97/2.11 tff(15165,plain,
% 1.97/2.11 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15164, 394])).
% 1.97/2.11 tff(15166,plain,
% 1.97/2.11 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15165])).
% 1.97/2.11 tff(15167,plain,
% 1.97/2.11 (~(op(e3, e2) = op(e2, e3))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[3429, 15166])).
% 1.97/2.11 tff(15168,plain,
% 1.97/2.11 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[500, 15167])).
% 1.97/2.11 tff(15169,plain,
% 1.97/2.11 (op(op(e2, e3), e3) = op(e2, e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15004])).
% 1.97/2.11 tff(15170,plain,
% 1.97/2.11 (op(e2, op(e2, e2)) = op(op(e2, e3), e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15005, 15126])).
% 1.97/2.11 tff(15171,plain,
% 1.97/2.11 (op(e2, op(e2, e2)) = e2),
% 1.97/2.11 inference(transitivity,[status(thm)],[15170, 15169, 15004])).
% 1.97/2.11 tff(15172,plain,
% 1.97/2.11 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[528, 15171])).
% 1.97/2.11 tff(15173,plain,
% 1.97/2.11 (op(e3, op(e2, e1)) = op(e3, op(e3, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15070])).
% 1.97/2.11 tff(15174,plain,
% 1.97/2.11 (op(e3, op(e2, e1)) = e3),
% 1.97/2.11 inference(transitivity,[status(thm)],[15173, 15087, 15097])).
% 1.97/2.11 tff(15175,plain,
% 1.97/2.11 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[6334, 15174])).
% 1.97/2.11 tff(15176,plain,
% 1.97/2.11 (op(e2, op(e1, e3)) = op(e2, e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[105])).
% 1.97/2.11 tff(15177,plain,
% 1.97/2.11 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e3) = e2)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15176])).
% 1.97/2.11 tff(15178,plain,
% 1.97/2.11 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15177])).
% 1.97/2.11 tff(15179,plain,
% 1.97/2.11 (op(e2, op(e1, e3)) = e2),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[15004, 15178])).
% 1.97/2.11 tff(15180,plain,
% 1.97/2.11 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 1.97/2.11 inference(unit_resolution,[status(thm)],[9084, 15179])).
% 1.97/2.11 tff(15181,plain,
% 1.97/2.11 (e3 = op(e1, e3)),
% 1.97/2.11 inference(symmetry,[status(thm)],[105])).
% 1.97/2.11 tff(15182,plain,
% 1.97/2.11 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15181])).
% 1.97/2.11 tff(15183,plain,
% 1.97/2.11 (e2 = op(e3, e1)),
% 1.97/2.11 inference(symmetry,[status(thm)],[15046])).
% 1.97/2.11 tff(15184,plain,
% 1.97/2.11 (op(e2, e3) = op(e3, e1)),
% 1.97/2.11 inference(transitivity,[status(thm)],[15004, 15183])).
% 1.97/2.11 tff(15185,plain,
% 1.97/2.11 ((op(e2, e3) = e3) <=> (op(e3, e1) = e3)),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15184])).
% 1.97/2.11 tff(15186,plain,
% 1.97/2.11 ((op(e2, e3) = e3) <=> (op(e1, e3) = op(e3, e1))),
% 1.97/2.11 inference(transitivity,[status(thm)],[15185, 15182, 6290])).
% 1.97/2.11 tff(15187,plain,
% 1.97/2.11 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 1.97/2.11 inference(monotonicity,[status(thm)],[15186])).
% 1.97/2.11 tff(15188,plain,
% 1.97/2.11 (~(op(e1, e3) = op(e3, e1))),
% 1.97/2.11 inference(modus_ponens,[status(thm)],[119, 15187])).
% 1.97/2.11 tff(15189,plain,
% 1.97/2.11 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[6307, 15188])).
% 1.97/2.12 tff(15190,plain,
% 1.97/2.12 (op(e1, op(e1, e1)) = op(e1, e1)),
% 1.97/2.12 inference(monotonicity,[status(thm)],[10357])).
% 1.97/2.12 tff(15191,plain,
% 1.97/2.12 (op(e1, op(e1, e1)) = e1),
% 1.97/2.12 inference(transitivity,[status(thm)],[15190, 10357])).
% 1.97/2.12 tff(15192,plain,
% 1.97/2.12 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[5678, 15191])).
% 1.97/2.12 tff(15193,plain,
% 1.97/2.12 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e1)),
% 1.97/2.12 inference(monotonicity,[status(thm)],[10582])).
% 1.97/2.12 tff(15194,plain,
% 1.97/2.12 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 1.97/2.12 inference(symmetry,[status(thm)],[15193])).
% 1.97/2.12 tff(15195,plain,
% 1.97/2.12 ((op(e3, e0) = e1) <=> (op(e0, e3) = op(e3, e0))),
% 1.97/2.12 inference(transitivity,[status(thm)],[15194, 453])).
% 1.97/2.12 tff(15196,plain,
% 1.97/2.12 ((~(op(e3, e0) = e1)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[15195])).
% 1.97/2.12 tff(15197,plain,
% 1.97/2.12 (~(op(e0, e3) = op(e3, e0))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[15047, 15196])).
% 1.97/2.12 tff(15198,plain,
% 1.97/2.12 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[496, 15197])).
% 1.97/2.12 tff(15199,plain,
% 1.97/2.12 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 1.97/2.12 inference(transitivity,[status(thm)],[15165, 395])).
% 1.97/2.12 tff(15200,plain,
% 1.97/2.12 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[15199])).
% 1.97/2.12 tff(15201,plain,
% 1.97/2.12 (~(op(e2, e3) = op(e3, e2))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[3429, 15200])).
% 1.97/2.12 tff(15202,plain,
% 1.97/2.12 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[430, 15201])).
% 1.97/2.12 tff(15203,plain,
% 1.97/2.12 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 1.97/2.12 inference(monotonicity,[status(thm)],[15088])).
% 1.97/2.12 tff(15204,plain,
% 1.97/2.12 (op(e3, op(e3, e3)) = e3),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[15097, 15203])).
% 1.97/2.12 tff(15205,plain,
% 1.97/2.12 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[6277, 15204])).
% 1.97/2.12 tff(15206,plain,
% 1.97/2.12 (op(e1, e2) = op(e2, e1)),
% 1.97/2.12 inference(transitivity,[status(thm)],[15134, 15055])).
% 1.97/2.12 tff(15207,plain,
% 1.97/2.12 (op(e3, op(e1, e2)) = op(e3, op(e2, e1))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[15206])).
% 1.97/2.12 tff(15208,plain,
% 1.97/2.12 (op(e3, op(e1, e2)) = e3),
% 1.97/2.12 inference(transitivity,[status(thm)],[15207, 15173, 15087, 15097])).
% 1.97/2.12 tff(15209,plain,
% 1.97/2.12 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[11442, 15208])).
% 1.97/2.12 tff(15210,plain,
% 1.97/2.12 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[5367, 15209, 15205, 15202, 15198, 15192, 15189, 15180, 15175, 15172, 15168, 15163, 15159, 15154, 15151])).
% 1.97/2.12 tff(15211,plain,
% 1.97/2.12 (~(op(e0, op(e0, e0)) = e0)),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[5598, 15210])).
% 1.97/2.12 tff(15212,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[15211, 15141])).
% 1.97/2.12 tff(15213,plain,((op(e1, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e3) | (op(e3, e2) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(15214,plain,
% 1.97/2.12 (op(e1, e3) = e1),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[15213, 85, 84, 75, 17, 80, 68, 72, 76])).
% 1.97/2.12 tff(15215,plain,
% 1.97/2.12 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 1.97/2.12 inference(monotonicity,[status(thm)],[15214])).
% 1.97/2.12 tff(15216,plain,
% 1.97/2.12 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15215])).
% 2.02/2.12 tff(15217,plain,
% 2.02/2.12 (~(op(e1, e1) = e1)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[619, 15216])).
% 2.02/2.12 tff(15218,plain,
% 2.02/2.12 (op(e1, e1) = e3),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[630, 15217, 68, 84])).
% 2.02/2.12 tff(15219,plain,
% 2.02/2.12 (e3 = op(e1, e1)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15218])).
% 2.02/2.12 tff(15220,plain,
% 2.02/2.12 (op(e2, e3) = op(e2, op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.12 tff(15221,plain,
% 2.02/2.12 (op(e2, op(e1, e1)) = op(e2, e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15220])).
% 2.02/2.12 tff(15222,plain,
% 2.02/2.12 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.12 tff(15223,plain,
% 2.02/2.12 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15222, 657])).
% 2.02/2.12 tff(15224,plain,
% 2.02/2.12 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15223])).
% 2.02/2.12 tff(15225,plain,
% 2.02/2.12 (~(op(e3, e3) = e1)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[571, 15224])).
% 2.02/2.12 tff(15226,plain,
% 2.02/2.12 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.12 tff(15227,plain,
% 2.02/2.12 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15226])).
% 2.02/2.12 tff(15228,plain,
% 2.02/2.12 (~(op(e0, e3) = e1)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[64, 15227])).
% 2.02/2.12 tff(15229,plain,
% 2.02/2.12 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.12 tff(15230,plain,
% 2.02/2.12 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15229])).
% 2.02/2.12 tff(15231,plain,
% 2.02/2.12 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15230])).
% 2.02/2.12 tff(15232,plain,
% 2.02/2.12 (~(op(e1, e3) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[303, 15231])).
% 2.02/2.12 tff(15233,plain,
% 2.02/2.12 (op(op(e1, e3), e3) = e1),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[137, 15214])).
% 2.02/2.12 tff(15234,plain,
% 2.02/2.12 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[130, 15233])).
% 2.02/2.12 tff(15235,plain,
% 2.02/2.12 ((op(e1, e3) = e3) | (op(e1, e2) = e3) | (op(e2, e3) = e3) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e0, e3) = e2) | (op(e1, e3) = e2)),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[8677, 15002])).
% 2.02/2.12 tff(15236,plain,
% 2.02/2.12 (op(e0, e3) = e2),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[15235, 124, 72, 75, 80, 15234, 15232, 15228])).
% 2.02/2.12 tff(15237,plain,
% 2.02/2.12 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15236])).
% 2.02/2.12 tff(15238,plain,
% 2.02/2.12 (op(e0, e2) = op(e0, op(e0, e3))),
% 2.02/2.12 inference(symmetry,[status(thm)],[15237])).
% 2.02/2.12 tff(15239,plain,
% 2.02/2.12 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15238])).
% 2.02/2.12 tff(15240,plain,
% 2.02/2.12 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15239])).
% 2.02/2.12 tff(15241,plain,
% 2.02/2.12 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15220])).
% 2.02/2.12 tff(15242,plain,
% 2.02/2.12 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, e3) = e2)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15241])).
% 2.02/2.12 tff(15243,plain,
% 2.02/2.12 ((e2 = op(e2, op(e1, e1))) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.12 inference(commutativity,[status(thm)],[])).
% 2.02/2.12 tff(15244,plain,
% 2.02/2.12 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, op(e1, e1)))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15236, 15220])).
% 2.02/2.12 tff(15245,plain,
% 2.02/2.12 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15244, 15243])).
% 2.02/2.12 tff(15246,plain,
% 2.02/2.12 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15245, 15242])).
% 2.02/2.12 tff(15247,plain,
% 2.02/2.12 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15246])).
% 2.02/2.12 tff(15248,plain,
% 2.02/2.12 (~(op(e2, e3) = e2)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[964, 15247])).
% 2.02/2.12 tff(15249,plain,
% 2.02/2.12 (op(e2, e3) = e0),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[206, 15248, 76, 124])).
% 2.02/2.12 tff(15250,plain,
% 2.02/2.12 (e0 = op(e2, e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15249])).
% 2.02/2.12 tff(15251,plain,
% 2.02/2.12 ((op(e0, e3) = e3) <=> (e2 = op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15236, 15219])).
% 2.02/2.12 tff(15252,plain,
% 2.02/2.12 ((op(e0, e3) = e3) <=> (op(e1, e1) = e2)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15251, 2166])).
% 2.02/2.12 tff(15253,plain,
% 2.02/2.12 ((op(e1, e1) = e2) <=> (op(e0, e3) = e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15252])).
% 2.02/2.12 tff(15254,plain,
% 2.02/2.12 ((~(op(e1, e1) = e2)) <=> (~(op(e0, e3) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15253])).
% 2.02/2.12 tff(15255,plain,
% 2.02/2.12 (~(op(e0, e3) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[68, 15254])).
% 2.02/2.12 tff(15256,plain,
% 2.02/2.12 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.12 tff(15257,plain,
% 2.02/2.12 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15256])).
% 2.02/2.12 tff(15258,plain,
% 2.02/2.12 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15257])).
% 2.02/2.12 tff(15259,plain,
% 2.02/2.12 (~(op(e0, e1) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[792, 15258])).
% 2.02/2.12 tff(15260,plain,
% 2.02/2.12 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.12 tff(15261,plain,
% 2.02/2.12 ((op(e2, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 2.02/2.12 inference(transitivity,[status(thm)],[15260, 8414])).
% 2.02/2.12 tff(15262,plain,
% 2.02/2.12 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15261])).
% 2.02/2.12 tff(15263,plain,
% 2.02/2.12 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15262])).
% 2.02/2.12 tff(15264,plain,
% 2.02/2.12 (~(op(e2, e1) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[225, 15263])).
% 2.02/2.12 tff(15265,plain,
% 2.02/2.12 (e2 = op(e0, e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15236])).
% 2.02/2.12 tff(15266,plain,
% 2.02/2.12 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15265])).
% 2.02/2.12 tff(15267,plain,
% 2.02/2.12 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15266])).
% 2.02/2.12 tff(15268,plain,
% 2.02/2.12 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15267])).
% 2.02/2.12 tff(15269,plain,
% 2.02/2.12 (~(op(e0, e1) = e2)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[818, 15268])).
% 2.02/2.12 tff(15270,plain,
% 2.02/2.12 (op(e2, e1) = e2),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[1993, 15269, 68, 82])).
% 2.02/2.12 tff(15271,plain,
% 2.02/2.12 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15270])).
% 2.02/2.12 tff(15272,plain,
% 2.02/2.12 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15271])).
% 2.02/2.12 tff(15273,plain,
% 2.02/2.12 (~(op(e2, e0) = e2)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[1966, 15272])).
% 2.02/2.12 tff(15274,plain,
% 2.02/2.12 (op(e2, e0) = e3),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[3293, 15273, 15264, 15236, 15249, 124])).
% 2.02/2.12 tff(15275,plain,
% 2.02/2.12 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15274])).
% 2.02/2.12 tff(15276,plain,
% 2.02/2.12 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15275])).
% 2.02/2.12 tff(15277,plain,
% 2.02/2.12 (~(op(e0, e0) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[359, 15276])).
% 2.02/2.12 tff(15278,plain,
% 2.02/2.12 (op(e0, e2) = e3),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[1495, 15277, 15259, 15255])).
% 2.02/2.12 tff(15279,plain,
% 2.02/2.12 (op(e0, op(e0, e3)) = e3),
% 2.02/2.12 inference(transitivity,[status(thm)],[15237, 15278])).
% 2.02/2.12 tff(15280,plain,
% 2.02/2.12 ((op(e0, op(e0, e3)) = e0) <=> (e3 = op(e2, e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15279, 15250])).
% 2.02/2.12 tff(15281,plain,
% 2.02/2.12 ((op(e0, op(e0, e3)) = e0) <=> (op(e2, e3) = e3)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15280, 112])).
% 2.02/2.12 tff(15282,plain,
% 2.02/2.12 ((op(e2, e3) = e3) <=> (op(e0, op(e0, e3)) = e0)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15281])).
% 2.02/2.12 tff(15283,plain,
% 2.02/2.12 ((op(e2, e3) = e3) <=> (op(e0, e2) = e0)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15282, 15240])).
% 2.02/2.12 tff(15284,plain,
% 2.02/2.12 ((~(op(e2, e3) = e3)) <=> (~(op(e0, e2) = e0))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15283])).
% 2.02/2.12 tff(15285,plain,
% 2.02/2.12 (~(op(e0, e2) = e0)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[124, 15284])).
% 2.02/2.12 tff(15286,plain,
% 2.02/2.12 (op(e0, e3) = op(e0, op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.12 tff(15287,plain,
% 2.02/2.12 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e1)) = e0)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15286])).
% 2.02/2.12 tff(15288,plain,
% 2.02/2.12 ((op(e0, op(e1, e1)) = e0) <=> (op(e0, e3) = e0)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15287])).
% 2.02/2.12 tff(15289,plain,
% 2.02/2.12 ((e0 = op(e0, op(e1, e1))) <=> (op(e0, op(e1, e1)) = e0)),
% 2.02/2.12 inference(commutativity,[status(thm)],[])).
% 2.02/2.12 tff(15290,plain,
% 2.02/2.12 (e2 = op(e0, op(e1, e1))),
% 2.02/2.12 inference(transitivity,[status(thm)],[15265, 15286])).
% 2.02/2.12 tff(15291,plain,
% 2.02/2.12 ((e0 = e2) <=> (e0 = op(e0, op(e1, e1)))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15290])).
% 2.02/2.12 tff(15292,plain,
% 2.02/2.12 ((e0 = e2) <=> (op(e0, op(e1, e1)) = e0)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15291, 15289])).
% 2.02/2.12 tff(15293,plain,
% 2.02/2.12 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15292, 15288])).
% 2.02/2.12 tff(15294,plain,
% 2.02/2.12 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15293])).
% 2.02/2.12 tff(15295,plain,
% 2.02/2.12 (~(op(e0, e3) = e0)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[14, 15294])).
% 2.02/2.12 tff(15296,plain,
% 2.02/2.12 (op(e3, e3) = e3),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[480, 15255, 15232, 124])).
% 2.02/2.12 tff(15297,plain,
% 2.02/2.12 (op(e3, e3) = op(e1, e1)),
% 2.02/2.12 inference(transitivity,[status(thm)],[15296, 15219])).
% 2.02/2.12 tff(15298,plain,
% 2.02/2.12 ((op(e3, e3) = e0) <=> (op(e1, e1) = e0)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15297])).
% 2.02/2.12 tff(15299,plain,
% 2.02/2.12 ((op(e1, e1) = e0) <=> (op(e3, e3) = e0)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15298])).
% 2.02/2.12 tff(15300,plain,
% 2.02/2.12 ((~(op(e1, e1) = e0)) <=> (~(op(e3, e3) = e0))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15299])).
% 2.02/2.12 tff(15301,plain,
% 2.02/2.12 (~(op(e3, e3) = e0)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[84, 15300])).
% 2.02/2.12 tff(15302,plain,
% 2.02/2.12 ((op(e3, e1) = op(e1, e1)) <=> (op(e1, e1) = op(e3, e1))),
% 2.02/2.12 inference(commutativity,[status(thm)],[])).
% 2.02/2.12 tff(15303,plain,
% 2.02/2.12 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e1))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.12 tff(15304,plain,
% 2.02/2.12 ((op(e3, e1) = e3) <=> (op(e1, e1) = op(e3, e1))),
% 2.02/2.12 inference(transitivity,[status(thm)],[15303, 15302])).
% 2.02/2.12 tff(15305,plain,
% 2.02/2.12 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15304])).
% 2.02/2.12 tff(15306,plain,
% 2.02/2.12 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15305])).
% 2.02/2.12 tff(15307,plain,
% 2.02/2.12 (~(op(e3, e1) = e3)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[945, 15306])).
% 2.02/2.12 tff(15308,plain,
% 2.02/2.12 (op(e2, e1) = op(e0, op(e1, e1))),
% 2.02/2.12 inference(transitivity,[status(thm)],[15270, 15265, 15286])).
% 2.02/2.12 tff(15309,plain,
% 2.02/2.12 ((op(e2, e1) = e0) <=> (op(e0, op(e1, e1)) = e0)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15308])).
% 2.02/2.12 tff(15310,plain,
% 2.02/2.12 ((op(e0, op(e1, e1)) = e0) <=> (op(e2, e1) = e0)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15309])).
% 2.02/2.12 tff(15311,plain,
% 2.02/2.12 ((~(op(e0, op(e1, e1)) = e0)) <=> (~(op(e2, e1) = e0))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15310])).
% 2.02/2.12 tff(15312,plain,
% 2.02/2.12 ((~(e0 = e2)) <=> (~(op(e0, op(e1, e1)) = e0))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15292])).
% 2.02/2.12 tff(15313,plain,
% 2.02/2.12 (~(op(e0, op(e1, e1)) = e0)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[14, 15312])).
% 2.02/2.12 tff(15314,plain,
% 2.02/2.12 (~(op(e2, e1) = e0)),
% 2.02/2.12 inference(modus_ponens,[status(thm)],[15313, 15311])).
% 2.02/2.12 tff(15315,plain,
% 2.02/2.12 (op(e1, e2) = e0),
% 2.02/2.12 inference(unit_resolution,[status(thm)],[973, 15285, 17, 85])).
% 2.02/2.12 tff(15316,plain,
% 2.02/2.12 (op(op(e1, e2), e1) = op(e0, e1)),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15315])).
% 2.02/2.12 tff(15317,plain,
% 2.02/2.12 ((op(op(e1, e2), e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 2.02/2.12 inference(monotonicity,[status(thm)],[15316, 15265])).
% 2.02/2.12 tff(15318,plain,
% 2.02/2.12 ((op(e0, e1) = op(e0, e3)) <=> (op(op(e1, e2), e1) = e2)),
% 2.02/2.12 inference(symmetry,[status(thm)],[15317])).
% 2.02/2.12 tff(15319,plain,
% 2.02/2.12 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15318])).
% 2.02/2.13 tff(15320,plain,
% 2.02/2.13 (~(op(op(e1, e2), e1) = e2)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[818, 15319])).
% 2.02/2.13 tff(15321,plain,
% 2.02/2.13 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[5959, 15320])).
% 2.02/2.13 tff(15322,plain,
% 2.02/2.13 (op(op(e0, e3), e3) = op(e2, op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15236, 15219])).
% 2.02/2.13 tff(15323,plain,
% 2.02/2.13 (op(e2, op(e2, e0)) = op(op(e0, e3), e3)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15265, 15274])).
% 2.02/2.13 tff(15324,plain,
% 2.02/2.13 (op(e2, op(e2, e0)) = e0),
% 2.02/2.13 inference(transitivity,[status(thm)],[15323, 15322, 15221, 15249])).
% 2.02/2.13 tff(15325,plain,
% 2.02/2.13 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[2653, 15324])).
% 2.02/2.13 tff(15326,plain,
% 2.02/2.13 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15322, 15221])).
% 2.02/2.13 tff(15327,plain,
% 2.02/2.13 ((op(op(e0, e3), e3) = e0) <=> (op(e2, e3) = e0)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15326])).
% 2.02/2.13 tff(15328,plain,
% 2.02/2.13 ((op(e2, e3) = e0) <=> (op(op(e0, e3), e3) = e0)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15327])).
% 2.02/2.13 tff(15329,plain,
% 2.02/2.13 (op(op(e0, e3), e3) = e0),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15249, 15328])).
% 2.02/2.13 tff(15330,plain,
% 2.02/2.13 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1361, 15329])).
% 2.02/2.13 tff(15331,plain,
% 2.02/2.13 (op(e1, op(e0, e3)) = op(e1, e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15236])).
% 2.02/2.13 tff(15332,plain,
% 2.02/2.13 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e0, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15265])).
% 2.02/2.13 tff(15333,plain,
% 2.02/2.13 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15332])).
% 2.02/2.13 tff(15334,plain,
% 2.02/2.13 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15333])).
% 2.02/2.13 tff(15335,plain,
% 2.02/2.13 (~(op(e0, e0) = e2)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[3414, 15334])).
% 2.02/2.13 tff(15336,plain,
% 2.02/2.13 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15265])).
% 2.02/2.13 tff(15337,plain,
% 2.02/2.13 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15336])).
% 2.02/2.13 tff(15338,plain,
% 2.02/2.13 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15337])).
% 2.02/2.13 tff(15339,plain,
% 2.02/2.13 (op(e2, op(e0, e3)) = op(e2, e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15236])).
% 2.02/2.13 tff(15340,plain,
% 2.02/2.13 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15339])).
% 2.02/2.13 tff(15341,plain,
% 2.02/2.13 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15340])).
% 2.02/2.13 tff(15342,plain,
% 2.02/2.13 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15270])).
% 2.02/2.13 tff(15343,plain,
% 2.02/2.13 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15342, 81])).
% 2.02/2.13 tff(15344,plain,
% 2.02/2.13 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, op(e0, e3)) = e2)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15343, 15341])).
% 2.02/2.13 tff(15345,plain,
% 2.02/2.13 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15344])).
% 2.02/2.13 tff(15346,plain,
% 2.02/2.13 (~(op(e2, op(e0, e3)) = e2)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[508, 15345])).
% 2.02/2.13 tff(15347,plain,
% 2.02/2.13 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15219])).
% 2.02/2.13 tff(15348,plain,
% 2.02/2.13 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15347])).
% 2.02/2.13 tff(15349,plain,
% 2.02/2.13 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15348])).
% 2.02/2.13 tff(15350,plain,
% 2.02/2.13 (~(op(e1, e0) = e3)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[737, 15349])).
% 2.02/2.13 tff(15351,plain,
% 2.02/2.13 ((~(op(e2, e3) = e3)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15282])).
% 2.02/2.13 tff(15352,plain,
% 2.02/2.13 (~(op(e0, op(e0, e3)) = e0)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[124, 15351])).
% 2.02/2.13 tff(15353,plain,
% 2.02/2.13 (~(op(e3, e0) = op(e0, e3))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[4069, 15352, 15232, 15228, 124, 15234, 72, 15264, 15217, 15350, 15259, 15255, 68, 15346, 84, 80, 15301])).
% 2.02/2.13 tff(15354,plain,
% 2.02/2.13 (~(op(e3, e0) = e2)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15353, 15338])).
% 2.02/2.13 tff(15355,plain,
% 2.02/2.13 (op(e1, e0) = e2),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[589, 15354, 15335, 15273])).
% 2.02/2.13 tff(15356,plain,
% 2.02/2.13 (op(e1, e0) = op(e0, e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15355, 15265])).
% 2.02/2.13 tff(15357,plain,
% 2.02/2.13 (op(e1, op(e1, e0)) = op(e1, op(e0, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15356])).
% 2.02/2.13 tff(15358,plain,
% 2.02/2.13 (op(e1, op(e1, e0)) = e0),
% 2.02/2.13 inference(transitivity,[status(thm)],[15357, 15331, 15315])).
% 2.02/2.13 tff(15359,plain,
% 2.02/2.13 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1836, 15358])).
% 2.02/2.13 tff(15360,plain,
% 2.02/2.13 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15236])).
% 2.02/2.13 tff(15361,plain,
% 2.02/2.13 (op(e3, e2) = op(e3, op(e0, e3))),
% 2.02/2.13 inference(symmetry,[status(thm)],[15360])).
% 2.02/2.13 tff(15362,plain,
% 2.02/2.13 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15361])).
% 2.02/2.13 tff(15363,plain,
% 2.02/2.13 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15362])).
% 2.02/2.13 tff(15364,plain,
% 2.02/2.13 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15361, 15296])).
% 2.02/2.13 tff(15365,plain,
% 2.02/2.13 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15364, 15363])).
% 2.02/2.13 tff(15366,plain,
% 2.02/2.13 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15365])).
% 2.02/2.13 tff(15367,plain,
% 2.02/2.13 (~(op(e3, e2) = e3)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[1888, 15366])).
% 2.02/2.13 tff(15368,plain,
% 2.02/2.13 (op(e2, e1) = op(e0, e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15270, 15265])).
% 2.02/2.13 tff(15369,plain,
% 2.02/2.13 ((op(e2, e1) = e1) <=> (op(e0, e3) = e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15368])).
% 2.02/2.13 tff(15370,plain,
% 2.02/2.13 ((op(e0, e3) = e1) <=> (op(e2, e1) = e1)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15369])).
% 2.02/2.13 tff(15371,plain,
% 2.02/2.13 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e1) = e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15370])).
% 2.02/2.13 tff(15372,plain,
% 2.02/2.13 (~(op(e2, e1) = e1)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15228, 15371])).
% 2.02/2.13 tff(15373,plain,
% 2.02/2.13 (op(e2, e0) = op(e1, e1)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15274, 15219])).
% 2.02/2.13 tff(15374,plain,
% 2.02/2.13 ((op(e2, e0) = e1) <=> (op(e1, e1) = e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15373])).
% 2.02/2.13 tff(15375,plain,
% 2.02/2.13 ((op(e1, e1) = e1) <=> (op(e2, e0) = e1)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15374])).
% 2.02/2.13 tff(15376,plain,
% 2.02/2.13 ((~(op(e1, e1) = e1)) <=> (~(op(e2, e0) = e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15375])).
% 2.02/2.13 tff(15377,plain,
% 2.02/2.13 (~(op(e2, e0) = e1)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15217, 15376])).
% 2.02/2.13 tff(15378,plain,
% 2.02/2.13 (op(e2, e2) = e1),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[345, 15377, 76, 15372])).
% 2.02/2.13 tff(15379,plain,
% 2.02/2.13 ((op(e2, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15378])).
% 2.02/2.13 tff(15380,plain,
% 2.02/2.13 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15379, 7171])).
% 2.02/2.13 tff(15381,plain,
% 2.02/2.13 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15380])).
% 2.02/2.13 tff(15382,plain,
% 2.02/2.13 (~(op(e3, e2) = e1)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[1546, 15381])).
% 2.02/2.13 tff(15383,plain,
% 2.02/2.13 (op(e3, e2) = e2),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1898, 15382, 85, 15367])).
% 2.02/2.13 tff(15384,plain,
% 2.02/2.13 (op(e3, e2) = op(e0, e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15383, 15265])).
% 2.02/2.13 tff(15385,plain,
% 2.02/2.13 (op(e3, op(e3, e2)) = op(e3, op(e0, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15384])).
% 2.02/2.13 tff(15386,plain,
% 2.02/2.13 (op(e3, op(e3, e2)) = e2),
% 2.02/2.13 inference(transitivity,[status(thm)],[15385, 15360, 15383])).
% 2.02/2.13 tff(15387,plain,
% 2.02/2.13 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1904, 15386])).
% 2.02/2.13 tff(15388,plain,
% 2.02/2.13 (op(op(e2, e1), e1) = op(e2, e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15270])).
% 2.02/2.13 tff(15389,plain,
% 2.02/2.13 (op(op(e2, e1), e1) = e2),
% 2.02/2.13 inference(transitivity,[status(thm)],[15388, 15270])).
% 2.02/2.13 tff(15390,plain,
% 2.02/2.13 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[2371, 15389])).
% 2.02/2.13 tff(15391,plain,
% 2.02/2.13 (op(e0, op(e1, e1)) = op(e0, e3)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15286])).
% 2.02/2.13 tff(15392,plain,
% 2.02/2.13 (op(op(e2, e3), e3) = op(e0, op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15249, 15219])).
% 2.02/2.13 tff(15393,plain,
% 2.02/2.13 (op(e0, op(e0, e2)) = op(op(e2, e3), e3)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15250, 15278])).
% 2.02/2.13 tff(15394,plain,
% 2.02/2.13 (op(e0, op(e0, e2)) = e2),
% 2.02/2.13 inference(transitivity,[status(thm)],[15393, 15392, 15391, 15236])).
% 2.02/2.13 tff(15395,plain,
% 2.02/2.13 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1331, 15394])).
% 2.02/2.13 tff(15396,plain,
% 2.02/2.13 (op(op(e2, e3), e3) = e2),
% 2.02/2.13 inference(transitivity,[status(thm)],[15392, 15391, 15236])).
% 2.02/2.13 tff(15397,plain,
% 2.02/2.13 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1288, 15396])).
% 2.02/2.13 tff(15398,plain,
% 2.02/2.13 (op(e3, e0) = e0),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1916, 183, 85, 656])).
% 2.02/2.13 tff(15399,plain,
% 2.02/2.13 (op(e3, e0) = op(e2, e3)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15398, 252])).
% 2.02/2.13 tff(15400,plain,
% 2.02/2.13 (op(e3, op(e3, e0)) = op(e3, op(e2, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15399])).
% 2.02/2.13 tff(15401,plain,
% 2.02/2.13 (op(e3, op(e3, e0)) = e0),
% 2.02/2.13 inference(transitivity,[status(thm)],[15400, 10439, 15398])).
% 2.02/2.13 tff(15402,plain,
% 2.02/2.13 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1345, 15401])).
% 2.02/2.13 tff(15403,plain,
% 2.02/2.13 (op(e3, e1) = e1),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[446, 183, 2839, 82])).
% 2.02/2.13 tff(15404,plain,
% 2.02/2.13 (op(e3, op(e3, e1)) = op(e3, e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15403])).
% 2.02/2.13 tff(15405,plain,
% 2.02/2.13 (op(e3, op(e3, e1)) = e1),
% 2.02/2.13 inference(transitivity,[status(thm)],[15404, 15403])).
% 2.02/2.13 tff(15406,plain,
% 2.02/2.13 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[2594, 15405])).
% 2.02/2.13 tff(15407,plain,
% 2.02/2.13 ($false),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[1459, 15406, 15402, 1347, 1363, 1936, 1304, 3341, 1357, 3342, 2421, 1358, 9836])).
% 2.02/2.13 tff(15408,plain,((op(e3, e1) = e0) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~(op(e2, e3) = e0)) | (op(e2, e1) = e0) | (op(e1, e1) = e0) | (op(e3, e1) = e3) | (op(e3, e1) = e2) | (op(e3, e2) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.13 tff(15409,plain,
% 2.02/2.13 (op(e3, e1) = e0),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[15408, 15397, 15395, 15390, 15234, 15387, 15359, 15330, 15325, 15321, 15249, 15314, 84, 15307, 82, 85, 15301])).
% 2.02/2.13 tff(15410,plain,
% 2.02/2.13 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15409])).
% 2.02/2.13 tff(15411,plain,
% 2.02/2.13 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15410])).
% 2.02/2.13 tff(15412,plain,
% 2.02/2.13 (~(op(e0, e1) = e0)),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[3046, 15411])).
% 2.02/2.13 tff(15413,plain,
% 2.02/2.13 (op(e0, e0) = e0),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[3976, 15412, 15295, 15285])).
% 2.02/2.13 tff(15414,plain,
% 2.02/2.13 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15413])).
% 2.02/2.13 tff(15415,plain,
% 2.02/2.13 (op(e0, op(e0, e0)) = e0),
% 2.02/2.13 inference(transitivity,[status(thm)],[15414, 15413])).
% 2.02/2.13 tff(15416,plain,
% 2.02/2.13 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15218])).
% 2.02/2.13 tff(15417,plain,
% 2.02/2.13 (op(e1, op(e2, e0)) = op(e1, op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15373])).
% 2.02/2.13 tff(15418,plain,
% 2.02/2.13 (op(e1, op(e2, e0)) = e1),
% 2.02/2.13 inference(transitivity,[status(thm)],[15417, 15416, 15214])).
% 2.02/2.13 tff(15419,plain,
% 2.02/2.13 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[5690, 15418])).
% 2.02/2.13 tff(15420,plain,
% 2.02/2.13 (op(e0, e2) = op(e1, e1)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15278, 15219])).
% 2.02/2.13 tff(15421,plain,
% 2.02/2.13 (op(e1, op(e0, e2)) = op(e1, op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15420])).
% 2.02/2.13 tff(15422,plain,
% 2.02/2.13 (op(e1, op(e0, e2)) = e1),
% 2.02/2.13 inference(transitivity,[status(thm)],[15421, 15416, 15214])).
% 2.02/2.13 tff(15423,plain,
% 2.02/2.13 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[14259, 15422])).
% 2.02/2.13 tff(15424,plain,
% 2.02/2.13 ((op(e0, e3) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e3))),
% 2.02/2.13 inference(commutativity,[status(thm)],[])).
% 2.02/2.13 tff(15425,plain,
% 2.02/2.13 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e3) = op(e0, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15356])).
% 2.02/2.13 tff(15426,plain,
% 2.02/2.13 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e3))),
% 2.02/2.13 inference(transitivity,[status(thm)],[15425, 15424])).
% 2.02/2.13 tff(15427,plain,
% 2.02/2.13 ((op(e0, e1) = op(e0, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 2.02/2.13 inference(symmetry,[status(thm)],[15426])).
% 2.02/2.13 tff(15428,plain,
% 2.02/2.13 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15427])).
% 2.02/2.13 tff(15429,plain,
% 2.02/2.13 (~(op(e1, e0) = op(e0, e1))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[818, 15428])).
% 2.02/2.13 tff(15430,plain,
% 2.02/2.13 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[613, 15429])).
% 2.02/2.13 tff(15431,plain,
% 2.02/2.13 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 2.02/2.13 inference(transitivity,[status(thm)],[15427, 596])).
% 2.02/2.13 tff(15432,plain,
% 2.02/2.13 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15431])).
% 2.02/2.13 tff(15433,plain,
% 2.02/2.13 (~(op(e0, e1) = op(e1, e0))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[818, 15432])).
% 2.02/2.13 tff(15434,plain,
% 2.02/2.13 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[609, 15433])).
% 2.02/2.13 tff(15435,plain,
% 2.02/2.13 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15250])).
% 2.02/2.13 tff(15436,plain,
% 2.02/2.13 ((~(op(e3, e2) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15435])).
% 2.02/2.13 tff(15437,plain,
% 2.02/2.13 (~(op(e3, e2) = op(e2, e3))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[85, 15436])).
% 2.02/2.13 tff(15438,plain,
% 2.02/2.13 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[500, 15437])).
% 2.02/2.13 tff(15439,plain,
% 2.02/2.13 (op(e2, op(e2, e2)) = op(e2, e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15378])).
% 2.02/2.13 tff(15440,plain,
% 2.02/2.13 (op(e2, op(e2, e2)) = e2),
% 2.02/2.13 inference(transitivity,[status(thm)],[15439, 15270])).
% 2.02/2.13 tff(15441,plain,
% 2.02/2.13 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[528, 15440])).
% 2.02/2.13 tff(15442,plain,
% 2.02/2.13 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15270])).
% 2.02/2.13 tff(15443,plain,
% 2.02/2.13 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.02/2.13 inference(transitivity,[status(thm)],[15442, 5762])).
% 2.02/2.13 tff(15444,plain,
% 2.02/2.13 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.02/2.13 inference(symmetry,[status(thm)],[15443])).
% 2.02/2.13 tff(15445,plain,
% 2.02/2.13 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15383])).
% 2.02/2.13 tff(15446,plain,
% 2.02/2.13 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 2.02/2.13 inference(transitivity,[status(thm)],[15445, 15444, 531])).
% 2.02/2.13 tff(15447,plain,
% 2.02/2.13 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15446])).
% 2.02/2.13 tff(15448,plain,
% 2.02/2.13 (~(op(e1, e2) = op(e2, e1))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[2292, 15447])).
% 2.02/2.13 tff(15449,plain,
% 2.02/2.13 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[539, 15448])).
% 2.02/2.13 tff(15450,plain,
% 2.02/2.13 (op(e2, op(e1, e3)) = op(e2, e1)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.13 tff(15451,plain,
% 2.02/2.13 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e1) = e2)),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15450])).
% 2.02/2.13 tff(15452,plain,
% 2.02/2.13 ((op(e2, e1) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 2.02/2.13 inference(symmetry,[status(thm)],[15451])).
% 2.02/2.13 tff(15453,plain,
% 2.02/2.13 (op(e2, op(e1, e3)) = e2),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15270, 15452])).
% 2.02/2.13 tff(15454,plain,
% 2.02/2.13 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[9084, 15453])).
% 2.02/2.13 tff(15455,plain,
% 2.02/2.13 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e1) = op(e1, e2))),
% 2.02/2.13 inference(transitivity,[status(thm)],[15445, 15444])).
% 2.02/2.13 tff(15456,plain,
% 2.02/2.13 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15455])).
% 2.02/2.13 tff(15457,plain,
% 2.02/2.13 (~(op(e2, e1) = op(e1, e2))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[2292, 15456])).
% 2.02/2.13 tff(15458,plain,
% 2.02/2.13 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[557, 15457])).
% 2.02/2.13 tff(15459,plain,
% 2.02/2.13 (op(e1, op(e1, e1)) = e1),
% 2.02/2.13 inference(transitivity,[status(thm)],[15416, 15214])).
% 2.02/2.13 tff(15460,plain,
% 2.02/2.13 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[5678, 15459])).
% 2.02/2.13 tff(15461,plain,
% 2.02/2.13 (~(op(e0, e3) = op(e3, e0))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[15353, 454])).
% 2.02/2.13 tff(15462,plain,
% 2.02/2.13 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[496, 15461])).
% 2.02/2.13 tff(15463,plain,
% 2.02/2.13 ((op(e3, e2) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 2.02/2.13 inference(transitivity,[status(thm)],[15435, 395])).
% 2.02/2.13 tff(15464,plain,
% 2.02/2.13 ((~(op(e3, e2) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15463])).
% 2.02/2.13 tff(15465,plain,
% 2.02/2.13 (~(op(e2, e3) = op(e3, e2))),
% 2.02/2.13 inference(modus_ponens,[status(thm)],[85, 15464])).
% 2.02/2.13 tff(15466,plain,
% 2.02/2.13 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.02/2.13 inference(unit_resolution,[status(thm)],[430, 15465])).
% 2.02/2.13 tff(15467,plain,
% 2.02/2.13 (op(e1, op(e3, e3)) = op(e1, op(e1, e1))),
% 2.02/2.13 inference(monotonicity,[status(thm)],[15297])).
% 2.02/2.13 tff(15468,plain,
% 2.02/2.13 (op(e1, op(e3, e3)) = e1),
% 2.02/2.13 inference(transitivity,[status(thm)],[15467, 15416, 15214])).
% 2.02/2.14 tff(15469,plain,
% 2.02/2.14 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[5685, 15468])).
% 2.02/2.14 tff(15470,plain,
% 2.02/2.14 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.14 tff(15471,plain,
% 2.02/2.14 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15470])).
% 2.02/2.14 tff(15472,plain,
% 2.02/2.14 (op(e3, e1) = op(e2, e3)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15409, 15250])).
% 2.02/2.14 tff(15473,plain,
% 2.02/2.14 ((op(e3, e1) = e1) <=> (op(e2, e3) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15472])).
% 2.02/2.14 tff(15474,plain,
% 2.02/2.14 ((op(e2, e3) = e1) <=> (op(e3, e1) = e1)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15473])).
% 2.02/2.14 tff(15475,plain,
% 2.02/2.14 ((op(e2, e3) = e1) <=> (op(e1, e3) = op(e3, e1))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15474, 15471, 6290])).
% 2.02/2.14 tff(15476,plain,
% 2.02/2.14 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15475])).
% 2.02/2.14 tff(15477,plain,
% 2.02/2.14 (~(op(e1, e3) = op(e3, e1))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[76, 15476])).
% 2.02/2.14 tff(15478,plain,
% 2.02/2.14 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[6307, 15477])).
% 2.02/2.14 tff(15479,plain,
% 2.02/2.14 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[5367, 15478, 15469, 15466, 15462, 15460, 15458, 15454, 15449, 15441, 15438, 15434, 15430, 15423, 15419])).
% 2.02/2.14 tff(15480,plain,
% 2.02/2.14 (~(op(e0, op(e0, e0)) = e0)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[5598, 15479])).
% 2.02/2.14 tff(15481,plain,
% 2.02/2.14 ($false),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[15480, 15415])).
% 2.02/2.14 tff(15482,plain,((op(e2, e3) = e3) | (op(e2, e3) = e1) | (op(e1, e1) = e0) | (op(e3, e1) = e2) | (op(e3, e2) = e0) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e1, e1) = e2) | (op(e1, e3) = e0) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.14 tff(15483,plain,
% 2.02/2.14 (op(e2, e3) = e3),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[15482, 82, 84, 76, 85, 17, 72, 68, 80, 75])).
% 2.02/2.14 tff(15484,plain,
% 2.02/2.14 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15483])).
% 2.02/2.14 tff(15485,plain,
% 2.02/2.14 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15484, 666])).
% 2.02/2.14 tff(15486,plain,
% 2.02/2.14 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15485])).
% 2.02/2.14 tff(15487,plain,
% 2.02/2.14 (~(op(e3, e3) = e3)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[368, 15486])).
% 2.02/2.14 tff(15488,plain,
% 2.02/2.14 (op(e3, e3) = e0),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[15018, 15487, 15225])).
% 2.02/2.14 tff(15489,plain,
% 2.02/2.14 (e0 = op(e3, e3)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15488])).
% 2.02/2.14 tff(15490,plain,
% 2.02/2.14 (op(e3, e0) = op(e3, op(e3, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15489])).
% 2.02/2.14 tff(15491,plain,
% 2.02/2.14 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15490])).
% 2.02/2.14 tff(15492,plain,
% 2.02/2.14 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15483])).
% 2.02/2.14 tff(15493,plain,
% 2.02/2.14 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15492])).
% 2.02/2.14 tff(15494,plain,
% 2.02/2.14 (~(op(e2, e0) = e3)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[989, 15493])).
% 2.02/2.14 tff(15495,plain,
% 2.02/2.14 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15214])).
% 2.02/2.14 tff(15496,plain,
% 2.02/2.14 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15495])).
% 2.02/2.14 tff(15497,plain,
% 2.02/2.14 (~(op(e1, e0) = e1)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[110, 15496])).
% 2.02/2.14 tff(15498,plain,
% 2.02/2.14 ((op(e3, op(e3, e3)) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 2.02/2.14 inference(commutativity,[status(thm)],[])).
% 2.02/2.14 tff(15499,plain,
% 2.02/2.14 ((op(e3, e0) = e1) <=> (op(e3, op(e3, e3)) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15490])).
% 2.02/2.14 tff(15500,plain,
% 2.02/2.14 ((op(e3, e0) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15499, 15498])).
% 2.02/2.14 tff(15501,plain,
% 2.02/2.14 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e1)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15500])).
% 2.02/2.14 tff(15502,plain,
% 2.02/2.14 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15489])).
% 2.02/2.14 tff(15503,plain,
% 2.02/2.14 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15502])).
% 2.02/2.14 tff(15504,plain,
% 2.02/2.14 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15503])).
% 2.02/2.14 tff(15505,plain,
% 2.02/2.14 (~(op(e3, e1) = e0)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[437, 15504])).
% 2.02/2.14 tff(15506,plain,
% 2.02/2.14 (op(e3, e1) = e1),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[446, 15505, 15307, 82])).
% 2.02/2.14 tff(15507,plain,
% 2.02/2.14 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, op(e3, e3)) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15490, 15506])).
% 2.02/2.14 tff(15508,plain,
% 2.02/2.14 ((op(e3, e0) = op(e3, e1)) <=> (e1 = op(e3, op(e3, e3)))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15507, 15498])).
% 2.02/2.14 tff(15509,plain,
% 2.02/2.14 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15508, 15501])).
% 2.02/2.14 tff(15510,plain,
% 2.02/2.14 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15509])).
% 2.02/2.14 tff(15511,plain,
% 2.02/2.14 (~(op(e3, e0) = e1)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[580, 15510])).
% 2.02/2.14 tff(15512,plain,
% 2.02/2.14 (op(e2, e3) = op(e1, e1)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15483, 15219])).
% 2.02/2.14 tff(15513,plain,
% 2.02/2.14 ((op(e2, e3) = e0) <=> (op(e1, e1) = e0)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15512])).
% 2.02/2.14 tff(15514,plain,
% 2.02/2.14 ((op(e1, e1) = e0) <=> (op(e2, e3) = e0)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15513])).
% 2.02/2.14 tff(15515,plain,
% 2.02/2.14 ((~(op(e1, e1) = e0)) <=> (~(op(e2, e3) = e0))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15514])).
% 2.02/2.14 tff(15516,plain,
% 2.02/2.14 (~(op(e2, e3) = e0)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[84, 15515])).
% 2.02/2.14 tff(15517,plain,
% 2.02/2.14 (op(e2, op(e1, e1)) = op(e2, e3)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15218])).
% 2.02/2.14 tff(15518,plain,
% 2.02/2.14 (op(e2, e3) = op(e2, op(e1, e1))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15517])).
% 2.02/2.14 tff(15519,plain,
% 2.02/2.14 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15518])).
% 2.02/2.14 tff(15520,plain,
% 2.02/2.14 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, e3) = e2)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15519])).
% 2.02/2.14 tff(15521,plain,
% 2.02/2.14 (op(e2, op(e1, e1)) = op(e1, e1)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15517, 15483, 15219])).
% 2.02/2.14 tff(15522,plain,
% 2.02/2.14 ((op(e2, op(e1, e1)) = e2) <=> (op(e1, e1) = e2)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15521])).
% 2.02/2.14 tff(15523,plain,
% 2.02/2.14 ((op(e1, e1) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15522])).
% 2.02/2.14 tff(15524,plain,
% 2.02/2.14 ((op(e1, e1) = e2) <=> (op(e2, e3) = e2)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15523, 15520])).
% 2.02/2.14 tff(15525,plain,
% 2.02/2.14 ((~(op(e1, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15524])).
% 2.02/2.14 tff(15526,plain,
% 2.02/2.14 (~(op(e2, e3) = e2)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[68, 15525])).
% 2.02/2.14 tff(15527,plain,
% 2.02/2.14 (op(e0, e3) = e2),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[15003, 15526, 72])).
% 2.02/2.14 tff(15528,plain,
% 2.02/2.14 (e2 = op(e0, e3)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15527])).
% 2.02/2.14 tff(15529,plain,
% 2.02/2.14 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15528])).
% 2.02/2.14 tff(15530,plain,
% 2.02/2.14 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15529])).
% 2.02/2.14 tff(15531,plain,
% 2.02/2.14 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15530])).
% 2.02/2.14 tff(15532,plain,
% 2.02/2.14 (~(op(e0, e1) = e2)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[818, 15531])).
% 2.02/2.14 tff(15533,plain,
% 2.02/2.14 (op(e2, e1) = e2),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[1993, 15532, 68, 82])).
% 2.02/2.14 tff(15534,plain,
% 2.02/2.14 (op(e2, e1) = op(e0, e3)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15533, 15528])).
% 2.02/2.14 tff(15535,plain,
% 2.02/2.14 ((op(e2, e1) = e0) <=> (op(e0, e3) = op(e3, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15534, 15489])).
% 2.02/2.14 tff(15536,plain,
% 2.02/2.14 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e1) = e0)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15535])).
% 2.02/2.14 tff(15537,plain,
% 2.02/2.14 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e1) = e0))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15536])).
% 2.02/2.14 tff(15538,plain,
% 2.02/2.14 (~(op(e2, e1) = e0)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[1077, 15537])).
% 2.02/2.14 tff(15539,plain,
% 2.02/2.14 (op(e2, e0) = e0),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[2311, 15538, 17, 15516])).
% 2.02/2.14 tff(15540,plain,
% 2.02/2.14 (op(e2, e0) = op(e3, e3)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15539, 15489])).
% 2.02/2.14 tff(15541,plain,
% 2.02/2.14 ((op(e2, e0) = e1) <=> (op(e3, e3) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15540])).
% 2.02/2.14 tff(15542,plain,
% 2.02/2.14 ((op(e3, e3) = e1) <=> (op(e2, e0) = e1)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15541])).
% 2.02/2.14 tff(15543,plain,
% 2.02/2.14 ((~(op(e3, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15542])).
% 2.02/2.14 tff(15544,plain,
% 2.02/2.14 (~(op(e2, e0) = e1)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15225, 15543])).
% 2.02/2.14 tff(15545,plain,
% 2.02/2.14 (op(e0, e0) = e1),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[1480, 15544, 15511, 15497])).
% 2.02/2.14 tff(15546,plain,
% 2.02/2.14 ((op(e0, e0) = e3) <=> (e1 = op(e1, e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15545, 15219])).
% 2.02/2.14 tff(15547,plain,
% 2.02/2.14 ((op(e0, e0) = e3) <=> (op(e1, e1) = e1)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15546, 8462])).
% 2.02/2.14 tff(15548,plain,
% 2.02/2.14 ((op(e1, e1) = e1) <=> (op(e0, e0) = e3)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15547])).
% 2.02/2.14 tff(15549,plain,
% 2.02/2.14 ((~(op(e1, e1) = e1)) <=> (~(op(e0, e0) = e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15548])).
% 2.02/2.14 tff(15550,plain,
% 2.02/2.14 (~(op(e0, e0) = e3)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15217, 15549])).
% 2.02/2.14 tff(15551,plain,
% 2.02/2.14 (op(e3, e0) = e3),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[2713, 15550, 15494, 15350])).
% 2.02/2.14 tff(15552,plain,
% 2.02/2.14 (op(e3, op(e3, e3)) = e3),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15551, 15491])).
% 2.02/2.14 tff(15553,plain,
% 2.02/2.14 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15527])).
% 2.02/2.14 tff(15554,plain,
% 2.02/2.14 (op(e0, e2) = op(e0, op(e0, e3))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15553])).
% 2.02/2.14 tff(15555,plain,
% 2.02/2.14 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, op(e0, e3)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15539, 15554])).
% 2.02/2.14 tff(15556,plain,
% 2.02/2.14 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15555, 2239])).
% 2.02/2.14 tff(15557,plain,
% 2.02/2.14 ((op(e0, op(e0, e3)) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15556])).
% 2.02/2.14 tff(15558,plain,
% 2.02/2.14 (op(e0, e1) = e0),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[292, 15538, 15505, 84])).
% 2.02/2.14 tff(15559,plain,
% 2.02/2.14 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, op(e0, e3)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15558, 15554])).
% 2.02/2.14 tff(15560,plain,
% 2.02/2.14 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15559, 2239])).
% 2.02/2.14 tff(15561,plain,
% 2.02/2.14 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = op(e2, e0))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15560, 15557, 6337])).
% 2.02/2.14 tff(15562,plain,
% 2.02/2.14 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15561])).
% 2.02/2.14 tff(15563,plain,
% 2.02/2.14 (~(op(e0, e2) = op(e2, e0))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[2102, 15562])).
% 2.02/2.14 tff(15564,plain,
% 2.02/2.14 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[6347, 15563])).
% 2.02/2.14 tff(15565,plain,
% 2.02/2.14 ((op(e0, e1) = op(e0, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15560, 15557])).
% 2.02/2.14 tff(15566,plain,
% 2.02/2.14 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15565])).
% 2.02/2.14 tff(15567,plain,
% 2.02/2.14 (~(op(e2, e0) = op(e0, e2))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[2102, 15566])).
% 2.02/2.14 tff(15568,plain,
% 2.02/2.14 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[6358, 15567])).
% 2.02/2.14 tff(15569,plain,
% 2.02/2.14 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15558])).
% 2.02/2.14 tff(15570,plain,
% 2.02/2.14 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15569])).
% 2.02/2.14 tff(15571,plain,
% 2.02/2.14 ((~(op(e1, e0) = e0)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15570])).
% 2.02/2.14 tff(15572,plain,
% 2.02/2.14 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15539])).
% 2.02/2.14 tff(15573,plain,
% 2.02/2.14 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15572])).
% 2.02/2.14 tff(15574,plain,
% 2.02/2.14 (~(op(e1, e0) = e0)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[756, 15573])).
% 2.02/2.14 tff(15575,plain,
% 2.02/2.14 (~(op(e1, e0) = op(e0, e1))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15574, 15571])).
% 2.02/2.14 tff(15576,plain,
% 2.02/2.14 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[613, 15575])).
% 2.02/2.14 tff(15577,plain,
% 2.02/2.14 ((op(e1, e0) = e0) <=> (op(e0, e1) = op(e1, e0))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15570, 596])).
% 2.02/2.14 tff(15578,plain,
% 2.02/2.14 ((~(op(e1, e0) = e0)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15577])).
% 2.02/2.14 tff(15579,plain,
% 2.02/2.14 (~(op(e0, e1) = op(e1, e0))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15574, 15578])).
% 2.02/2.14 tff(15580,plain,
% 2.02/2.14 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[609, 15579])).
% 2.02/2.14 tff(15581,plain,
% 2.02/2.14 (op(e1, op(e2, e3)) = op(e1, op(e1, e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15512])).
% 2.02/2.14 tff(15582,plain,
% 2.02/2.14 (op(e1, op(e2, e3)) = e1),
% 2.02/2.14 inference(transitivity,[status(thm)],[15581, 15416, 15214])).
% 2.02/2.14 tff(15583,plain,
% 2.02/2.14 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[10724, 15582])).
% 2.02/2.14 tff(15584,plain,
% 2.02/2.14 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15483])).
% 2.02/2.14 tff(15585,plain,
% 2.02/2.14 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15584])).
% 2.02/2.14 tff(15586,plain,
% 2.02/2.14 (~(op(e2, e2) = e3)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[515, 15585])).
% 2.02/2.14 tff(15587,plain,
% 2.02/2.14 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15533])).
% 2.02/2.14 tff(15588,plain,
% 2.02/2.14 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15587, 81])).
% 2.02/2.14 tff(15589,plain,
% 2.02/2.14 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15588])).
% 2.02/2.14 tff(15590,plain,
% 2.02/2.14 (~(op(e2, e2) = e2)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[508, 15589])).
% 2.02/2.14 tff(15591,plain,
% 2.02/2.14 (op(e2, e2) = e1),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[524, 15590, 17, 15586])).
% 2.02/2.14 tff(15592,plain,
% 2.02/2.14 (op(e0, op(e2, e2)) = op(e0, e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15591])).
% 2.02/2.14 tff(15593,plain,
% 2.02/2.14 (op(e0, op(e2, e2)) = e0),
% 2.02/2.14 inference(transitivity,[status(thm)],[15592, 15558])).
% 2.02/2.14 tff(15594,plain,
% 2.02/2.14 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[5619, 15593])).
% 2.02/2.14 tff(15595,plain,
% 2.02/2.14 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15533])).
% 2.02/2.14 tff(15596,plain,
% 2.02/2.14 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15595, 5762])).
% 2.02/2.14 tff(15597,plain,
% 2.02/2.14 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.02/2.14 inference(symmetry,[status(thm)],[15596])).
% 2.02/2.14 tff(15598,plain,
% 2.02/2.14 (op(e1, e2) = e0),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[1830, 15574, 80, 84])).
% 2.02/2.14 tff(15599,plain,
% 2.02/2.14 (op(e1, e2) = op(e3, e3)),
% 2.02/2.14 inference(transitivity,[status(thm)],[15598, 15489])).
% 2.02/2.14 tff(15600,plain,
% 2.02/2.14 ((op(e1, e2) = e2) <=> (op(e3, e3) = op(e0, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15599, 15528])).
% 2.02/2.14 tff(15601,plain,
% 2.02/2.14 ((op(e1, e2) = e2) <=> (op(e0, e3) = op(e3, e3))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15600, 659])).
% 2.02/2.14 tff(15602,plain,
% 2.02/2.14 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e2) = e2)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15601])).
% 2.02/2.14 tff(15603,plain,
% 2.02/2.14 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15602, 15597, 531])).
% 2.02/2.14 tff(15604,plain,
% 2.02/2.14 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15603])).
% 2.02/2.14 tff(15605,plain,
% 2.02/2.14 (~(op(e1, e2) = op(e2, e1))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[1077, 15604])).
% 2.02/2.14 tff(15606,plain,
% 2.02/2.14 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[539, 15605])).
% 2.02/2.14 tff(15607,plain,
% 2.02/2.14 (op(e2, op(e1, e3)) = e2),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[15533, 15452])).
% 2.02/2.14 tff(15608,plain,
% 2.02/2.14 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[9084, 15607])).
% 2.02/2.14 tff(15609,plain,
% 2.02/2.14 ((op(e0, e3) = op(e3, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15602, 15597])).
% 2.02/2.14 tff(15610,plain,
% 2.02/2.14 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15609])).
% 2.02/2.14 tff(15611,plain,
% 2.02/2.14 (~(op(e2, e1) = op(e1, e2))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[1077, 15610])).
% 2.02/2.14 tff(15612,plain,
% 2.02/2.14 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[557, 15611])).
% 2.02/2.14 tff(15613,plain,
% 2.02/2.14 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15490])).
% 2.02/2.14 tff(15614,plain,
% 2.02/2.14 ((e2 = op(e3, op(e3, e3))) <=> (op(e0, e3) = op(e3, e0))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15528, 15613])).
% 2.02/2.14 tff(15615,plain,
% 2.02/2.14 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = op(e0, e3))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15614, 452])).
% 2.02/2.14 tff(15616,plain,
% 2.02/2.14 (op(e1, e0) = e2),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[728, 15574, 15350, 15497])).
% 2.02/2.14 tff(15617,plain,
% 2.02/2.14 ((op(e1, e0) = op(e3, e0)) <=> (e2 = op(e3, op(e3, e3)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15616, 15490])).
% 2.02/2.14 tff(15618,plain,
% 2.02/2.14 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.02/2.14 inference(transitivity,[status(thm)],[15617, 15615, 453])).
% 2.02/2.14 tff(15619,plain,
% 2.02/2.14 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15618])).
% 2.02/2.14 tff(15620,plain,
% 2.02/2.14 (~(op(e0, e3) = op(e3, e0))),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[410, 15619])).
% 2.02/2.14 tff(15621,plain,
% 2.02/2.14 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.02/2.14 inference(unit_resolution,[status(thm)],[496, 15620])).
% 2.02/2.14 tff(15622,plain,
% 2.02/2.14 (e3 = op(e2, e3)),
% 2.02/2.14 inference(symmetry,[status(thm)],[15483])).
% 2.02/2.14 tff(15623,plain,
% 2.02/2.14 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15622])).
% 2.02/2.14 tff(15624,plain,
% 2.02/2.14 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15591])).
% 2.02/2.14 tff(15625,plain,
% 2.02/2.14 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15624])).
% 2.02/2.14 tff(15626,plain,
% 2.02/2.14 (~(op(e0, e2) = e1)),
% 2.02/2.14 inference(modus_ponens,[status(thm)],[2736, 15625])).
% 2.02/2.14 tff(15627,plain,
% 2.02/2.14 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 2.02/2.14 inference(monotonicity,[status(thm)],[15528])).
% 2.02/2.14 tff(15628,plain,
% 2.02/2.14 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15627])).
% 2.02/2.15 tff(15629,plain,
% 2.02/2.15 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15628])).
% 2.02/2.15 tff(15630,plain,
% 2.02/2.15 (~(op(e0, e2) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[918, 15629])).
% 2.02/2.15 tff(15631,plain,
% 2.02/2.15 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15554])).
% 2.02/2.15 tff(15632,plain,
% 2.02/2.15 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15631])).
% 2.02/2.15 tff(15633,plain,
% 2.02/2.15 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15560, 15632])).
% 2.02/2.15 tff(15634,plain,
% 2.02/2.15 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15633])).
% 2.02/2.15 tff(15635,plain,
% 2.02/2.15 (~(op(e0, e2) = e0)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[2102, 15634])).
% 2.02/2.15 tff(15636,plain,
% 2.02/2.15 (op(e0, e2) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[2745, 15635, 15630, 15626])).
% 2.02/2.15 tff(15637,plain,
% 2.02/2.15 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15636])).
% 2.02/2.15 tff(15638,plain,
% 2.02/2.15 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15637, 3423])).
% 2.02/2.15 tff(15639,plain,
% 2.02/2.15 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.02/2.15 inference(transitivity,[status(thm)],[15638, 15623, 395])).
% 2.02/2.15 tff(15640,plain,
% 2.02/2.15 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15639])).
% 2.02/2.15 tff(15641,plain,
% 2.02/2.15 (~(op(e2, e3) = op(e3, e2))),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[1467, 15640])).
% 2.02/2.15 tff(15642,plain,
% 2.02/2.15 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[430, 15641])).
% 2.02/2.15 tff(15643,plain,
% 2.02/2.15 (op(e2, op(e3, e1)) = op(e2, e1)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15506])).
% 2.02/2.15 tff(15644,plain,
% 2.02/2.15 (op(e2, op(e3, e1)) = e2),
% 2.02/2.15 inference(transitivity,[status(thm)],[15643, 15533])).
% 2.02/2.15 tff(15645,plain,
% 2.02/2.15 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[14271, 15644])).
% 2.02/2.15 tff(15646,plain,
% 2.02/2.15 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15545])).
% 2.02/2.15 tff(15647,plain,
% 2.02/2.15 (op(e0, op(e0, e0)) = e0),
% 2.02/2.15 inference(transitivity,[status(thm)],[15646, 15558])).
% 2.02/2.15 tff(15648,plain,
% 2.02/2.15 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[5598, 15647])).
% 2.02/2.15 tff(15649,plain,
% 2.02/2.15 (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[5367, 15648, 15645, 15642, 15621, 15460, 15612, 15608, 15606, 15594, 15583, 15580, 15576, 15568, 15564])).
% 2.02/2.15 tff(15650,plain,
% 2.02/2.15 (~(op(e3, op(e3, e3)) = e3)),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[6277, 15649])).
% 2.02/2.15 tff(15651,plain,
% 2.02/2.15 ($false),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15650, 15552])).
% 2.02/2.15 tff(15652,plain,((op(e3, e1) = e2) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e1) | (op(e3, e2) = e0) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.15 tff(15653,plain,
% 2.02/2.15 (op(e3, e1) = e2),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15652, 85, 84, 17, 68, 72, 76, 80, 75])).
% 2.02/2.15 tff(15654,plain,
% 2.02/2.15 (op(op(e3, e1), e3) = op(e2, op(e1, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15653, 15219])).
% 2.02/2.15 tff(15655,plain,
% 2.02/2.15 (op(op(e3, e1), e3) = op(e2, e3)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15654, 15221])).
% 2.02/2.15 tff(15656,plain,
% 2.02/2.15 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15655])).
% 2.02/2.15 tff(15657,plain,
% 2.02/2.15 ((op(e2, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15656])).
% 2.02/2.15 tff(15658,plain,
% 2.02/2.15 ((~(op(e2, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15657])).
% 2.02/2.15 tff(15659,plain,
% 2.02/2.15 (~(op(op(e3, e1), e3) = e1)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[76, 15658])).
% 2.02/2.15 tff(15660,plain,
% 2.02/2.15 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[1050, 15659])).
% 2.02/2.15 tff(15661,plain,
% 2.02/2.15 (e2 = op(e3, e1)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15653])).
% 2.02/2.15 tff(15662,plain,
% 2.02/2.15 ((e0 = e2) <=> (e0 = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15661])).
% 2.02/2.15 tff(15663,plain,
% 2.02/2.15 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15662, 5470])).
% 2.02/2.15 tff(15664,plain,
% 2.02/2.15 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15663])).
% 2.02/2.15 tff(15665,plain,
% 2.02/2.15 (~(op(e3, e1) = e0)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[14, 15664])).
% 2.02/2.15 tff(15666,plain,
% 2.02/2.15 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[4971])).
% 2.02/2.15 tff(15667,plain,
% 2.02/2.15 ((op(e2, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 2.02/2.15 inference(transitivity,[status(thm)],[15666, 8414])).
% 2.02/2.15 tff(15668,plain,
% 2.02/2.15 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15667])).
% 2.02/2.15 tff(15669,plain,
% 2.02/2.15 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15668])).
% 2.02/2.15 tff(15670,plain,
% 2.02/2.15 (~(op(e2, e1) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[225, 15669])).
% 2.02/2.15 tff(15671,plain,
% 2.02/2.15 (op(e3, e3) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15018, 656, 926])).
% 2.02/2.15 tff(15672,plain,
% 2.02/2.15 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15671])).
% 2.02/2.15 tff(15673,plain,
% 2.02/2.15 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15672])).
% 2.02/2.15 tff(15674,plain,
% 2.02/2.15 (~(op(e2, e3) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[368, 15673])).
% 2.02/2.15 tff(15675,plain,
% 2.02/2.15 (op(e0, e3) = e0),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[1098, 656, 80, 1063])).
% 2.02/2.15 tff(15676,plain,
% 2.02/2.15 ((op(e0, e3) = e2) <=> (e0 = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15675, 8644])).
% 2.02/2.15 tff(15677,plain,
% 2.02/2.15 ((op(e0, e3) = e2) <=> (op(e3, e1) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15676, 5470])).
% 2.02/2.15 tff(15678,plain,
% 2.02/2.15 ((op(e3, e1) = e0) <=> (op(e0, e3) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15677])).
% 2.02/2.15 tff(15679,plain,
% 2.02/2.15 ((~(op(e3, e1) = e0)) <=> (~(op(e0, e3) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15678])).
% 2.02/2.15 tff(15680,plain,
% 2.02/2.15 ((e0 = e2) <=> (e0 = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[8644])).
% 2.02/2.15 tff(15681,plain,
% 2.02/2.15 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15680, 5470])).
% 2.02/2.15 tff(15682,plain,
% 2.02/2.15 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15681])).
% 2.02/2.15 tff(15683,plain,
% 2.02/2.15 (~(op(e3, e1) = e0)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[14, 15682])).
% 2.02/2.15 tff(15684,plain,
% 2.02/2.15 (~(op(e0, e3) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[15683, 15679])).
% 2.02/2.15 tff(15685,plain,
% 2.02/2.15 ($false),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15235, 15684, 15674, 72, 75, 80, 1304, 1080, 121])).
% 2.02/2.15 tff(15686,plain,((op(e3, e3) = e0) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e3) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e1, e3) = e3) | (op(e0, e3) = e1) | (~(op(e3, e1) = e2)) | (op(e2, e3) = e0) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.15 tff(15687,plain,
% 2.02/2.15 (op(e3, e3) = e0),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15686, 1063, 75, 80, 1304, 1080, 121, 6684, 72, 926])).
% 2.02/2.15 tff(15688,plain,
% 2.02/2.15 (e0 = op(e3, e3)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15687])).
% 2.02/2.15 tff(15689,plain,
% 2.02/2.15 (op(e2, e0) = op(e2, op(e3, e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15688])).
% 2.02/2.15 tff(15690,plain,
% 2.02/2.15 ((op(e2, e0) = e2) <=> (op(e2, op(e3, e3)) = e2)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15689])).
% 2.02/2.15 tff(15691,plain,
% 2.02/2.15 ((op(e2, op(e3, e3)) = e2) <=> (op(e2, e0) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15690])).
% 2.02/2.15 tff(15692,plain,
% 2.02/2.15 ((e1 = e2) <=> (e1 = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[8644])).
% 2.02/2.15 tff(15693,plain,
% 2.02/2.15 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15692, 7793])).
% 2.02/2.15 tff(15694,plain,
% 2.02/2.15 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15693])).
% 2.02/2.15 tff(15695,plain,
% 2.02/2.15 (~(op(e3, e1) = e1)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[708, 15694])).
% 2.02/2.15 tff(15696,plain,
% 2.02/2.15 (~(op(e3, e0) = e1)),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[8647, 15687, 6684])).
% 2.02/2.15 tff(15697,plain,
% 2.02/2.15 (op(e3, e2) = e1),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[939, 15696, 926, 15695])).
% 2.02/2.15 tff(15698,plain,
% 2.02/2.15 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15697])).
% 2.02/2.15 tff(15699,plain,
% 2.02/2.15 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15698])).
% 2.02/2.15 tff(15700,plain,
% 2.02/2.15 (~(op(e2, e2) = e1)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[1546, 15699])).
% 2.02/2.15 tff(15701,plain,
% 2.02/2.15 ((op(e3, e3) = e3) <=> (e0 = op(e1, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15687, 4971])).
% 2.02/2.15 tff(15702,plain,
% 2.02/2.15 ((op(e3, e3) = e3) <=> (op(e1, e1) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15701, 122])).
% 2.02/2.15 tff(15703,plain,
% 2.02/2.15 ((op(e1, e1) = e0) <=> (op(e3, e3) = e3)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15702])).
% 2.02/2.15 tff(15704,plain,
% 2.02/2.15 ((~(op(e1, e1) = e0)) <=> (~(op(e3, e3) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15703])).
% 2.02/2.15 tff(15705,plain,
% 2.02/2.15 (~(op(e3, e3) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[84, 15704])).
% 2.02/2.15 tff(15706,plain,
% 2.02/2.15 (op(e0, e3) = e2),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15235, 124, 72, 75, 80, 1304, 1080, 121])).
% 2.02/2.15 tff(15707,plain,
% 2.02/2.15 (op(e0, e3) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[480, 124, 1080, 468])).
% 2.02/2.15 tff(15708,plain,
% 2.02/2.15 (e3 = op(e0, e3)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15707])).
% 2.02/2.15 tff(15709,plain,
% 2.02/2.15 (op(e1, e1) = op(e3, e1)),
% 2.02/2.15 inference(transitivity,[status(thm)],[4960, 15708, 15706, 8644])).
% 2.02/2.15 tff(15710,plain,
% 2.02/2.15 ($false),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[945, 15709])).
% 2.02/2.15 tff(15711,plain,((op(e2, e3) = e3) | (~(op(e1, e1) = e3)) | (~(op(e3, e1) = e2)) | (op(e1, e3) = e3) | (op(e3, e3) = e3) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e3) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.15 tff(15712,plain,
% 2.02/2.15 (op(e2, e3) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15711, 15705, 6684, 1080, 4960, 72, 75, 80, 1304, 121])).
% 2.02/2.15 tff(15713,plain,
% 2.02/2.15 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15712])).
% 2.02/2.15 tff(15714,plain,
% 2.02/2.15 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15713])).
% 2.02/2.15 tff(15715,plain,
% 2.02/2.15 (~(op(e2, e2) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[515, 15714])).
% 2.02/2.15 tff(15716,plain,
% 2.02/2.15 (op(e2, e2) = e2),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[524, 15715, 17, 15700])).
% 2.02/2.15 tff(15717,plain,
% 2.02/2.15 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, op(e3, e3)) = e2)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15689, 15716])).
% 2.02/2.15 tff(15718,plain,
% 2.02/2.15 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e2)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15717, 15691])).
% 2.02/2.15 tff(15719,plain,
% 2.02/2.15 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15718])).
% 2.02/2.15 tff(15720,plain,
% 2.02/2.15 (~(op(e2, e0) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[2228, 15719])).
% 2.02/2.15 tff(15721,plain,
% 2.02/2.15 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[8644])).
% 2.02/2.15 tff(15722,plain,
% 2.02/2.15 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15721])).
% 2.02/2.15 tff(15723,plain,
% 2.02/2.15 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15722])).
% 2.02/2.15 tff(15724,plain,
% 2.02/2.15 (~(op(e3, e0) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[580, 15723])).
% 2.02/2.15 tff(15725,plain,
% 2.02/2.15 (op(e2, op(e1, e1)) = op(e2, e3)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[4960])).
% 2.02/2.15 tff(15726,plain,
% 2.02/2.15 (op(e2, e3) = op(e2, op(e1, e1))),
% 2.02/2.15 inference(symmetry,[status(thm)],[15725])).
% 2.02/2.15 tff(15727,plain,
% 2.02/2.15 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15726])).
% 2.02/2.15 tff(15728,plain,
% 2.02/2.15 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, e3) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15727])).
% 2.02/2.15 tff(15729,plain,
% 2.02/2.15 (op(e2, op(e1, e1)) = op(e1, e1)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15725, 15712, 4971])).
% 2.02/2.15 tff(15730,plain,
% 2.02/2.15 ((op(e2, op(e1, e1)) = e2) <=> (op(e1, e1) = op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15729, 8644])).
% 2.02/2.15 tff(15731,plain,
% 2.02/2.15 ((op(e1, e1) = op(e3, e1)) <=> (op(e2, op(e1, e1)) = e2)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15730])).
% 2.02/2.15 tff(15732,plain,
% 2.02/2.15 ((op(e1, e1) = op(e3, e1)) <=> (op(e2, e3) = e2)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15731, 15728])).
% 2.02/2.15 tff(15733,plain,
% 2.02/2.15 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e2, e3) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15732])).
% 2.02/2.15 tff(15734,plain,
% 2.02/2.15 (~(op(e2, e3) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[945, 15733])).
% 2.02/2.15 tff(15735,plain,
% 2.02/2.15 (op(e0, e3) = e2),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[15003, 15734, 72])).
% 2.02/2.15 tff(15736,plain,
% 2.02/2.15 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15735])).
% 2.02/2.15 tff(15737,plain,
% 2.02/2.15 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15736])).
% 2.02/2.15 tff(15738,plain,
% 2.02/2.15 (~(op(e0, e0) = e2)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[3414, 15737])).
% 2.02/2.15 tff(15739,plain,
% 2.02/2.15 (op(e1, e0) = e2),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[589, 15738, 15724, 15720])).
% 2.02/2.15 tff(15740,plain,
% 2.02/2.15 (op(e1, op(e3, e3)) = op(e1, e0)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15687])).
% 2.02/2.15 tff(15741,plain,
% 2.02/2.15 (op(e0, op(e3, e1)) = op(e0, e2)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[6684])).
% 2.02/2.15 tff(15742,plain,
% 2.02/2.15 (op(e0, e2) = op(e0, op(e3, e1))),
% 2.02/2.15 inference(symmetry,[status(thm)],[15741])).
% 2.02/2.15 tff(15743,plain,
% 2.02/2.15 ((op(e0, e2) = e0) <=> (op(e0, op(e3, e1)) = e0)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15742])).
% 2.02/2.15 tff(15744,plain,
% 2.02/2.15 ((op(e0, op(e3, e1)) = e0) <=> (op(e0, e2) = e0)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15743])).
% 2.02/2.15 tff(15745,plain,
% 2.02/2.15 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15688])).
% 2.02/2.15 tff(15746,plain,
% 2.02/2.15 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15745])).
% 2.02/2.15 tff(15747,plain,
% 2.02/2.15 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15746])).
% 2.02/2.15 tff(15748,plain,
% 2.02/2.15 (~(op(e3, e0) = e0)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[157, 15747])).
% 2.02/2.15 tff(15749,plain,
% 2.02/2.15 (op(e3, e0) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[5422, 15748, 15724, 15696])).
% 2.02/2.15 tff(15750,plain,
% 2.02/2.15 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15749])).
% 2.02/2.15 tff(15751,plain,
% 2.02/2.15 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15750])).
% 2.02/2.15 tff(15752,plain,
% 2.02/2.15 (~(op(e0, e0) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[6384, 15751])).
% 2.02/2.15 tff(15753,plain,
% 2.02/2.15 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[4971])).
% 2.02/2.15 tff(15754,plain,
% 2.02/2.15 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15753])).
% 2.02/2.15 tff(15755,plain,
% 2.02/2.15 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15754])).
% 2.02/2.15 tff(15756,plain,
% 2.02/2.15 (~(op(e0, e1) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[792, 15755])).
% 2.02/2.15 tff(15757,plain,
% 2.02/2.15 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15712])).
% 2.02/2.15 tff(15758,plain,
% 2.02/2.15 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15757])).
% 2.02/2.15 tff(15759,plain,
% 2.02/2.15 (~(op(e0, e3) = e3)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[964, 15758])).
% 2.02/2.15 tff(15760,plain,
% 2.02/2.15 (op(e0, e2) = e3),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[1495, 15759, 15756, 15752])).
% 2.02/2.15 tff(15761,plain,
% 2.02/2.15 (op(e0, op(e3, e1)) = e3),
% 2.02/2.15 inference(transitivity,[status(thm)],[15741, 15760])).
% 2.02/2.15 tff(15762,plain,
% 2.02/2.15 ((op(e0, op(e3, e1)) = e0) <=> (e3 = op(e3, e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15761, 15688])).
% 2.02/2.15 tff(15763,plain,
% 2.02/2.15 ((op(e0, op(e3, e1)) = e0) <=> (op(e3, e3) = e3)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15762, 666])).
% 2.02/2.15 tff(15764,plain,
% 2.02/2.15 ((op(e3, e3) = e3) <=> (op(e0, op(e3, e1)) = e0)),
% 2.02/2.15 inference(symmetry,[status(thm)],[15763])).
% 2.02/2.15 tff(15765,plain,
% 2.02/2.15 ((op(e3, e3) = e3) <=> (op(e0, e2) = e0)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15764, 15744])).
% 2.02/2.15 tff(15766,plain,
% 2.02/2.15 ((~(op(e3, e3) = e3)) <=> (~(op(e0, e2) = e0))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15765])).
% 2.02/2.15 tff(15767,plain,
% 2.02/2.15 (~(op(e0, e2) = e0)),
% 2.02/2.15 inference(modus_ponens,[status(thm)],[15705, 15766])).
% 2.02/2.15 tff(15768,plain,
% 2.02/2.15 (op(e1, e2) = e0),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[973, 15767, 17, 85])).
% 2.02/2.15 tff(15769,plain,
% 2.02/2.15 (op(e1, e2) = op(e3, e3)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15768, 15688])).
% 2.02/2.15 tff(15770,plain,
% 2.02/2.15 (op(e1, op(e1, e2)) = op(e1, op(e3, e3))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15769])).
% 2.02/2.15 tff(15771,plain,
% 2.02/2.15 (op(e1, op(e1, e2)) = e2),
% 2.02/2.15 inference(transitivity,[status(thm)],[15770, 15740, 15739])).
% 2.02/2.15 tff(15772,plain,
% 2.02/2.15 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[2377, 15771])).
% 2.02/2.15 tff(15773,plain,
% 2.02/2.15 (op(e0, e3) = op(e3, e1)),
% 2.02/2.15 inference(transitivity,[status(thm)],[15735, 8644])).
% 2.02/2.15 tff(15774,plain,
% 2.02/2.15 (op(e0, op(e0, e3)) = op(e0, op(e3, e1))),
% 2.02/2.15 inference(monotonicity,[status(thm)],[15773])).
% 2.02/2.15 tff(15775,plain,
% 2.02/2.15 (op(e0, op(e0, e3)) = e3),
% 2.02/2.15 inference(transitivity,[status(thm)],[15774, 15741, 15760])).
% 2.02/2.15 tff(15776,plain,
% 2.02/2.15 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.02/2.15 inference(unit_resolution,[status(thm)],[1938, 15775])).
% 2.02/2.16 tff(15777,plain,
% 2.02/2.16 (op(e1, op(e3, e1)) = op(e1, e2)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[6684])).
% 2.02/2.16 tff(15778,plain,
% 2.02/2.16 (op(e1, e0) = op(e3, e1)),
% 2.02/2.16 inference(transitivity,[status(thm)],[15739, 8644])).
% 2.02/2.16 tff(15779,plain,
% 2.02/2.16 (op(e1, op(e1, e0)) = op(e1, op(e3, e1))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15778])).
% 2.02/2.16 tff(15780,plain,
% 2.02/2.16 (op(e1, op(e1, e0)) = e0),
% 2.02/2.16 inference(transitivity,[status(thm)],[15779, 15777, 15768])).
% 2.02/2.16 tff(15781,plain,
% 2.02/2.16 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[1836, 15780])).
% 2.02/2.16 tff(15782,plain,
% 2.02/2.16 (op(e0, op(e1, e1)) = op(e0, e3)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[4960])).
% 2.02/2.16 tff(15783,plain,
% 2.02/2.16 (op(e0, e2) = op(e1, e1)),
% 2.02/2.16 inference(transitivity,[status(thm)],[15760, 4971])).
% 2.02/2.16 tff(15784,plain,
% 2.02/2.16 (op(e0, op(e0, e2)) = op(e0, op(e1, e1))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15783])).
% 2.02/2.16 tff(15785,plain,
% 2.02/2.16 (op(e0, op(e0, e2)) = e2),
% 2.02/2.16 inference(transitivity,[status(thm)],[15784, 15782, 15735])).
% 2.02/2.16 tff(15786,plain,
% 2.02/2.16 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[1331, 15785])).
% 2.02/2.16 tff(15787,plain,
% 2.02/2.16 (op(op(e3, e1), e3) = op(e2, op(e1, e1))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[6684, 4971])).
% 2.02/2.16 tff(15788,plain,
% 2.02/2.16 (op(e2, op(e2, e3)) = op(op(e3, e1), e3)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[8644, 15712])).
% 2.02/2.16 tff(15789,plain,
% 2.02/2.16 (op(e2, op(e2, e3)) = e3),
% 2.02/2.16 inference(transitivity,[status(thm)],[15788, 15787, 15725, 15712])).
% 2.02/2.16 tff(15790,plain,
% 2.02/2.16 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[2344, 15789])).
% 2.02/2.16 tff(15791,plain,
% 2.02/2.16 (op(e3, op(e3, e2)) = op(e3, e1)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15697])).
% 2.02/2.16 tff(15792,plain,
% 2.02/2.16 (op(e3, op(e3, e2)) = e2),
% 2.02/2.16 inference(transitivity,[status(thm)],[15791, 6684])).
% 2.02/2.16 tff(15793,plain,
% 2.02/2.16 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[1904, 15792])).
% 2.02/2.16 tff(15794,plain,
% 2.02/2.16 (op(e2, e0) = op(e3, e3)),
% 2.02/2.16 inference(transitivity,[status(thm)],[12956, 4451])).
% 2.02/2.16 tff(15795,plain,
% 2.02/2.16 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15794])).
% 2.02/2.16 tff(15796,plain,
% 2.02/2.16 (op(e2, op(e2, e0)) = e0),
% 2.02/2.16 inference(transitivity,[status(thm)],[15795, 4551, 12956])).
% 2.02/2.16 tff(15797,plain,
% 2.02/2.16 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[2653, 15796])).
% 2.02/2.16 tff(15798,plain,
% 2.02/2.16 (~(op(e3, e0) = e1)),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[8647, 3066, 6684])).
% 2.02/2.16 tff(15799,plain,
% 2.02/2.16 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[4451])).
% 2.02/2.16 tff(15800,plain,
% 2.02/2.16 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.02/2.16 inference(symmetry,[status(thm)],[15799])).
% 2.02/2.16 tff(15801,plain,
% 2.02/2.16 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15800])).
% 2.02/2.16 tff(15802,plain,
% 2.02/2.16 (~(op(e3, e0) = e0)),
% 2.02/2.16 inference(modus_ponens,[status(thm)],[157, 15801])).
% 2.02/2.16 tff(15803,plain,
% 2.02/2.16 (op(e3, e0) = e3),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[5422, 15802, 15724, 15798])).
% 2.02/2.16 tff(15804,plain,
% 2.02/2.16 (op(op(e3, e0), e0) = op(e3, op(e3, e3))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15803, 4451])).
% 2.02/2.16 tff(15805,plain,
% 2.02/2.16 (op(op(e3, e0), e0) = e3),
% 2.02/2.16 inference(transitivity,[status(thm)],[15804, 3067, 15803])).
% 2.02/2.16 tff(15806,plain,
% 2.02/2.16 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[4026, 15805])).
% 2.02/2.16 tff(15807,plain,
% 2.02/2.16 (op(e0, e1) = e0),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[292, 2559, 15683, 84])).
% 2.02/2.16 tff(15808,plain,
% 2.02/2.16 (op(op(e0, e1), e1) = op(e0, e1)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15807])).
% 2.02/2.16 tff(15809,plain,
% 2.02/2.16 (op(op(e0, e1), e1) = e0),
% 2.02/2.16 inference(transitivity,[status(thm)],[15808, 15807])).
% 2.02/2.16 tff(15810,plain,
% 2.02/2.16 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[2650, 15809])).
% 2.02/2.16 tff(15811,plain,
% 2.02/2.16 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e3, e1))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[8644])).
% 2.02/2.16 tff(15812,plain,
% 2.02/2.16 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.02/2.16 inference(symmetry,[status(thm)],[15811])).
% 2.02/2.16 tff(15813,plain,
% 2.02/2.16 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.02/2.16 inference(monotonicity,[status(thm)],[15812])).
% 2.02/2.16 tff(15814,plain,
% 2.02/2.16 (~(op(e2, e1) = e2)),
% 2.02/2.16 inference(modus_ponens,[status(thm)],[402, 15813])).
% 2.02/2.16 tff(15815,plain,
% 2.02/2.16 (op(e2, e1) = e1),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[2367, 2559, 3271, 15814])).
% 2.02/2.16 tff(15816,plain,
% 2.02/2.16 (op(op(e3, e1), e1) = op(e2, e1)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[6684])).
% 2.02/2.16 tff(15817,plain,
% 2.02/2.16 (op(e2, op(e2, e1)) = op(op(e3, e1), e1)),
% 2.02/2.16 inference(monotonicity,[status(thm)],[8644, 15815])).
% 2.02/2.16 tff(15818,plain,
% 2.02/2.16 (op(e2, op(e2, e1)) = e1),
% 2.02/2.16 inference(transitivity,[status(thm)],[15817, 15816, 15815])).
% 2.02/2.16 tff(15819,plain,
% 2.02/2.16 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[1355, 15818])).
% 2.02/2.16 tff(15820,plain,
% 2.02/2.16 ($false),
% 2.02/2.16 inference(unit_resolution,[status(thm)],[1459, 15819, 15810, 3341, 15806, 1347, 1304, 1363, 1357, 3342, 15797, 1358, 1275])).
% 2.02/2.16 tff(15821,plain,((op(e2, e1) = e0) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~(op(e3, e1) = e2)) | (~(op(e3, e3) = e0)) | (op(e2, e1) = e3) | (op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.16 tff(15822,plain,
% 2.06/2.16 (op(e2, e1) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[15821, 15793, 15790, 1304, 15786, 15781, 15776, 15772, 1275, 6684, 15687, 15670, 84, 17, 1063])).
% 2.06/2.16 tff(15823,plain,
% 2.06/2.16 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e0)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15822])).
% 2.06/2.16 tff(15824,plain,
% 2.06/2.16 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e2, e1))),
% 2.06/2.16 inference(symmetry,[status(thm)],[15823])).
% 2.06/2.16 tff(15825,plain,
% 2.06/2.16 ((op(e3, e0) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15749])).
% 2.06/2.16 tff(15826,plain,
% 2.06/2.16 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15825, 1364])).
% 2.06/2.16 tff(15827,plain,
% 2.06/2.16 ((op(e0, e3) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.16 inference(symmetry,[status(thm)],[15826])).
% 2.06/2.16 tff(15828,plain,
% 2.06/2.16 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.16 inference(transitivity,[status(thm)],[15757, 15827])).
% 2.06/2.16 tff(15829,plain,
% 2.06/2.16 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e0) = op(e0, e3)))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15828])).
% 2.06/2.16 tff(15830,plain,
% 2.06/2.16 (~(op(e3, e0) = op(e0, e3))),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[964, 15829])).
% 2.06/2.16 tff(15831,plain,
% 2.06/2.16 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[4971])).
% 2.06/2.16 tff(15832,plain,
% 2.06/2.16 ((op(e3, e1) = e3) <=> (op(e1, e1) = op(e3, e1))),
% 2.06/2.16 inference(transitivity,[status(thm)],[15831, 15302])).
% 2.06/2.16 tff(15833,plain,
% 2.06/2.16 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15832])).
% 2.06/2.16 tff(15834,plain,
% 2.06/2.16 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15833])).
% 2.06/2.16 tff(15835,plain,
% 2.06/2.16 (~(op(e3, e1) = e3)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[945, 15834])).
% 2.06/2.16 tff(15836,plain,
% 2.06/2.16 (op(e0, e1) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[6478, 15822, 80, 121, 72, 15835, 15683, 15756, 15830])).
% 2.06/2.16 tff(15837,plain,
% 2.06/2.16 (op(e0, e1) = op(e2, e1)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[15836, 15824])).
% 2.06/2.16 tff(15838,plain,
% 2.06/2.16 ($false),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[606, 15837])).
% 2.06/2.16 tff(15839,plain,((op(e2, e3) = e0) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e2) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~(op(e3, e1) = e2)) | (op(e1, e1) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0) | (~(op(e1, e1) = e3)) | (op(e1, e3) = e3) | (op(e1, e2) = e3) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.16 tff(15840,plain,
% 2.06/2.16 (op(e2, e3) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[15839, 15228, 80, 72, 15234, 15660, 15653, 84, 17, 85, 15218, 15232, 75, 15225])).
% 2.06/2.16 tff(15841,plain,
% 2.06/2.16 (e0 = op(e2, e3)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15840])).
% 2.06/2.16 tff(15842,plain,
% 2.06/2.16 ((op(e3, e3) = e0) <=> (op(e3, e3) = op(e2, e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15841])).
% 2.06/2.16 tff(15843,plain,
% 2.06/2.16 ((op(e3, e3) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 2.06/2.16 inference(transitivity,[status(thm)],[15842, 2820])).
% 2.06/2.16 tff(15844,plain,
% 2.06/2.16 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15843])).
% 2.06/2.16 tff(15845,plain,
% 2.06/2.16 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15844])).
% 2.06/2.16 tff(15846,plain,
% 2.06/2.16 (~(op(e3, e3) = e0)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[368, 15845])).
% 2.06/2.16 tff(15847,plain,
% 2.06/2.16 (op(e3, e0) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1916, 15846, 85, 15665])).
% 2.06/2.16 tff(15848,plain,
% 2.06/2.16 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e0)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15847])).
% 2.06/2.16 tff(15849,plain,
% 2.06/2.16 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e0))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15848])).
% 2.06/2.16 tff(15850,plain,
% 2.06/2.16 (~(op(e1, e0) = e0)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[410, 15849])).
% 2.06/2.16 tff(15851,plain,
% 2.06/2.16 (op(e1, e0) = e2),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[728, 15850, 15350, 15497])).
% 2.06/2.16 tff(15852,plain,
% 2.06/2.16 (op(e1, op(e2, e3)) = op(e1, e0)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15840])).
% 2.06/2.16 tff(15853,plain,
% 2.06/2.16 (op(e0, op(e3, e1)) = op(e0, e2)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15653])).
% 2.06/2.16 tff(15854,plain,
% 2.06/2.16 (op(e0, e2) = op(e0, op(e3, e1))),
% 2.06/2.16 inference(symmetry,[status(thm)],[15853])).
% 2.06/2.16 tff(15855,plain,
% 2.06/2.16 ((op(e0, e2) = e0) <=> (op(e0, op(e3, e1)) = e0)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15854])).
% 2.06/2.16 tff(15856,plain,
% 2.06/2.16 ((op(e0, op(e3, e1)) = e0) <=> (op(e0, e2) = e0)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15855])).
% 2.06/2.16 tff(15857,plain,
% 2.06/2.16 ((e0 = op(e0, op(e3, e1))) <=> (op(e0, op(e3, e1)) = e0)),
% 2.06/2.16 inference(commutativity,[status(thm)],[])).
% 2.06/2.16 tff(15858,plain,
% 2.06/2.16 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15841])).
% 2.06/2.16 tff(15859,plain,
% 2.06/2.16 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15858])).
% 2.06/2.16 tff(15860,plain,
% 2.06/2.16 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15859])).
% 2.06/2.16 tff(15861,plain,
% 2.06/2.16 (~(op(e2, e1) = e0)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[197, 15860])).
% 2.06/2.16 tff(15862,plain,
% 2.06/2.16 (op(e0, e1) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[292, 15861, 15665, 84])).
% 2.06/2.16 tff(15863,plain,
% 2.06/2.16 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, op(e3, e1)))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15862, 15854])).
% 2.06/2.16 tff(15864,plain,
% 2.06/2.16 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e3, e1)) = e0)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15863, 15857])).
% 2.06/2.16 tff(15865,plain,
% 2.06/2.16 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15864, 15856])).
% 2.06/2.16 tff(15866,plain,
% 2.06/2.16 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15865])).
% 2.06/2.16 tff(15867,plain,
% 2.06/2.16 (~(op(e0, e2) = e0)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[2102, 15866])).
% 2.06/2.16 tff(15868,plain,
% 2.06/2.16 (op(e1, e2) = e0),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[973, 15867, 17, 85])).
% 2.06/2.16 tff(15869,plain,
% 2.06/2.16 (op(e1, e2) = op(e2, e3)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15868, 15841])).
% 2.06/2.16 tff(15870,plain,
% 2.06/2.16 (op(e1, op(e1, e2)) = op(e1, op(e2, e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15869])).
% 2.06/2.16 tff(15871,plain,
% 2.06/2.16 (op(e1, op(e1, e2)) = e2),
% 2.06/2.16 inference(transitivity,[status(thm)],[15870, 15852, 15851])).
% 2.06/2.16 tff(15872,plain,
% 2.06/2.16 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[2377, 15871])).
% 2.06/2.16 tff(15873,plain,
% 2.06/2.16 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e3, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15661])).
% 2.06/2.16 tff(15874,plain,
% 2.06/2.16 ((op(e3, e2) = e2) <=> (op(e3, e1) = op(e3, e2))),
% 2.06/2.16 inference(transitivity,[status(thm)],[15873, 4845])).
% 2.06/2.16 tff(15875,plain,
% 2.06/2.16 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15874])).
% 2.06/2.16 tff(15876,plain,
% 2.06/2.16 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15875])).
% 2.06/2.16 tff(15877,plain,
% 2.06/2.16 (~(op(e3, e2) = e2)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[3429, 15876])).
% 2.06/2.16 tff(15878,plain,
% 2.06/2.16 (op(e3, op(e3, e1)) = op(e3, e2)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15653])).
% 2.06/2.16 tff(15879,plain,
% 2.06/2.16 (op(e3, e2) = op(e3, op(e3, e1))),
% 2.06/2.16 inference(symmetry,[status(thm)],[15878])).
% 2.06/2.16 tff(15880,plain,
% 2.06/2.16 ((op(e3, e2) = e3) <=> (op(e3, op(e3, e1)) = e3)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15879])).
% 2.06/2.16 tff(15881,plain,
% 2.06/2.16 ((op(e3, op(e3, e1)) = e3) <=> (op(e3, e2) = e3)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15880])).
% 2.06/2.16 tff(15882,plain,
% 2.06/2.16 ((op(e2, e3) = e3) <=> (e0 = op(e1, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15840, 15219])).
% 2.06/2.16 tff(15883,plain,
% 2.06/2.16 ((op(e2, e3) = e3) <=> (op(e1, e1) = e0)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15882, 122])).
% 2.06/2.16 tff(15884,plain,
% 2.06/2.16 ((op(e1, e1) = e0) <=> (op(e2, e3) = e3)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15883])).
% 2.06/2.16 tff(15885,plain,
% 2.06/2.16 ((~(op(e1, e1) = e0)) <=> (~(op(e2, e3) = e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15884])).
% 2.06/2.16 tff(15886,plain,
% 2.06/2.16 (~(op(e2, e3) = e3)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[84, 15885])).
% 2.06/2.16 tff(15887,plain,
% 2.06/2.16 (op(e3, e3) = e3),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[15711, 15886, 15653, 15232, 15218, 72, 75, 80, 15234, 15228])).
% 2.06/2.16 tff(15888,plain,
% 2.06/2.16 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(e3, e1)) = e3)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15879, 15887])).
% 2.06/2.16 tff(15889,plain,
% 2.06/2.16 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15888, 15881])).
% 2.06/2.16 tff(15890,plain,
% 2.06/2.16 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15889])).
% 2.06/2.16 tff(15891,plain,
% 2.06/2.16 (~(op(e3, e2) = e3)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[1888, 15890])).
% 2.06/2.16 tff(15892,plain,
% 2.06/2.16 (op(e3, e2) = e1),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1898, 15891, 85, 15877])).
% 2.06/2.16 tff(15893,plain,
% 2.06/2.16 (op(e3, op(e3, e2)) = op(e3, e1)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15892])).
% 2.06/2.16 tff(15894,plain,
% 2.06/2.16 (op(e3, op(e3, e2)) = e2),
% 2.06/2.16 inference(transitivity,[status(thm)],[15893, 15653])).
% 2.06/2.16 tff(15895,plain,
% 2.06/2.16 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1904, 15894])).
% 2.06/2.16 tff(15896,plain,
% 2.06/2.16 (op(e0, e3) = e2),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[15235, 15886, 72, 75, 80, 15234, 15232, 15228])).
% 2.06/2.16 tff(15897,plain,
% 2.06/2.16 (op(e0, e3) = op(e3, e1)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15896, 15661])).
% 2.06/2.16 tff(15898,plain,
% 2.06/2.16 (op(op(e0, e3), e3) = op(op(e3, e1), e3)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15897])).
% 2.06/2.16 tff(15899,plain,
% 2.06/2.16 (op(op(e0, e3), e3) = e0),
% 2.06/2.16 inference(transitivity,[status(thm)],[15898, 15654, 15221, 15840])).
% 2.06/2.16 tff(15900,plain,
% 2.06/2.16 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1361, 15899])).
% 2.06/2.16 tff(15901,plain,
% 2.06/2.16 (op(e1, op(e3, e1)) = op(e1, e2)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15653])).
% 2.06/2.16 tff(15902,plain,
% 2.06/2.16 (op(e1, e0) = op(e3, e1)),
% 2.06/2.16 inference(transitivity,[status(thm)],[15851, 15661])).
% 2.06/2.16 tff(15903,plain,
% 2.06/2.16 (op(e1, op(e1, e0)) = op(e1, op(e3, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15902])).
% 2.06/2.16 tff(15904,plain,
% 2.06/2.16 (op(e1, op(e1, e0)) = e0),
% 2.06/2.16 inference(transitivity,[status(thm)],[15903, 15901, 15868])).
% 2.06/2.16 tff(15905,plain,
% 2.06/2.16 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1836, 15904])).
% 2.06/2.16 tff(15906,plain,
% 2.06/2.16 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e3, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15661])).
% 2.06/2.16 tff(15907,plain,
% 2.06/2.16 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.06/2.16 inference(symmetry,[status(thm)],[15906])).
% 2.06/2.16 tff(15908,plain,
% 2.06/2.16 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15907])).
% 2.06/2.16 tff(15909,plain,
% 2.06/2.16 (~(op(e2, e1) = e2)),
% 2.06/2.16 inference(modus_ponens,[status(thm)],[402, 15908])).
% 2.06/2.16 tff(15910,plain,
% 2.06/2.16 (op(e2, e1) = e1),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[2367, 15861, 15264, 15909])).
% 2.06/2.16 tff(15911,plain,
% 2.06/2.16 (op(op(e3, e1), e1) = op(e2, e1)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15653])).
% 2.06/2.16 tff(15912,plain,
% 2.06/2.16 (op(e2, op(e2, e1)) = op(op(e3, e1), e1)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15661, 15910])).
% 2.06/2.16 tff(15913,plain,
% 2.06/2.16 (op(e2, op(e2, e1)) = e1),
% 2.06/2.16 inference(transitivity,[status(thm)],[15912, 15911, 15910])).
% 2.06/2.16 tff(15914,plain,
% 2.06/2.16 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.06/2.16 inference(unit_resolution,[status(thm)],[1355, 15913])).
% 2.06/2.16 tff(15915,plain,
% 2.06/2.16 (op(e0, op(e1, e1)) = op(e0, e3)),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15218])).
% 2.06/2.16 tff(15916,plain,
% 2.06/2.16 (op(op(e2, e3), e3) = op(e0, op(e1, e1))),
% 2.06/2.16 inference(monotonicity,[status(thm)],[15840, 15219])).
% 2.06/2.17 tff(15917,plain,
% 2.06/2.17 (op(op(e2, e3), e3) = op(e0, e3)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15916, 15915])).
% 2.06/2.17 tff(15918,plain,
% 2.06/2.17 ((op(op(e2, e3), e3) = e2) <=> (op(e0, e3) = e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15917])).
% 2.06/2.17 tff(15919,plain,
% 2.06/2.17 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15918])).
% 2.06/2.17 tff(15920,plain,
% 2.06/2.17 (op(op(e2, e3), e3) = e2),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[15896, 15919])).
% 2.06/2.17 tff(15921,plain,
% 2.06/2.17 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1288, 15920])).
% 2.06/2.17 tff(15922,plain,
% 2.06/2.17 (op(e3, op(e2, e3)) = op(e3, e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15840])).
% 2.06/2.17 tff(15923,plain,
% 2.06/2.17 (op(e3, e0) = op(e2, e3)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15847, 15841])).
% 2.06/2.17 tff(15924,plain,
% 2.06/2.17 (op(e3, op(e3, e0)) = op(e3, op(e2, e3))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15923])).
% 2.06/2.17 tff(15925,plain,
% 2.06/2.17 (op(e3, op(e3, e0)) = e0),
% 2.06/2.17 inference(transitivity,[status(thm)],[15924, 15922, 15847])).
% 2.06/2.17 tff(15926,plain,
% 2.06/2.17 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1345, 15925])).
% 2.06/2.17 tff(15927,plain,
% 2.06/2.17 (op(op(e0, e1), e1) = op(e0, e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15862])).
% 2.06/2.17 tff(15928,plain,
% 2.06/2.17 (op(op(e0, e1), e1) = e0),
% 2.06/2.17 inference(transitivity,[status(thm)],[15927, 15862])).
% 2.06/2.17 tff(15929,plain,
% 2.06/2.17 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2650, 15928])).
% 2.06/2.17 tff(15930,plain,
% 2.06/2.17 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15896])).
% 2.06/2.17 tff(15931,plain,
% 2.06/2.17 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15930])).
% 2.06/2.17 tff(15932,plain,
% 2.06/2.17 (~(op(e0, e2) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[918, 15931])).
% 2.06/2.17 tff(15933,plain,
% 2.06/2.17 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15892])).
% 2.06/2.17 tff(15934,plain,
% 2.06/2.17 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15933])).
% 2.06/2.17 tff(15935,plain,
% 2.06/2.17 (~(op(e0, e2) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1467, 15934])).
% 2.06/2.17 tff(15936,plain,
% 2.06/2.17 (op(e0, e2) = e3),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2745, 15935, 15932, 15867])).
% 2.06/2.17 tff(15937,plain,
% 2.06/2.17 (op(e0, op(e0, e2)) = op(op(e2, e3), e3)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15841, 15936])).
% 2.06/2.17 tff(15938,plain,
% 2.06/2.17 (op(e0, op(e0, e2)) = e2),
% 2.06/2.17 inference(transitivity,[status(thm)],[15937, 15916, 15915, 15896])).
% 2.06/2.17 tff(15939,plain,
% 2.06/2.17 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1331, 15938])).
% 2.06/2.17 tff(15940,plain,
% 2.06/2.17 (op(e3, e0) = op(e3, op(e2, e3))),
% 2.06/2.17 inference(symmetry,[status(thm)],[15922])).
% 2.06/2.17 tff(15941,plain,
% 2.06/2.17 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15940])).
% 2.06/2.17 tff(15942,plain,
% 2.06/2.17 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e0) = e3)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15941])).
% 2.06/2.17 tff(15943,plain,
% 2.06/2.17 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, op(e2, e3)) = e3)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15940, 15887])).
% 2.06/2.17 tff(15944,plain,
% 2.06/2.17 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15943, 15942])).
% 2.06/2.17 tff(15945,plain,
% 2.06/2.17 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15944])).
% 2.06/2.17 tff(15946,plain,
% 2.06/2.17 (~(op(e3, e0) = e3)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[157, 15945])).
% 2.06/2.17 tff(15947,plain,
% 2.06/2.17 ((op(e3, e0) = e1) <=> (op(e2, e3) = e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15923])).
% 2.06/2.17 tff(15948,plain,
% 2.06/2.17 ((op(e2, e3) = e1) <=> (op(e3, e0) = e1)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15947])).
% 2.06/2.17 tff(15949,plain,
% 2.06/2.17 ((~(op(e2, e3) = e1)) <=> (~(op(e3, e0) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15948])).
% 2.06/2.17 tff(15950,plain,
% 2.06/2.17 (~(op(e3, e0) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[76, 15949])).
% 2.06/2.17 tff(15951,plain,
% 2.06/2.17 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15910])).
% 2.06/2.17 tff(15952,plain,
% 2.06/2.17 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15951])).
% 2.06/2.17 tff(15953,plain,
% 2.06/2.17 (~(op(e2, e0) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1966, 15952])).
% 2.06/2.17 tff(15954,plain,
% 2.06/2.17 (op(e0, e0) = e1),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1480, 15953, 15950, 15497])).
% 2.06/2.17 tff(15955,plain,
% 2.06/2.17 ((op(e0, e0) = e3) <=> (e1 = op(e1, e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15954, 15219])).
% 2.06/2.17 tff(15956,plain,
% 2.06/2.17 ((op(e0, e0) = e3) <=> (op(e1, e1) = e1)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15955, 8462])).
% 2.06/2.17 tff(15957,plain,
% 2.06/2.17 ((op(e1, e1) = e1) <=> (op(e0, e0) = e3)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15956])).
% 2.06/2.17 tff(15958,plain,
% 2.06/2.17 ((~(op(e1, e1) = e1)) <=> (~(op(e0, e0) = e3))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15957])).
% 2.06/2.17 tff(15959,plain,
% 2.06/2.17 (~(op(e0, e0) = e3)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[15217, 15958])).
% 2.06/2.17 tff(15960,plain,
% 2.06/2.17 (op(e2, e0) = e3),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2713, 15959, 15946, 15350])).
% 2.06/2.17 tff(15961,plain,
% 2.06/2.17 (op(e2, op(e2, e0)) = op(op(e3, e1), e3)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15661, 15960])).
% 2.06/2.17 tff(15962,plain,
% 2.06/2.17 (op(e2, op(e2, e0)) = e0),
% 2.06/2.17 inference(transitivity,[status(thm)],[15961, 15654, 15221, 15840])).
% 2.06/2.17 tff(15963,plain,
% 2.06/2.17 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2653, 15962])).
% 2.06/2.17 tff(15964,plain,
% 2.06/2.17 ($false),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1459, 15963, 15939, 15929, 15926, 15921, 15234, 15914, 15905, 15900, 15895, 15872, 15660])).
% 2.06/2.17 tff(15965,plain,((op(e3, e2) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e1, e1) = e0) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (op(e1, e3) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.17 tff(15966,plain,
% 2.06/2.17 (op(e3, e2) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[15965, 84, 76, 17, 72, 75, 80, 68])).
% 2.06/2.17 tff(15967,plain,
% 2.06/2.17 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15966])).
% 2.06/2.17 tff(15968,plain,
% 2.06/2.17 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15967])).
% 2.06/2.17 tff(15969,plain,
% 2.06/2.17 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15968])).
% 2.06/2.17 tff(15970,plain,
% 2.06/2.17 (~(op(e3, e2) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[14, 15969])).
% 2.06/2.17 tff(15971,plain,
% 2.06/2.17 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2)),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2015, 15002])).
% 2.06/2.17 tff(15972,plain,
% 2.06/2.17 (op(e3, e0) = e2),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[15971, 15970, 82])).
% 2.06/2.17 tff(15973,plain,
% 2.06/2.17 (op(e0, op(e3, e0)) = op(e0, e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15972])).
% 2.06/2.17 tff(15974,plain,
% 2.06/2.17 (e2 = op(e3, e0)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15972])).
% 2.06/2.17 tff(15975,plain,
% 2.06/2.17 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15966])).
% 2.06/2.17 tff(15976,plain,
% 2.06/2.17 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15975])).
% 2.06/2.17 tff(15977,plain,
% 2.06/2.17 (~(op(e1, e2) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[2292, 15976])).
% 2.06/2.17 tff(15978,plain,
% 2.06/2.17 (op(e1, e0) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1830, 15977, 80, 84])).
% 2.06/2.17 tff(15979,plain,
% 2.06/2.17 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15978])).
% 2.06/2.17 tff(15980,plain,
% 2.06/2.17 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15979, 4499])).
% 2.06/2.17 tff(15981,plain,
% 2.06/2.17 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15980])).
% 2.06/2.17 tff(15982,plain,
% 2.06/2.17 (~(op(e2, e0) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[756, 15981])).
% 2.06/2.17 tff(15983,plain,
% 2.06/2.17 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15966])).
% 2.06/2.17 tff(15984,plain,
% 2.06/2.17 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15983])).
% 2.06/2.17 tff(15985,plain,
% 2.06/2.17 (~(op(e3, e0) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1133, 15984])).
% 2.06/2.17 tff(15986,plain,
% 2.06/2.17 ((op(e3, e2) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15966])).
% 2.06/2.17 tff(15987,plain,
% 2.06/2.17 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15986, 3077])).
% 2.06/2.17 tff(15988,plain,
% 2.06/2.17 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15987])).
% 2.06/2.17 tff(15989,plain,
% 2.06/2.17 (~(op(e3, e3) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1888, 15988])).
% 2.06/2.17 tff(15990,plain,
% 2.06/2.17 (op(e2, e1) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2311, 1063, 17, 983])).
% 2.06/2.17 tff(15991,plain,
% 2.06/2.17 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[3716])).
% 2.06/2.17 tff(15992,plain,
% 2.06/2.17 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15991])).
% 2.06/2.17 tff(15993,plain,
% 2.06/2.17 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15992])).
% 2.06/2.17 tff(15994,plain,
% 2.06/2.17 (~(op(e0, e3) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[26, 15993])).
% 2.06/2.17 tff(15995,plain,
% 2.06/2.17 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[9333])).
% 2.06/2.17 tff(15996,plain,
% 2.06/2.17 ((op(e0, e3) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.17 inference(transitivity,[status(thm)],[15995, 452])).
% 2.06/2.17 tff(15997,plain,
% 2.06/2.17 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[15996])).
% 2.06/2.17 tff(15998,plain,
% 2.06/2.17 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[3716])).
% 2.06/2.17 tff(15999,plain,
% 2.06/2.17 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.17 inference(symmetry,[status(thm)],[15998])).
% 2.06/2.17 tff(16000,plain,
% 2.06/2.17 ((op(e3, e0) = e0) <=> (op(e0, e3) = e2)),
% 2.06/2.17 inference(transitivity,[status(thm)],[15999, 15997])).
% 2.06/2.17 tff(16001,plain,
% 2.06/2.17 ((~(op(e3, e0) = e0)) <=> (~(op(e0, e3) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16000])).
% 2.06/2.17 tff(16002,plain,
% 2.06/2.17 (~(op(e0, e3) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1908, 16001])).
% 2.06/2.17 tff(16003,plain,
% 2.06/2.17 ($false),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[7365, 16002, 15994, 80, 656, 15990])).
% 2.06/2.17 tff(16004,plain,((op(e2, e3) = e0) | (op(e1, e3) = e0) | (op(e3, e3) = e0) | (op(e3, e0) = e0) | (~(op(e3, e0) = e2)) | (op(e2, e2) = e0) | (op(e2, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.17 tff(16005,plain,
% 2.06/2.17 (op(e2, e3) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[16004, 15989, 80, 15985, 15972, 17, 15982])).
% 2.06/2.17 tff(16006,plain,
% 2.06/2.17 ((op(e2, e3) = e2) <=> (e0 = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16005, 15974])).
% 2.06/2.17 tff(16007,plain,
% 2.06/2.17 ((op(e2, e3) = e2) <=> (op(e3, e0) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16006, 8115])).
% 2.06/2.17 tff(16008,plain,
% 2.06/2.17 ((op(e3, e0) = e0) <=> (op(e2, e3) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16007])).
% 2.06/2.17 tff(16009,plain,
% 2.06/2.17 ((~(op(e3, e0) = e0)) <=> (~(op(e2, e3) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16008])).
% 2.06/2.17 tff(16010,plain,
% 2.06/2.17 (~(op(e2, e3) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[15985, 16009])).
% 2.06/2.17 tff(16011,plain,
% 2.06/2.17 (op(e0, e3) = e2),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[15003, 16010, 72])).
% 2.06/2.17 tff(16012,plain,
% 2.06/2.17 (op(e0, e3) = op(e3, e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16011, 15974])).
% 2.06/2.17 tff(16013,plain,
% 2.06/2.17 (op(e0, op(e0, e3)) = op(e0, op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16012])).
% 2.06/2.17 tff(16014,plain,
% 2.06/2.17 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16013, 15973])).
% 2.06/2.17 tff(16015,plain,
% 2.06/2.17 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16014])).
% 2.06/2.17 tff(16016,plain,
% 2.06/2.17 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16015])).
% 2.06/2.17 tff(16017,plain,
% 2.06/2.17 ((~(op(e0, e2) = e0)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16016])).
% 2.06/2.17 tff(16018,plain,
% 2.06/2.17 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15966])).
% 2.06/2.17 tff(16019,plain,
% 2.06/2.17 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16018])).
% 2.06/2.17 tff(16020,plain,
% 2.06/2.17 (~(op(e0, e2) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1467, 16019])).
% 2.06/2.17 tff(16021,plain,
% 2.06/2.17 (~(op(e0, op(e0, e3)) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[16020, 16017])).
% 2.06/2.17 tff(16022,plain,
% 2.06/2.17 (op(e2, op(e0, e3)) = op(e2, e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16011])).
% 2.06/2.17 tff(16023,plain,
% 2.06/2.17 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16022])).
% 2.06/2.17 tff(16024,plain,
% 2.06/2.17 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16023])).
% 2.06/2.17 tff(16025,plain,
% 2.06/2.17 ((~(op(e2, e2) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16024])).
% 2.06/2.17 tff(16026,plain,
% 2.06/2.17 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15974])).
% 2.06/2.17 tff(16027,plain,
% 2.06/2.17 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16026])).
% 2.06/2.17 tff(16028,plain,
% 2.06/2.17 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16027])).
% 2.06/2.17 tff(16029,plain,
% 2.06/2.17 (~(op(e1, e0) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[410, 16028])).
% 2.06/2.17 tff(16030,plain,
% 2.06/2.17 (op(e1, e2) = e2),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2285, 16029, 68, 72])).
% 2.06/2.17 tff(16031,plain,
% 2.06/2.17 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16030])).
% 2.06/2.17 tff(16032,plain,
% 2.06/2.17 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16031, 81])).
% 2.06/2.17 tff(16033,plain,
% 2.06/2.17 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16032])).
% 2.06/2.17 tff(16034,plain,
% 2.06/2.17 (~(op(e2, e2) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[1273, 16033])).
% 2.06/2.17 tff(16035,plain,
% 2.06/2.17 (~(op(e2, op(e0, e3)) = e2)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[16034, 16025])).
% 2.06/2.17 tff(16036,plain,
% 2.06/2.17 (op(e1, op(e3, e0)) = op(e1, e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15972])).
% 2.06/2.17 tff(16037,plain,
% 2.06/2.17 (op(e1, op(e0, e3)) = op(e1, op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16012])).
% 2.06/2.17 tff(16038,plain,
% 2.06/2.17 (op(e1, op(e0, e3)) = op(e3, e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16037, 16036, 16030, 15974])).
% 2.06/2.17 tff(16039,plain,
% 2.06/2.17 ((op(e1, op(e0, e3)) = e1) <=> (op(e3, e0) = e1)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16038])).
% 2.06/2.17 tff(16040,plain,
% 2.06/2.17 ((op(e3, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16039])).
% 2.06/2.17 tff(16041,plain,
% 2.06/2.17 ((~(op(e3, e0) = e1)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16040])).
% 2.06/2.17 tff(16042,plain,
% 2.06/2.17 ((e1 = e2) <=> (e1 = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15974])).
% 2.06/2.17 tff(16043,plain,
% 2.06/2.17 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16042, 6411])).
% 2.06/2.17 tff(16044,plain,
% 2.06/2.17 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16043])).
% 2.06/2.17 tff(16045,plain,
% 2.06/2.17 (~(op(e3, e0) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[708, 16044])).
% 2.06/2.17 tff(16046,plain,
% 2.06/2.17 (~(op(e1, op(e0, e3)) = e1)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[16045, 16041])).
% 2.06/2.17 tff(16047,plain,
% 2.06/2.17 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15974])).
% 2.06/2.17 tff(16048,plain,
% 2.06/2.17 ((op(e0, e3) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.17 inference(transitivity,[status(thm)],[16047, 452])).
% 2.06/2.17 tff(16049,plain,
% 2.06/2.17 (op(e3, e0) = op(e0, e3)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[16011, 16048])).
% 2.06/2.17 tff(16050,plain,
% 2.06/2.17 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[15972])).
% 2.06/2.17 tff(16051,plain,
% 2.06/2.17 (op(e3, op(e0, e3)) = op(e3, op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16012])).
% 2.06/2.17 tff(16052,plain,
% 2.06/2.17 (op(e3, op(e0, e3)) = e0),
% 2.06/2.17 inference(transitivity,[status(thm)],[16051, 16050, 15966])).
% 2.06/2.17 tff(16053,plain,
% 2.06/2.17 ((op(e3, op(e0, e3)) = e3) <=> (e0 = e3)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16052])).
% 2.06/2.17 tff(16054,plain,
% 2.06/2.17 ((e0 = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16053])).
% 2.06/2.17 tff(16055,plain,
% 2.06/2.17 ((~(e0 = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16054])).
% 2.06/2.17 tff(16056,plain,
% 2.06/2.17 (~(op(e3, op(e0, e3)) = e3)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[181, 16055])).
% 2.06/2.17 tff(16057,plain,
% 2.06/2.17 ((~((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3))) | (~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)),
% 2.06/2.17 inference(tautology,[status(thm)],[])).
% 2.06/2.17 tff(16058,plain,
% 2.06/2.17 ((~(op(e3, e0) = op(e0, e3))) | (op(e0, op(e0, e3)) = e0) | (op(e1, op(e0, e3)) = e1) | (op(e2, op(e0, e3)) = e2) | (op(e3, op(e0, e3)) = e3)),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[16057, 5196])).
% 2.06/2.17 tff(16059,plain,
% 2.06/2.17 ($false),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[16058, 16056, 16049, 16046, 16035, 16021])).
% 2.06/2.17 tff(16060,plain,((op(e1, e1) = e0) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e3, e1) = e2) | (op(e2, e3) = e1) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.17 tff(16061,plain,
% 2.06/2.17 (op(e1, e1) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[16060, 82, 80, 17, 68, 72, 76, 75])).
% 2.06/2.17 tff(16062,plain,
% 2.06/2.17 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16061])).
% 2.06/2.17 tff(16063,plain,
% 2.06/2.17 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16062, 83])).
% 2.06/2.17 tff(16064,plain,
% 2.06/2.17 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16063])).
% 2.06/2.17 tff(16065,plain,
% 2.06/2.17 (~(op(e2, e1) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[225, 16064])).
% 2.06/2.17 tff(16066,plain,
% 2.06/2.17 (op(e2, e0) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[2311, 1063, 17, 16065])).
% 2.06/2.17 tff(16067,plain,
% 2.06/2.17 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16066])).
% 2.06/2.17 tff(16068,plain,
% 2.06/2.17 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16067])).
% 2.06/2.17 tff(16069,plain,
% 2.06/2.17 (~(op(e0, e0) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[359, 16068])).
% 2.06/2.17 tff(16070,plain,
% 2.06/2.17 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16061])).
% 2.06/2.17 tff(16071,plain,
% 2.06/2.17 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16070])).
% 2.06/2.17 tff(16072,plain,
% 2.06/2.17 (~(op(e0, e1) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[792, 16071])).
% 2.06/2.17 tff(16073,plain,
% 2.06/2.17 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16061])).
% 2.06/2.17 tff(16074,plain,
% 2.06/2.17 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16073, 5470])).
% 2.06/2.17 tff(16075,plain,
% 2.06/2.17 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16074])).
% 2.06/2.17 tff(16076,plain,
% 2.06/2.17 (~(op(e3, e1) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[945, 16075])).
% 2.06/2.17 tff(16077,plain,
% 2.06/2.17 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16066])).
% 2.06/2.17 tff(16078,plain,
% 2.06/2.17 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.06/2.17 inference(transitivity,[status(thm)],[16077, 8115])).
% 2.06/2.17 tff(16079,plain,
% 2.06/2.17 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16078])).
% 2.06/2.17 tff(16080,plain,
% 2.06/2.17 (~(op(e3, e0) = e0)),
% 2.06/2.17 inference(modus_ponens,[status(thm)],[747, 16079])).
% 2.06/2.17 tff(16081,plain,
% 2.06/2.17 (op(e3, e2) = e0),
% 2.06/2.17 inference(unit_resolution,[status(thm)],[1916, 656, 1908, 183])).
% 2.06/2.17 tff(16082,plain,
% 2.06/2.17 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 2.06/2.17 inference(monotonicity,[status(thm)],[16081])).
% 2.06/2.17 tff(16083,plain,
% 2.06/2.17 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 2.06/2.17 inference(symmetry,[status(thm)],[16082])).
% 2.06/2.17 tff(16084,plain,
% 2.06/2.18 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16083])).
% 2.06/2.18 tff(16085,plain,
% 2.06/2.18 (~(op(e3, e2) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[14, 16084])).
% 2.06/2.18 tff(16086,plain,
% 2.06/2.18 (op(e3, e0) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[15971, 16085, 82])).
% 2.06/2.18 tff(16087,plain,
% 2.06/2.18 (e2 = op(e3, e0)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16086])).
% 2.06/2.18 tff(16088,plain,
% 2.06/2.18 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16087])).
% 2.06/2.18 tff(16089,plain,
% 2.06/2.18 ((op(e3, e0) = e3) <=> (e2 = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16088])).
% 2.06/2.18 tff(16090,plain,
% 2.06/2.18 ((op(e0, e3) = e1) <=> (e0 = e1)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[15675])).
% 2.06/2.18 tff(16091,plain,
% 2.06/2.18 ((e0 = e1) <=> (op(e0, e3) = e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16090])).
% 2.06/2.18 tff(16092,plain,
% 2.06/2.18 ((~(e0 = e1)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16091])).
% 2.06/2.18 tff(16093,plain,
% 2.06/2.18 (~(op(e0, e3) = e1)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[26, 16092])).
% 2.06/2.18 tff(16094,plain,
% 2.06/2.18 ((op(e0, e3) = e2) <=> (e0 = e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[15675])).
% 2.06/2.18 tff(16095,plain,
% 2.06/2.18 ((e0 = e2) <=> (op(e0, e3) = e2)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16094])).
% 2.06/2.18 tff(16096,plain,
% 2.06/2.18 ((~(e0 = e2)) <=> (~(op(e0, e3) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16095])).
% 2.06/2.18 tff(16097,plain,
% 2.06/2.18 (~(op(e0, e3) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[14, 16096])).
% 2.06/2.18 tff(16098,plain,
% 2.06/2.18 ((op(e1, e3) = e2) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e1)),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[9642, 15002])).
% 2.06/2.18 tff(16099,plain,
% 2.06/2.18 (op(e2, e3) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[16098, 16097, 72, 76, 80, 16093])).
% 2.06/2.18 tff(16100,plain,
% 2.06/2.18 (op(e2, e3) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[15003, 16097, 72])).
% 2.06/2.18 tff(16101,plain,
% 2.06/2.18 (e2 = op(e2, e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16100])).
% 2.06/2.18 tff(16102,plain,
% 2.06/2.18 (op(e3, e0) = e3),
% 2.06/2.18 inference(transitivity,[status(thm)],[16086, 16101, 16099])).
% 2.06/2.18 tff(16103,plain,
% 2.06/2.18 (e2 = e3),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16102, 16089])).
% 2.06/2.18 tff(16104,plain,
% 2.06/2.18 ($false),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[1321, 16103])).
% 2.06/2.18 tff(16105,plain,((op(e3, e3) = e0) | (op(e1, e3) = e2) | (op(e2, e3) = e1) | (op(e1, e3) = e0) | (op(e3, e1) = e2) | (op(e2, e3) = e0) | (op(e3, e0) = e0) | (op(e3, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.18 tff(16106,plain,
% 2.06/2.18 (op(e3, e3) = e0),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[16105, 1063, 76, 80, 82, 72, 16080, 16076])).
% 2.06/2.18 tff(16107,plain,
% 2.06/2.18 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16106])).
% 2.06/2.18 tff(16108,plain,
% 2.06/2.18 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16107])).
% 2.06/2.18 tff(16109,plain,
% 2.06/2.18 (~(op(e0, e3) = e0)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1077, 16108])).
% 2.06/2.18 tff(16110,plain,
% 2.06/2.18 (op(e0, e2) = e0),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[3976, 16109, 16072, 16069])).
% 2.06/2.18 tff(16111,plain,
% 2.06/2.18 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16110])).
% 2.06/2.18 tff(16112,plain,
% 2.06/2.18 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16111])).
% 2.06/2.18 tff(16113,plain,
% 2.06/2.18 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16112])).
% 2.06/2.18 tff(16114,plain,
% 2.06/2.18 (~(op(e0, e2) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[181, 16113])).
% 2.06/2.18 tff(16115,plain,
% 2.06/2.18 (op(e2, e3) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[15003, 79, 72])).
% 2.06/2.18 tff(16116,plain,
% 2.06/2.18 ((op(e2, e3) = e3) <=> (e2 = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16115])).
% 2.06/2.18 tff(16117,plain,
% 2.06/2.18 ((e2 = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16116])).
% 2.06/2.18 tff(16118,plain,
% 2.06/2.18 ((~(e2 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16117])).
% 2.06/2.18 tff(16119,plain,
% 2.06/2.18 (~(op(e2, e3) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1321, 16118])).
% 2.06/2.18 tff(16120,plain,
% 2.06/2.18 (op(e0, e3) = e1),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[10335, 16119, 79, 72, 76, 80])).
% 2.06/2.18 tff(16121,plain,
% 2.06/2.18 (op(e0, e1) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[5000, 16120, 4412, 3849])).
% 2.06/2.18 tff(16122,plain,
% 2.06/2.18 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16115])).
% 2.06/2.18 tff(16123,plain,
% 2.06/2.18 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16122])).
% 2.06/2.18 tff(16124,plain,
% 2.06/2.18 (~(op(e2, e1) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[197, 16123])).
% 2.06/2.18 tff(16125,plain,
% 2.06/2.18 (op(e0, e1) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[1993, 16124, 68, 82])).
% 2.06/2.18 tff(16126,plain,
% 2.06/2.18 (e2 = op(e0, e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16125])).
% 2.06/2.18 tff(16127,plain,
% 2.06/2.18 (e2 = e3),
% 2.06/2.18 inference(transitivity,[status(thm)],[16126, 16121])).
% 2.06/2.18 tff(16128,plain,
% 2.06/2.18 ($false),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[1321, 16127])).
% 2.06/2.18 tff(16129,plain,((op(e0, e3) = e2) | (op(e0, e2) = e3) | (op(e0, e1) = e0) | (op(e1, e1) = e2) | (op(e3, e1) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e1) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.18 tff(16130,plain,
% 2.06/2.18 (op(e0, e3) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[16129, 16114, 16072, 68, 82, 72, 76, 80])).
% 2.06/2.18 tff(16131,plain,
% 2.06/2.18 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16130])).
% 2.06/2.18 tff(16132,plain,
% 2.06/2.18 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16131])).
% 2.06/2.18 tff(16133,plain,
% 2.06/2.18 (~(op(e0, e0) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[3414, 16132])).
% 2.06/2.18 tff(16134,plain,
% 2.06/2.18 (e0 = op(e1, e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16061])).
% 2.06/2.18 tff(16135,plain,
% 2.06/2.18 ((e0 = e3) <=> (op(e1, e1) = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16134])).
% 2.06/2.18 tff(16136,plain,
% 2.06/2.18 ((~(e0 = e3)) <=> (~(op(e1, e1) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16135])).
% 2.06/2.18 tff(16137,plain,
% 2.06/2.18 (~(op(e1, e1) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[181, 16136])).
% 2.06/2.18 tff(16138,plain,
% 2.06/2.18 ((op(e3, e3) = e1) <=> (e0 = e1)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16106])).
% 2.06/2.18 tff(16139,plain,
% 2.06/2.18 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16138])).
% 2.06/2.18 tff(16140,plain,
% 2.06/2.18 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16139])).
% 2.06/2.18 tff(16141,plain,
% 2.06/2.18 (~(op(e3, e3) = e1)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[26, 16140])).
% 2.06/2.18 tff(16142,plain,
% 2.06/2.18 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16130])).
% 2.06/2.18 tff(16143,plain,
% 2.06/2.18 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16142, 69])).
% 2.06/2.18 tff(16144,plain,
% 2.06/2.18 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16143])).
% 2.06/2.18 tff(16145,plain,
% 2.06/2.18 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16144])).
% 2.06/2.18 tff(16146,plain,
% 2.06/2.18 (~(op(e0, e3) = e1)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[708, 16145])).
% 2.06/2.18 tff(16147,plain,
% 2.06/2.18 (op(e1, e3) = e1),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[151, 16146, 76, 16141])).
% 2.06/2.18 tff(16148,plain,
% 2.06/2.18 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16147])).
% 2.06/2.18 tff(16149,plain,
% 2.06/2.18 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16148])).
% 2.06/2.18 tff(16150,plain,
% 2.06/2.18 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16149])).
% 2.06/2.18 tff(16151,plain,
% 2.06/2.18 (~(op(e1, e3) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[303, 16150])).
% 2.06/2.18 tff(16152,plain,
% 2.06/2.18 (op(e1, e0) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[247, 16151, 75, 16137])).
% 2.06/2.18 tff(16153,plain,
% 2.06/2.18 (e3 = op(e1, e0)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16152])).
% 2.06/2.18 tff(16154,plain,
% 2.06/2.18 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16153])).
% 2.06/2.18 tff(16155,plain,
% 2.06/2.18 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16154])).
% 2.06/2.18 tff(16156,plain,
% 2.06/2.18 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16155])).
% 2.06/2.18 tff(16157,plain,
% 2.06/2.18 (~(op(e0, e0) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[2471, 16156])).
% 2.06/2.18 tff(16158,plain,
% 2.06/2.18 (op(e0, e0) = e1),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[3612, 16157, 16133, 16069])).
% 2.06/2.18 tff(16159,plain,
% 2.06/2.18 (e1 = op(e0, e0)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16158, 74])).
% 2.06/2.18 tff(16160,plain,
% 2.06/2.18 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16158])).
% 2.06/2.18 tff(16161,plain,
% 2.06/2.18 (op(e0, e1) = op(e0, op(e0, e0))),
% 2.06/2.18 inference(symmetry,[status(thm)],[16160])).
% 2.06/2.18 tff(16162,plain,
% 2.06/2.18 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16130])).
% 2.06/2.18 tff(16163,plain,
% 2.06/2.18 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16162])).
% 2.06/2.18 tff(16164,plain,
% 2.06/2.18 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16163])).
% 2.06/2.18 tff(16165,plain,
% 2.06/2.18 (~(op(e0, e3) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1321, 16164])).
% 2.06/2.18 tff(16166,plain,
% 2.06/2.18 (op(e0, e1) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[1495, 16157, 16114, 16165])).
% 2.06/2.18 tff(16167,plain,
% 2.06/2.18 (e3 = op(e0, e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16166])).
% 2.06/2.18 tff(16168,plain,
% 2.06/2.18 (e3 = op(e0, op(e0, e0))),
% 2.06/2.18 inference(transitivity,[status(thm)],[16167, 16161])).
% 2.06/2.18 tff(16169,plain,
% 2.06/2.18 (op(e0, op(e0, e0)) = op(e1, e0)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16160, 16166, 16153])).
% 2.06/2.18 tff(16170,plain,
% 2.06/2.18 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e0))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16169])).
% 2.06/2.18 tff(16171,plain,
% 2.06/2.18 (op(e0, op(e1, e0)) = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.18 inference(symmetry,[status(thm)],[16170])).
% 2.06/2.18 tff(16172,plain,
% 2.06/2.18 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16130])).
% 2.06/2.18 tff(16173,plain,
% 2.06/2.18 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16172, 120])).
% 2.06/2.18 tff(16174,plain,
% 2.06/2.18 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16173])).
% 2.06/2.18 tff(16175,plain,
% 2.06/2.18 (~(op(e2, e3) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[964, 16174])).
% 2.06/2.18 tff(16176,plain,
% 2.06/2.18 (op(e2, e3) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[206, 16175, 76, 1063])).
% 2.06/2.18 tff(16177,plain,
% 2.06/2.18 (e3 = op(e2, e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16176])).
% 2.06/2.18 tff(16178,plain,
% 2.06/2.18 (op(e1, e0) = op(e2, e3)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16152, 16177])).
% 2.06/2.18 tff(16179,plain,
% 2.06/2.18 (op(e0, op(e1, e0)) = op(e0, op(e2, e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16178])).
% 2.06/2.18 tff(16180,plain,
% 2.06/2.18 (op(e0, op(e2, e3)) = op(e0, op(e1, e0))),
% 2.06/2.18 inference(symmetry,[status(thm)],[16179])).
% 2.06/2.18 tff(16181,plain,
% 2.06/2.18 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16176])).
% 2.06/2.18 tff(16182,plain,
% 2.06/2.18 (op(e0, e3) = op(e0, op(e2, e3))),
% 2.06/2.18 inference(symmetry,[status(thm)],[16181])).
% 2.06/2.18 tff(16183,plain,
% 2.06/2.18 (e2 = op(e0, e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16130])).
% 2.06/2.18 tff(16184,plain,
% 2.06/2.18 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.18 inference(transitivity,[status(thm)],[16183, 16182, 16180, 16171])).
% 2.06/2.18 tff(16185,plain,
% 2.06/2.18 ((~(~((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0))))))) <=> ((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))))),
% 2.06/2.18 inference(rewrite,[status(thm)],[])).
% 2.06/2.18 tff(16186,plain,
% 2.06/2.18 (((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))) <=> (~((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0))))))),
% 2.06/2.18 inference(rewrite,[status(thm)],[])).
% 2.06/2.18 tff(16187,plain,
% 2.06/2.18 ((~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~(~((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))))))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16186])).
% 2.06/2.18 tff(16188,plain,
% 2.06/2.18 ((~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> ((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))))),
% 2.06/2.18 inference(transitivity,[status(thm)],[16187, 16185])).
% 2.06/2.18 tff(16189,plain,
% 2.06/2.18 ((~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))))),
% 2.06/2.18 inference(rewrite,[status(thm)],[])).
% 2.06/2.18 tff(16190,plain,
% 2.06/2.18 ((~(((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0))) & (e2 = op(e0, op(e0, op(e0, e0)))))) <=> (~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0))))))),
% 2.06/2.18 inference(rewrite,[status(thm)],[])).
% 2.06/2.18 tff(16191,axiom,(~(((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0))) & (e2 = op(e0, op(e0, op(e0, e0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax10')).
% 2.06/2.18 tff(16192,plain,
% 2.06/2.18 (~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16191, 16190])).
% 2.06/2.18 tff(16193,plain,
% 2.06/2.18 (~((e3 = op(e0, op(e0, e0))) & (e1 = op(e0, e0)) & (e2 = op(e0, op(e0, op(e0, e0)))))),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16192, 16189])).
% 2.06/2.18 tff(16194,plain,
% 2.06/2.18 ((~(e2 = op(e0, op(e0, op(e0, e0))))) | (~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0))))),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16193, 16188])).
% 2.06/2.18 tff(16195,plain,
% 2.06/2.18 ($false),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[16194, 16184, 16168, 16159])).
% 2.06/2.18 tff(16196,plain,((op(e2, e3) = e0) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (op(e1, e1) = e2) | (op(e3, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.18 tff(16197,plain,
% 2.06/2.18 (op(e2, e3) = e0),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[16196, 82, 76, 68, 75, 72, 80, 17])).
% 2.06/2.18 tff(16198,plain,
% 2.06/2.18 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16197])).
% 2.06/2.18 tff(16199,plain,
% 2.06/2.18 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16198])).
% 2.06/2.18 tff(16200,plain,
% 2.06/2.18 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16199])).
% 2.06/2.18 tff(16201,plain,
% 2.06/2.18 (~(op(e2, e3) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[14, 16200])).
% 2.06/2.18 tff(16202,plain,
% 2.06/2.18 (op(e0, e3) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[15003, 16201, 72])).
% 2.06/2.18 tff(16203,plain,
% 2.06/2.18 (e2 = op(e0, e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16202])).
% 2.06/2.18 tff(16204,plain,
% 2.06/2.18 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e0, e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.18 tff(16205,plain,
% 2.06/2.18 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16204])).
% 2.06/2.18 tff(16206,plain,
% 2.06/2.18 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16205])).
% 2.06/2.18 tff(16207,plain,
% 2.06/2.18 (~(op(e0, e1) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[818, 16206])).
% 2.06/2.18 tff(16208,plain,
% 2.06/2.18 (op(e2, e1) = e2),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[1993, 16207, 68, 82])).
% 2.06/2.18 tff(16209,plain,
% 2.06/2.18 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16208])).
% 2.06/2.18 tff(16210,plain,
% 2.06/2.18 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16209, 81])).
% 2.06/2.18 tff(16211,plain,
% 2.06/2.18 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16210])).
% 2.06/2.18 tff(16212,plain,
% 2.06/2.18 (~(op(e2, e2) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[508, 16211])).
% 2.06/2.18 tff(16213,plain,
% 2.06/2.18 ((op(e2, e3) = e3) <=> (e0 = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16197])).
% 2.06/2.18 tff(16214,plain,
% 2.06/2.18 ((e0 = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16213])).
% 2.06/2.18 tff(16215,plain,
% 2.06/2.18 ((~(e0 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16214])).
% 2.06/2.18 tff(16216,plain,
% 2.06/2.18 (~(op(e2, e3) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[181, 16215])).
% 2.06/2.18 tff(16217,plain,
% 2.06/2.18 (op(e2, e1) = op(e0, e3)),
% 2.06/2.18 inference(transitivity,[status(thm)],[16208, 16203])).
% 2.06/2.18 tff(16218,plain,
% 2.06/2.18 ((op(e2, e1) = e3) <=> (op(e0, e3) = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16217])).
% 2.06/2.18 tff(16219,plain,
% 2.06/2.18 ((op(e0, e3) = e3) <=> (op(e2, e1) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16218])).
% 2.06/2.18 tff(16220,plain,
% 2.06/2.18 ((~(op(e0, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16219])).
% 2.06/2.18 tff(16221,plain,
% 2.06/2.18 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.18 tff(16222,plain,
% 2.06/2.18 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16221])).
% 2.06/2.18 tff(16223,plain,
% 2.06/2.18 (~(op(e0, e3) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1321, 16222])).
% 2.06/2.18 tff(16224,plain,
% 2.06/2.18 (~(op(e2, e1) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[16223, 16220])).
% 2.06/2.18 tff(16225,plain,
% 2.06/2.18 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16208])).
% 2.06/2.18 tff(16226,plain,
% 2.06/2.18 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16225])).
% 2.06/2.18 tff(16227,plain,
% 2.06/2.18 (~(op(e2, e0) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1966, 16226])).
% 2.06/2.18 tff(16228,plain,
% 2.06/2.18 (op(e2, e0) = e3),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[3293, 16227, 16197, 16224, 16202, 16216])).
% 2.06/2.18 tff(16229,plain,
% 2.06/2.18 (e3 = op(e2, e0)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16228])).
% 2.06/2.18 tff(16230,plain,
% 2.06/2.18 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e0))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16229])).
% 2.06/2.18 tff(16231,plain,
% 2.06/2.18 ((op(e2, e2) = e3) <=> (op(e2, e0) = op(e2, e2))),
% 2.06/2.18 inference(transitivity,[status(thm)],[16230, 6116])).
% 2.06/2.18 tff(16232,plain,
% 2.06/2.18 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16231])).
% 2.06/2.18 tff(16233,plain,
% 2.06/2.18 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16232])).
% 2.06/2.18 tff(16234,plain,
% 2.06/2.18 (~(op(e2, e2) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[2228, 16233])).
% 2.06/2.18 tff(16235,plain,
% 2.06/2.18 (op(e2, e2) = e1),
% 2.06/2.18 inference(unit_resolution,[status(thm)],[524, 16234, 17, 16212])).
% 2.06/2.18 tff(16236,plain,
% 2.06/2.18 (e1 = op(e2, e2)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16235])).
% 2.06/2.18 tff(16237,plain,
% 2.06/2.18 (op(e1, op(e0, e3)) = op(e1, e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16202])).
% 2.06/2.18 tff(16238,plain,
% 2.06/2.18 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = op(e2, e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16237, 16236])).
% 2.06/2.18 tff(16239,plain,
% 2.06/2.18 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, op(e0, e3)) = e1)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16238])).
% 2.06/2.18 tff(16240,plain,
% 2.06/2.18 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16239])).
% 2.06/2.18 tff(16241,plain,
% 2.06/2.18 (~(op(e1, op(e0, e3)) = e1)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[1273, 16240])).
% 2.06/2.18 tff(16242,plain,
% 2.06/2.18 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16202])).
% 2.06/2.18 tff(16243,plain,
% 2.06/2.18 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16242])).
% 2.06/2.18 tff(16244,plain,
% 2.06/2.18 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16243])).
% 2.06/2.18 tff(16245,plain,
% 2.06/2.18 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e2, e0))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16229])).
% 2.06/2.18 tff(16246,plain,
% 2.06/2.18 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16245])).
% 2.06/2.18 tff(16247,plain,
% 2.06/2.18 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16246])).
% 2.06/2.18 tff(16248,plain,
% 2.06/2.18 (~(op(e0, e0) = e3)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[359, 16247])).
% 2.06/2.18 tff(16249,plain,
% 2.06/2.18 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e0, e3))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.18 tff(16250,plain,
% 2.06/2.18 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.06/2.18 inference(symmetry,[status(thm)],[16249])).
% 2.06/2.18 tff(16251,plain,
% 2.06/2.18 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16250])).
% 2.06/2.18 tff(16252,plain,
% 2.06/2.18 (~(op(e0, e0) = e2)),
% 2.06/2.18 inference(modus_ponens,[status(thm)],[3414, 16251])).
% 2.06/2.18 tff(16253,plain,
% 2.06/2.18 (op(e1, op(e2, e0)) = op(e1, e3)),
% 2.06/2.18 inference(monotonicity,[status(thm)],[16228])).
% 2.06/2.18 tff(16254,plain,
% 2.06/2.18 (op(e1, e3) = op(e1, op(e2, e0))),
% 2.06/2.18 inference(symmetry,[status(thm)],[16253])).
% 2.06/2.18 tff(16255,plain,
% 2.06/2.18 ((op(e1, e3) = e1) <=> (op(e1, op(e2, e0)) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16254])).
% 2.06/2.19 tff(16256,plain,
% 2.06/2.19 ((op(e1, op(e2, e0)) = e1) <=> (op(e1, e3) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16255])).
% 2.06/2.19 tff(16257,plain,
% 2.06/2.19 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16229])).
% 2.06/2.19 tff(16258,plain,
% 2.06/2.19 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e3)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16257])).
% 2.06/2.19 tff(16259,plain,
% 2.06/2.19 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16258])).
% 2.06/2.19 tff(16260,plain,
% 2.06/2.19 (~(op(e1, e0) = e3)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[756, 16259])).
% 2.06/2.19 tff(16261,plain,
% 2.06/2.19 (op(e1, e3) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[247, 16260, 75, 16137])).
% 2.06/2.19 tff(16262,plain,
% 2.06/2.19 (op(e1, op(e2, e0)) = op(e2, e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16253, 16261, 16229])).
% 2.06/2.19 tff(16263,plain,
% 2.06/2.19 ((op(e1, op(e2, e0)) = e1) <=> (op(e2, e0) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16262])).
% 2.06/2.19 tff(16264,plain,
% 2.06/2.19 ((op(e2, e0) = e1) <=> (op(e1, op(e2, e0)) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16263])).
% 2.06/2.19 tff(16265,plain,
% 2.06/2.19 ((op(e2, e0) = e1) <=> (op(e1, e3) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16264, 16256])).
% 2.06/2.19 tff(16266,plain,
% 2.06/2.19 ((~(op(e2, e0) = e1)) <=> (~(op(e1, e3) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16265])).
% 2.06/2.19 tff(16267,plain,
% 2.06/2.19 ((e1 = e3) <=> (e1 = op(e2, e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16229])).
% 2.06/2.19 tff(16268,plain,
% 2.06/2.19 ((e1 = e3) <=> (op(e2, e0) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16267, 16])).
% 2.06/2.19 tff(16269,plain,
% 2.06/2.19 ((~(e1 = e3)) <=> (~(op(e2, e0) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16268])).
% 2.06/2.19 tff(16270,plain,
% 2.06/2.19 (~(op(e2, e0) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[303, 16269])).
% 2.06/2.19 tff(16271,plain,
% 2.06/2.19 (~(op(e1, e3) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[16270, 16266])).
% 2.06/2.19 tff(16272,plain,
% 2.06/2.19 ((op(e1, e1) = e1) <=> (e0 = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16061])).
% 2.06/2.19 tff(16273,plain,
% 2.06/2.19 ((e0 = e1) <=> (op(e1, e1) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16272])).
% 2.06/2.19 tff(16274,plain,
% 2.06/2.19 ((~(e0 = e1)) <=> (~(op(e1, e1) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16273])).
% 2.06/2.19 tff(16275,plain,
% 2.06/2.19 (~(op(e1, e1) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[26, 16274])).
% 2.06/2.19 tff(16276,plain,
% 2.06/2.19 (op(e1, e2) = op(e1, op(e0, e3))),
% 2.06/2.19 inference(symmetry,[status(thm)],[16237])).
% 2.06/2.19 tff(16277,plain,
% 2.06/2.19 ((op(e1, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16276])).
% 2.06/2.19 tff(16278,plain,
% 2.06/2.19 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16277])).
% 2.06/2.19 tff(16279,plain,
% 2.06/2.19 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16239, 16278])).
% 2.06/2.19 tff(16280,plain,
% 2.06/2.19 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16279])).
% 2.06/2.19 tff(16281,plain,
% 2.06/2.19 (~(op(e1, e2) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[1273, 16280])).
% 2.06/2.19 tff(16282,plain,
% 2.06/2.19 (op(e1, e0) = e1),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[954, 16281, 16275, 16271])).
% 2.06/2.19 tff(16283,plain,
% 2.06/2.19 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16282])).
% 2.06/2.19 tff(16284,plain,
% 2.06/2.19 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16283])).
% 2.06/2.19 tff(16285,plain,
% 2.06/2.19 (~(op(e0, e0) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[2471, 16284])).
% 2.06/2.19 tff(16286,plain,
% 2.06/2.19 (op(e0, e0) = e0),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[3612, 16285, 16252, 16248])).
% 2.06/2.19 tff(16287,plain,
% 2.06/2.19 ((op(e0, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16286])).
% 2.06/2.19 tff(16288,plain,
% 2.06/2.19 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16287, 10200])).
% 2.06/2.19 tff(16289,plain,
% 2.06/2.19 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16288, 16244])).
% 2.06/2.19 tff(16290,plain,
% 2.06/2.19 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16289])).
% 2.06/2.19 tff(16291,plain,
% 2.06/2.19 (~(op(e0, op(e0, e3)) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[3603, 16290])).
% 2.06/2.19 tff(16292,plain,
% 2.06/2.19 (op(e2, op(e0, e3)) = op(e2, e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16202])).
% 2.06/2.19 tff(16293,plain,
% 2.06/2.19 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16292])).
% 2.06/2.19 tff(16294,plain,
% 2.06/2.19 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16293])).
% 2.06/2.19 tff(16295,plain,
% 2.06/2.19 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, op(e0, e3)) = e2)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16210, 16294])).
% 2.06/2.19 tff(16296,plain,
% 2.06/2.19 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16295])).
% 2.06/2.19 tff(16297,plain,
% 2.06/2.19 (~(op(e2, op(e0, e3)) = e2)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[508, 16296])).
% 2.06/2.19 tff(16298,plain,
% 2.06/2.19 ((e1 = e2) <=> (e1 = op(e0, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.19 tff(16299,plain,
% 2.06/2.19 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16298, 10225])).
% 2.06/2.19 tff(16300,plain,
% 2.06/2.19 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16299])).
% 2.06/2.19 tff(16301,plain,
% 2.06/2.19 (~(op(e0, e3) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[708, 16300])).
% 2.06/2.19 tff(16302,plain,
% 2.06/2.19 ((op(e2, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16197])).
% 2.06/2.19 tff(16303,plain,
% 2.06/2.19 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16302, 3077])).
% 2.06/2.19 tff(16304,plain,
% 2.06/2.19 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16303])).
% 2.06/2.19 tff(16305,plain,
% 2.06/2.19 (~(op(e3, e3) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[368, 16304])).
% 2.06/2.19 tff(16306,plain,
% 2.06/2.19 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.19 tff(16307,plain,
% 2.06/2.19 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16061])).
% 2.06/2.19 tff(16308,plain,
% 2.06/2.19 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16307, 67])).
% 2.06/2.19 tff(16309,plain,
% 2.06/2.19 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16308])).
% 2.06/2.19 tff(16310,plain,
% 2.06/2.19 (~(op(e1, e2) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[1604, 16309])).
% 2.06/2.19 tff(16311,plain,
% 2.06/2.19 (op(e1, e2) = e2),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1859, 16281, 75, 16310])).
% 2.06/2.19 tff(16312,plain,
% 2.06/2.19 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16311])).
% 2.06/2.19 tff(16313,plain,
% 2.06/2.19 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16312, 2234])).
% 2.06/2.19 tff(16314,plain,
% 2.06/2.19 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16313])).
% 2.06/2.19 tff(16315,plain,
% 2.06/2.19 (~(op(e3, e2) = e2)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[2292, 16314])).
% 2.06/2.19 tff(16316,plain,
% 2.06/2.19 (op(e3, e0) = e2),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[15971, 16315, 82])).
% 2.06/2.19 tff(16317,plain,
% 2.06/2.19 (op(e3, e0) = op(e0, e3)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[16316, 16306])).
% 2.06/2.19 tff(16318,plain,
% 2.06/2.19 (op(e3, e2) = op(e3, op(e0, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16203])).
% 2.06/2.19 tff(16319,plain,
% 2.06/2.19 (op(e3, e3) = e1),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[151, 16271, 76, 16301])).
% 2.06/2.19 tff(16320,plain,
% 2.06/2.19 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16319])).
% 2.06/2.19 tff(16321,plain,
% 2.06/2.19 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16320])).
% 2.06/2.19 tff(16322,plain,
% 2.06/2.19 (~(op(e3, e1) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[437, 16321])).
% 2.06/2.19 tff(16323,plain,
% 2.06/2.19 (op(e3, e1) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[446, 16322, 82, 16076])).
% 2.06/2.19 tff(16324,plain,
% 2.06/2.19 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, op(e0, e3)))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16323, 16318])).
% 2.06/2.19 tff(16325,plain,
% 2.06/2.19 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16324, 10461])).
% 2.06/2.19 tff(16326,plain,
% 2.06/2.19 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16325])).
% 2.06/2.19 tff(16327,plain,
% 2.06/2.19 (~(op(e3, op(e0, e3)) = e3)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[3429, 16326])).
% 2.06/2.19 tff(16328,plain,
% 2.06/2.19 ($false),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[3664, 16327, 16317, 16137, 16305, 80, 16223, 16301, 16297, 16291, 16241])).
% 2.06/2.19 tff(16329,plain,((op(e3, e1) = e2) | (op(e1, e3) = e0) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.19 tff(16330,plain,
% 2.06/2.19 (op(e3, e1) = e2),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[16329, 80, 75, 76, 17, 68, 72])).
% 2.06/2.19 tff(16331,plain,
% 2.06/2.19 (op(op(e3, e1), e3) = op(e2, e3)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.19 tff(16332,plain,
% 2.06/2.19 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16331])).
% 2.06/2.19 tff(16333,plain,
% 2.06/2.19 ((op(e2, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16332])).
% 2.06/2.19 tff(16334,plain,
% 2.06/2.19 ((~(op(e2, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16333])).
% 2.06/2.19 tff(16335,plain,
% 2.06/2.19 (~(op(op(e3, e1), e3) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[76, 16334])).
% 2.06/2.19 tff(16336,plain,
% 2.06/2.19 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1050, 16335])).
% 2.06/2.19 tff(16337,plain,
% 2.06/2.19 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16120])).
% 2.06/2.19 tff(16338,plain,
% 2.06/2.19 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16337, 657])).
% 2.06/2.19 tff(16339,plain,
% 2.06/2.19 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16338])).
% 2.06/2.19 tff(16340,plain,
% 2.06/2.19 (~(op(e3, e3) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[1077, 16339])).
% 2.06/2.19 tff(16341,plain,
% 2.06/2.19 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.19 tff(16342,plain,
% 2.06/2.19 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16341, 69])).
% 2.06/2.19 tff(16343,plain,
% 2.06/2.19 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16342])).
% 2.06/2.19 tff(16344,plain,
% 2.06/2.19 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16343])).
% 2.06/2.19 tff(16345,plain,
% 2.06/2.19 (~(op(e3, e1) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[708, 16344])).
% 2.06/2.19 tff(16346,plain,
% 2.06/2.19 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16120])).
% 2.06/2.19 tff(16347,plain,
% 2.06/2.19 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16346, 18])).
% 2.06/2.19 tff(16348,plain,
% 2.06/2.19 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16347])).
% 2.06/2.19 tff(16349,plain,
% 2.06/2.19 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16348])).
% 2.06/2.19 tff(16350,plain,
% 2.06/2.19 (~(op(e0, e3) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[26, 16349])).
% 2.06/2.19 tff(16351,plain,
% 2.06/2.19 (op(e3, e3) = e0),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1098, 16350, 80, 1063])).
% 2.06/2.19 tff(16352,plain,
% 2.06/2.19 (~(op(e3, e0) = e1)),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[8647, 16351, 16330])).
% 2.06/2.19 tff(16353,plain,
% 2.06/2.19 (op(e3, e2) = e1),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[939, 16352, 16345, 16340])).
% 2.06/2.19 tff(16354,plain,
% 2.06/2.19 (e1 = op(e3, e2)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16353])).
% 2.06/2.19 tff(16355,plain,
% 2.06/2.19 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16354])).
% 2.06/2.19 tff(16356,plain,
% 2.06/2.19 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16355])).
% 2.06/2.19 tff(16357,plain,
% 2.06/2.19 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16356])).
% 2.06/2.19 tff(16358,plain,
% 2.06/2.19 (~(op(e1, e2) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[2292, 16357])).
% 2.06/2.19 tff(16359,plain,
% 2.06/2.19 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16351])).
% 2.06/2.19 tff(16360,plain,
% 2.06/2.19 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16359])).
% 2.06/2.19 tff(16361,plain,
% 2.06/2.19 (~(op(e3, e2) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[1888, 16360])).
% 2.06/2.19 tff(16362,plain,
% 2.06/2.19 (op(e1, e1) = e0),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[15965, 16361, 76, 17, 72, 75, 80, 68])).
% 2.06/2.19 tff(16363,plain,
% 2.06/2.19 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16362])).
% 2.06/2.19 tff(16364,plain,
% 2.06/2.19 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16363, 67])).
% 2.06/2.19 tff(16365,plain,
% 2.06/2.19 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16364])).
% 2.06/2.19 tff(16366,plain,
% 2.06/2.19 (~(op(e1, e2) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[1604, 16365])).
% 2.06/2.19 tff(16367,plain,
% 2.06/2.19 (op(e1, e2) = e2),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1859, 16366, 75, 16358])).
% 2.06/2.19 tff(16368,plain,
% 2.06/2.19 (op(op(e3, e2), e2) = op(e1, e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16353])).
% 2.06/2.19 tff(16369,plain,
% 2.06/2.19 (op(e1, op(e1, e2)) = op(op(e3, e2), e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16354, 16367])).
% 2.06/2.19 tff(16370,plain,
% 2.06/2.19 (op(e1, op(e1, e2)) = e2),
% 2.06/2.19 inference(transitivity,[status(thm)],[16369, 16368, 16367])).
% 2.06/2.19 tff(16371,plain,
% 2.06/2.19 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[2377, 16370])).
% 2.06/2.19 tff(16372,plain,
% 2.06/2.19 ((op(e0, e3) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16120])).
% 2.06/2.19 tff(16373,plain,
% 2.06/2.19 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16372, 28])).
% 2.06/2.19 tff(16374,plain,
% 2.06/2.19 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16373])).
% 2.06/2.19 tff(16375,plain,
% 2.06/2.19 (~(op(e1, e3) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[64, 16374])).
% 2.06/2.19 tff(16376,plain,
% 2.06/2.19 (op(e1, e3) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[104, 16375, 72, 80])).
% 2.06/2.19 tff(16377,plain,
% 2.06/2.19 (op(op(e1, e3), e1) = op(e3, e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16376])).
% 2.06/2.19 tff(16378,plain,
% 2.06/2.19 (e3 = op(e1, e3)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16376])).
% 2.06/2.19 tff(16379,plain,
% 2.06/2.19 (op(e3, op(e3, e2)) = op(op(e1, e3), e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16378, 16353])).
% 2.06/2.19 tff(16380,plain,
% 2.06/2.19 (op(e3, op(e3, e2)) = e2),
% 2.06/2.19 inference(transitivity,[status(thm)],[16379, 16377, 16330])).
% 2.06/2.19 tff(16381,plain,
% 2.06/2.19 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1904, 16380])).
% 2.06/2.19 tff(16382,plain,
% 2.06/2.19 (op(op(e0, e3), e0) = op(e1, e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16120])).
% 2.06/2.19 tff(16383,plain,
% 2.06/2.19 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16382])).
% 2.06/2.19 tff(16384,plain,
% 2.06/2.19 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16383])).
% 2.06/2.19 tff(16385,plain,
% 2.06/2.19 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16378])).
% 2.06/2.19 tff(16386,plain,
% 2.06/2.19 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16385])).
% 2.06/2.19 tff(16387,plain,
% 2.06/2.19 ((op(e1, e0) = op(e1, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16386, 16384])).
% 2.06/2.19 tff(16388,plain,
% 2.06/2.19 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16387])).
% 2.06/2.19 tff(16389,plain,
% 2.06/2.19 (~(op(op(e0, e3), e0) = e3)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[110, 16388])).
% 2.06/2.19 tff(16390,plain,
% 2.06/2.19 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[2635, 16389])).
% 2.06/2.19 tff(16391,plain,
% 2.06/2.19 ((op(e1, e1) = e1) <=> (e0 = op(e3, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16362, 16354])).
% 2.06/2.19 tff(16392,plain,
% 2.06/2.19 ((op(e1, e1) = e1) <=> (op(e3, e2) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16391, 4959])).
% 2.06/2.19 tff(16393,plain,
% 2.06/2.19 ((op(e3, e2) = e0) <=> (op(e1, e1) = e1)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16392])).
% 2.06/2.19 tff(16394,plain,
% 2.06/2.19 ((~(op(e3, e2) = e0)) <=> (~(op(e1, e1) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16393])).
% 2.06/2.19 tff(16395,plain,
% 2.06/2.19 (~(op(e1, e1) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[16361, 16394])).
% 2.06/2.19 tff(16396,plain,
% 2.06/2.19 (op(e1, e0) = e1),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[954, 16395, 16358, 16375])).
% 2.06/2.19 tff(16397,plain,
% 2.06/2.19 (op(e1, op(e1, e0)) = op(e1, e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16396])).
% 2.06/2.19 tff(16398,plain,
% 2.06/2.19 (op(e1, op(e1, e0)) = e0),
% 2.06/2.19 inference(transitivity,[status(thm)],[16397, 16362])).
% 2.06/2.19 tff(16399,plain,
% 2.06/2.19 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1836, 16398])).
% 2.06/2.19 tff(16400,plain,
% 2.06/2.19 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16120])).
% 2.06/2.19 tff(16401,plain,
% 2.06/2.19 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16400])).
% 2.06/2.19 tff(16402,plain,
% 2.06/2.19 (~(op(e0, e1) = e1)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[818, 16401])).
% 2.06/2.19 tff(16403,plain,
% 2.06/2.19 (op(e2, e1) = e1),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1252, 16395, 16345, 16402])).
% 2.06/2.19 tff(16404,plain,
% 2.06/2.19 (op(e2, op(e3, e2)) = op(e2, e1)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16353])).
% 2.06/2.19 tff(16405,plain,
% 2.06/2.19 (op(e2, e1) = op(e3, e2)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16403, 16354])).
% 2.06/2.19 tff(16406,plain,
% 2.06/2.19 (op(e2, op(e2, e1)) = op(e2, op(e3, e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16405])).
% 2.06/2.19 tff(16407,plain,
% 2.06/2.19 (op(e2, op(e2, e1)) = e1),
% 2.06/2.19 inference(transitivity,[status(thm)],[16406, 16404, 16403])).
% 2.06/2.19 tff(16408,plain,
% 2.06/2.19 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1355, 16407])).
% 2.06/2.19 tff(16409,plain,
% 2.06/2.19 ($false),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[104, 138, 170, 72, 80])).
% 2.06/2.19 tff(16410,plain,(((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e1, e3) = e2) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.19 tff(16411,plain,
% 2.06/2.19 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[16410, 80, 72])).
% 2.06/2.19 tff(16412,plain,
% 2.06/2.19 (op(op(e2, e3), e3) = op(e2, e3)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16115])).
% 2.06/2.19 tff(16413,plain,
% 2.06/2.19 (op(op(e2, e3), e3) = e2),
% 2.06/2.19 inference(transitivity,[status(thm)],[16412, 16115])).
% 2.06/2.19 tff(16414,plain,
% 2.06/2.19 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1288, 16413])).
% 2.06/2.19 tff(16415,plain,
% 2.06/2.19 (op(e0, e2) = e0),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[973, 16366, 17, 16361])).
% 2.06/2.19 tff(16416,plain,
% 2.06/2.19 (op(op(e0, e2), e2) = op(e0, e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16415])).
% 2.06/2.19 tff(16417,plain,
% 2.06/2.19 (op(op(e0, e2), e2) = e0),
% 2.06/2.19 inference(transitivity,[status(thm)],[16416, 16415])).
% 2.06/2.19 tff(16418,plain,
% 2.06/2.19 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1956, 16417])).
% 2.06/2.19 tff(16419,plain,
% 2.06/2.19 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.19 tff(16420,plain,
% 2.06/2.19 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16419])).
% 2.06/2.19 tff(16421,plain,
% 2.06/2.19 (~(op(e3, e0) = e2)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[580, 16420])).
% 2.06/2.19 tff(16422,plain,
% 2.06/2.19 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16351])).
% 2.06/2.19 tff(16423,plain,
% 2.06/2.19 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16422])).
% 2.06/2.19 tff(16424,plain,
% 2.06/2.19 (~(op(e3, e0) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[157, 16423])).
% 2.06/2.19 tff(16425,plain,
% 2.06/2.19 (op(e3, e0) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[5422, 16424, 16421, 16352])).
% 2.06/2.19 tff(16426,plain,
% 2.06/2.19 (op(e3, op(e3, e0)) = op(e3, e3)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16425])).
% 2.06/2.19 tff(16427,plain,
% 2.06/2.19 (op(e3, op(e3, e0)) = e0),
% 2.06/2.19 inference(transitivity,[status(thm)],[16426, 16351])).
% 2.06/2.19 tff(16428,plain,
% 2.06/2.19 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1345, 16427])).
% 2.06/2.19 tff(16429,plain,
% 2.06/2.19 (op(e0, op(e1, e3)) = op(e0, e3)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16376])).
% 2.06/2.19 tff(16430,plain,
% 2.06/2.19 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.19 tff(16431,plain,
% 2.06/2.19 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16430])).
% 2.06/2.19 tff(16432,plain,
% 2.06/2.19 (~(op(e0, e1) = e2)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[3046, 16431])).
% 2.06/2.19 tff(16433,plain,
% 2.06/2.19 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16362])).
% 2.06/2.19 tff(16434,plain,
% 2.06/2.19 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16433])).
% 2.06/2.19 tff(16435,plain,
% 2.06/2.19 (~(op(e0, e1) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[792, 16434])).
% 2.06/2.19 tff(16436,plain,
% 2.06/2.19 (op(e0, e1) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[829, 16435, 16402, 16432])).
% 2.06/2.19 tff(16437,plain,
% 2.06/2.19 (op(e0, e1) = op(e1, e3)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16436, 16378])).
% 2.06/2.19 tff(16438,plain,
% 2.06/2.19 (op(e0, op(e0, e1)) = op(e0, op(e1, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16437])).
% 2.06/2.19 tff(16439,plain,
% 2.06/2.19 (op(e0, op(e0, e1)) = e1),
% 2.06/2.19 inference(transitivity,[status(thm)],[16438, 16429, 16120])).
% 2.06/2.19 tff(16440,plain,
% 2.06/2.19 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[2449, 16439])).
% 2.06/2.19 tff(16441,plain,
% 2.06/2.19 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16362])).
% 2.06/2.19 tff(16442,plain,
% 2.06/2.19 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16441, 83])).
% 2.06/2.19 tff(16443,plain,
% 2.06/2.19 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16442])).
% 2.06/2.19 tff(16444,plain,
% 2.06/2.19 (~(op(e2, e1) = e0)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[225, 16443])).
% 2.06/2.19 tff(16445,plain,
% 2.06/2.19 (op(e2, e0) = e0),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[2311, 16444, 17, 1063])).
% 2.06/2.19 tff(16446,plain,
% 2.06/2.19 (op(e2, op(e2, e0)) = op(e2, e0)),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16445])).
% 2.06/2.19 tff(16447,plain,
% 2.06/2.19 (op(e2, op(e2, e0)) = e0),
% 2.06/2.19 inference(transitivity,[status(thm)],[16446, 16445])).
% 2.06/2.19 tff(16448,plain,
% 2.06/2.19 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[2653, 16447])).
% 2.06/2.19 tff(16449,plain,
% 2.06/2.19 ($false),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[1459, 16448, 16440, 16428, 16418, 16414, 16411, 16408, 16399, 16390, 16381, 16371, 16336])).
% 2.06/2.19 tff(16450,plain,((op(e0, e3) = e2) | (op(e1, e2) = e3) | (op(e2, e2) = e0) | (op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.19 tff(16451,plain,
% 2.06/2.19 (op(e0, e3) = e2),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[16450, 1063, 17, 75, 76, 72, 80, 68])).
% 2.06/2.19 tff(16452,plain,
% 2.06/2.19 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16451])).
% 2.06/2.19 tff(16453,plain,
% 2.06/2.19 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.06/2.19 inference(transitivity,[status(thm)],[16452, 120])).
% 2.06/2.19 tff(16454,plain,
% 2.06/2.19 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.06/2.19 inference(monotonicity,[status(thm)],[16453])).
% 2.06/2.19 tff(16455,plain,
% 2.06/2.19 (~(op(e2, e3) = e2)),
% 2.06/2.19 inference(modus_ponens,[status(thm)],[964, 16454])).
% 2.06/2.19 tff(16456,plain,
% 2.06/2.19 (op(e2, e3) = e3),
% 2.06/2.19 inference(unit_resolution,[status(thm)],[206, 16455, 76, 1063])).
% 2.06/2.19 tff(16457,plain,
% 2.06/2.19 (e3 = op(e2, e3)),
% 2.06/2.19 inference(symmetry,[status(thm)],[16456])).
% 2.06/2.19 tff(16458,plain,
% 2.06/2.19 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16457])).
% 2.06/2.20 tff(16459,plain,
% 2.06/2.20 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16458])).
% 2.06/2.20 tff(16460,plain,
% 2.06/2.20 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16459])).
% 2.06/2.20 tff(16461,plain,
% 2.06/2.20 (~(op(e1, e3) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[118, 16460])).
% 2.06/2.20 tff(16462,plain,
% 2.06/2.20 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16451])).
% 2.06/2.20 tff(16463,plain,
% 2.06/2.20 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16462, 1])).
% 2.06/2.20 tff(16464,plain,
% 2.06/2.20 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16463])).
% 2.06/2.20 tff(16465,plain,
% 2.06/2.20 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16464])).
% 2.06/2.20 tff(16466,plain,
% 2.06/2.20 (~(op(e0, e3) = e0)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[14, 16465])).
% 2.06/2.20 tff(16467,plain,
% 2.06/2.20 (op(e3, e3) = e0),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[1098, 16466, 80, 1063])).
% 2.06/2.20 tff(16468,plain,
% 2.06/2.20 (~(op(e3, e0) = e1)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[8647, 16467, 16330])).
% 2.06/2.20 tff(16469,plain,
% 2.06/2.20 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16467])).
% 2.06/2.20 tff(16470,plain,
% 2.06/2.20 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16469])).
% 2.06/2.20 tff(16471,plain,
% 2.06/2.20 (~(op(e3, e0) = e0)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[157, 16470])).
% 2.06/2.20 tff(16472,plain,
% 2.06/2.20 (op(e3, e0) = e3),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[5422, 16471, 16421, 16468])).
% 2.06/2.20 tff(16473,plain,
% 2.06/2.20 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16472])).
% 2.06/2.20 tff(16474,plain,
% 2.06/2.20 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16473])).
% 2.06/2.20 tff(16475,plain,
% 2.06/2.20 (~(op(e1, e0) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[410, 16474])).
% 2.06/2.20 tff(16476,plain,
% 2.06/2.20 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16467])).
% 2.06/2.20 tff(16477,plain,
% 2.06/2.20 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16476])).
% 2.06/2.20 tff(16478,plain,
% 2.06/2.20 (~(op(e3, e2) = e0)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[1888, 16477])).
% 2.06/2.20 tff(16479,plain,
% 2.06/2.20 (op(e1, e1) = e0),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[15965, 16478, 76, 17, 72, 75, 80, 68])).
% 2.06/2.20 tff(16480,plain,
% 2.06/2.20 ((op(e1, e1) = e3) <=> (e0 = op(e2, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16479, 16457])).
% 2.06/2.20 tff(16481,plain,
% 2.06/2.20 ((op(e1, e1) = e3) <=> (op(e2, e3) = e0)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16480, 86])).
% 2.06/2.20 tff(16482,plain,
% 2.06/2.20 ((op(e2, e3) = e0) <=> (op(e1, e1) = e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16481])).
% 2.06/2.20 tff(16483,plain,
% 2.06/2.20 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e1) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16482])).
% 2.06/2.20 tff(16484,plain,
% 2.06/2.20 (~(op(e1, e1) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[1063, 16483])).
% 2.06/2.20 tff(16485,plain,
% 2.06/2.20 ($false),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[247, 16484, 16475, 75, 16461])).
% 2.06/2.20 tff(16486,plain,((op(e2, e3) = e0) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.20 tff(16487,plain,
% 2.06/2.20 (op(e2, e3) = e0),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[16486, 80, 76, 17, 72, 75, 68])).
% 2.06/2.20 tff(16488,plain,
% 2.06/2.20 (e0 = op(e2, e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16487])).
% 2.06/2.20 tff(16489,plain,
% 2.06/2.20 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.20 tff(16490,plain,
% 2.06/2.20 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16489, 2234])).
% 2.06/2.20 tff(16491,plain,
% 2.06/2.20 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16490])).
% 2.06/2.20 tff(16492,plain,
% 2.06/2.20 (~(op(e3, e2) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[3429, 16491])).
% 2.06/2.20 tff(16493,plain,
% 2.06/2.20 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16487])).
% 2.06/2.20 tff(16494,plain,
% 2.06/2.20 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16493])).
% 2.06/2.20 tff(16495,plain,
% 2.06/2.20 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16494])).
% 2.06/2.20 tff(16496,plain,
% 2.06/2.20 (~(op(e2, e3) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[14, 16495])).
% 2.06/2.20 tff(16497,plain,
% 2.06/2.20 (op(e0, e3) = e2),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[15003, 16496, 72])).
% 2.06/2.20 tff(16498,plain,
% 2.06/2.20 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16497])).
% 2.06/2.20 tff(16499,plain,
% 2.06/2.20 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16498, 69])).
% 2.06/2.20 tff(16500,plain,
% 2.06/2.20 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16499])).
% 2.06/2.20 tff(16501,plain,
% 2.06/2.20 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16500])).
% 2.06/2.20 tff(16502,plain,
% 2.06/2.20 (~(op(e0, e3) = e1)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[708, 16501])).
% 2.06/2.20 tff(16503,plain,
% 2.06/2.20 (op(e1, e0) = op(e2, e3)),
% 2.06/2.20 inference(transitivity,[status(thm)],[15978, 16488])).
% 2.06/2.20 tff(16504,plain,
% 2.06/2.20 ((op(e1, e0) = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16503])).
% 2.06/2.20 tff(16505,plain,
% 2.06/2.20 ((op(e2, e3) = e3) <=> (op(e1, e0) = e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16504])).
% 2.06/2.20 tff(16506,plain,
% 2.06/2.20 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e0) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16505])).
% 2.06/2.20 tff(16507,plain,
% 2.06/2.20 ((e0 = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16488])).
% 2.06/2.20 tff(16508,plain,
% 2.06/2.20 ((~(e0 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16507])).
% 2.06/2.20 tff(16509,plain,
% 2.06/2.20 (~(op(e2, e3) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[181, 16508])).
% 2.06/2.20 tff(16510,plain,
% 2.06/2.20 (~(op(e1, e0) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16509, 16506])).
% 2.06/2.20 tff(16511,plain,
% 2.06/2.20 (op(e2, op(e2, e3)) = op(e2, e0)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16487])).
% 2.06/2.20 tff(16512,plain,
% 2.06/2.20 (op(e2, e0) = op(e2, op(e2, e3))),
% 2.06/2.20 inference(symmetry,[status(thm)],[16511])).
% 2.06/2.20 tff(16513,plain,
% 2.06/2.20 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16512])).
% 2.06/2.20 tff(16514,plain,
% 2.06/2.20 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e0) = e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16513])).
% 2.06/2.20 tff(16515,plain,
% 2.06/2.20 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16497])).
% 2.06/2.20 tff(16516,plain,
% 2.06/2.20 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16515])).
% 2.06/2.20 tff(16517,plain,
% 2.06/2.20 (~(op(e0, e0) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[3414, 16516])).
% 2.06/2.20 tff(16518,plain,
% 2.06/2.20 ((op(e1, e0) = e2) <=> (op(e2, e3) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16503])).
% 2.06/2.20 tff(16519,plain,
% 2.06/2.20 ((op(e2, e3) = e2) <=> (op(e1, e0) = e2)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16518])).
% 2.06/2.20 tff(16520,plain,
% 2.06/2.20 ((~(op(e2, e3) = e2)) <=> (~(op(e1, e0) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16519])).
% 2.06/2.20 tff(16521,plain,
% 2.06/2.20 (~(op(e1, e0) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16496, 16520])).
% 2.06/2.20 tff(16522,plain,
% 2.06/2.20 (op(e2, e0) = e2),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[589, 16521, 16421, 16517])).
% 2.06/2.20 tff(16523,plain,
% 2.06/2.20 (op(e2, op(e2, e3)) = e2),
% 2.06/2.20 inference(transitivity,[status(thm)],[16511, 16522])).
% 2.06/2.20 tff(16524,plain,
% 2.06/2.20 ((op(e2, op(e2, e3)) = e3) <=> (e2 = e3)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16523])).
% 2.06/2.20 tff(16525,plain,
% 2.06/2.20 ((e2 = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16524])).
% 2.06/2.20 tff(16526,plain,
% 2.06/2.20 ((e2 = e3) <=> (op(e2, e0) = e3)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16525, 16514])).
% 2.06/2.20 tff(16527,plain,
% 2.06/2.20 ((~(e2 = e3)) <=> (~(op(e2, e0) = e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16526])).
% 2.06/2.20 tff(16528,plain,
% 2.06/2.20 (~(op(e2, e0) = e3)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[1321, 16527])).
% 2.06/2.20 tff(16529,plain,
% 2.06/2.20 ((op(e2, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16522])).
% 2.06/2.20 tff(16530,plain,
% 2.06/2.20 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16529, 3491])).
% 2.06/2.20 tff(16531,plain,
% 2.06/2.20 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.06/2.20 inference(symmetry,[status(thm)],[16530])).
% 2.06/2.20 tff(16532,plain,
% 2.06/2.20 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.06/2.20 inference(transitivity,[status(thm)],[16531, 6337])).
% 2.06/2.20 tff(16533,plain,
% 2.06/2.20 ((~(op(e0, e2) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16532])).
% 2.06/2.20 tff(16534,plain,
% 2.06/2.20 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16497])).
% 2.06/2.20 tff(16535,plain,
% 2.06/2.20 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16534])).
% 2.06/2.20 tff(16536,plain,
% 2.06/2.20 (~(op(e0, e2) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[918, 16535])).
% 2.06/2.20 tff(16537,plain,
% 2.06/2.20 (~(op(e0, e2) = op(e2, e0))),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16536, 16533])).
% 2.06/2.20 tff(16538,plain,
% 2.06/2.20 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[6347, 16537])).
% 2.06/2.20 tff(16539,plain,
% 2.06/2.20 (op(e1, e2) = e2),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[2285, 16521, 68, 72])).
% 2.06/2.20 tff(16540,plain,
% 2.06/2.20 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16539])).
% 2.06/2.20 tff(16541,plain,
% 2.06/2.20 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.06/2.20 inference(symmetry,[status(thm)],[16540])).
% 2.06/2.20 tff(16542,plain,
% 2.06/2.20 ((~(op(e2, e1) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16541])).
% 2.06/2.20 tff(16543,plain,
% 2.06/2.20 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.20 tff(16544,plain,
% 2.06/2.20 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16543])).
% 2.06/2.20 tff(16545,plain,
% 2.06/2.20 (~(op(e2, e1) = e2)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[402, 16544])).
% 2.06/2.20 tff(16546,plain,
% 2.06/2.20 (~(op(e2, e1) = op(e1, e2))),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16545, 16542])).
% 2.06/2.20 tff(16547,plain,
% 2.06/2.20 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[557, 16546])).
% 2.06/2.20 tff(16548,plain,
% 2.06/2.20 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16488])).
% 2.06/2.20 tff(16549,plain,
% 2.06/2.20 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16548])).
% 2.06/2.20 tff(16550,plain,
% 2.06/2.20 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16549])).
% 2.06/2.20 tff(16551,plain,
% 2.06/2.20 (~(op(e2, e1) = e0)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[197, 16550])).
% 2.06/2.20 tff(16552,plain,
% 2.06/2.20 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.20 tff(16553,plain,
% 2.06/2.20 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16552, 1])).
% 2.06/2.20 tff(16554,plain,
% 2.06/2.20 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16553])).
% 2.06/2.20 tff(16555,plain,
% 2.06/2.20 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16554])).
% 2.06/2.20 tff(16556,plain,
% 2.06/2.20 (~(op(e3, e1) = e0)),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[14, 16555])).
% 2.06/2.20 tff(16557,plain,
% 2.06/2.20 (op(e0, e1) = e0),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[292, 84, 16556, 16551])).
% 2.06/2.20 tff(16558,plain,
% 2.06/2.20 (op(e0, e1) = op(e2, e3)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16557, 16488])).
% 2.06/2.20 tff(16559,plain,
% 2.06/2.20 (op(e2, op(e0, e1)) = op(e2, op(e2, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16558])).
% 2.06/2.20 tff(16560,plain,
% 2.06/2.20 ((op(e2, op(e0, e1)) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16559])).
% 2.06/2.20 tff(16561,plain,
% 2.06/2.20 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, op(e0, e1)) = e2)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16560])).
% 2.06/2.20 tff(16562,plain,
% 2.06/2.20 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16512])).
% 2.06/2.20 tff(16563,plain,
% 2.06/2.20 ((op(e2, e0) = e2) <=> (op(e2, op(e0, e1)) = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16562, 16561])).
% 2.06/2.20 tff(16564,plain,
% 2.06/2.20 (op(e2, op(e0, e1)) = e2),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16522, 16563])).
% 2.06/2.20 tff(16565,plain,
% 2.06/2.20 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[9902, 16564])).
% 2.06/2.20 tff(16566,plain,
% 2.06/2.20 (op(e2, op(e1, e0)) = op(e2, op(e2, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16503])).
% 2.06/2.20 tff(16567,plain,
% 2.06/2.20 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16566])).
% 2.06/2.20 tff(16568,plain,
% 2.06/2.20 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.06/2.20 inference(symmetry,[status(thm)],[16567])).
% 2.06/2.20 tff(16569,plain,
% 2.06/2.20 ((op(e2, e0) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16562, 16568])).
% 2.06/2.20 tff(16570,plain,
% 2.06/2.20 (op(e2, op(e1, e0)) = e2),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16522, 16569])).
% 2.06/2.20 tff(16571,plain,
% 2.06/2.20 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[10735, 16570])).
% 2.06/2.20 tff(16572,plain,
% 2.06/2.20 (op(e2, op(e2, e3)) = e2),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16522, 16562])).
% 2.06/2.20 tff(16573,plain,
% 2.06/2.20 (((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)) | (~(op(e2, op(e2, e3)) = e2))),
% 2.06/2.20 inference(tautology,[status(thm)],[])).
% 2.06/2.20 tff(16574,plain,
% 2.06/2.20 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[16573, 16572])).
% 2.06/2.20 tff(16575,plain,
% 2.06/2.20 ((op(e2, e1) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.06/2.20 inference(transitivity,[status(thm)],[16541, 531])).
% 2.06/2.20 tff(16576,plain,
% 2.06/2.20 ((~(op(e2, e1) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16575])).
% 2.06/2.20 tff(16577,plain,
% 2.06/2.20 (~(op(e1, e2) = op(e2, e1))),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16545, 16576])).
% 2.06/2.20 tff(16578,plain,
% 2.06/2.20 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[539, 16577])).
% 2.06/2.20 tff(16579,plain,
% 2.06/2.20 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16330])).
% 2.06/2.20 tff(16580,plain,
% 2.06/2.20 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.06/2.20 inference(transitivity,[status(thm)],[16579, 66])).
% 2.06/2.20 tff(16581,plain,
% 2.06/2.20 ((op(e1, e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.06/2.20 inference(symmetry,[status(thm)],[16580])).
% 2.06/2.20 tff(16582,plain,
% 2.06/2.20 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16581])).
% 2.06/2.20 tff(16583,plain,
% 2.06/2.20 (~(op(e3, e1) = op(e1, e3))),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[72, 16582])).
% 2.06/2.20 tff(16584,plain,
% 2.06/2.20 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[6362, 16583])).
% 2.06/2.20 tff(16585,plain,
% 2.06/2.20 ((~(op(e0, e2) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16531])).
% 2.06/2.20 tff(16586,plain,
% 2.06/2.20 (~(op(e2, e0) = op(e0, e2))),
% 2.06/2.20 inference(modus_ponens,[status(thm)],[16536, 16585])).
% 2.06/2.20 tff(16587,plain,
% 2.06/2.20 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.06/2.20 inference(unit_resolution,[status(thm)],[6358, 16586])).
% 2.06/2.20 tff(16588,plain,
% 2.06/2.20 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.06/2.20 inference(monotonicity,[status(thm)],[16497])).
% 2.06/2.20 tff(16589,plain,
% 2.06/2.20 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.20 inference(symmetry,[status(thm)],[16588])).
% 2.06/2.20 tff(16590,plain,
% 2.06/2.20 ((op(e3, e0) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.06/2.20 inference(transitivity,[status(thm)],[16589, 453])).
% 2.06/2.21 tff(16591,plain,
% 2.06/2.21 ((~(op(e3, e0) = e2)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16590])).
% 2.06/2.21 tff(16592,plain,
% 2.06/2.21 (~(op(e0, e3) = op(e3, e0))),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[16421, 16591])).
% 2.06/2.21 tff(16593,plain,
% 2.06/2.21 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[496, 16592])).
% 2.06/2.21 tff(16594,plain,
% 2.06/2.21 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.06/2.21 inference(transitivity,[status(thm)],[16581, 6290])).
% 2.06/2.21 tff(16595,plain,
% 2.06/2.21 ((~(op(e1, e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16594])).
% 2.06/2.21 tff(16596,plain,
% 2.06/2.21 (~(op(e1, e3) = op(e3, e1))),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[72, 16595])).
% 2.06/2.21 tff(16597,plain,
% 2.06/2.21 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[6307, 16596])).
% 2.06/2.21 tff(16598,plain,
% 2.06/2.21 (op(e3, e2) = op(e2, e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[15966, 16488])).
% 2.06/2.21 tff(16599,plain,
% 2.06/2.21 (op(e2, op(e3, e2)) = op(e2, op(e2, e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16598])).
% 2.06/2.21 tff(16600,plain,
% 2.06/2.21 ((op(e2, op(e3, e2)) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16599])).
% 2.06/2.21 tff(16601,plain,
% 2.06/2.21 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, op(e3, e2)) = e2)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16600])).
% 2.06/2.21 tff(16602,plain,
% 2.06/2.21 ((op(e2, e0) = e2) <=> (op(e2, op(e3, e2)) = e2)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16562, 16601])).
% 2.06/2.21 tff(16603,plain,
% 2.06/2.21 (op(e2, op(e3, e2)) = e2),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[16522, 16602])).
% 2.06/2.21 tff(16604,plain,
% 2.06/2.21 (((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)) | (~(op(e2, op(e3, e2)) = e2))),
% 2.06/2.21 inference(tautology,[status(thm)],[])).
% 2.06/2.21 tff(16605,plain,
% 2.06/2.21 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[16604, 16603])).
% 2.06/2.21 tff(16606,plain,
% 2.06/2.21 (op(e1, e1) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[247, 1080, 75, 2168])).
% 2.06/2.21 tff(16607,plain,
% 2.06/2.21 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16606])).
% 2.06/2.21 tff(16608,plain,
% 2.06/2.21 (op(e1, op(e1, e1)) = e1),
% 2.06/2.21 inference(transitivity,[status(thm)],[16607, 3699])).
% 2.06/2.21 tff(16609,plain,
% 2.06/2.21 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[5678, 16608])).
% 2.06/2.21 tff(16610,plain,
% 2.06/2.21 (op(e0, e3) = e2),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[15003, 5019, 72])).
% 2.06/2.21 tff(16611,plain,
% 2.06/2.21 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.21 tff(16612,plain,
% 2.06/2.21 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16611])).
% 2.06/2.21 tff(16613,plain,
% 2.06/2.21 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16612])).
% 2.06/2.21 tff(16614,plain,
% 2.06/2.21 (~(op(e0, e3) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[1321, 16613])).
% 2.06/2.21 tff(16615,plain,
% 2.06/2.21 ((e0 = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[252])).
% 2.06/2.21 tff(16616,plain,
% 2.06/2.21 ((~(e0 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16615])).
% 2.06/2.21 tff(16617,plain,
% 2.06/2.21 (~(op(e2, e3) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[181, 16616])).
% 2.06/2.21 tff(16618,plain,
% 2.06/2.21 (op(e3, e3) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[480, 1080, 16617, 16614])).
% 2.06/2.21 tff(16619,plain,
% 2.06/2.21 (op(e1, op(e3, e3)) = op(e1, e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16618])).
% 2.06/2.21 tff(16620,plain,
% 2.06/2.21 (op(e1, op(e3, e3)) = e1),
% 2.06/2.21 inference(transitivity,[status(thm)],[16619, 3699])).
% 2.06/2.21 tff(16621,plain,
% 2.06/2.21 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[5685, 16620])).
% 2.06/2.21 tff(16622,plain,
% 2.06/2.21 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, op(e2, e3)) = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[12148, 16618])).
% 2.06/2.21 tff(16623,plain,
% 2.06/2.21 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16622, 12150])).
% 2.06/2.21 tff(16624,plain,
% 2.06/2.21 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16623])).
% 2.06/2.21 tff(16625,plain,
% 2.06/2.21 (~(op(e3, e0) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[157, 16624])).
% 2.06/2.21 tff(16626,plain,
% 2.06/2.21 (op(e0, e0) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[2713, 16625, 2168, 3272])).
% 2.06/2.21 tff(16627,plain,
% 2.06/2.21 (op(e1, op(e0, e0)) = op(e1, e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16626])).
% 2.06/2.21 tff(16628,plain,
% 2.06/2.21 (op(e1, op(e0, e0)) = e1),
% 2.06/2.21 inference(transitivity,[status(thm)],[16627, 3699])).
% 2.06/2.21 tff(16629,plain,
% 2.06/2.21 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[6717, 16628])).
% 2.06/2.21 tff(16630,plain,
% 2.06/2.21 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16606])).
% 2.06/2.21 tff(16631,plain,
% 2.06/2.21 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16630, 1262])).
% 2.06/2.21 tff(16632,plain,
% 2.06/2.21 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16631])).
% 2.06/2.21 tff(16633,plain,
% 2.06/2.21 (~(op(e2, e1) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[225, 16632])).
% 2.06/2.21 tff(16634,plain,
% 2.06/2.21 (op(e2, e2) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[1559, 16633, 16617, 3272])).
% 2.06/2.21 tff(16635,plain,
% 2.06/2.21 (op(e1, op(e2, e2)) = op(e1, e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16634])).
% 2.06/2.21 tff(16636,plain,
% 2.06/2.21 (op(e1, op(e2, e2)) = e1),
% 2.06/2.21 inference(transitivity,[status(thm)],[16635, 3699])).
% 2.06/2.21 tff(16637,plain,
% 2.06/2.21 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[6714, 16636])).
% 2.06/2.21 tff(16638,plain,
% 2.06/2.21 ($false),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[5367, 16637, 16629, 5669, 5668, 5670, 5674, 16621, 5511, 16609, 5673, 5671, 5681, 5675, 5680, 9846])).
% 2.06/2.21 tff(16639,plain,((op(e1, e3) = e3) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (op(e2, e0) = e3) | (op(e1, e0) = e3) | (~(op(e2, e3) = e0)) | (op(e1, e2) = e3) | (op(e1, e3) = e2) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.21 tff(16640,plain,
% 2.06/2.21 (op(e1, e3) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[16639, 16605, 16597, 16593, 16587, 16584, 16578, 16574, 16571, 16565, 16547, 16538, 16528, 16510, 16487, 75, 72, 80])).
% 2.06/2.21 tff(16641,plain,
% 2.06/2.21 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16640])).
% 2.06/2.21 tff(16642,plain,
% 2.06/2.21 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16641, 128])).
% 2.06/2.21 tff(16643,plain,
% 2.06/2.21 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16642])).
% 2.06/2.21 tff(16644,plain,
% 2.06/2.21 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16643])).
% 2.06/2.21 tff(16645,plain,
% 2.06/2.21 (~(op(e1, e3) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[303, 16644])).
% 2.06/2.21 tff(16646,plain,
% 2.06/2.21 (op(e3, e3) = e1),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[151, 16645, 76, 16502])).
% 2.06/2.21 tff(16647,plain,
% 2.06/2.21 (e1 = op(e3, e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[16646, 658])).
% 2.06/2.21 tff(16648,plain,
% 2.06/2.21 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16646])).
% 2.06/2.21 tff(16649,plain,
% 2.06/2.21 (op(e3, e1) = op(e3, op(e3, e3))),
% 2.06/2.21 inference(symmetry,[status(thm)],[16648])).
% 2.06/2.21 tff(16650,plain,
% 2.06/2.21 (e2 = op(e3, e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16330])).
% 2.06/2.21 tff(16651,plain,
% 2.06/2.21 (e2 = op(e3, op(e3, e3))),
% 2.06/2.21 inference(transitivity,[status(thm)],[16650, 16649])).
% 2.06/2.21 tff(16652,plain,
% 2.06/2.21 (op(e3, op(e3, e3)) = e2),
% 2.06/2.21 inference(transitivity,[status(thm)],[16648, 16330])).
% 2.06/2.21 tff(16653,plain,
% 2.06/2.21 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16652])).
% 2.06/2.21 tff(16654,plain,
% 2.06/2.21 (op(e3, e2) = op(e3, op(e3, op(e3, e3)))),
% 2.06/2.21 inference(symmetry,[status(thm)],[16653])).
% 2.06/2.21 tff(16655,plain,
% 2.06/2.21 (e0 = op(e3, e2)),
% 2.06/2.21 inference(symmetry,[status(thm)],[15966])).
% 2.06/2.21 tff(16656,plain,
% 2.06/2.21 (e0 = op(e3, op(e3, op(e3, e3)))),
% 2.06/2.21 inference(transitivity,[status(thm)],[16655, 16654])).
% 2.06/2.21 tff(16657,plain,
% 2.06/2.21 ($false),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[2034, 16656, 16651, 16647])).
% 2.06/2.21 tff(16658,plain,((op(e1, e1) = e0) | (op(e2, e3) = e1) | (op(e1, e2) = e3) | (op(e1, e3) = e2) | (op(e1, e3) = e0) | (op(e1, e1) = e2) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.21 tff(16659,plain,
% 2.06/2.21 (op(e1, e1) = e0),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[16658, 80, 75, 72, 76, 68, 17])).
% 2.06/2.21 tff(16660,plain,
% 2.06/2.21 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16618])).
% 2.06/2.21 tff(16661,plain,
% 2.06/2.21 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16660])).
% 2.06/2.21 tff(16662,plain,
% 2.06/2.21 (~(op(e3, e2) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[1888, 16661])).
% 2.06/2.21 tff(16663,plain,
% 2.06/2.21 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[11829])).
% 2.06/2.21 tff(16664,plain,
% 2.06/2.21 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e0) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16663])).
% 2.06/2.21 tff(16665,plain,
% 2.06/2.21 ((op(e1, e1) = e3) <=> (op(e2, e3) = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[253])).
% 2.06/2.21 tff(16666,plain,
% 2.06/2.21 ((op(e2, e3) = e3) <=> (op(e1, e1) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16665])).
% 2.06/2.21 tff(16667,plain,
% 2.06/2.21 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e1) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16666])).
% 2.06/2.21 tff(16668,plain,
% 2.06/2.21 (~(op(e1, e1) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[16617, 16667])).
% 2.06/2.21 tff(16669,plain,
% 2.06/2.21 (op(e1, e0) = e3),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[247, 1080, 75, 16668])).
% 2.06/2.21 tff(16670,plain,
% 2.06/2.21 (e3 = op(e1, e0)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16669])).
% 2.06/2.21 tff(16671,plain,
% 2.06/2.21 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[11212, 16670])).
% 2.06/2.21 tff(16672,plain,
% 2.06/2.21 ((op(e2, op(e2, e3)) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 2.06/2.21 inference(transitivity,[status(thm)],[16671, 749])).
% 2.06/2.21 tff(16673,plain,
% 2.06/2.21 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, op(e2, e3)) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16672])).
% 2.06/2.21 tff(16674,plain,
% 2.06/2.21 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16673, 16664])).
% 2.06/2.21 tff(16675,plain,
% 2.06/2.21 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16674])).
% 2.06/2.21 tff(16676,plain,
% 2.06/2.21 (~(op(e2, e0) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[756, 16675])).
% 2.06/2.21 tff(16677,plain,
% 2.06/2.21 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[3699])).
% 2.06/2.21 tff(16678,plain,
% 2.06/2.21 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16677])).
% 2.06/2.21 tff(16679,plain,
% 2.06/2.21 (~(op(e1, e2) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[1850, 16678])).
% 2.06/2.21 tff(16680,plain,
% 2.06/2.21 (op(e1, e2) = e2),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[1859, 16679, 75, 13143])).
% 2.06/2.21 tff(16681,plain,
% 2.06/2.21 (op(e1, op(e1, e2)) = op(e1, e2)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16680])).
% 2.06/2.21 tff(16682,plain,
% 2.06/2.21 (op(e1, op(e1, e2)) = e2),
% 2.06/2.21 inference(transitivity,[status(thm)],[16681, 16680])).
% 2.06/2.21 tff(16683,plain,
% 2.06/2.21 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[2377, 16682])).
% 2.06/2.21 tff(16684,plain,
% 2.06/2.21 (op(op(e1, e0), e1) = op(e3, e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16669])).
% 2.06/2.21 tff(16685,plain,
% 2.06/2.21 (op(op(e1, e0), e1) = e2),
% 2.06/2.21 inference(transitivity,[status(thm)],[16684, 6684])).
% 2.06/2.21 tff(16686,plain,
% 2.06/2.21 ((op(op(e1, e0), e1) = e0) <=> (e2 = op(e2, e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16685, 252])).
% 2.06/2.21 tff(16687,plain,
% 2.06/2.21 ((op(op(e1, e0), e1) = e0) <=> (op(e2, e3) = e2)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16686, 120])).
% 2.06/2.21 tff(16688,plain,
% 2.06/2.21 ((op(e2, e3) = e2) <=> (op(op(e1, e0), e1) = e0)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16687])).
% 2.06/2.21 tff(16689,plain,
% 2.06/2.21 ((~(op(e2, e3) = e2)) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16688])).
% 2.06/2.21 tff(16690,plain,
% 2.06/2.21 (~(op(op(e1, e0), e1) = e0)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[5019, 16689])).
% 2.06/2.21 tff(16691,plain,
% 2.06/2.21 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[1302, 16690])).
% 2.06/2.21 tff(16692,plain,
% 2.06/2.21 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[3699])).
% 2.06/2.21 tff(16693,plain,
% 2.06/2.21 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16692, 657])).
% 2.06/2.21 tff(16694,plain,
% 2.06/2.21 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16693])).
% 2.06/2.21 tff(16695,plain,
% 2.06/2.21 (~(op(e3, e3) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[571, 16694])).
% 2.06/2.21 tff(16696,plain,
% 2.06/2.21 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[6684])).
% 2.06/2.21 tff(16697,plain,
% 2.06/2.21 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16696, 69])).
% 2.06/2.21 tff(16698,plain,
% 2.06/2.21 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16697])).
% 2.06/2.21 tff(16699,plain,
% 2.06/2.21 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16698])).
% 2.06/2.21 tff(16700,plain,
% 2.06/2.21 (~(op(e3, e1) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[708, 16699])).
% 2.06/2.21 tff(16701,plain,
% 2.06/2.21 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.21 tff(16702,plain,
% 2.06/2.21 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16701])).
% 2.06/2.21 tff(16703,plain,
% 2.06/2.21 (~(op(e0, e0) = e2)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[3414, 16702])).
% 2.06/2.21 tff(16704,plain,
% 2.06/2.21 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16669])).
% 2.06/2.21 tff(16705,plain,
% 2.06/2.21 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16704, 1314])).
% 2.06/2.21 tff(16706,plain,
% 2.06/2.21 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16705])).
% 2.06/2.21 tff(16707,plain,
% 2.06/2.21 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16706])).
% 2.06/2.21 tff(16708,plain,
% 2.06/2.21 (~(op(e1, e0) = e2)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[1321, 16707])).
% 2.06/2.21 tff(16709,plain,
% 2.06/2.21 (op(e2, e0) = e2),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[589, 16708, 6692, 16703])).
% 2.06/2.21 tff(16710,plain,
% 2.06/2.21 ((op(e2, e0) = e1) <=> (e2 = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16709])).
% 2.06/2.21 tff(16711,plain,
% 2.06/2.21 ((op(e2, e0) = e1) <=> (e1 = e2)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16710, 69])).
% 2.06/2.21 tff(16712,plain,
% 2.06/2.21 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16711])).
% 2.06/2.21 tff(16713,plain,
% 2.06/2.21 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16712])).
% 2.06/2.21 tff(16714,plain,
% 2.06/2.21 (~(op(e2, e0) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[708, 16713])).
% 2.06/2.21 tff(16715,plain,
% 2.06/2.21 (op(e1, e0) = op(e1, op(e2, e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[252])).
% 2.06/2.21 tff(16716,plain,
% 2.06/2.21 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16715])).
% 2.06/2.21 tff(16717,plain,
% 2.06/2.21 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16716])).
% 2.06/2.21 tff(16718,plain,
% 2.06/2.21 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, op(e2, e3)) = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16715, 3699])).
% 2.06/2.21 tff(16719,plain,
% 2.06/2.21 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16718, 16717])).
% 2.06/2.21 tff(16720,plain,
% 2.06/2.21 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16719])).
% 2.06/2.21 tff(16721,plain,
% 2.06/2.21 (~(op(e1, e0) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[110, 16720])).
% 2.06/2.21 tff(16722,plain,
% 2.06/2.21 ((op(e3, e3) = e0) <=> (op(e3, e3) = op(e2, e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[252])).
% 2.06/2.21 tff(16723,plain,
% 2.06/2.21 ((op(e3, e3) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 2.06/2.21 inference(transitivity,[status(thm)],[16722, 2820])).
% 2.06/2.21 tff(16724,plain,
% 2.06/2.21 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16723])).
% 2.06/2.21 tff(16725,plain,
% 2.06/2.21 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16724])).
% 2.06/2.21 tff(16726,plain,
% 2.06/2.21 (~(op(e3, e3) = e0)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[368, 16725])).
% 2.06/2.21 tff(16727,plain,
% 2.06/2.21 (op(e3, e0) = e0),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[1916, 85, 16726, 183])).
% 2.06/2.21 tff(16728,plain,
% 2.06/2.21 (op(e3, e0) = op(e2, e3)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16727, 252])).
% 2.06/2.21 tff(16729,plain,
% 2.06/2.21 ((op(e3, e0) = e1) <=> (op(e2, e3) = e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16728])).
% 2.06/2.21 tff(16730,plain,
% 2.06/2.21 ((op(e2, e3) = e1) <=> (op(e3, e0) = e1)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16729])).
% 2.06/2.21 tff(16731,plain,
% 2.06/2.21 ((~(op(e2, e3) = e1)) <=> (~(op(e3, e0) = e1))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16730])).
% 2.06/2.21 tff(16732,plain,
% 2.06/2.21 (~(op(e3, e0) = e1)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[76, 16731])).
% 2.06/2.21 tff(16733,plain,
% 2.06/2.21 (op(e0, e0) = e1),
% 2.06/2.21 inference(unit_resolution,[status(thm)],[1480, 16732, 929, 1349])).
% 2.06/2.21 tff(16734,plain,
% 2.06/2.21 (e1 = op(e0, e0)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[16733, 74])).
% 2.06/2.21 tff(16735,plain,
% 2.06/2.21 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16733])).
% 2.06/2.21 tff(16736,plain,
% 2.06/2.21 (op(e0, e1) = op(e0, op(e0, e0))),
% 2.06/2.21 inference(symmetry,[status(thm)],[16735])).
% 2.06/2.21 tff(16737,plain,
% 2.06/2.21 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.06/2.21 inference(monotonicity,[status(thm)],[2])).
% 2.06/2.21 tff(16738,plain,
% 2.06/2.21 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16737])).
% 2.06/2.21 tff(16739,plain,
% 2.06/2.21 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16738])).
% 2.06/2.21 tff(16740,plain,
% 2.06/2.21 (~(op(e0, e3) = e3)),
% 2.06/2.21 inference(modus_ponens,[status(thm)],[1321, 16739])).
% 2.06/2.21 tff(16741,plain,
% 2.06/2.21 ((e0 = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 2.06/2.21 inference(commutativity,[status(thm)],[])).
% 2.06/2.21 tff(16742,plain,
% 2.06/2.21 ((op(e0, e2) = e3) <=> (e0 = op(e1, e0))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[10155, 259])).
% 2.06/2.21 tff(16743,plain,
% 2.06/2.21 ((op(e0, e2) = e3) <=> (op(e1, e0) = e0)),
% 2.06/2.21 inference(transitivity,[status(thm)],[16742, 16741])).
% 2.06/2.21 tff(16744,plain,
% 2.06/2.21 ((op(e1, e0) = e0) <=> (op(e0, e2) = e3)),
% 2.06/2.21 inference(symmetry,[status(thm)],[16743])).
% 2.06/2.21 tff(16745,plain,
% 2.06/2.21 ((~(op(e1, e0) = e0)) <=> (~(op(e0, e2) = e3))),
% 2.06/2.21 inference(monotonicity,[status(thm)],[16744])).
% 2.06/2.22 tff(16746,plain,
% 2.06/2.22 (~(op(e0, e2) = e3)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[2167, 16745])).
% 2.06/2.22 tff(16747,plain,
% 2.06/2.22 (op(e0, e1) = e3),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1495, 16746, 11542, 16740])).
% 2.06/2.22 tff(16748,plain,
% 2.06/2.22 (e3 = op(e0, e1)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16747])).
% 2.06/2.22 tff(16749,plain,
% 2.06/2.22 (e3 = op(e0, op(e0, e0))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16748, 16736])).
% 2.06/2.22 tff(16750,plain,
% 2.06/2.22 (op(e0, op(e0, e0)) = op(e1, e0)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16735, 16747, 259])).
% 2.06/2.22 tff(16751,plain,
% 2.06/2.22 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e0))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16750])).
% 2.06/2.22 tff(16752,plain,
% 2.06/2.22 (op(e0, op(e1, e0)) = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.22 inference(symmetry,[status(thm)],[16751])).
% 2.06/2.22 tff(16753,plain,
% 2.06/2.22 (op(e0, op(e1, e0)) = op(op(e2, e3), e3)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[252, 258])).
% 2.06/2.22 tff(16754,plain,
% 2.06/2.22 (op(op(e2, e3), e3) = op(e0, op(e1, e0))),
% 2.06/2.22 inference(symmetry,[status(thm)],[16753])).
% 2.06/2.22 tff(16755,plain,
% 2.06/2.22 (op(e0, e3) = op(op(e2, e3), e3)),
% 2.06/2.22 inference(symmetry,[status(thm)],[10444])).
% 2.06/2.22 tff(16756,plain,
% 2.06/2.22 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.22 inference(transitivity,[status(thm)],[2560, 16755, 16754, 16752])).
% 2.06/2.22 tff(16757,plain,
% 2.06/2.22 ($false),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[16194, 16756, 16749, 16734])).
% 2.06/2.22 tff(16758,plain,((op(e3, e2) = e0) | (~(op(e0, e3) = e2)) | (~(op(e1, e0) = e3)) | (~(op(e2, e3) = e0)) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e1, e0) = e0) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e2) = e0) | (op(e3, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.22 tff(16759,plain,
% 2.06/2.22 (op(e3, e2) = e0),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[16758, 16669, 16610, 251, 16721, 16714, 13237, 76, 17, 13143, 8495])).
% 2.06/2.22 tff(16760,plain,
% 2.06/2.22 (op(e3, e2) = op(e2, e3)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16759, 252])).
% 2.06/2.22 tff(16761,plain,
% 2.06/2.22 ((op(e3, e2) = e1) <=> (op(e2, e3) = e1)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16760])).
% 2.06/2.22 tff(16762,plain,
% 2.06/2.22 ((op(e2, e3) = e1) <=> (op(e3, e2) = e1)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16761])).
% 2.06/2.22 tff(16763,plain,
% 2.06/2.22 ((~(op(e2, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16762])).
% 2.06/2.22 tff(16764,plain,
% 2.06/2.22 (~(op(e3, e2) = e1)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[76, 16763])).
% 2.06/2.22 tff(16765,plain,
% 2.06/2.22 (op(e3, e0) = e1),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[939, 16764, 16700, 16695])).
% 2.06/2.22 tff(16766,plain,
% 2.06/2.22 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16765])).
% 2.06/2.22 tff(16767,plain,
% 2.06/2.22 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16766])).
% 2.06/2.22 tff(16768,plain,
% 2.06/2.22 (~(op(e0, e0) = e1)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[6384, 16767])).
% 2.06/2.22 tff(16769,plain,
% 2.06/2.22 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.22 tff(16770,plain,
% 2.06/2.22 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16769, 69])).
% 2.06/2.22 tff(16771,plain,
% 2.06/2.22 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16770])).
% 2.06/2.22 tff(16772,plain,
% 2.06/2.22 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16771])).
% 2.06/2.22 tff(16773,plain,
% 2.06/2.22 (~(op(e0, e3) = e1)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[708, 16772])).
% 2.06/2.22 tff(16774,plain,
% 2.06/2.22 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16755])).
% 2.06/2.22 tff(16775,plain,
% 2.06/2.22 (op(op(e2, e3), e3) = e2),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16610, 16774])).
% 2.06/2.22 tff(16776,plain,
% 2.06/2.22 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1288, 16775])).
% 2.06/2.22 tff(16777,plain,
% 2.06/2.22 (op(op(e3, e1), e3) = op(e2, e3)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[6684])).
% 2.06/2.22 tff(16778,plain,
% 2.06/2.22 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16777])).
% 2.06/2.22 tff(16779,plain,
% 2.06/2.22 ((op(e2, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16778])).
% 2.06/2.22 tff(16780,plain,
% 2.06/2.22 ((~(op(e2, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16779])).
% 2.06/2.22 tff(16781,plain,
% 2.06/2.22 (~(op(op(e3, e1), e3) = e1)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[76, 16780])).
% 2.06/2.22 tff(16782,plain,
% 2.06/2.22 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1050, 16781])).
% 2.06/2.22 tff(16783,plain,
% 2.06/2.22 (op(e1, op(e2, e3)) = op(e1, e0)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16715])).
% 2.06/2.22 tff(16784,plain,
% 2.06/2.22 (op(op(e3, e0), e0) = op(e1, op(e2, e3))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16765, 252])).
% 2.06/2.22 tff(16785,plain,
% 2.06/2.22 (op(op(e3, e0), e0) = e3),
% 2.06/2.22 inference(transitivity,[status(thm)],[16784, 16783, 16669])).
% 2.06/2.22 tff(16786,plain,
% 2.06/2.22 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[4026, 16785])).
% 2.06/2.22 tff(16787,plain,
% 2.06/2.22 (op(op(e2, e0), e0) = op(e2, op(e2, e3))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16709, 252])).
% 2.06/2.22 tff(16788,plain,
% 2.06/2.22 (op(op(e2, e0), e0) = e2),
% 2.06/2.22 inference(transitivity,[status(thm)],[16787, 11212, 16709])).
% 2.06/2.22 tff(16789,plain,
% 2.06/2.22 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1945, 16788])).
% 2.06/2.22 tff(16790,plain,
% 2.06/2.22 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.22 tff(16791,plain,
% 2.06/2.22 (op(op(e0, e3), e3) = e0),
% 2.06/2.22 inference(transitivity,[status(thm)],[16790, 251])).
% 2.06/2.22 tff(16792,plain,
% 2.06/2.22 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1361, 16791])).
% 2.06/2.22 tff(16793,plain,
% 2.06/2.22 ((op(e2, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16709])).
% 2.06/2.22 tff(16794,plain,
% 2.06/2.22 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16793, 3491])).
% 2.06/2.22 tff(16795,plain,
% 2.06/2.22 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.06/2.22 inference(symmetry,[status(thm)],[16794])).
% 2.06/2.22 tff(16796,plain,
% 2.06/2.22 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16795, 6337])).
% 2.06/2.22 tff(16797,plain,
% 2.06/2.22 ((~(op(e0, e2) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16796])).
% 2.06/2.22 tff(16798,plain,
% 2.06/2.22 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.22 tff(16799,plain,
% 2.06/2.22 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16798])).
% 2.06/2.22 tff(16800,plain,
% 2.06/2.22 (~(op(e0, e2) = e2)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[918, 16799])).
% 2.06/2.22 tff(16801,plain,
% 2.06/2.22 (~(op(e0, e2) = op(e2, e0))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16800, 16797])).
% 2.06/2.22 tff(16802,plain,
% 2.06/2.22 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[6347, 16801])).
% 2.06/2.22 tff(16803,plain,
% 2.06/2.22 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16680])).
% 2.06/2.22 tff(16804,plain,
% 2.06/2.22 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.06/2.22 inference(symmetry,[status(thm)],[16803])).
% 2.06/2.22 tff(16805,plain,
% 2.06/2.22 ((~(op(e2, e1) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16804])).
% 2.06/2.22 tff(16806,plain,
% 2.06/2.22 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[6684])).
% 2.06/2.22 tff(16807,plain,
% 2.06/2.22 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16806])).
% 2.06/2.22 tff(16808,plain,
% 2.06/2.22 (~(op(e2, e1) = e2)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[402, 16807])).
% 2.06/2.22 tff(16809,plain,
% 2.06/2.22 (~(op(e2, e1) = op(e1, e2))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16808, 16805])).
% 2.06/2.22 tff(16810,plain,
% 2.06/2.22 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[557, 16809])).
% 2.06/2.22 tff(16811,plain,
% 2.06/2.22 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16759])).
% 2.06/2.22 tff(16812,plain,
% 2.06/2.22 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16811])).
% 2.06/2.22 tff(16813,plain,
% 2.06/2.22 (~(op(e0, e2) = e0)),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[1467, 16812])).
% 2.06/2.22 tff(16814,plain,
% 2.06/2.22 (op(e0, e0) = e0),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[3976, 16813, 13158, 12526])).
% 2.06/2.22 tff(16815,plain,
% 2.06/2.22 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16814])).
% 2.06/2.22 tff(16816,plain,
% 2.06/2.22 (op(e0, op(e0, e0)) = e0),
% 2.06/2.22 inference(transitivity,[status(thm)],[16815, 16814])).
% 2.06/2.22 tff(16817,plain,
% 2.06/2.22 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[5598, 16816])).
% 2.06/2.22 tff(16818,plain,
% 2.06/2.22 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[11829])).
% 2.06/2.22 tff(16819,plain,
% 2.06/2.22 (op(e2, op(e2, e3)) = e2),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16709, 16818])).
% 2.06/2.22 tff(16820,plain,
% 2.06/2.22 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[16573, 16819])).
% 2.06/2.22 tff(16821,plain,
% 2.06/2.22 ((op(e2, e1) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16804, 531])).
% 2.06/2.22 tff(16822,plain,
% 2.06/2.22 ((~(op(e2, e1) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16821])).
% 2.06/2.22 tff(16823,plain,
% 2.06/2.22 (~(op(e1, e2) = op(e2, e1))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16808, 16822])).
% 2.06/2.22 tff(16824,plain,
% 2.06/2.22 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[539, 16823])).
% 2.06/2.22 tff(16825,plain,
% 2.06/2.22 (op(e2, op(e1, e1)) = op(e2, op(e2, e3))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[253])).
% 2.06/2.22 tff(16826,plain,
% 2.06/2.22 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16825])).
% 2.06/2.22 tff(16827,plain,
% 2.06/2.22 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.06/2.22 inference(symmetry,[status(thm)],[16826])).
% 2.06/2.22 tff(16828,plain,
% 2.06/2.22 ((op(e2, e0) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16818, 16827])).
% 2.06/2.22 tff(16829,plain,
% 2.06/2.22 (op(e2, op(e1, e1)) = e2),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16709, 16828])).
% 2.06/2.22 tff(16830,plain,
% 2.06/2.22 (((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)) | (~(op(e2, op(e1, e1)) = e2))),
% 2.06/2.22 inference(tautology,[status(thm)],[])).
% 2.06/2.22 tff(16831,plain,
% 2.06/2.22 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[16830, 16829])).
% 2.06/2.22 tff(16832,plain,
% 2.06/2.22 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[8644])).
% 2.06/2.22 tff(16833,plain,
% 2.06/2.22 ((op(e1, e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16832, 1674])).
% 2.06/2.22 tff(16834,plain,
% 2.06/2.22 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16833])).
% 2.06/2.22 tff(16835,plain,
% 2.06/2.22 (~(op(e3, e1) = op(e1, e3))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[72, 16834])).
% 2.06/2.22 tff(16836,plain,
% 2.06/2.22 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[6362, 16835])).
% 2.06/2.22 tff(16837,plain,
% 2.06/2.22 ((~(op(e0, e2) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16795])).
% 2.06/2.22 tff(16838,plain,
% 2.06/2.22 (~(op(e2, e0) = op(e0, e2))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[16800, 16837])).
% 2.06/2.22 tff(16839,plain,
% 2.06/2.22 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[6358, 16838])).
% 2.06/2.22 tff(16840,plain,
% 2.06/2.22 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16610])).
% 2.06/2.22 tff(16841,plain,
% 2.06/2.22 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.06/2.22 inference(symmetry,[status(thm)],[16840])).
% 2.06/2.22 tff(16842,plain,
% 2.06/2.22 ((op(e3, e0) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16841, 453])).
% 2.06/2.22 tff(16843,plain,
% 2.06/2.22 ((~(op(e3, e0) = e2)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16842])).
% 2.06/2.22 tff(16844,plain,
% 2.06/2.22 (~(op(e0, e3) = op(e3, e0))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[6692, 16843])).
% 2.06/2.22 tff(16845,plain,
% 2.06/2.22 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[496, 16844])).
% 2.06/2.22 tff(16846,plain,
% 2.06/2.22 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.06/2.22 inference(transitivity,[status(thm)],[16833, 6290])).
% 2.06/2.22 tff(16847,plain,
% 2.06/2.22 ((~(op(e1, e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16846])).
% 2.06/2.22 tff(16848,plain,
% 2.06/2.22 (~(op(e1, e3) = op(e3, e1))),
% 2.06/2.22 inference(modus_ponens,[status(thm)],[72, 16847])).
% 2.06/2.22 tff(16849,plain,
% 2.06/2.22 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[6307, 16848])).
% 2.06/2.22 tff(16850,plain,
% 2.06/2.22 (op(e2, op(e3, e2)) = op(e2, op(e2, e3))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16760])).
% 2.06/2.22 tff(16851,plain,
% 2.06/2.22 (op(e2, op(e3, e2)) = e2),
% 2.06/2.22 inference(transitivity,[status(thm)],[16850, 11212, 16709])).
% 2.06/2.22 tff(16852,plain,
% 2.06/2.22 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[16604, 16851])).
% 2.06/2.22 tff(16853,plain,
% 2.06/2.22 (op(e1, op(e1, e0)) = e1),
% 2.06/2.22 inference(transitivity,[status(thm)],[781, 132])).
% 2.06/2.22 tff(16854,plain,
% 2.06/2.22 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[13418, 16853])).
% 2.06/2.22 tff(16855,plain,
% 2.06/2.22 (op(e0, e1) = e3),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[1495, 4412, 11542, 661])).
% 2.06/2.22 tff(16856,plain,
% 2.06/2.22 (op(e0, e1) = op(e1, e0)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16855, 259])).
% 2.06/2.22 tff(16857,plain,
% 2.06/2.22 (op(e1, op(e0, e1)) = op(e1, op(e1, e0))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16856])).
% 2.06/2.22 tff(16858,plain,
% 2.06/2.22 (op(e1, op(e0, e1)) = e1),
% 2.06/2.22 inference(transitivity,[status(thm)],[16857, 781, 132])).
% 2.06/2.22 tff(16859,plain,
% 2.06/2.22 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[13426, 16858])).
% 2.06/2.22 tff(16860,plain,
% 2.06/2.22 (op(e2, e2) = e3),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[2111, 4412, 75, 1890])).
% 2.06/2.22 tff(16861,plain,
% 2.06/2.22 (op(e2, e2) = op(e1, e0)),
% 2.06/2.22 inference(transitivity,[status(thm)],[16860, 259])).
% 2.06/2.22 tff(16862,plain,
% 2.06/2.22 (op(e1, op(e2, e2)) = op(e1, op(e1, e0))),
% 2.06/2.22 inference(monotonicity,[status(thm)],[16861])).
% 2.06/2.22 tff(16863,plain,
% 2.06/2.22 (op(e1, op(e2, e2)) = e1),
% 2.06/2.22 inference(transitivity,[status(thm)],[16862, 781, 132])).
% 2.06/2.22 tff(16864,plain,
% 2.06/2.22 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[6714, 16863])).
% 2.06/2.22 tff(16865,plain,
% 2.06/2.22 ($false),
% 2.06/2.22 inference(unit_resolution,[status(thm)],[5367, 16864, 16859, 5669, 5668, 5670, 5674, 6688, 5511, 6689, 5673, 5671, 16854, 5667, 5680, 9846])).
% 2.06/2.22 tff(16866,plain,((op(e0, e2) = e3) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e1, e3) = e1)) | (~(op(e1, e0) = e3)) | (op(e1, e2) = e3) | (op(e3, e2) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.23 tff(16867,plain,
% 2.06/2.23 (op(e0, e2) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[16866, 16852, 16849, 16845, 16839, 16621, 16836, 16831, 16824, 16820, 16817, 16810, 16802, 3699, 16669, 75, 16662, 16614])).
% 2.06/2.23 tff(16868,plain,
% 2.06/2.23 ((op(e0, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16867])).
% 2.06/2.23 tff(16869,plain,
% 2.06/2.23 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16868, 502])).
% 2.06/2.23 tff(16870,plain,
% 2.06/2.23 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16869])).
% 2.06/2.23 tff(16871,plain,
% 2.06/2.23 (~(op(e2, e2) = e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[2736, 16870])).
% 2.06/2.23 tff(16872,plain,
% 2.06/2.23 (op(op(e3, e2), e2) = op(op(e2, e3), e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16760])).
% 2.06/2.23 tff(16873,plain,
% 2.06/2.23 (op(op(e3, e2), e2) = op(e0, e2)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16872, 5088])).
% 2.06/2.23 tff(16874,plain,
% 2.06/2.23 ((op(op(e3, e2), e2) = e3) <=> (op(e0, e2) = e3)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16873])).
% 2.06/2.23 tff(16875,plain,
% 2.06/2.23 ((op(e0, e2) = e3) <=> (op(op(e3, e2), e2) = e3)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16874])).
% 2.06/2.23 tff(16876,plain,
% 2.06/2.23 (op(op(e3, e2), e2) = e3),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[16867, 16875])).
% 2.06/2.23 tff(16877,plain,
% 2.06/2.23 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1339, 16876])).
% 2.06/2.23 tff(16878,plain,
% 2.06/2.23 ($false),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[8597, 16877, 16871, 6684, 16792, 16411, 16759, 16789, 16786, 16782, 16776, 16773, 16768, 16691, 16683, 16676, 16617, 75, 16662])).
% 2.06/2.23 tff(16879,plain,((op(e1, e3) = e3) | (~(op(e3, e1) = e2)) | (op(e1, e2) = e3) | (~(op(e2, e3) = e0)) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (~(op(e1, e1) = e0)) | (op(e1, e3) = e2) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.23 tff(16880,plain,
% 2.06/2.23 (op(e1, e3) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[16879, 16330, 75, 16487, 76, 17, 16659, 72, 80])).
% 2.06/2.23 tff(16881,plain,
% 2.06/2.23 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16880])).
% 2.06/2.23 tff(16882,plain,
% 2.06/2.23 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16881, 128])).
% 2.06/2.23 tff(16883,plain,
% 2.06/2.23 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16882])).
% 2.06/2.23 tff(16884,plain,
% 2.06/2.23 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16883])).
% 2.06/2.23 tff(16885,plain,
% 2.06/2.23 (~(op(e1, e3) = e1)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[303, 16884])).
% 2.06/2.23 tff(16886,plain,
% 2.06/2.23 (op(e3, e3) = e1),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[151, 16885, 76, 16502])).
% 2.06/2.23 tff(16887,plain,
% 2.06/2.23 (e1 = op(e3, e3)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16886])).
% 2.06/2.23 tff(16888,plain,
% 2.06/2.23 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16887])).
% 2.06/2.23 tff(16889,plain,
% 2.06/2.23 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16888])).
% 2.06/2.23 tff(16890,plain,
% 2.06/2.23 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16889])).
% 2.06/2.23 tff(16891,plain,
% 2.06/2.23 (~(op(e3, e2) = e1)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[1888, 16890])).
% 2.06/2.23 tff(16892,plain,
% 2.06/2.23 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16488])).
% 2.06/2.23 tff(16893,plain,
% 2.06/2.23 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e0)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16892])).
% 2.06/2.23 tff(16894,plain,
% 2.06/2.23 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16886])).
% 2.06/2.23 tff(16895,plain,
% 2.06/2.23 (op(e3, op(e3, e3)) = e2),
% 2.06/2.23 inference(transitivity,[status(thm)],[16894, 16330])).
% 2.06/2.23 tff(16896,plain,
% 2.06/2.23 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16895])).
% 2.06/2.23 tff(16897,plain,
% 2.06/2.23 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e3) = op(e3, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16488, 16896])).
% 2.06/2.23 tff(16898,plain,
% 2.06/2.23 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e2, e3))),
% 2.06/2.23 inference(transitivity,[status(thm)],[16897, 394])).
% 2.06/2.23 tff(16899,plain,
% 2.06/2.23 ((e0 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e0)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16898, 16893])).
% 2.06/2.23 tff(16900,plain,
% 2.06/2.23 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e0))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16899])).
% 2.06/2.23 tff(16901,plain,
% 2.06/2.23 (e1 = op(e3, e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[16886, 658])).
% 2.06/2.23 tff(16902,plain,
% 2.06/2.23 (op(e3, e1) = op(e3, op(e3, e3))),
% 2.06/2.23 inference(symmetry,[status(thm)],[16894])).
% 2.06/2.23 tff(16903,plain,
% 2.06/2.23 (e2 = op(e3, op(e3, e3))),
% 2.06/2.23 inference(transitivity,[status(thm)],[16650, 16902])).
% 2.06/2.23 tff(16904,plain,
% 2.06/2.23 (~(e0 = op(e3, op(e3, op(e3, e3))))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[2034, 16903, 16901])).
% 2.06/2.23 tff(16905,plain,
% 2.06/2.23 (~(op(e3, e2) = e0)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[16904, 16900])).
% 2.06/2.23 tff(16906,plain,
% 2.06/2.23 (op(e3, e2) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1898, 16905, 16891, 16492])).
% 2.06/2.23 tff(16907,plain,
% 2.06/2.23 (e3 = op(e3, e2)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16906])).
% 2.06/2.23 tff(16908,plain,
% 2.06/2.23 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e3, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16907])).
% 2.06/2.23 tff(16909,plain,
% 2.06/2.23 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16908])).
% 2.06/2.23 tff(16910,plain,
% 2.06/2.23 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16909])).
% 2.06/2.23 tff(16911,plain,
% 2.06/2.23 (~(op(e2, e2) = e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[1546, 16910])).
% 2.06/2.23 tff(16912,plain,
% 2.06/2.23 ((op(e3, e3) = e0) <=> (op(e3, e3) = op(e2, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16488])).
% 2.06/2.23 tff(16913,plain,
% 2.06/2.23 ((op(e3, e3) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 2.06/2.23 inference(transitivity,[status(thm)],[16912, 2820])).
% 2.06/2.23 tff(16914,plain,
% 2.06/2.23 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16913])).
% 2.06/2.23 tff(16915,plain,
% 2.06/2.23 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16914])).
% 2.06/2.23 tff(16916,plain,
% 2.06/2.23 (~(op(e3, e3) = e0)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[368, 16915])).
% 2.06/2.23 tff(16917,plain,
% 2.06/2.23 (op(e3, e0) = e0),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1916, 16905, 16916, 16556])).
% 2.06/2.23 tff(16918,plain,
% 2.06/2.23 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e0)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16917])).
% 2.06/2.23 tff(16919,plain,
% 2.06/2.23 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e0))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16918])).
% 2.06/2.23 tff(16920,plain,
% 2.06/2.23 (~(op(e0, e0) = e0)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[6384, 16919])).
% 2.06/2.23 tff(16921,plain,
% 2.06/2.23 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[2])).
% 2.06/2.23 tff(16922,plain,
% 2.06/2.23 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16921])).
% 2.06/2.23 tff(16923,plain,
% 2.06/2.23 (~(op(e0, e0) = e2)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[3414, 16922])).
% 2.06/2.23 tff(16924,plain,
% 2.06/2.23 (op(e0, e0) = e1),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[3612, 10447, 16923, 6213])).
% 2.06/2.23 tff(16925,plain,
% 2.06/2.23 (e1 = op(e0, e0)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[16924, 74])).
% 2.06/2.23 tff(16926,plain,
% 2.06/2.23 (op(e0, e0) = op(e3, e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16924, 306])).
% 2.06/2.23 tff(16927,plain,
% 2.06/2.23 (op(e0, op(e0, e0)) = op(e0, op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16926])).
% 2.06/2.23 tff(16928,plain,
% 2.06/2.23 (op(e0, op(e3, e3)) = op(e0, op(e0, e0))),
% 2.06/2.23 inference(symmetry,[status(thm)],[16927])).
% 2.06/2.23 tff(16929,plain,
% 2.06/2.23 (e3 = op(e3, e2)),
% 2.06/2.23 inference(symmetry,[status(thm)],[856])).
% 2.06/2.23 tff(16930,plain,
% 2.06/2.23 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e3, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16929])).
% 2.06/2.23 tff(16931,plain,
% 2.06/2.23 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16930])).
% 2.06/2.23 tff(16932,plain,
% 2.06/2.23 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16931])).
% 2.06/2.23 tff(16933,plain,
% 2.06/2.23 (~(op(e0, e2) = e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[1467, 16932])).
% 2.06/2.23 tff(16934,plain,
% 2.06/2.23 (op(e0, e1) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1495, 10447, 16933, 16740])).
% 2.06/2.23 tff(16935,plain,
% 2.06/2.23 (e3 = op(e0, e1)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16934])).
% 2.06/2.23 tff(16936,plain,
% 2.06/2.23 (e3 = op(e0, op(e0, e0))),
% 2.06/2.23 inference(transitivity,[status(thm)],[16935, 8888, 16928])).
% 2.06/2.23 tff(16937,plain,
% 2.06/2.23 (op(e0, op(e0, e0)) = op(e3, e2)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16927, 3348, 16934, 16929])).
% 2.06/2.23 tff(16938,plain,
% 2.06/2.23 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e3, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16937])).
% 2.06/2.23 tff(16939,plain,
% 2.06/2.23 (op(e0, op(e3, e2)) = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.23 inference(symmetry,[status(thm)],[16938])).
% 2.06/2.23 tff(16940,plain,
% 2.06/2.23 (op(e0, op(e3, e2)) = op(op(e2, e3), e3)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[252, 856])).
% 2.06/2.23 tff(16941,plain,
% 2.06/2.23 (op(op(e2, e3), e3) = op(e0, op(e3, e2))),
% 2.06/2.23 inference(symmetry,[status(thm)],[16940])).
% 2.06/2.23 tff(16942,plain,
% 2.06/2.23 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.06/2.23 inference(transitivity,[status(thm)],[2560, 16755, 16941, 16939])).
% 2.06/2.23 tff(16943,plain,
% 2.06/2.23 ($false),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[16194, 16942, 16936, 16925])).
% 2.06/2.23 tff(16944,plain,((op(e0, e0) = e3) | (~(op(e0, e3) = e2)) | (~(op(e3, e2) = e3)) | (~(op(e2, e3) = e0)) | (~(op(e3, e3) = e1)) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.23 tff(16945,plain,
% 2.06/2.23 (op(e0, e0) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[16944, 16497, 16906, 16487, 16886, 16920])).
% 2.06/2.23 tff(16946,plain,
% 2.06/2.23 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, op(e2, e3)))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16945, 16512])).
% 2.06/2.23 tff(16947,plain,
% 2.06/2.23 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, op(e2, e3)) = e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16946, 2881])).
% 2.06/2.23 tff(16948,plain,
% 2.06/2.23 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16947, 16514])).
% 2.06/2.23 tff(16949,plain,
% 2.06/2.23 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16948])).
% 2.06/2.23 tff(16950,plain,
% 2.06/2.23 (~(op(e2, e0) = e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[359, 16949])).
% 2.06/2.23 tff(16951,plain,
% 2.06/2.23 (op(e2, e1) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1559, 16950, 16509, 16911])).
% 2.06/2.23 tff(16952,plain,
% 2.06/2.23 (op(e2, op(e3, e3)) = op(e2, e1)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16886])).
% 2.06/2.23 tff(16953,plain,
% 2.06/2.23 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16880])).
% 2.06/2.23 tff(16954,plain,
% 2.06/2.23 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16953])).
% 2.06/2.23 tff(16955,plain,
% 2.06/2.23 (~(op(e1, e0) = e3)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[110, 16954])).
% 2.06/2.23 tff(16956,plain,
% 2.06/2.23 (op(op(e3, e2), e2) = e3),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[7919, 16906])).
% 2.06/2.23 tff(16957,plain,
% 2.06/2.23 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1339, 16956])).
% 2.06/2.23 tff(16958,plain,
% 2.06/2.23 (op(op(e2, e1), e1) = op(e3, op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16951, 16887])).
% 2.06/2.23 tff(16959,plain,
% 2.06/2.23 (op(op(e2, e1), e1) = e2),
% 2.06/2.23 inference(transitivity,[status(thm)],[16958, 16894, 16330])).
% 2.06/2.23 tff(16960,plain,
% 2.06/2.23 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[2371, 16959])).
% 2.06/2.23 tff(16961,plain,
% 2.06/2.23 ((op(e1, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16659])).
% 2.06/2.23 tff(16962,plain,
% 2.06/2.23 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16961, 67])).
% 2.06/2.23 tff(16963,plain,
% 2.06/2.23 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16962])).
% 2.06/2.23 tff(16964,plain,
% 2.06/2.23 (~(op(e1, e2) = e0)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[1604, 16963])).
% 2.06/2.23 tff(16965,plain,
% 2.06/2.23 (op(e0, e2) = e0),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[973, 16905, 17, 16964])).
% 2.06/2.23 tff(16966,plain,
% 2.06/2.23 (op(op(e2, e3), e2) = op(e0, e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16487])).
% 2.06/2.23 tff(16967,plain,
% 2.06/2.23 (op(e0, e2) = op(e2, e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16965, 16488])).
% 2.06/2.23 tff(16968,plain,
% 2.06/2.23 (op(op(e0, e2), e2) = op(op(e2, e3), e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16967])).
% 2.06/2.23 tff(16969,plain,
% 2.06/2.23 (op(op(e0, e2), e2) = e0),
% 2.06/2.23 inference(transitivity,[status(thm)],[16968, 16966, 16965])).
% 2.06/2.23 tff(16970,plain,
% 2.06/2.23 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1956, 16969])).
% 2.06/2.23 tff(16971,plain,
% 2.06/2.23 ((op(e0, e2) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16967, 16887])).
% 2.06/2.23 tff(16972,plain,
% 2.06/2.23 ((op(e2, e3) = op(e3, e3)) <=> (op(e0, e2) = e1)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16971])).
% 2.06/2.23 tff(16973,plain,
% 2.06/2.23 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e0, e2) = e1))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16972])).
% 2.06/2.23 tff(16974,plain,
% 2.06/2.23 (~(op(e0, e2) = e1)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[368, 16973])).
% 2.06/2.23 tff(16975,plain,
% 2.06/2.23 (op(e0, e0) = op(e3, e2)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16945, 16907])).
% 2.06/2.23 tff(16976,plain,
% 2.06/2.23 ((op(e0, e0) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16975, 16887])).
% 2.06/2.23 tff(16977,plain,
% 2.06/2.23 ((op(e3, e2) = op(e3, e3)) <=> (op(e0, e0) = e1)),
% 2.06/2.23 inference(symmetry,[status(thm)],[16976])).
% 2.06/2.23 tff(16978,plain,
% 2.06/2.23 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e0, e0) = e1))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16977])).
% 2.06/2.23 tff(16979,plain,
% 2.06/2.23 (~(op(e0, e0) = e1)),
% 2.06/2.23 inference(modus_ponens,[status(thm)],[1888, 16978])).
% 2.06/2.23 tff(16980,plain,
% 2.06/2.23 (op(e0, e1) = e1),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[384, 16979, 16502, 16974])).
% 2.06/2.23 tff(16981,plain,
% 2.06/2.23 (op(e0, op(e3, e3)) = op(e0, e1)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16886])).
% 2.06/2.23 tff(16982,plain,
% 2.06/2.23 (op(e0, e1) = op(e3, e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16980, 16887])).
% 2.06/2.23 tff(16983,plain,
% 2.06/2.23 (op(e0, op(e0, e1)) = op(e0, op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16982])).
% 2.06/2.23 tff(16984,plain,
% 2.06/2.23 (op(e0, op(e0, e1)) = e1),
% 2.06/2.23 inference(transitivity,[status(thm)],[16983, 16981, 16980])).
% 2.06/2.23 tff(16985,plain,
% 2.06/2.23 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[2449, 16984])).
% 2.06/2.23 tff(16986,plain,
% 2.06/2.23 (op(e3, op(e2, e3)) = op(e3, e0)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16487])).
% 2.06/2.23 tff(16987,plain,
% 2.06/2.23 (op(e3, e0) = op(e2, e3)),
% 2.06/2.23 inference(transitivity,[status(thm)],[16917, 16488])).
% 2.06/2.23 tff(16988,plain,
% 2.06/2.23 (op(e3, op(e3, e0)) = op(e3, op(e2, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16987])).
% 2.06/2.23 tff(16989,plain,
% 2.06/2.23 (op(e3, op(e3, e0)) = e0),
% 2.06/2.23 inference(transitivity,[status(thm)],[16988, 16986, 16917])).
% 2.06/2.23 tff(16990,plain,
% 2.06/2.23 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1345, 16989])).
% 2.06/2.23 tff(16991,plain,
% 2.06/2.23 (op(e1, e2) = e2),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[2285, 6687, 68, 72])).
% 2.06/2.23 tff(16992,plain,
% 2.06/2.23 (op(e1, op(e1, e2)) = op(e1, e2)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16991])).
% 2.06/2.23 tff(16993,plain,
% 2.06/2.23 (op(e1, op(e1, e2)) = e2),
% 2.06/2.23 inference(transitivity,[status(thm)],[16992, 16991])).
% 2.06/2.23 tff(16994,plain,
% 2.06/2.23 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[2377, 16993])).
% 2.06/2.23 tff(16995,plain,
% 2.06/2.23 (op(e1, e0) = e1),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[728, 6687, 13237, 2168])).
% 2.06/2.23 tff(16996,plain,
% 2.06/2.23 (op(e1, op(e1, e0)) = op(e1, e1)),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16995])).
% 2.06/2.23 tff(16997,plain,
% 2.06/2.23 (op(e1, op(e1, e0)) = e0),
% 2.06/2.23 inference(transitivity,[status(thm)],[16996, 249])).
% 2.06/2.23 tff(16998,plain,
% 2.06/2.23 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1836, 16997])).
% 2.06/2.23 tff(16999,plain,
% 2.06/2.23 (op(e2, e0) = e2),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[589, 6687, 3786, 16703])).
% 2.06/2.23 tff(17000,plain,
% 2.06/2.23 (op(op(e2, e0), e0) = op(e2, op(e2, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[16999, 252])).
% 2.06/2.23 tff(17001,plain,
% 2.06/2.23 (op(op(e2, e0), e0) = e2),
% 2.06/2.23 inference(transitivity,[status(thm)],[17000, 11212, 16999])).
% 2.06/2.23 tff(17002,plain,
% 2.06/2.23 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1945, 17001])).
% 2.06/2.23 tff(17003,plain,
% 2.06/2.23 ($false),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[1459, 17002, 16998, 1926, 4549, 16776, 1304, 1363, 1936, 16792, 3341, 16994, 1275])).
% 2.06/2.23 tff(17004,plain,((op(e1, e0) = e2) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~(op(e2, e3) = e0)) | (~(op(e1, e1) = e0)) | (op(e3, e0) = e2) | (op(e1, e0) = e3) | (op(e1, e1) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.06/2.23 tff(17005,plain,
% 2.06/2.23 (op(e1, e0) = e2),
% 2.06/2.23 inference(unit_resolution,[status(thm)],[17004, 16990, 16985, 16411, 16970, 16960, 16957, 16336, 16487, 16659, 16421, 16955, 68, 72])).
% 2.06/2.23 tff(17006,plain,
% 2.06/2.23 (op(op(e1, e0), e1) = op(e2, op(e3, e3))),
% 2.06/2.23 inference(monotonicity,[status(thm)],[17005, 16887])).
% 2.06/2.24 tff(17007,plain,
% 2.06/2.24 (op(op(e1, e0), e1) = op(e3, e2)),
% 2.06/2.24 inference(transitivity,[status(thm)],[17006, 16952, 16951, 16907])).
% 2.06/2.24 tff(17008,plain,
% 2.06/2.24 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 2.06/2.24 inference(monotonicity,[status(thm)],[17007, 16488])).
% 2.06/2.24 tff(17009,plain,
% 2.06/2.24 ((op(e3, e2) = op(e2, e3)) <=> (op(op(e1, e0), e1) = e0)),
% 2.06/2.24 inference(symmetry,[status(thm)],[17008])).
% 2.06/2.24 tff(17010,plain,
% 2.06/2.24 ((~(op(e3, e2) = op(e2, e3))) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.24 inference(monotonicity,[status(thm)],[17009])).
% 2.06/2.24 tff(17011,plain,
% 2.06/2.24 ((~(e0 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.06/2.24 inference(monotonicity,[status(thm)],[16898])).
% 2.06/2.24 tff(17012,plain,
% 2.06/2.24 (~(op(e3, e2) = op(e2, e3))),
% 2.06/2.24 inference(modus_ponens,[status(thm)],[16904, 17011])).
% 2.06/2.24 tff(17013,plain,
% 2.06/2.24 (~(op(op(e1, e0), e1) = e0)),
% 2.06/2.24 inference(modus_ponens,[status(thm)],[17012, 17010])).
% 2.06/2.24 tff(17014,plain,
% 2.06/2.24 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.06/2.24 inference(unit_resolution,[status(thm)],[1302, 17013])).
% 2.14/2.24 tff(17015,plain,
% 2.14/2.24 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[16497])).
% 2.14/2.24 tff(17016,plain,
% 2.14/2.24 (op(op(e0, e3), e3) = e0),
% 2.14/2.24 inference(transitivity,[status(thm)],[17015, 16487])).
% 2.14/2.24 tff(17017,plain,
% 2.14/2.24 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1361, 17016])).
% 2.14/2.24 tff(17018,plain,
% 2.14/2.24 (op(op(e2, e3), e3) = op(e0, e3)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[16487])).
% 2.14/2.24 tff(17019,plain,
% 2.14/2.24 (op(e0, e3) = op(op(e2, e3), e3)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17018])).
% 2.14/2.24 tff(17020,plain,
% 2.14/2.24 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17019])).
% 2.14/2.24 tff(17021,plain,
% 2.14/2.24 (op(op(e2, e3), e3) = e2),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[16497, 17020])).
% 2.14/2.24 tff(17022,plain,
% 2.14/2.24 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1288, 17021])).
% 2.14/2.24 tff(17023,plain,
% 2.14/2.24 (op(e1, e1) = op(e2, e3)),
% 2.14/2.24 inference(transitivity,[status(thm)],[16659, 16488])).
% 2.14/2.24 tff(17024,plain,
% 2.14/2.24 ((op(e1, e1) = e1) <=> (op(e2, e3) = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17023])).
% 2.14/2.24 tff(17025,plain,
% 2.14/2.24 ((op(e2, e3) = e1) <=> (op(e1, e1) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17024])).
% 2.14/2.24 tff(17026,plain,
% 2.14/2.24 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e1) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17025])).
% 2.14/2.24 tff(17027,plain,
% 2.14/2.24 (~(op(e1, e1) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[76, 17026])).
% 2.14/2.24 tff(17028,plain,
% 2.14/2.24 (op(e1, op(e2, e3)) = op(e1, e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[16487])).
% 2.14/2.24 tff(17029,plain,
% 2.14/2.24 (op(e1, e0) = op(e1, op(e2, e3))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17028])).
% 2.14/2.24 tff(17030,plain,
% 2.14/2.24 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17029])).
% 2.14/2.24 tff(17031,plain,
% 2.14/2.24 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17030])).
% 2.14/2.24 tff(17032,plain,
% 2.14/2.24 (op(e1, op(e2, e3)) = e2),
% 2.14/2.24 inference(transitivity,[status(thm)],[17028, 17005])).
% 2.14/2.24 tff(17033,plain,
% 2.14/2.24 ((op(e1, op(e2, e3)) = e1) <=> (e2 = op(e3, e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17032, 16887])).
% 2.14/2.24 tff(17034,plain,
% 2.14/2.24 ((op(e1, op(e2, e3)) = e1) <=> (op(e3, e3) = e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17033, 565])).
% 2.14/2.24 tff(17035,plain,
% 2.14/2.24 ((op(e3, e3) = e2) <=> (op(e1, op(e2, e3)) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17034])).
% 2.14/2.24 tff(17036,plain,
% 2.14/2.24 ((op(e3, e3) = e2) <=> (op(e1, e0) = e1)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17035, 17031])).
% 2.14/2.24 tff(17037,plain,
% 2.14/2.24 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e0) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17036])).
% 2.14/2.24 tff(17038,plain,
% 2.14/2.24 (~(op(e1, e0) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[15002, 17037])).
% 2.14/2.24 tff(17039,plain,
% 2.14/2.24 (op(e1, e2) = e1),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[954, 17038, 17027, 16885])).
% 2.14/2.24 tff(17040,plain,
% 2.14/2.24 (op(op(e1, e2), e2) = op(e1, e2)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17039])).
% 2.14/2.24 tff(17041,plain,
% 2.14/2.24 (op(op(e1, e2), e2) = e1),
% 2.14/2.24 inference(transitivity,[status(thm)],[17040, 17039])).
% 2.14/2.24 tff(17042,plain,
% 2.14/2.24 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1335, 17041])).
% 2.14/2.24 tff(17043,plain,
% 2.14/2.24 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[16887])).
% 2.14/2.24 tff(17044,plain,
% 2.14/2.24 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17043])).
% 2.14/2.24 tff(17045,plain,
% 2.14/2.24 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17044])).
% 2.14/2.24 tff(17046,plain,
% 2.14/2.24 (~(op(e3, e0) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[157, 17045])).
% 2.14/2.24 tff(17047,plain,
% 2.14/2.24 (op(e2, e0) = e1),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1480, 17038, 17046, 16979])).
% 2.14/2.24 tff(17048,plain,
% 2.14/2.24 (op(op(e2, e0), e0) = op(e1, op(e2, e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17047, 16488])).
% 2.14/2.24 tff(17049,plain,
% 2.14/2.24 (op(op(e2, e0), e0) = e2),
% 2.14/2.24 inference(transitivity,[status(thm)],[17048, 17028, 17005])).
% 2.14/2.24 tff(17050,plain,
% 2.14/2.24 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1945, 17049])).
% 2.14/2.24 tff(17051,plain,
% 2.14/2.24 ($false),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1459, 17050, 17042, 16990, 16985, 17022, 16411, 16970, 16960, 17017, 16957, 17014, 16336])).
% 2.14/2.24 tff(17052,plain,((op(e1, e3) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.24 tff(17053,plain,
% 2.14/2.24 (op(e1, e3) = e0),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[17052, 76, 72, 17, 68, 75])).
% 2.14/2.24 tff(17054,plain,
% 2.14/2.24 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.24 tff(17055,plain,
% 2.14/2.24 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17054])).
% 2.14/2.24 tff(17056,plain,
% 2.14/2.24 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17055])).
% 2.14/2.24 tff(17057,plain,
% 2.14/2.24 (~(op(e1, e3) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[26, 17056])).
% 2.14/2.24 tff(17058,plain,
% 2.14/2.24 (op(e0, e1) = e2),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1993, 82, 68, 16124])).
% 2.14/2.24 tff(17059,plain,
% 2.14/2.24 ((op(e0, e1) = e3) <=> (e2 = e3)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.24 tff(17060,plain,
% 2.14/2.24 ((e2 = e3) <=> (op(e0, e1) = e3)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17059])).
% 2.14/2.24 tff(17061,plain,
% 2.14/2.24 ((~(e2 = e3)) <=> (~(op(e0, e1) = e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17060])).
% 2.14/2.24 tff(17062,plain,
% 2.14/2.24 (~(op(e0, e1) = e3)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[1321, 17061])).
% 2.14/2.24 tff(17063,plain,
% 2.14/2.24 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.24 tff(17064,plain,
% 2.14/2.24 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17063, 69])).
% 2.14/2.24 tff(17065,plain,
% 2.14/2.24 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17064])).
% 2.14/2.24 tff(17066,plain,
% 2.14/2.24 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17065])).
% 2.14/2.24 tff(17067,plain,
% 2.14/2.24 (~(op(e0, e1) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[708, 17066])).
% 2.14/2.24 tff(17068,plain,
% 2.14/2.24 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.24 tff(17069,plain,
% 2.14/2.24 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17068])).
% 2.14/2.24 tff(17070,plain,
% 2.14/2.24 (~(op(e0, e0) = e2)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[811, 17069])).
% 2.14/2.24 tff(17071,plain,
% 2.14/2.24 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.24 tff(17072,plain,
% 2.14/2.24 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17071, 3491])).
% 2.14/2.24 tff(17073,plain,
% 2.14/2.24 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17072])).
% 2.14/2.24 tff(17074,plain,
% 2.14/2.24 (~(op(e0, e2) = e2)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[2102, 17073])).
% 2.14/2.24 tff(17075,plain,
% 2.14/2.24 (op(e3, e3) = e1),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[12046, 85, 17, 76, 2672, 72, 2605, 2527])).
% 2.14/2.24 tff(17076,plain,
% 2.14/2.24 (e1 = op(e3, e3)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[17075, 658])).
% 2.14/2.24 tff(17077,plain,
% 2.14/2.24 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17075])).
% 2.14/2.24 tff(17078,plain,
% 2.14/2.24 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17077])).
% 2.14/2.24 tff(17079,plain,
% 2.14/2.24 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17078, 5470])).
% 2.14/2.24 tff(17080,plain,
% 2.14/2.24 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17079])).
% 2.14/2.24 tff(17081,plain,
% 2.14/2.24 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[1219])).
% 2.14/2.24 tff(17082,plain,
% 2.14/2.24 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17081, 3077])).
% 2.14/2.24 tff(17083,plain,
% 2.14/2.24 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17082])).
% 2.14/2.24 tff(17084,plain,
% 2.14/2.24 (~(op(e3, e3) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[571, 17083])).
% 2.14/2.24 tff(17085,plain,
% 2.14/2.24 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[1219])).
% 2.14/2.24 tff(17086,plain,
% 2.14/2.24 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17085])).
% 2.14/2.24 tff(17087,plain,
% 2.14/2.24 (~(op(e1, e2) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[1850, 17086])).
% 2.14/2.24 tff(17088,plain,
% 2.14/2.24 (op(e0, e2) = e0),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[973, 85, 17, 17087])).
% 2.14/2.24 tff(17089,plain,
% 2.14/2.24 (e0 = op(e0, e2)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17088])).
% 2.14/2.24 tff(17090,plain,
% 2.14/2.24 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[16115])).
% 2.14/2.24 tff(17091,plain,
% 2.14/2.24 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17090])).
% 2.14/2.24 tff(17092,plain,
% 2.14/2.24 (~(op(e2, e0) = e2)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[989, 17091])).
% 2.14/2.24 tff(17093,plain,
% 2.14/2.24 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17075])).
% 2.14/2.24 tff(17094,plain,
% 2.14/2.24 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17093])).
% 2.14/2.24 tff(17095,plain,
% 2.14/2.24 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17094])).
% 2.14/2.24 tff(17096,plain,
% 2.14/2.24 (~(op(e3, e3) = e3)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[303, 17095])).
% 2.14/2.24 tff(17097,plain,
% 2.14/2.24 (op(e0, e3) = e3),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[480, 17096, 2605, 16119])).
% 2.14/2.24 tff(17098,plain,
% 2.14/2.24 (e3 = op(e0, e3)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17097])).
% 2.14/2.24 tff(17099,plain,
% 2.14/2.24 ((op(e1, e0) = op(e0, e0)) <=> (op(e0, e0) = op(e1, e0))),
% 2.14/2.24 inference(commutativity,[status(thm)],[])).
% 2.14/2.24 tff(17100,plain,
% 2.14/2.24 ((e0 = e1) <=> (op(e0, e2) = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17089])).
% 2.14/2.24 tff(17101,plain,
% 2.14/2.24 ((~(e0 = e1)) <=> (~(op(e0, e2) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17100])).
% 2.14/2.24 tff(17102,plain,
% 2.14/2.24 (~(op(e0, e2) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[26, 17101])).
% 2.14/2.24 tff(17103,plain,
% 2.14/2.24 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e1)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17075])).
% 2.14/2.24 tff(17104,plain,
% 2.14/2.24 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17103])).
% 2.14/2.24 tff(17105,plain,
% 2.14/2.24 (~(op(e0, e3) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[1077, 17104])).
% 2.14/2.24 tff(17106,plain,
% 2.14/2.24 (op(e0, e0) = e1),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[384, 17105, 3528, 17102])).
% 2.14/2.24 tff(17107,plain,
% 2.14/2.24 (e1 = op(e0, e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17106])).
% 2.14/2.24 tff(17108,plain,
% 2.14/2.24 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e0, e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17107])).
% 2.14/2.24 tff(17109,plain,
% 2.14/2.24 ((op(e1, e0) = e1) <=> (op(e0, e0) = op(e1, e0))),
% 2.14/2.24 inference(transitivity,[status(thm)],[17108, 17099])).
% 2.14/2.24 tff(17110,plain,
% 2.14/2.24 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17109])).
% 2.14/2.24 tff(17111,plain,
% 2.14/2.24 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17110])).
% 2.14/2.24 tff(17112,plain,
% 2.14/2.24 (~(op(e1, e0) = e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[2471, 17111])).
% 2.14/2.24 tff(17113,plain,
% 2.14/2.24 (op(e1, e1) = e3),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[247, 2168, 75, 2605])).
% 2.14/2.24 tff(17114,plain,
% 2.14/2.24 (e3 = op(e1, e1)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[17113, 1740])).
% 2.14/2.24 tff(17115,plain,
% 2.14/2.24 (op(e1, e1) = op(e0, e3)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17113, 1870])).
% 2.14/2.24 tff(17116,plain,
% 2.14/2.24 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17115])).
% 2.14/2.24 tff(17117,plain,
% 2.14/2.24 (op(e1, op(e0, e3)) = op(e1, op(e1, e1))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17116])).
% 2.14/2.24 tff(17118,plain,
% 2.14/2.24 (e0 = op(e1, op(e1, e1))),
% 2.14/2.24 inference(transitivity,[status(thm)],[2909, 12238, 17117])).
% 2.14/2.24 tff(17119,plain,
% 2.14/2.24 (e0 = op(e0, e2)),
% 2.14/2.24 inference(symmetry,[status(thm)],[4938])).
% 2.14/2.24 tff(17120,plain,
% 2.14/2.24 (op(e1, op(e1, e1)) = op(e0, e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17116, 9798, 1219, 17119])).
% 2.14/2.24 tff(17121,plain,
% 2.14/2.24 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e0, e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17120])).
% 2.14/2.24 tff(17122,plain,
% 2.14/2.24 (op(e1, op(e0, e2)) = op(e1, op(e1, op(e1, e1)))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17121])).
% 2.14/2.24 tff(17123,plain,
% 2.14/2.24 (op(e1, op(e0, e2)) = op(e1, e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[4938])).
% 2.14/2.24 tff(17124,plain,
% 2.14/2.24 (op(e1, e0) = op(e1, op(e0, e2))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17123])).
% 2.14/2.24 tff(17125,plain,
% 2.14/2.24 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[1219])).
% 2.14/2.24 tff(17126,plain,
% 2.14/2.24 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17125])).
% 2.14/2.24 tff(17127,plain,
% 2.14/2.24 (~(op(e1, e0) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[110, 17126])).
% 2.14/2.24 tff(17128,plain,
% 2.14/2.24 (op(e1, e0) = e2),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[728, 2168, 17127, 929])).
% 2.14/2.24 tff(17129,plain,
% 2.14/2.24 (e2 = op(e1, e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17128])).
% 2.14/2.24 tff(17130,plain,
% 2.14/2.24 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.14/2.24 inference(transitivity,[status(thm)],[17129, 17124, 17122])).
% 2.14/2.24 tff(17131,plain,
% 2.14/2.24 ($false),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[3009, 17130, 17118, 17114])).
% 2.14/2.24 tff(17132,plain,((op(e1, e0) = e3) | (~(op(e0, e2) = e0)) | (~(op(e1, e3) = e0)) | (~(op(e0, e3) = e3)) | (op(e1, e0) = e1) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.24 tff(17133,plain,
% 2.14/2.24 (op(e1, e0) = e3),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[17132, 17088, 1219, 17097, 17112, 75])).
% 2.14/2.24 tff(17134,plain,
% 2.14/2.24 (op(e1, e0) = op(e0, e3)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17133, 17098])).
% 2.14/2.24 tff(17135,plain,
% 2.14/2.24 ((op(e1, e0) = e2) <=> (op(e0, e3) = e2)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17134])).
% 2.14/2.24 tff(17136,plain,
% 2.14/2.24 ((op(e0, e3) = e2) <=> (op(e1, e0) = e2)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17135])).
% 2.14/2.24 tff(17137,plain,
% 2.14/2.24 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e0) = e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17136])).
% 2.14/2.24 tff(17138,plain,
% 2.14/2.24 (~(op(e1, e0) = e2)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[79, 17137])).
% 2.14/2.24 tff(17139,plain,
% 2.14/2.24 (op(e3, e0) = e2),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[589, 17138, 17092, 12721])).
% 2.14/2.24 tff(17140,plain,
% 2.14/2.24 ((op(e3, e0) = e0) <=> (e2 = op(e0, e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17139, 17089])).
% 2.14/2.24 tff(17141,plain,
% 2.14/2.24 ((op(e3, e0) = e0) <=> (op(e0, e2) = e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17140, 3491])).
% 2.14/2.24 tff(17142,plain,
% 2.14/2.24 ((op(e0, e2) = e2) <=> (op(e3, e0) = e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17141])).
% 2.14/2.24 tff(17143,plain,
% 2.14/2.24 ((~(op(e0, e2) = e2)) <=> (~(op(e3, e0) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17142])).
% 2.14/2.24 tff(17144,plain,
% 2.14/2.24 (~(op(e3, e0) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[6229, 17143])).
% 2.14/2.24 tff(17145,plain,
% 2.14/2.24 (op(e3, e1) = e0),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[1916, 17144, 17084, 85])).
% 2.14/2.24 tff(17146,plain,
% 2.14/2.24 (e0 = op(e3, op(e3, e3))),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[17145, 17080])).
% 2.14/2.24 tff(17147,plain,
% 2.14/2.24 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17077])).
% 2.14/2.24 tff(17148,plain,
% 2.14/2.24 (op(e3, op(e3, e1)) = op(e3, op(e3, op(e3, e3)))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17147])).
% 2.14/2.24 tff(17149,plain,
% 2.14/2.24 (op(e3, op(e3, e1)) = op(op(e0, e3), e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17098, 17145])).
% 2.14/2.24 tff(17150,plain,
% 2.14/2.24 (op(op(e0, e3), e0) = op(e3, op(e3, e1))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17149])).
% 2.14/2.24 tff(17151,plain,
% 2.14/2.24 (op(op(e0, e3), e0) = op(e3, op(e0, e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17097, 17089])).
% 2.14/2.24 tff(17152,plain,
% 2.14/2.24 (op(e3, op(e0, e2)) = op(op(e0, e3), e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17151])).
% 2.14/2.24 tff(17153,plain,
% 2.14/2.24 (op(e3, op(e0, e2)) = op(e3, e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17088])).
% 2.14/2.24 tff(17154,plain,
% 2.14/2.24 (op(e3, e0) = op(e3, op(e0, e2))),
% 2.14/2.24 inference(symmetry,[status(thm)],[17153])).
% 2.14/2.24 tff(17155,plain,
% 2.14/2.24 (e2 = op(e3, e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17139])).
% 2.14/2.24 tff(17156,plain,
% 2.14/2.24 (e2 = op(e3, op(e3, op(e3, e3)))),
% 2.14/2.24 inference(transitivity,[status(thm)],[17155, 17154, 17152, 17150, 17148])).
% 2.14/2.24 tff(17157,plain,
% 2.14/2.24 ($false),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[5397, 17156, 17146, 17076])).
% 2.14/2.24 tff(17158,plain,((op(e3, e2) = e0) | (op(e0, e2) = e2) | (op(e0, e0) = e2) | (op(e0, e3) = e2) | (~(op(e1, e3) = e0)) | (op(e1, e2) = e3) | (op(e0, e1) = e1) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e1, e3) = e2) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.24 tff(17159,plain,
% 2.14/2.24 (op(e3, e2) = e0),
% 2.14/2.24 inference(unit_resolution,[status(thm)],[17158, 17074, 17070, 79, 17053, 75, 17067, 17, 76, 72, 17062])).
% 2.14/2.24 tff(17160,plain,
% 2.14/2.24 (e0 = op(e3, e2)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17159])).
% 2.14/2.24 tff(17161,plain,
% 2.14/2.24 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.24 tff(17162,plain,
% 2.14/2.24 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 2.14/2.24 inference(transitivity,[status(thm)],[17161, 1])).
% 2.14/2.24 tff(17163,plain,
% 2.14/2.24 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17162])).
% 2.14/2.24 tff(17164,plain,
% 2.14/2.24 ((~(e0 = e2)) <=> (~(op(e0, e1) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17163])).
% 2.14/2.24 tff(17165,plain,
% 2.14/2.24 (~(op(e0, e1) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[14, 17164])).
% 2.14/2.24 tff(17166,plain,
% 2.14/2.24 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.24 tff(17167,plain,
% 2.14/2.24 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17166])).
% 2.14/2.24 tff(17168,plain,
% 2.14/2.24 (~(op(e1, e1) = e0)),
% 2.14/2.24 inference(modus_ponens,[status(thm)],[619, 17167])).
% 2.14/2.24 tff(17169,plain,
% 2.14/2.24 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17160])).
% 2.14/2.24 tff(17170,plain,
% 2.14/2.24 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 2.14/2.24 inference(symmetry,[status(thm)],[17169])).
% 2.14/2.24 tff(17171,plain,
% 2.14/2.24 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 2.14/2.24 inference(monotonicity,[status(thm)],[17170])).
% 2.14/2.25 tff(17172,plain,
% 2.14/2.25 (~(op(e3, e1) = e0)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[3429, 17171])).
% 2.14/2.25 tff(17173,plain,
% 2.14/2.25 (op(e2, e1) = e0),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[292, 17172, 17168, 17165])).
% 2.14/2.25 tff(17174,plain,
% 2.14/2.25 (op(e2, e1) = op(e3, e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17173, 17160])).
% 2.14/2.25 tff(17175,plain,
% 2.14/2.25 ((op(e2, e1) = op(e1, e2)) <=> (op(e3, e2) = op(e1, e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17174])).
% 2.14/2.25 tff(17176,plain,
% 2.14/2.25 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = op(e3, e2))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17175, 3635])).
% 2.14/2.25 tff(17177,plain,
% 2.14/2.25 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e1) = op(e1, e2))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17176])).
% 2.14/2.25 tff(17178,plain,
% 2.14/2.25 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17177])).
% 2.14/2.25 tff(17179,plain,
% 2.14/2.25 (~(op(e2, e1) = op(e1, e2))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[2292, 17178])).
% 2.14/2.25 tff(17180,plain,
% 2.14/2.25 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[557, 17179])).
% 2.14/2.25 tff(17181,plain,
% 2.14/2.25 ((op(e2, e1) = e1) <=> (op(e3, e2) = e1)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17174])).
% 2.14/2.25 tff(17182,plain,
% 2.14/2.25 ((op(e3, e2) = e1) <=> (op(e2, e1) = e1)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17181])).
% 2.14/2.25 tff(17183,plain,
% 2.14/2.25 ((~(op(e3, e2) = e1)) <=> (~(op(e2, e1) = e1))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17182])).
% 2.14/2.25 tff(17184,plain,
% 2.14/2.25 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17159])).
% 2.14/2.25 tff(17185,plain,
% 2.14/2.25 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17184])).
% 2.14/2.25 tff(17186,plain,
% 2.14/2.25 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17185])).
% 2.14/2.25 tff(17187,plain,
% 2.14/2.25 (~(op(e3, e2) = e1)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[26, 17186])).
% 2.14/2.25 tff(17188,plain,
% 2.14/2.25 (~(op(e2, e1) = e1)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[17187, 17183])).
% 2.14/2.25 tff(17189,plain,
% 2.14/2.25 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[16115])).
% 2.14/2.25 tff(17190,plain,
% 2.14/2.25 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17189])).
% 2.14/2.25 tff(17191,plain,
% 2.14/2.25 (~(op(e2, e2) = e2)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[515, 17190])).
% 2.14/2.25 tff(17192,plain,
% 2.14/2.25 (op(e2, e2) = e3),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[7007, 17173, 16119, 17191])).
% 2.14/2.25 tff(17193,plain,
% 2.14/2.25 (e3 = op(e2, e2)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17192])).
% 2.14/2.25 tff(17194,plain,
% 2.14/2.25 ((e1 = e3) <=> (e1 = op(e2, e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17193])).
% 2.14/2.25 tff(17195,plain,
% 2.14/2.25 ((e1 = e3) <=> (op(e2, e2) = e1)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17194, 316])).
% 2.14/2.25 tff(17196,plain,
% 2.14/2.25 ((~(e1 = e3)) <=> (~(op(e2, e2) = e1))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17195])).
% 2.14/2.25 tff(17197,plain,
% 2.14/2.25 (~(op(e2, e2) = e1)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[303, 17196])).
% 2.14/2.25 tff(17198,plain,
% 2.14/2.25 (op(e2, op(e2, e2)) = op(e2, e3)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17192])).
% 2.14/2.25 tff(17199,plain,
% 2.14/2.25 (op(e2, op(e2, e2)) = e2),
% 2.14/2.25 inference(transitivity,[status(thm)],[17198, 16115])).
% 2.14/2.25 tff(17200,plain,
% 2.14/2.25 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[528, 17199])).
% 2.14/2.25 tff(17201,plain,
% 2.14/2.25 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17177, 531])).
% 2.14/2.25 tff(17202,plain,
% 2.14/2.25 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17201])).
% 2.14/2.25 tff(17203,plain,
% 2.14/2.25 (~(op(e1, e2) = op(e2, e1))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[2292, 17202])).
% 2.14/2.25 tff(17204,plain,
% 2.14/2.25 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[539, 17203])).
% 2.14/2.25 tff(17205,plain,
% 2.14/2.25 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[16115])).
% 2.14/2.25 tff(17206,plain,
% 2.14/2.25 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17205])).
% 2.14/2.25 tff(17207,plain,
% 2.14/2.25 ((op(e3, e2) = e2) <=> (e0 = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17159])).
% 2.14/2.25 tff(17208,plain,
% 2.14/2.25 ((e0 = e2) <=> (op(e3, e2) = e2)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17207])).
% 2.14/2.25 tff(17209,plain,
% 2.14/2.25 ((e0 = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17208, 17206, 395])).
% 2.14/2.25 tff(17210,plain,
% 2.14/2.25 ((~(e0 = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17209])).
% 2.14/2.25 tff(17211,plain,
% 2.14/2.25 (~(op(e2, e3) = op(e3, e2))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[14, 17210])).
% 2.14/2.25 tff(17212,plain,
% 2.14/2.25 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[430, 17211])).
% 2.14/2.25 tff(17213,plain,
% 2.14/2.25 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e0)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.25 tff(17214,plain,
% 2.14/2.25 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17213])).
% 2.14/2.25 tff(17215,plain,
% 2.14/2.25 ((op(e3, e1) = op(e3, e2)) <=> (op(e1, e3) = op(e3, e1))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17170, 17214, 6290])).
% 2.14/2.25 tff(17216,plain,
% 2.14/2.25 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17215])).
% 2.14/2.25 tff(17217,plain,
% 2.14/2.25 (~(op(e1, e3) = op(e3, e1))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[3429, 17216])).
% 2.14/2.25 tff(17218,plain,
% 2.14/2.25 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[6307, 17217])).
% 2.14/2.25 tff(17219,plain,
% 2.14/2.25 ((~(e0 = e2)) <=> (~(op(e3, e2) = e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17208])).
% 2.14/2.25 tff(17220,plain,
% 2.14/2.25 (~(op(e3, e2) = e2)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[14, 17219])).
% 2.14/2.25 tff(17221,plain,
% 2.14/2.25 (op(e3, e0) = e2),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[15971, 17220, 82])).
% 2.14/2.25 tff(17222,plain,
% 2.14/2.25 ((op(e3, e0) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17221])).
% 2.14/2.25 tff(17223,plain,
% 2.14/2.25 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17222, 1681])).
% 2.14/2.25 tff(17224,plain,
% 2.14/2.25 ((op(e0, e3) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17223])).
% 2.14/2.25 tff(17225,plain,
% 2.14/2.25 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17224, 453])).
% 2.14/2.25 tff(17226,plain,
% 2.14/2.25 ((~(op(e0, e3) = e2)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17225])).
% 2.14/2.25 tff(17227,plain,
% 2.14/2.25 (~(op(e0, e3) = op(e3, e0))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[79, 17226])).
% 2.14/2.25 tff(17228,plain,
% 2.14/2.25 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[496, 17227])).
% 2.14/2.25 tff(17229,plain,
% 2.14/2.25 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.25 tff(17230,plain,
% 2.14/2.25 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17229])).
% 2.14/2.25 tff(17231,plain,
% 2.14/2.25 (~(op(e0, e3) = e0)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[64, 17230])).
% 2.14/2.25 tff(17232,plain,
% 2.14/2.25 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e3, e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17160])).
% 2.14/2.25 tff(17233,plain,
% 2.14/2.25 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17232])).
% 2.14/2.25 tff(17234,plain,
% 2.14/2.25 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17233])).
% 2.14/2.25 tff(17235,plain,
% 2.14/2.25 (~(op(e0, e2) = e0)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[1467, 17234])).
% 2.14/2.25 tff(17236,plain,
% 2.14/2.25 (op(e0, e0) = e0),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[3976, 17235, 17165, 17231])).
% 2.14/2.25 tff(17237,plain,
% 2.14/2.25 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17236])).
% 2.14/2.25 tff(17238,plain,
% 2.14/2.25 (op(e0, op(e0, e0)) = e0),
% 2.14/2.25 inference(transitivity,[status(thm)],[17237, 17236])).
% 2.14/2.25 tff(17239,plain,
% 2.14/2.25 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[5598, 17238])).
% 2.14/2.25 tff(17240,plain,
% 2.14/2.25 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17058])).
% 2.14/2.25 tff(17241,plain,
% 2.14/2.25 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17240])).
% 2.14/2.25 tff(17242,plain,
% 2.14/2.25 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17221])).
% 2.14/2.25 tff(17243,plain,
% 2.14/2.25 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17242, 17241])).
% 2.14/2.25 tff(17244,plain,
% 2.14/2.25 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17243])).
% 2.14/2.25 tff(17245,plain,
% 2.14/2.25 (~(op(e1, e0) = op(e0, e1))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[410, 17244])).
% 2.14/2.25 tff(17246,plain,
% 2.14/2.25 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[613, 17245])).
% 2.14/2.25 tff(17247,plain,
% 2.14/2.25 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e1) = op(e1, e0))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17242, 17241, 596])).
% 2.14/2.25 tff(17248,plain,
% 2.14/2.25 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17247])).
% 2.14/2.25 tff(17249,plain,
% 2.14/2.25 (~(op(e0, e1) = op(e1, e0))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[410, 17248])).
% 2.14/2.25 tff(17250,plain,
% 2.14/2.25 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[609, 17249])).
% 2.14/2.25 tff(17251,plain,
% 2.14/2.25 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17193])).
% 2.14/2.25 tff(17252,plain,
% 2.14/2.25 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17251])).
% 2.14/2.25 tff(17253,plain,
% 2.14/2.25 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17252])).
% 2.14/2.25 tff(17254,plain,
% 2.14/2.25 (~(op(e0, e2) = e3)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[2736, 17253])).
% 2.14/2.25 tff(17255,plain,
% 2.14/2.25 (~(op(e0, e3) = e1)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[5000, 17254, 17062, 17165])).
% 2.14/2.25 tff(17256,plain,
% 2.14/2.25 ((e0 = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17208, 17206])).
% 2.14/2.25 tff(17257,plain,
% 2.14/2.25 ((~(e0 = e2)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17256])).
% 2.14/2.25 tff(17258,plain,
% 2.14/2.25 (~(op(e3, e2) = op(e2, e3))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[14, 17257])).
% 2.14/2.25 tff(17259,plain,
% 2.14/2.25 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[500, 17258])).
% 2.14/2.25 tff(17260,plain,
% 2.14/2.25 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 2.14/2.25 inference(transitivity,[status(thm)],[17170, 17214])).
% 2.14/2.25 tff(17261,plain,
% 2.14/2.25 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17260])).
% 2.14/2.25 tff(17262,plain,
% 2.14/2.25 (~(op(e3, e1) = op(e1, e3))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[3429, 17261])).
% 2.14/2.25 tff(17263,plain,
% 2.14/2.25 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[6362, 17262])).
% 2.14/2.25 tff(17264,plain,
% 2.14/2.25 (op(e1, e2) = e2),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[1151, 17220, 17191, 17074])).
% 2.14/2.25 tff(17265,plain,
% 2.14/2.25 ((op(e1, e2) = e1) <=> (e2 = e1)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17264])).
% 2.14/2.25 tff(17266,plain,
% 2.14/2.25 ((op(e1, e2) = e1) <=> (e1 = e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17265, 69])).
% 2.14/2.25 tff(17267,plain,
% 2.14/2.25 ((e1 = e2) <=> (op(e1, e2) = e1)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17266])).
% 2.14/2.25 tff(17268,plain,
% 2.14/2.25 ((~(e1 = e2)) <=> (~(op(e1, e2) = e1))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17267])).
% 2.14/2.25 tff(17269,plain,
% 2.14/2.25 (~(op(e1, e2) = e1)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[708, 17268])).
% 2.14/2.25 tff(17270,plain,
% 2.14/2.25 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e2, e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17193])).
% 2.14/2.25 tff(17271,plain,
% 2.14/2.25 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17270])).
% 2.14/2.25 tff(17272,plain,
% 2.14/2.25 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17271])).
% 2.14/2.25 tff(17273,plain,
% 2.14/2.25 (~(op(e2, e0) = e3)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[2228, 17272])).
% 2.14/2.25 tff(17274,plain,
% 2.14/2.25 (op(e0, e0) = op(e3, e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17236, 17160])).
% 2.14/2.25 tff(17275,plain,
% 2.14/2.25 ((op(e0, e0) = e3) <=> (op(e3, e2) = e3)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17274])).
% 2.14/2.25 tff(17276,plain,
% 2.14/2.25 ((op(e3, e2) = e3) <=> (op(e0, e0) = e3)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17275])).
% 2.14/2.25 tff(17277,plain,
% 2.14/2.25 ((~(op(e3, e2) = e3)) <=> (~(op(e0, e0) = e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17276])).
% 2.14/2.25 tff(17278,plain,
% 2.14/2.25 ((e0 = e3) <=> (op(e3, e2) = e3)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17160])).
% 2.14/2.25 tff(17279,plain,
% 2.14/2.25 ((~(e0 = e3)) <=> (~(op(e3, e2) = e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17278])).
% 2.14/2.25 tff(17280,plain,
% 2.14/2.25 (~(op(e3, e2) = e3)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[181, 17279])).
% 2.14/2.25 tff(17281,plain,
% 2.14/2.25 (~(op(e0, e0) = e3)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[17280, 17277])).
% 2.14/2.25 tff(17282,plain,
% 2.14/2.25 ((op(e3, e0) = e3) <=> (e2 = e3)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17221])).
% 2.14/2.25 tff(17283,plain,
% 2.14/2.25 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17282])).
% 2.14/2.25 tff(17284,plain,
% 2.14/2.25 ((~(e2 = e3)) <=> (~(op(e3, e0) = e3))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17283])).
% 2.14/2.25 tff(17285,plain,
% 2.14/2.25 (~(op(e3, e0) = e3)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[1321, 17284])).
% 2.14/2.25 tff(17286,plain,
% 2.14/2.25 (op(e1, e0) = e3),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[2713, 17285, 17281, 17273])).
% 2.14/2.25 tff(17287,plain,
% 2.14/2.25 (op(e1, e0) = op(e2, e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17286, 17193])).
% 2.14/2.25 tff(17288,plain,
% 2.14/2.25 ((op(e1, e0) = e1) <=> (op(e2, e2) = e1)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17287])).
% 2.14/2.25 tff(17289,plain,
% 2.14/2.25 ((op(e2, e2) = e1) <=> (op(e1, e0) = e1)),
% 2.14/2.25 inference(symmetry,[status(thm)],[17288])).
% 2.14/2.25 tff(17290,plain,
% 2.14/2.25 ((~(op(e2, e2) = e1)) <=> (~(op(e1, e0) = e1))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17289])).
% 2.14/2.25 tff(17291,plain,
% 2.14/2.25 (~(op(e1, e0) = e1)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[17197, 17290])).
% 2.14/2.25 tff(17292,plain,
% 2.14/2.25 (op(e1, e1) = e1),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[954, 17291, 17269, 17057])).
% 2.14/2.25 tff(17293,plain,
% 2.14/2.25 ((~(op(e0, e3) = e2)) <=> (~(op(e3, e0) = op(e0, e3)))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17224])).
% 2.14/2.25 tff(17294,plain,
% 2.14/2.25 (~(op(e3, e0) = op(e0, e3))),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[79, 17293])).
% 2.14/2.25 tff(17295,plain,
% 2.14/2.25 (op(e0, e3) = e3),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[1495, 17281, 17062, 17254])).
% 2.14/2.25 tff(17296,plain,
% 2.14/2.25 (op(e3, e1) = e3),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[6055, 17295, 17280, 17294])).
% 2.14/2.25 tff(17297,plain,
% 2.14/2.25 (op(e0, e2) = e1),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[2745, 17254, 17074, 17235])).
% 2.14/2.25 tff(17298,plain,
% 2.14/2.25 (op(e3, op(e0, e2)) = op(e3, e1)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17297])).
% 2.14/2.25 tff(17299,plain,
% 2.14/2.25 (op(e3, op(e0, e2)) = e3),
% 2.14/2.25 inference(transitivity,[status(thm)],[17298, 17296])).
% 2.14/2.25 tff(17300,plain,
% 2.14/2.25 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[5635, 17299])).
% 2.14/2.25 tff(17301,plain,
% 2.14/2.25 ($false),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[5693, 17300, 17292, 17263, 17259, 17255, 17250, 17246, 76, 17239, 17228, 17218, 17212, 17204, 17200, 17197, 17188, 17180, 17057])).
% 2.14/2.25 tff(17302,plain,((op(e3, e1) = e2) | (op(e2, e3) = e1) | (op(e0, e3) = e2) | (op(e1, e2) = e3) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.25 tff(17303,plain,
% 2.14/2.25 (op(e3, e1) = e2),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[17302, 79, 76, 75, 17, 72, 68])).
% 2.14/2.25 tff(17304,plain,
% 2.14/2.25 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17303])).
% 2.14/2.25 tff(17305,plain,
% 2.14/2.25 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17304])).
% 2.14/2.25 tff(17306,plain,
% 2.14/2.25 (~(op(e3, e0) = e2)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[580, 17305])).
% 2.14/2.25 tff(17307,plain,
% 2.14/2.25 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17113])).
% 2.14/2.25 tff(17308,plain,
% 2.14/2.25 (op(e1, op(e1, e1)) = e0),
% 2.14/2.25 inference(transitivity,[status(thm)],[17307, 1219])).
% 2.14/2.25 tff(17309,plain,
% 2.14/2.25 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17308])).
% 2.14/2.25 tff(17310,plain,
% 2.14/2.25 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17309])).
% 2.14/2.25 tff(17311,plain,
% 2.14/2.25 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.14/2.25 inference(transitivity,[status(thm)],[17310, 2154])).
% 2.14/2.25 tff(17312,plain,
% 2.14/2.25 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.14/2.25 inference(monotonicity,[status(thm)],[17311])).
% 2.14/2.25 tff(17313,plain,
% 2.14/2.25 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.14/2.25 inference(symmetry,[status(thm)],[17307])).
% 2.14/2.25 tff(17314,plain,
% 2.14/2.25 (e0 = op(e1, op(e1, e1))),
% 2.14/2.25 inference(transitivity,[status(thm)],[2909, 17313])).
% 2.14/2.25 tff(17315,plain,
% 2.14/2.25 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[3009, 17314, 17114])).
% 2.14/2.25 tff(17316,plain,
% 2.14/2.25 (~(op(e1, e0) = e2)),
% 2.14/2.25 inference(modus_ponens,[status(thm)],[17315, 17312])).
% 2.14/2.25 tff(17317,plain,
% 2.14/2.25 (op(e1, e0) = e1),
% 2.14/2.25 inference(unit_resolution,[status(thm)],[728, 17316, 17127, 2168])).
% 2.14/2.25 tff(17318,plain,
% 2.14/2.26 (e1 = op(e1, e0)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17317])).
% 2.14/2.26 tff(17319,plain,
% 2.14/2.26 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17318])).
% 2.14/2.26 tff(17320,plain,
% 2.14/2.26 ((op(e3, e0) = e1) <=> (op(e1, e0) = op(e3, e0))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17319, 2294])).
% 2.14/2.26 tff(17321,plain,
% 2.14/2.26 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17320])).
% 2.14/2.26 tff(17322,plain,
% 2.14/2.26 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17321])).
% 2.14/2.26 tff(17323,plain,
% 2.14/2.26 (~(op(e3, e0) = e1)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[410, 17322])).
% 2.14/2.26 tff(17324,plain,
% 2.14/2.26 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17113])).
% 2.14/2.26 tff(17325,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17324])).
% 2.14/2.26 tff(17326,plain,
% 2.14/2.26 (~(op(e0, e1) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[792, 17325])).
% 2.14/2.26 tff(17327,plain,
% 2.14/2.26 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[6684])).
% 2.14/2.26 tff(17328,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17327])).
% 2.14/2.26 tff(17329,plain,
% 2.14/2.26 (~(op(e0, e1) = e2)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[3046, 17328])).
% 2.14/2.26 tff(17330,plain,
% 2.14/2.26 (op(e2, e1) = e0),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[292, 3849, 84, 183])).
% 2.14/2.26 tff(17331,plain,
% 2.14/2.26 (op(e0, e1) = e1),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[829, 3849, 5828, 2527])).
% 2.14/2.26 tff(17332,plain,
% 2.14/2.26 ($false),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[5928, 17331, 17330, 76, 5900, 124])).
% 2.14/2.26 tff(17333,plain,((op(e0, e1) = e0) | (op(e2, e3) = e1) | (~(op(e1, e0) = e1)) | (op(e2, e3) = e3) | (op(e0, e1) = e2) | (op(e0, e1) = e3) | (op(e1, e1) = e0) | (op(e3, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.26 tff(17334,plain,
% 2.14/2.26 (op(e0, e1) = e0),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[17333, 17317, 76, 124, 17329, 17326, 2639, 8495])).
% 2.14/2.26 tff(17335,plain,
% 2.14/2.26 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17334])).
% 2.14/2.26 tff(17336,plain,
% 2.14/2.26 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17335, 10200])).
% 2.14/2.26 tff(17337,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17336])).
% 2.14/2.26 tff(17338,plain,
% 2.14/2.26 (~(op(e0, e2) = e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[2102, 17337])).
% 2.14/2.26 tff(17339,plain,
% 2.14/2.26 (op(e3, e2) = e0),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[973, 17338, 17, 17087])).
% 2.14/2.26 tff(17340,plain,
% 2.14/2.26 ((op(e3, e2) = e1) <=> (e0 = op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17339, 17318])).
% 2.14/2.26 tff(17341,plain,
% 2.14/2.26 ((op(e3, e2) = e1) <=> (op(e1, e0) = e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17340, 16741])).
% 2.14/2.26 tff(17342,plain,
% 2.14/2.26 ((op(e1, e0) = e0) <=> (op(e3, e2) = e1)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17341])).
% 2.14/2.26 tff(17343,plain,
% 2.14/2.26 ((~(op(e1, e0) = e0)) <=> (~(op(e3, e2) = e1))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17342])).
% 2.14/2.26 tff(17344,plain,
% 2.14/2.26 (~(op(e3, e2) = e1)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[17127, 17343])).
% 2.14/2.26 tff(17345,plain,
% 2.14/2.26 (op(e3, e3) = e1),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[939, 17344, 16700, 17323])).
% 2.14/2.26 tff(17346,plain,
% 2.14/2.26 (e1 = op(e3, e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[17345, 658])).
% 2.14/2.26 tff(17347,plain,
% 2.14/2.26 (op(e3, e3) = op(e1, e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17345, 17318])).
% 2.14/2.26 tff(17348,plain,
% 2.14/2.26 (op(e3, op(e3, e3)) = op(e3, op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17347])).
% 2.14/2.26 tff(17349,plain,
% 2.14/2.26 (op(e3, op(e1, e0)) = op(e3, op(e3, e3))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17348])).
% 2.14/2.26 tff(17350,plain,
% 2.14/2.26 (op(e3, op(e1, e0)) = op(e3, e1)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17317])).
% 2.14/2.26 tff(17351,plain,
% 2.14/2.26 (op(e3, e1) = op(e3, op(e1, e0))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17350])).
% 2.14/2.26 tff(17352,plain,
% 2.14/2.26 (e2 = op(e3, op(e3, e3))),
% 2.14/2.26 inference(transitivity,[status(thm)],[8644, 17351, 17349])).
% 2.14/2.26 tff(17353,plain,
% 2.14/2.26 (op(e3, op(e3, e3)) = e2),
% 2.14/2.26 inference(transitivity,[status(thm)],[17348, 17350, 6684])).
% 2.14/2.26 tff(17354,plain,
% 2.14/2.26 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17353])).
% 2.14/2.26 tff(17355,plain,
% 2.14/2.26 (op(e3, e2) = op(e3, op(e3, op(e3, e3)))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17354])).
% 2.14/2.26 tff(17356,plain,
% 2.14/2.26 (e0 = op(e3, e2)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17339])).
% 2.14/2.26 tff(17357,plain,
% 2.14/2.26 (e0 = op(e3, op(e3, op(e3, e3)))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17356, 17355])).
% 2.14/2.26 tff(17358,plain,
% 2.14/2.26 ($false),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[2034, 17357, 17352, 17346])).
% 2.14/2.26 tff(17359,plain,((op(e1, e0) = e3) | (~(op(e3, e1) = e2)) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (~(op(e1, e3) = e0)) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.26 tff(17360,plain,
% 2.14/2.26 (op(e1, e0) = e3),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[17359, 17303, 17, 76, 16119, 17053, 75])).
% 2.14/2.26 tff(17361,plain,
% 2.14/2.26 ((op(e1, e0) = e2) <=> (e3 = e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17360])).
% 2.14/2.26 tff(17362,plain,
% 2.14/2.26 ((op(e1, e0) = e2) <=> (e2 = e3)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17361, 1314])).
% 2.14/2.26 tff(17363,plain,
% 2.14/2.26 ((e2 = e3) <=> (op(e1, e0) = e2)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17362])).
% 2.14/2.26 tff(17364,plain,
% 2.14/2.26 ((~(e2 = e3)) <=> (~(op(e1, e0) = e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17363])).
% 2.14/2.26 tff(17365,plain,
% 2.14/2.26 (~(op(e1, e0) = e2)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[1321, 17364])).
% 2.14/2.26 tff(17366,plain,
% 2.14/2.26 (op(e0, e0) = e2),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[589, 17365, 17092, 17306])).
% 2.14/2.26 tff(17367,plain,
% 2.14/2.26 (e2 = op(e0, e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[17366, 78])).
% 2.14/2.26 tff(17368,plain,
% 2.14/2.26 (op(e0, op(e0, e0)) = op(e0, e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17366])).
% 2.14/2.26 tff(17369,plain,
% 2.14/2.26 ((e3 = op(e0, op(e0, e0))) <=> (e3 = op(e0, e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17368])).
% 2.14/2.26 tff(17370,plain,
% 2.14/2.26 ((e3 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e3)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17369, 4221])).
% 2.14/2.26 tff(17371,plain,
% 2.14/2.26 ((op(e0, e2) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17370])).
% 2.14/2.26 tff(17372,plain,
% 2.14/2.26 (e3 = op(e1, e0)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17360])).
% 2.14/2.26 tff(17373,plain,
% 2.14/2.26 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17372])).
% 2.14/2.26 tff(17374,plain,
% 2.14/2.26 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17373])).
% 2.14/2.26 tff(17375,plain,
% 2.14/2.26 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17374])).
% 2.14/2.26 tff(17376,plain,
% 2.14/2.26 (~(op(e0, e0) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[2471, 17375])).
% 2.14/2.26 tff(17377,plain,
% 2.14/2.26 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17372])).
% 2.14/2.26 tff(17378,plain,
% 2.14/2.26 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17377, 595])).
% 2.14/2.26 tff(17379,plain,
% 2.14/2.26 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17378])).
% 2.14/2.26 tff(17380,plain,
% 2.14/2.26 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.26 tff(17381,plain,
% 2.14/2.26 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17380])).
% 2.14/2.26 tff(17382,plain,
% 2.14/2.26 (~(op(e1, e2) = e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[1850, 17381])).
% 2.14/2.26 tff(17383,plain,
% 2.14/2.26 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.26 tff(17384,plain,
% 2.14/2.26 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17383, 3077])).
% 2.14/2.26 tff(17385,plain,
% 2.14/2.26 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17384])).
% 2.14/2.26 tff(17386,plain,
% 2.14/2.26 (~(op(e3, e3) = e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[571, 17385])).
% 2.14/2.26 tff(17387,plain,
% 2.14/2.26 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17303])).
% 2.14/2.26 tff(17388,plain,
% 2.14/2.26 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17387, 1])).
% 2.14/2.26 tff(17389,plain,
% 2.14/2.26 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17388])).
% 2.14/2.26 tff(17390,plain,
% 2.14/2.26 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17389])).
% 2.14/2.26 tff(17391,plain,
% 2.14/2.26 (~(op(e3, e1) = e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[14, 17390])).
% 2.14/2.26 tff(17392,plain,
% 2.14/2.26 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17372])).
% 2.14/2.26 tff(17393,plain,
% 2.14/2.26 ((op(e1, e1) = e3) <=> (op(e1, e0) = op(e1, e1))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17392, 710])).
% 2.14/2.26 tff(17394,plain,
% 2.14/2.26 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17393])).
% 2.14/2.26 tff(17395,plain,
% 2.14/2.26 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17394])).
% 2.14/2.26 tff(17396,plain,
% 2.14/2.26 (~(op(e1, e1) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[737, 17395])).
% 2.14/2.26 tff(17397,plain,
% 2.14/2.26 (op(e1, e1) = e1),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[630, 17396, 68, 17168])).
% 2.14/2.26 tff(17398,plain,
% 2.14/2.26 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17397])).
% 2.14/2.26 tff(17399,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17398])).
% 2.14/2.26 tff(17400,plain,
% 2.14/2.26 (~(op(e0, e1) = e1)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[792, 17399])).
% 2.14/2.26 tff(17401,plain,
% 2.14/2.26 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17303])).
% 2.14/2.26 tff(17402,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17401])).
% 2.14/2.26 tff(17403,plain,
% 2.14/2.26 (~(op(e0, e1) = e2)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[3046, 17402])).
% 2.14/2.26 tff(17404,plain,
% 2.14/2.26 ((op(e1, e3) = e3) <=> (e0 = e3)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.26 tff(17405,plain,
% 2.14/2.26 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17404])).
% 2.14/2.26 tff(17406,plain,
% 2.14/2.26 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17405])).
% 2.14/2.26 tff(17407,plain,
% 2.14/2.26 (~(op(e1, e3) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[181, 17406])).
% 2.14/2.26 tff(17408,plain,
% 2.14/2.26 (op(e1, e2) = e2),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[2285, 17365, 68, 72])).
% 2.14/2.26 tff(17409,plain,
% 2.14/2.26 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e2)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17408])).
% 2.14/2.26 tff(17410,plain,
% 2.14/2.26 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17409])).
% 2.14/2.26 tff(17411,plain,
% 2.14/2.26 ((~(op(e2, e1) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17410])).
% 2.14/2.26 tff(17412,plain,
% 2.14/2.26 (~(op(e2, e1) = op(e1, e2))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[16124, 17411])).
% 2.14/2.26 tff(17413,plain,
% 2.14/2.26 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[557, 17412])).
% 2.14/2.26 tff(17414,plain,
% 2.14/2.26 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17303])).
% 2.14/2.26 tff(17415,plain,
% 2.14/2.26 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17414, 2234])).
% 2.14/2.26 tff(17416,plain,
% 2.14/2.26 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17415, 17206])).
% 2.14/2.26 tff(17417,plain,
% 2.14/2.26 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17416])).
% 2.14/2.26 tff(17418,plain,
% 2.14/2.26 (~(op(e3, e2) = op(e2, e3))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[3429, 17417])).
% 2.14/2.26 tff(17419,plain,
% 2.14/2.26 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[500, 17418])).
% 2.14/2.26 tff(17420,plain,
% 2.14/2.26 ((op(e2, e1) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17410, 531])).
% 2.14/2.26 tff(17421,plain,
% 2.14/2.26 ((~(op(e2, e1) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17420])).
% 2.14/2.26 tff(17422,plain,
% 2.14/2.26 (~(op(e1, e2) = op(e2, e1))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[16124, 17421])).
% 2.14/2.26 tff(17423,plain,
% 2.14/2.26 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[539, 17422])).
% 2.14/2.26 tff(17424,plain,
% 2.14/2.26 (op(e1, op(e1, e1)) = op(e1, e1)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17397])).
% 2.14/2.26 tff(17425,plain,
% 2.14/2.26 (op(e1, op(e1, e1)) = e1),
% 2.14/2.26 inference(transitivity,[status(thm)],[17424, 17397])).
% 2.14/2.26 tff(17426,plain,
% 2.14/2.26 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[5678, 17425])).
% 2.14/2.26 tff(17427,plain,
% 2.14/2.26 ((e0 = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17389, 17214])).
% 2.14/2.26 tff(17428,plain,
% 2.14/2.26 ((~(e0 = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17427])).
% 2.14/2.26 tff(17429,plain,
% 2.14/2.26 (~(op(e3, e1) = op(e1, e3))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[14, 17428])).
% 2.14/2.26 tff(17430,plain,
% 2.14/2.26 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[6362, 17429])).
% 2.14/2.26 tff(17431,plain,
% 2.14/2.26 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17415, 17206, 395])).
% 2.14/2.26 tff(17432,plain,
% 2.14/2.26 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17431])).
% 2.14/2.26 tff(17433,plain,
% 2.14/2.26 (~(op(e2, e3) = op(e3, e2))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[3429, 17432])).
% 2.14/2.26 tff(17434,plain,
% 2.14/2.26 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[430, 17433])).
% 2.14/2.26 tff(17435,plain,
% 2.14/2.26 ((e0 = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17389, 17214, 6290])).
% 2.14/2.26 tff(17436,plain,
% 2.14/2.26 ((~(e0 = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17435])).
% 2.14/2.26 tff(17437,plain,
% 2.14/2.26 (~(op(e1, e3) = op(e3, e1))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[14, 17436])).
% 2.14/2.26 tff(17438,plain,
% 2.14/2.26 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[6307, 17437])).
% 2.14/2.26 tff(17439,plain,
% 2.14/2.26 (op(e2, op(e1, e0)) = op(e2, e3)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[258])).
% 2.14/2.26 tff(17440,plain,
% 2.14/2.26 ((op(e2, e3) = e3) <=> (e2 = e3)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[3787])).
% 2.14/2.26 tff(17441,plain,
% 2.14/2.26 ((e2 = e3) <=> (op(e2, e3) = e3)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17440])).
% 2.14/2.26 tff(17442,plain,
% 2.14/2.26 ((~(e2 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17441])).
% 2.14/2.26 tff(17443,plain,
% 2.14/2.26 (~(op(e2, e3) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[1321, 17442])).
% 2.14/2.26 tff(17444,plain,
% 2.14/2.26 (e0 = op(e0, e2)),
% 2.14/2.26 inference(symmetry,[status(thm)],[10155])).
% 2.14/2.26 tff(17445,plain,
% 2.14/2.26 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17444])).
% 2.14/2.26 tff(17446,plain,
% 2.14/2.26 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17445])).
% 2.14/2.26 tff(17447,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17446])).
% 2.14/2.26 tff(17448,plain,
% 2.14/2.26 (~(op(e0, e1) = e0)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[2102, 17447])).
% 2.14/2.26 tff(17449,plain,
% 2.14/2.26 (op(e0, e1) = e3),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[829, 17448, 5828, 3528])).
% 2.14/2.26 tff(17450,plain,
% 2.14/2.26 ((op(e0, e1) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17449])).
% 2.14/2.26 tff(17451,plain,
% 2.14/2.26 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17450, 1364])).
% 2.14/2.26 tff(17452,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17451])).
% 2.14/2.26 tff(17453,plain,
% 2.14/2.26 (~(op(e0, e3) = e3)),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[818, 17452])).
% 2.14/2.26 tff(17454,plain,
% 2.14/2.26 (op(e3, e3) = e3),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[480, 17453, 1080, 17443])).
% 2.14/2.26 tff(17455,plain,
% 2.14/2.26 (op(e3, e3) = op(e1, e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17454, 259])).
% 2.14/2.26 tff(17456,plain,
% 2.14/2.26 (op(e2, op(e3, e3)) = op(e2, op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17455])).
% 2.14/2.26 tff(17457,plain,
% 2.14/2.26 (op(e2, op(e3, e3)) = e2),
% 2.14/2.26 inference(transitivity,[status(thm)],[17456, 17439, 3787])).
% 2.14/2.26 tff(17458,plain,
% 2.14/2.26 (op(e3, e0) = op(e0, e2)),
% 2.14/2.26 inference(transitivity,[status(thm)],[10159, 17444])).
% 2.14/2.26 tff(17459,plain,
% 2.14/2.26 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = op(e0, e2))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17458])).
% 2.14/2.26 tff(17460,plain,
% 2.14/2.26 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e2) = op(e2, e0))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17459, 6337])).
% 2.14/2.26 tff(17461,plain,
% 2.14/2.26 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17460])).
% 2.14/2.26 tff(17462,plain,
% 2.14/2.26 (~(op(e0, e2) = op(e2, e0))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[747, 17461])).
% 2.14/2.26 tff(17463,plain,
% 2.14/2.26 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[6347, 17462])).
% 2.14/2.26 tff(17464,plain,
% 2.14/2.26 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e2) = e0)),
% 2.14/2.26 inference(monotonicity,[status(thm)],[2381])).
% 2.14/2.26 tff(17465,plain,
% 2.14/2.26 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.14/2.26 inference(symmetry,[status(thm)],[17464])).
% 2.14/2.26 tff(17466,plain,
% 2.14/2.26 (op(e0, op(e0, e0)) = e0),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[10155, 17465])).
% 2.14/2.26 tff(17467,plain,
% 2.14/2.26 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[5598, 17466])).
% 2.14/2.26 tff(17468,plain,
% 2.14/2.26 (op(e2, op(e1, e0)) = e2),
% 2.14/2.26 inference(transitivity,[status(thm)],[17439, 3787])).
% 2.14/2.26 tff(17469,plain,
% 2.14/2.26 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[10735, 17468])).
% 2.14/2.26 tff(17470,plain,
% 2.14/2.26 (op(e0, e1) = op(e1, e0)),
% 2.14/2.26 inference(transitivity,[status(thm)],[17449, 259])).
% 2.14/2.26 tff(17471,plain,
% 2.14/2.26 (op(e2, op(e0, e1)) = op(e2, op(e1, e0))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17470])).
% 2.14/2.26 tff(17472,plain,
% 2.14/2.26 (op(e2, op(e0, e1)) = e2),
% 2.14/2.26 inference(transitivity,[status(thm)],[17471, 17439, 3787])).
% 2.14/2.26 tff(17473,plain,
% 2.14/2.26 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[9902, 17472])).
% 2.14/2.26 tff(17474,plain,
% 2.14/2.26 ((op(e3, e0) = op(e0, e3)) <=> (op(e0, e2) = op(e0, e3))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17458])).
% 2.14/2.26 tff(17475,plain,
% 2.14/2.26 ((op(e0, e2) = op(e0, e3)) <=> (op(e3, e0) = op(e0, e3))),
% 2.14/2.26 inference(symmetry,[status(thm)],[17474])).
% 2.14/2.26 tff(17476,plain,
% 2.14/2.26 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = op(e3, e0))),
% 2.14/2.26 inference(transitivity,[status(thm)],[17475, 453])).
% 2.14/2.26 tff(17477,plain,
% 2.14/2.26 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17476])).
% 2.14/2.26 tff(17478,plain,
% 2.14/2.26 (~(op(e0, e3) = op(e3, e0))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[918, 17477])).
% 2.14/2.26 tff(17479,plain,
% 2.14/2.26 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.14/2.26 inference(unit_resolution,[status(thm)],[496, 17478])).
% 2.14/2.26 tff(17480,plain,
% 2.14/2.26 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.14/2.26 inference(monotonicity,[status(thm)],[17459])).
% 2.14/2.26 tff(17481,plain,
% 2.14/2.26 (~(op(e2, e0) = op(e0, e2))),
% 2.14/2.26 inference(modus_ponens,[status(thm)],[747, 17480])).
% 2.14/2.27 tff(17482,plain,
% 2.14/2.27 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[6358, 17481])).
% 2.14/2.27 tff(17483,plain,
% 2.14/2.27 (op(e2, e1) = e0),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[292, 17448, 84, 183])).
% 2.14/2.27 tff(17484,plain,
% 2.14/2.27 (op(e2, e2) = e3),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[7007, 17483, 17443, 9283])).
% 2.14/2.27 tff(17485,plain,
% 2.14/2.27 (op(e2, e2) = op(e1, e0)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17484, 259])).
% 2.14/2.27 tff(17486,plain,
% 2.14/2.27 (op(e2, op(e2, e2)) = op(e2, op(e1, e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17485])).
% 2.14/2.27 tff(17487,plain,
% 2.14/2.27 (op(e2, op(e2, e2)) = e2),
% 2.14/2.27 inference(transitivity,[status(thm)],[17486, 17439, 3787])).
% 2.14/2.27 tff(17488,plain,
% 2.14/2.27 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[528, 17487])).
% 2.14/2.27 tff(17489,plain,
% 2.14/2.27 (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[5367, 17488, 5669, 5668, 17482, 17479, 17473, 5511, 6689, 5673, 5671, 17469, 17467, 5680, 17463])).
% 2.14/2.27 tff(17490,plain,
% 2.14/2.27 (~(op(e2, op(e3, e3)) = e2)),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[14770, 17489])).
% 2.14/2.27 tff(17491,plain,
% 2.14/2.27 ($false),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[17490, 17457])).
% 2.14/2.27 tff(17492,plain,((op(e3, e2) = e0) | (~(op(e2, e3) = e2)) | (~(op(e1, e0) = e3)) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (op(e1, e3) = e3) | (op(e0, e1) = e2) | (op(e0, e1) = e1) | (op(e1, e1) = e0) | (op(e3, e1) = e0) | (~(op(e0, e0) = e2)) | (op(e3, e3) = e0) | (op(e2, e2) = e0) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.27 tff(17493,plain,
% 2.14/2.27 (op(e3, e2) = e0),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[17492, 16115, 17360, 17438, 17434, 17430, 17426, 17423, 17419, 17413, 17407, 17403, 17400, 17168, 17391, 17366, 17386, 17, 17382])).
% 2.14/2.27 tff(17494,plain,
% 2.14/2.27 (e0 = op(e3, e2)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17493])).
% 2.14/2.27 tff(17495,plain,
% 2.14/2.27 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17366])).
% 2.14/2.27 tff(17496,plain,
% 2.14/2.27 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17495, 1])).
% 2.14/2.27 tff(17497,plain,
% 2.14/2.27 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17496])).
% 2.14/2.27 tff(17498,plain,
% 2.14/2.27 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17497])).
% 2.14/2.27 tff(17499,plain,
% 2.14/2.27 (~(op(e0, e0) = e0)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[14, 17498])).
% 2.14/2.27 tff(17500,plain,
% 2.14/2.27 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e3, e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17494])).
% 2.14/2.27 tff(17501,plain,
% 2.14/2.27 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17500])).
% 2.14/2.27 tff(17502,plain,
% 2.14/2.27 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17501])).
% 2.14/2.27 tff(17503,plain,
% 2.14/2.27 (~(op(e0, e2) = e0)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[1467, 17502])).
% 2.14/2.27 tff(17504,plain,
% 2.14/2.27 (op(e0, e1) = e0),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[3976, 17503, 17499, 17231])).
% 2.14/2.27 tff(17505,plain,
% 2.14/2.27 (op(e0, e1) = op(e3, e2)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17504, 17494])).
% 2.14/2.27 tff(17506,plain,
% 2.14/2.27 ((op(e1, e0) = op(e0, e1)) <=> (e3 = op(e3, e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17360, 17505])).
% 2.14/2.27 tff(17507,plain,
% 2.14/2.27 ((op(e1, e0) = op(e0, e1)) <=> (op(e3, e2) = e3)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17506, 3423])).
% 2.14/2.27 tff(17508,plain,
% 2.14/2.27 ((op(e3, e2) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17507])).
% 2.14/2.27 tff(17509,plain,
% 2.14/2.27 ((op(e3, e2) = e3) <=> (op(e0, e1) = e3)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17508, 17379])).
% 2.14/2.27 tff(17510,plain,
% 2.14/2.27 ((~(op(e3, e2) = e3)) <=> (~(op(e0, e1) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17509])).
% 2.14/2.27 tff(17511,plain,
% 2.14/2.27 ((op(e1, e0) = e0) <=> (e3 = op(e3, e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17360, 17494])).
% 2.14/2.27 tff(17512,plain,
% 2.14/2.27 ((op(e1, e0) = e0) <=> (op(e3, e2) = e3)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17511, 3423])).
% 2.14/2.27 tff(17513,plain,
% 2.14/2.27 ((~(op(e1, e0) = e0)) <=> (~(op(e3, e2) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17512])).
% 2.14/2.27 tff(17514,plain,
% 2.14/2.27 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e0)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.27 tff(17515,plain,
% 2.14/2.27 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17514])).
% 2.14/2.27 tff(17516,plain,
% 2.14/2.27 (~(op(e1, e0) = e0)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[110, 17515])).
% 2.14/2.27 tff(17517,plain,
% 2.14/2.27 (~(op(e3, e2) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17516, 17513])).
% 2.14/2.27 tff(17518,plain,
% 2.14/2.27 (~(op(e0, e1) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17517, 17510])).
% 2.14/2.27 tff(17519,plain,
% 2.14/2.27 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e1, e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17372])).
% 2.14/2.27 tff(17520,plain,
% 2.14/2.27 ((op(e3, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 2.14/2.27 inference(transitivity,[status(thm)],[17519, 2294])).
% 2.14/2.27 tff(17521,plain,
% 2.14/2.27 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17520])).
% 2.14/2.27 tff(17522,plain,
% 2.14/2.27 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17521])).
% 2.14/2.27 tff(17523,plain,
% 2.14/2.27 (~(op(e3, e0) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[410, 17522])).
% 2.14/2.27 tff(17524,plain,
% 2.14/2.27 ((op(e3, e1) = e3) <=> (e2 = e3)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17303])).
% 2.14/2.27 tff(17525,plain,
% 2.14/2.27 ((e2 = e3) <=> (op(e3, e1) = e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17524])).
% 2.14/2.27 tff(17526,plain,
% 2.14/2.27 ((~(e2 = e3)) <=> (~(op(e3, e1) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17525])).
% 2.14/2.27 tff(17527,plain,
% 2.14/2.27 (~(op(e3, e1) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[1321, 17526])).
% 2.14/2.27 tff(17528,plain,
% 2.14/2.27 (op(e3, e3) = e3),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[422, 17517, 17527, 17523])).
% 2.14/2.27 tff(17529,plain,
% 2.14/2.27 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e3)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17528])).
% 2.14/2.27 tff(17530,plain,
% 2.14/2.27 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17529])).
% 2.14/2.27 tff(17531,plain,
% 2.14/2.27 (~(op(e0, e3) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[1077, 17530])).
% 2.14/2.27 tff(17532,plain,
% 2.14/2.27 (op(e0, e2) = e3),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[1495, 17531, 17518, 17376])).
% 2.14/2.27 tff(17533,plain,
% 2.14/2.27 (e3 = op(e0, op(e0, e0))),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17532, 17371])).
% 2.14/2.27 tff(17534,plain,
% 2.14/2.27 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17368])).
% 2.14/2.27 tff(17535,plain,
% 2.14/2.27 (op(e0, op(e0, e2)) = op(e0, op(e0, op(e0, e0)))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17534])).
% 2.14/2.27 tff(17536,plain,
% 2.14/2.27 (op(e0, op(e0, e2)) = op(op(e3, e2), e3)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17494, 17532])).
% 2.14/2.27 tff(17537,plain,
% 2.14/2.27 (op(op(e3, e2), e3) = op(e0, op(e0, e2))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17536])).
% 2.14/2.27 tff(17538,plain,
% 2.14/2.27 (op(op(e3, e2), e3) = op(e0, op(e1, e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17493, 17372])).
% 2.14/2.27 tff(17539,plain,
% 2.14/2.27 (op(e0, op(e1, e0)) = op(op(e3, e2), e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17538])).
% 2.14/2.27 tff(17540,plain,
% 2.14/2.27 (op(e0, op(e1, e0)) = op(e0, e3)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17360])).
% 2.14/2.27 tff(17541,plain,
% 2.14/2.27 (op(e0, e3) = op(e0, op(e1, e0))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17540])).
% 2.14/2.27 tff(17542,plain,
% 2.14/2.27 (op(e3, e3) = op(e1, e0)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17528, 17372])).
% 2.14/2.27 tff(17543,plain,
% 2.14/2.27 ((op(e3, e3) = e1) <=> (op(e1, e0) = e1)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17542])).
% 2.14/2.27 tff(17544,plain,
% 2.14/2.27 ((op(e1, e0) = e1) <=> (op(e3, e3) = e1)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17543])).
% 2.14/2.27 tff(17545,plain,
% 2.14/2.27 ((~(op(e1, e0) = e1)) <=> (~(op(e3, e3) = e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17544])).
% 2.14/2.27 tff(17546,plain,
% 2.14/2.27 ((e1 = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 2.14/2.27 inference(commutativity,[status(thm)],[])).
% 2.14/2.27 tff(17547,plain,
% 2.14/2.27 ((e1 = e3) <=> (e1 = op(e1, e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17372])).
% 2.14/2.27 tff(17548,plain,
% 2.14/2.27 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17547, 17546])).
% 2.14/2.27 tff(17549,plain,
% 2.14/2.27 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17548])).
% 2.14/2.27 tff(17550,plain,
% 2.14/2.27 (~(op(e1, e0) = e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[303, 17549])).
% 2.14/2.27 tff(17551,plain,
% 2.14/2.27 (~(op(e3, e3) = e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17550, 17545])).
% 2.14/2.27 tff(17552,plain,
% 2.14/2.27 (op(e0, e3) = e1),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[151, 17551, 76, 17057])).
% 2.14/2.27 tff(17553,plain,
% 2.14/2.27 (e1 = op(e0, e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17552])).
% 2.14/2.27 tff(17554,plain,
% 2.14/2.27 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.14/2.27 inference(transitivity,[status(thm)],[17553, 17541, 17539, 17537, 17535])).
% 2.14/2.27 tff(17555,plain,
% 2.14/2.27 ($false),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[10921, 17554, 17533, 17367])).
% 2.14/2.27 tff(17556,plain,((op(e0, e3) = e2) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.27 tff(17557,plain,
% 2.14/2.27 (op(e0, e3) = e2),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[17556, 76, 17, 68, 72, 75])).
% 2.14/2.27 tff(17558,plain,
% 2.14/2.27 (e2 = op(e0, e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17557])).
% 2.14/2.27 tff(17559,plain,
% 2.14/2.27 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17558])).
% 2.14/2.27 tff(17560,plain,
% 2.14/2.27 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17559])).
% 2.14/2.27 tff(17561,plain,
% 2.14/2.27 (op(e1, e1) = e3),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[247, 2168, 75, 17407])).
% 2.14/2.27 tff(17562,plain,
% 2.14/2.27 ((op(e1, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17561])).
% 2.14/2.27 tff(17563,plain,
% 2.14/2.27 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17562, 396])).
% 2.14/2.27 tff(17564,plain,
% 2.14/2.27 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17563])).
% 2.14/2.27 tff(17565,plain,
% 2.14/2.27 (~(op(e3, e1) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[945, 17564])).
% 2.14/2.27 tff(17566,plain,
% 2.14/2.27 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.27 tff(17567,plain,
% 2.14/2.27 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17566, 86])).
% 2.14/2.27 tff(17568,plain,
% 2.14/2.27 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17567])).
% 2.14/2.27 tff(17569,plain,
% 2.14/2.27 (~(op(e2, e3) = e0)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[118, 17568])).
% 2.14/2.27 tff(17570,plain,
% 2.14/2.27 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17558])).
% 2.14/2.27 tff(17571,plain,
% 2.14/2.27 ((op(e2, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 2.14/2.27 inference(transitivity,[status(thm)],[17570, 925])).
% 2.14/2.27 tff(17572,plain,
% 2.14/2.27 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17571])).
% 2.14/2.27 tff(17573,plain,
% 2.14/2.27 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17572])).
% 2.14/2.27 tff(17574,plain,
% 2.14/2.27 (~(op(e2, e3) = e2)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[964, 17573])).
% 2.14/2.27 tff(17575,plain,
% 2.14/2.27 (op(e2, e3) = e3),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[206, 17574, 76, 17569])).
% 2.14/2.27 tff(17576,plain,
% 2.14/2.27 (op(e1, op(e2, e3)) = op(e1, e3)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17575])).
% 2.14/2.27 tff(17577,plain,
% 2.14/2.27 (e3 = op(e2, e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17575])).
% 2.14/2.27 tff(17578,plain,
% 2.14/2.27 (op(e1, e1) = op(e2, e3)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17561, 17577])).
% 2.14/2.27 tff(17579,plain,
% 2.14/2.27 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17578])).
% 2.14/2.27 tff(17580,plain,
% 2.14/2.27 (op(e1, op(e1, e1)) = e0),
% 2.14/2.27 inference(transitivity,[status(thm)],[17579, 17576, 17053])).
% 2.14/2.27 tff(17581,plain,
% 2.14/2.27 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17580])).
% 2.14/2.27 tff(17582,plain,
% 2.14/2.27 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17581])).
% 2.14/2.27 tff(17583,plain,
% 2.14/2.27 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17582, 2154])).
% 2.14/2.27 tff(17584,plain,
% 2.14/2.27 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17583])).
% 2.14/2.27 tff(17585,plain,
% 2.14/2.27 (e3 = op(e1, e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17561, 1740])).
% 2.14/2.27 tff(17586,plain,
% 2.14/2.27 (op(e1, op(e2, e3)) = op(e1, op(e1, e1))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17579])).
% 2.14/2.27 tff(17587,plain,
% 2.14/2.27 (op(e1, e3) = op(e1, op(e2, e3))),
% 2.14/2.27 inference(symmetry,[status(thm)],[17576])).
% 2.14/2.27 tff(17588,plain,
% 2.14/2.27 (e0 = op(e1, e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17053])).
% 2.14/2.27 tff(17589,plain,
% 2.14/2.27 (e0 = op(e1, op(e1, e1))),
% 2.14/2.27 inference(transitivity,[status(thm)],[17588, 17587, 17586])).
% 2.14/2.27 tff(17590,plain,
% 2.14/2.27 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[3009, 17589, 17585])).
% 2.14/2.27 tff(17591,plain,
% 2.14/2.27 (~(op(e1, e0) = e2)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[17590, 17584])).
% 2.14/2.27 tff(17592,plain,
% 2.14/2.27 (op(e1, e0) = e1),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[728, 17591, 17516, 2168])).
% 2.14/2.27 tff(17593,plain,
% 2.14/2.27 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e1)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17592])).
% 2.14/2.27 tff(17594,plain,
% 2.14/2.27 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17593])).
% 2.14/2.27 tff(17595,plain,
% 2.14/2.27 (~(op(e0, e0) = e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[2471, 17594])).
% 2.14/2.27 tff(17596,plain,
% 2.14/2.27 ((e1 = e2) <=> (e1 = op(e0, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17558])).
% 2.14/2.27 tff(17597,plain,
% 2.14/2.27 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17596, 10225])).
% 2.14/2.27 tff(17598,plain,
% 2.14/2.27 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17597])).
% 2.14/2.27 tff(17599,plain,
% 2.14/2.27 (~(op(e0, e3) = e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[708, 17598])).
% 2.14/2.27 tff(17600,plain,
% 2.14/2.27 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17577])).
% 2.14/2.27 tff(17601,plain,
% 2.14/2.27 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17600])).
% 2.14/2.27 tff(17602,plain,
% 2.14/2.27 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17601])).
% 2.14/2.27 tff(17603,plain,
% 2.14/2.27 (~(op(e2, e2) = e3)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[515, 17602])).
% 2.14/2.27 tff(17604,plain,
% 2.14/2.27 (op(e1, e2) = e2),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[2285, 17591, 68, 72])).
% 2.14/2.27 tff(17605,plain,
% 2.14/2.27 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17604])).
% 2.14/2.27 tff(17606,plain,
% 2.14/2.27 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17605, 81])).
% 2.14/2.27 tff(17607,plain,
% 2.14/2.27 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17606])).
% 2.14/2.27 tff(17608,plain,
% 2.14/2.27 (~(op(e2, e2) = e2)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[1273, 17607])).
% 2.14/2.27 tff(17609,plain,
% 2.14/2.27 (op(e2, e2) = e1),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[524, 17608, 17, 17603])).
% 2.14/2.27 tff(17610,plain,
% 2.14/2.27 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17609])).
% 2.14/2.27 tff(17611,plain,
% 2.14/2.27 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17610])).
% 2.14/2.27 tff(17612,plain,
% 2.14/2.27 (~(op(e0, e2) = e1)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[2736, 17611])).
% 2.14/2.27 tff(17613,plain,
% 2.14/2.27 (op(e0, e1) = e1),
% 2.14/2.27 inference(unit_resolution,[status(thm)],[384, 17612, 17599, 17595])).
% 2.14/2.27 tff(17614,plain,
% 2.14/2.27 ((op(e0, e1) = e0) <=> (e1 = e0)),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17613])).
% 2.14/2.27 tff(17615,plain,
% 2.14/2.27 ((op(e0, e1) = e0) <=> (e0 = e1)),
% 2.14/2.27 inference(transitivity,[status(thm)],[17614, 18])).
% 2.14/2.27 tff(17616,plain,
% 2.14/2.27 ((e0 = e1) <=> (op(e0, e1) = e0)),
% 2.14/2.27 inference(symmetry,[status(thm)],[17615])).
% 2.14/2.27 tff(17617,plain,
% 2.14/2.27 ((~(e0 = e1)) <=> (~(op(e0, e1) = e0))),
% 2.14/2.27 inference(monotonicity,[status(thm)],[17616])).
% 2.14/2.27 tff(17618,plain,
% 2.14/2.27 (~(op(e0, e1) = e0)),
% 2.14/2.27 inference(modus_ponens,[status(thm)],[26, 17617])).
% 2.14/2.27 tff(17619,plain,
% 2.14/2.28 (op(e3, e3) = e1),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[151, 17599, 76, 17057])).
% 2.14/2.28 tff(17620,plain,
% 2.14/2.28 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17604])).
% 2.14/2.28 tff(17621,plain,
% 2.14/2.28 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17620, 2234])).
% 2.14/2.28 tff(17622,plain,
% 2.14/2.28 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17621])).
% 2.14/2.28 tff(17623,plain,
% 2.14/2.28 (~(op(e3, e2) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[2292, 17622])).
% 2.14/2.28 tff(17624,plain,
% 2.14/2.28 (op(op(e1, e0), e0) = op(e1, e0)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17592])).
% 2.14/2.28 tff(17625,plain,
% 2.14/2.28 (op(op(e1, e0), e0) = e1),
% 2.14/2.28 inference(transitivity,[status(thm)],[17624, 17592])).
% 2.14/2.28 tff(17626,plain,
% 2.14/2.28 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[3015, 17625])).
% 2.14/2.28 tff(17627,plain,
% 2.14/2.28 (op(e1, op(e0, e3)) = op(e1, e2)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17557])).
% 2.14/2.28 tff(17628,plain,
% 2.14/2.28 (op(e1, e2) = op(e0, e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17604, 17558])).
% 2.14/2.28 tff(17629,plain,
% 2.14/2.28 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17628])).
% 2.14/2.28 tff(17630,plain,
% 2.14/2.28 (op(e1, op(e1, e2)) = e2),
% 2.14/2.28 inference(transitivity,[status(thm)],[17629, 17627, 17604])).
% 2.14/2.28 tff(17631,plain,
% 2.14/2.28 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2377, 17630])).
% 2.14/2.28 tff(17632,plain,
% 2.14/2.28 (op(e0, op(e0, e1)) = op(e0, e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17613])).
% 2.14/2.28 tff(17633,plain,
% 2.14/2.28 (op(e0, op(e0, e1)) = e1),
% 2.14/2.28 inference(transitivity,[status(thm)],[17632, 17613])).
% 2.14/2.28 tff(17634,plain,
% 2.14/2.28 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2449, 17633])).
% 2.14/2.28 tff(17635,plain,
% 2.14/2.28 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.28 tff(17636,plain,
% 2.14/2.28 ((op(op(e1, e3), e1) = e3) <=> (op(e0, e1) = e3)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17635])).
% 2.14/2.28 tff(17637,plain,
% 2.14/2.28 ((op(e0, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17636])).
% 2.14/2.28 tff(17638,plain,
% 2.14/2.28 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e3)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17561])).
% 2.14/2.28 tff(17639,plain,
% 2.14/2.28 ((op(e0, e1) = op(e1, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17638, 17637])).
% 2.14/2.28 tff(17640,plain,
% 2.14/2.28 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17639])).
% 2.14/2.28 tff(17641,plain,
% 2.14/2.28 (~(op(op(e1, e3), e1) = e3)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[792, 17640])).
% 2.14/2.28 tff(17642,plain,
% 2.14/2.28 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[160, 17641])).
% 2.14/2.28 tff(17643,plain,
% 2.14/2.28 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[2560])).
% 2.14/2.28 tff(17644,plain,
% 2.14/2.28 ((op(e2, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 2.14/2.28 inference(transitivity,[status(thm)],[17643, 925])).
% 2.14/2.28 tff(17645,plain,
% 2.14/2.28 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17644])).
% 2.14/2.28 tff(17646,plain,
% 2.14/2.28 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17645])).
% 2.14/2.28 tff(17647,plain,
% 2.14/2.28 (~(op(e2, e3) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[964, 17646])).
% 2.14/2.28 tff(17648,plain,
% 2.14/2.28 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[305])).
% 2.14/2.28 tff(17649,plain,
% 2.14/2.28 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17648])).
% 2.14/2.28 tff(17650,plain,
% 2.14/2.28 (~(op(e3, e1) = e1)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[437, 17649])).
% 2.14/2.28 tff(17651,plain,
% 2.14/2.28 (op(e3, e1) = e2),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[446, 183, 17650, 2839])).
% 2.14/2.28 tff(17652,plain,
% 2.14/2.28 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17651])).
% 2.14/2.28 tff(17653,plain,
% 2.14/2.28 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17652])).
% 2.14/2.28 tff(17654,plain,
% 2.14/2.28 (~(op(e2, e1) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[402, 17653])).
% 2.14/2.28 tff(17655,plain,
% 2.14/2.28 (op(e2, e0) = e2),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2088, 17654, 17647, 5548])).
% 2.14/2.28 tff(17656,plain,
% 2.14/2.28 (op(e2, e1) = e0),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[292, 183, 84, 3849])).
% 2.14/2.28 tff(17657,plain,
% 2.14/2.28 (op(e2, op(e2, e1)) = op(op(e0, e3), e0)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[2560, 17656])).
% 2.14/2.28 tff(17658,plain,
% 2.14/2.28 (e0 = op(e2, e1)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17656])).
% 2.14/2.28 tff(17659,plain,
% 2.14/2.28 (op(op(e2, e0), e0) = op(e2, op(e2, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17655, 17658])).
% 2.14/2.28 tff(17660,plain,
% 2.14/2.28 (op(op(e2, e0), e0) = e2),
% 2.14/2.28 inference(transitivity,[status(thm)],[17659, 17657, 2583, 17655])).
% 2.14/2.28 tff(17661,plain,
% 2.14/2.28 (~(op(e3, e2) = e0)),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[6787, 17651, 6778, 305])).
% 2.14/2.28 tff(17662,plain,
% 2.14/2.28 (op(e0, e2) = e0),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[973, 17661, 17, 1947])).
% 2.14/2.28 tff(17663,plain,
% 2.14/2.28 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[2])).
% 2.14/2.28 tff(17664,plain,
% 2.14/2.28 (op(op(e2, e1), e2) = op(e0, op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17656, 2560])).
% 2.14/2.28 tff(17665,plain,
% 2.14/2.28 (op(op(e2, e1), e2) = op(e2, e1)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17664, 17663, 17662, 17658])).
% 2.14/2.28 tff(17666,plain,
% 2.14/2.28 ((op(op(e2, e1), e2) = e1) <=> (op(e2, e1) = e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17665])).
% 2.14/2.28 tff(17667,plain,
% 2.14/2.28 ((op(e2, e1) = e1) <=> (op(op(e2, e1), e2) = e1)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17666])).
% 2.14/2.28 tff(17668,plain,
% 2.14/2.28 ((~(op(e2, e1) = e1)) <=> (~(op(op(e2, e1), e2) = e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17667])).
% 2.14/2.28 tff(17669,plain,
% 2.14/2.28 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[6779])).
% 2.14/2.28 tff(17670,plain,
% 2.14/2.28 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17669])).
% 2.14/2.28 tff(17671,plain,
% 2.14/2.28 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17670])).
% 2.14/2.28 tff(17672,plain,
% 2.14/2.28 (~(op(e2, e2) = e3)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[515, 17671])).
% 2.14/2.28 tff(17673,plain,
% 2.14/2.28 (op(e2, e2) = e1),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[524, 5548, 17, 17672])).
% 2.14/2.28 tff(17674,plain,
% 2.14/2.28 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17673])).
% 2.14/2.28 tff(17675,plain,
% 2.14/2.28 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17674])).
% 2.14/2.28 tff(17676,plain,
% 2.14/2.28 (~(op(e2, e1) = e1)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[508, 17675])).
% 2.14/2.28 tff(17677,plain,
% 2.14/2.28 (~(op(op(e2, e1), e2) = e1)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17676, 17668])).
% 2.14/2.28 tff(17678,plain,
% 2.14/2.28 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[5808, 17677])).
% 2.14/2.28 tff(17679,plain,
% 2.14/2.28 (op(e3, e0) = e0),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1916, 17661, 656, 183])).
% 2.14/2.28 tff(17680,plain,
% 2.14/2.28 (op(e3, op(e2, e1)) = op(e3, e0)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17656])).
% 2.14/2.28 tff(17681,plain,
% 2.14/2.28 (op(e3, e0) = op(e2, e1)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17679, 17658])).
% 2.14/2.28 tff(17682,plain,
% 2.14/2.28 (op(e3, op(e3, e0)) = op(e3, op(e2, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17681])).
% 2.14/2.28 tff(17683,plain,
% 2.14/2.28 (op(e3, op(e3, e0)) = e0),
% 2.14/2.28 inference(transitivity,[status(thm)],[17682, 17680, 17679])).
% 2.14/2.28 tff(17684,plain,
% 2.14/2.28 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1345, 17683])).
% 2.14/2.28 tff(17685,plain,
% 2.14/2.28 (op(e0, e2) = op(e2, e1)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17662, 17658])).
% 2.14/2.28 tff(17686,plain,
% 2.14/2.28 (op(op(e0, e2), e2) = op(op(e2, e1), e2)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17685])).
% 2.14/2.28 tff(17687,plain,
% 2.14/2.28 (op(op(e0, e2), e2) = e0),
% 2.14/2.28 inference(transitivity,[status(thm)],[17686, 17664, 17663, 17662])).
% 2.14/2.28 tff(17688,plain,
% 2.14/2.28 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1956, 17687])).
% 2.14/2.28 tff(17689,plain,
% 2.14/2.28 (op(e2, op(e2, e3)) = op(op(e0, e3), e3)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[2560, 6778])).
% 2.14/2.28 tff(17690,plain,
% 2.14/2.28 (op(e2, op(e2, e3)) = e3),
% 2.14/2.28 inference(transitivity,[status(thm)],[17689, 2607, 6778])).
% 2.14/2.28 tff(17691,plain,
% 2.14/2.28 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2344, 17690])).
% 2.14/2.28 tff(17692,plain,
% 2.14/2.28 (op(e3, e2) = e3),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1898, 17661, 10457, 2386])).
% 2.14/2.28 tff(17693,plain,
% 2.14/2.28 (op(op(e3, e2), e2) = e3),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[7919, 17692])).
% 2.14/2.28 tff(17694,plain,
% 2.14/2.28 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1339, 17693])).
% 2.14/2.28 tff(17695,plain,
% 2.14/2.28 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[2583])).
% 2.14/2.28 tff(17696,plain,
% 2.14/2.28 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17695])).
% 2.14/2.28 tff(17697,plain,
% 2.14/2.28 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e2, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[6779])).
% 2.14/2.28 tff(17698,plain,
% 2.14/2.28 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17697])).
% 2.14/2.28 tff(17699,plain,
% 2.14/2.28 ((op(e2, e0) = op(e2, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17698, 17696])).
% 2.14/2.28 tff(17700,plain,
% 2.14/2.28 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17699])).
% 2.14/2.28 tff(17701,plain,
% 2.14/2.28 (~(op(op(e0, e3), e0) = e3)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[989, 17700])).
% 2.14/2.28 tff(17702,plain,
% 2.14/2.28 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2635, 17701])).
% 2.14/2.28 tff(17703,plain,
% 2.14/2.28 (op(op(e3, e1), e3) = op(e2, op(e2, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17651, 6779])).
% 2.14/2.28 tff(17704,plain,
% 2.14/2.28 (op(op(e3, e1), e3) = op(e2, e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17703, 17689, 2607])).
% 2.14/2.28 tff(17705,plain,
% 2.14/2.28 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17704])).
% 2.14/2.28 tff(17706,plain,
% 2.14/2.28 ((op(e2, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17705])).
% 2.14/2.28 tff(17707,plain,
% 2.14/2.28 ((~(op(e2, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17706])).
% 2.14/2.28 tff(17708,plain,
% 2.14/2.28 (~(op(op(e3, e1), e3) = e1)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[76, 17707])).
% 2.14/2.28 tff(17709,plain,
% 2.14/2.28 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1050, 17708])).
% 2.14/2.28 tff(17710,plain,
% 2.14/2.28 (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1459, 17709, 17702, 17694, 17691, 1304, 4549, 1358, 17688, 17684, 1357, 17678])).
% 2.14/2.28 tff(17711,plain,
% 2.14/2.28 (~(op(op(e2, e0), e0) = e2)),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1945, 17710])).
% 2.14/2.28 tff(17712,plain,
% 2.14/2.28 ($false),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[17711, 17660])).
% 2.14/2.28 tff(17713,plain,((op(e3, e1) = e0) | (~(op(e0, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (op(e2, e2) = e2) | (op(e2, e3) = e1) | (~(op(e2, e3) = e3)) | (op(e3, e2) = e2) | (op(e3, e3) = e0) | (op(e2, e2) = e0) | (op(e1, e2) = e0) | (~(op(e3, e3) = e1)) | (op(e1, e1) = e0) | (op(e0, e1) = e0) | (op(e3, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.28 tff(17714,plain,
% 2.14/2.28 (op(e3, e1) = e0),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[17713, 17642, 17557, 17634, 17631, 17626, 17608, 76, 17575, 17623, 17386, 17, 17382, 17619, 17168, 17618, 17565])).
% 2.14/2.28 tff(17715,plain,
% 2.14/2.28 (e0 = op(e3, e1)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17714])).
% 2.14/2.28 tff(17716,plain,
% 2.14/2.28 (op(e3, e0) = op(e3, op(e3, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17715])).
% 2.14/2.28 tff(17717,plain,
% 2.14/2.28 (op(e3, op(e3, e1)) = op(e3, e0)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17716])).
% 2.14/2.28 tff(17718,plain,
% 2.14/2.28 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17619])).
% 2.14/2.28 tff(17719,plain,
% 2.14/2.28 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17718])).
% 2.14/2.28 tff(17720,plain,
% 2.14/2.28 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17719, 17717])).
% 2.14/2.28 tff(17721,plain,
% 2.14/2.28 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e0, e3) = op(e3, e0))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17558, 17720])).
% 2.14/2.28 tff(17722,plain,
% 2.14/2.28 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = op(e0, e3))),
% 2.14/2.28 inference(transitivity,[status(thm)],[17721, 452])).
% 2.14/2.28 tff(17723,plain,
% 2.14/2.28 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17722, 17560])).
% 2.14/2.28 tff(17724,plain,
% 2.14/2.28 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17723])).
% 2.14/2.28 tff(17725,plain,
% 2.14/2.28 (e1 = op(e3, e3)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17619, 658])).
% 2.14/2.28 tff(17726,plain,
% 2.14/2.28 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17718])).
% 2.14/2.28 tff(17727,plain,
% 2.14/2.28 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17726, 5470])).
% 2.14/2.28 tff(17728,plain,
% 2.14/2.28 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.14/2.28 inference(symmetry,[status(thm)],[17727])).
% 2.14/2.28 tff(17729,plain,
% 2.14/2.28 (e0 = op(e3, op(e3, e3))),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17714, 17728])).
% 2.14/2.28 tff(17730,plain,
% 2.14/2.28 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[5397, 17729, 17725])).
% 2.14/2.28 tff(17731,plain,
% 2.14/2.28 (~(op(e3, e0) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17730, 17724])).
% 2.14/2.28 tff(17732,plain,
% 2.14/2.28 ((op(e3, e1) = e2) <=> (e0 = op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17714, 17558])).
% 2.14/2.28 tff(17733,plain,
% 2.14/2.28 ((op(e3, e1) = e2) <=> (op(e0, e3) = e0)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17732, 1079])).
% 2.14/2.28 tff(17734,plain,
% 2.14/2.28 ((op(e0, e3) = e0) <=> (op(e3, e1) = e2)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17733])).
% 2.14/2.28 tff(17735,plain,
% 2.14/2.28 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e1) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17734])).
% 2.14/2.28 tff(17736,plain,
% 2.14/2.28 (~(op(e3, e1) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17231, 17735])).
% 2.14/2.28 tff(17737,plain,
% 2.14/2.28 (op(e3, e0) = e2),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[15971, 17736, 17623])).
% 2.14/2.28 tff(17738,plain,
% 2.14/2.28 ($false),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[17737, 17731])).
% 2.14/2.28 tff(17739,plain,((op(e1, e0) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.28 tff(17740,plain,
% 2.14/2.28 (op(e1, e0) = e3),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[17739, 76, 17, 68, 72, 75])).
% 2.14/2.28 tff(17741,plain,
% 2.14/2.28 ((op(e1, e0) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17740])).
% 2.14/2.28 tff(17742,plain,
% 2.14/2.28 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17741, 1112])).
% 2.14/2.28 tff(17743,plain,
% 2.14/2.28 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17742])).
% 2.14/2.28 tff(17744,plain,
% 2.14/2.28 (~(op(e1, e1) = e3)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[737, 17743])).
% 2.14/2.28 tff(17745,plain,
% 2.14/2.28 (op(e1, e0) = op(e2, e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17740, 17577])).
% 2.14/2.28 tff(17746,plain,
% 2.14/2.28 ((op(e1, e0) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17745, 17558])).
% 2.14/2.28 tff(17747,plain,
% 2.14/2.28 ((op(e1, e0) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 2.14/2.28 inference(transitivity,[status(thm)],[17746, 925])).
% 2.14/2.28 tff(17748,plain,
% 2.14/2.28 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e0) = e2)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17747])).
% 2.14/2.28 tff(17749,plain,
% 2.14/2.28 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e0) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17748])).
% 2.14/2.28 tff(17750,plain,
% 2.14/2.28 (~(op(e1, e0) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[964, 17749])).
% 2.14/2.28 tff(17751,plain,
% 2.14/2.28 (op(e1, e2) = e2),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2285, 17750, 68, 72])).
% 2.14/2.28 tff(17752,plain,
% 2.14/2.28 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17751])).
% 2.14/2.28 tff(17753,plain,
% 2.14/2.28 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17752, 2234])).
% 2.14/2.28 tff(17754,plain,
% 2.14/2.28 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17753])).
% 2.14/2.28 tff(17755,plain,
% 2.14/2.28 (~(op(e3, e2) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[2292, 17754])).
% 2.14/2.28 tff(17756,plain,
% 2.14/2.28 ((op(e1, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17751])).
% 2.14/2.28 tff(17757,plain,
% 2.14/2.28 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17756, 81])).
% 2.14/2.28 tff(17758,plain,
% 2.14/2.28 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17757])).
% 2.14/2.28 tff(17759,plain,
% 2.14/2.28 (~(op(e2, e2) = e2)),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[1273, 17758])).
% 2.14/2.28 tff(17760,plain,
% 2.14/2.28 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17745])).
% 2.14/2.28 tff(17761,plain,
% 2.14/2.28 (op(e1, op(e1, e0)) = e0),
% 2.14/2.28 inference(transitivity,[status(thm)],[17760, 17576, 17053])).
% 2.14/2.28 tff(17762,plain,
% 2.14/2.28 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[1836, 17761])).
% 2.14/2.28 tff(17763,plain,
% 2.14/2.28 (op(e1, e2) = op(e0, e3)),
% 2.14/2.28 inference(transitivity,[status(thm)],[17751, 17558])).
% 2.14/2.28 tff(17764,plain,
% 2.14/2.28 (op(e1, op(e1, e2)) = op(e1, op(e0, e3))),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17763])).
% 2.14/2.28 tff(17765,plain,
% 2.14/2.28 (op(e1, op(e1, e2)) = e2),
% 2.14/2.28 inference(transitivity,[status(thm)],[17764, 17627, 17751])).
% 2.14/2.28 tff(17766,plain,
% 2.14/2.28 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[2377, 17765])).
% 2.14/2.28 tff(17767,plain,
% 2.14/2.28 (op(e1, op(e1, e3)) = op(e1, e0)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17053])).
% 2.14/2.28 tff(17768,plain,
% 2.14/2.28 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e0) = e3)),
% 2.14/2.28 inference(monotonicity,[status(thm)],[17767])).
% 2.14/2.28 tff(17769,plain,
% 2.14/2.28 ((op(e1, e0) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 2.14/2.28 inference(symmetry,[status(thm)],[17768])).
% 2.14/2.28 tff(17770,plain,
% 2.14/2.28 (op(e1, op(e1, e3)) = e3),
% 2.14/2.28 inference(modus_ponens,[status(thm)],[17740, 17769])).
% 2.14/2.28 tff(17771,plain,
% 2.14/2.28 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.14/2.28 inference(unit_resolution,[status(thm)],[162, 17770])).
% 2.14/2.29 tff(17772,plain,
% 2.14/2.29 (op(e2, e3) = e3),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[206, 17647, 76, 2558])).
% 2.14/2.29 tff(17773,plain,
% 2.14/2.29 (e3 = op(e2, e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17772])).
% 2.14/2.29 tff(17774,plain,
% 2.14/2.29 ((e1 = e2) <=> (e1 = op(e0, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[2560])).
% 2.14/2.29 tff(17775,plain,
% 2.14/2.29 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17774, 10225])).
% 2.14/2.29 tff(17776,plain,
% 2.14/2.29 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17775])).
% 2.14/2.29 tff(17777,plain,
% 2.14/2.29 (~(op(e0, e3) = e1)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[708, 17776])).
% 2.14/2.29 tff(17778,plain,
% 2.14/2.29 (op(e3, e3) = e1),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[151, 17777, 76, 2672])).
% 2.14/2.29 tff(17779,plain,
% 2.14/2.29 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17778])).
% 2.14/2.29 tff(17780,plain,
% 2.14/2.29 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17779])).
% 2.14/2.29 tff(17781,plain,
% 2.14/2.29 (~(op(e3, e1) = e1)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[437, 17780])).
% 2.14/2.29 tff(17782,plain,
% 2.14/2.29 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17773])).
% 2.14/2.29 tff(17783,plain,
% 2.14/2.29 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17782])).
% 2.14/2.29 tff(17784,plain,
% 2.14/2.29 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17783])).
% 2.14/2.29 tff(17785,plain,
% 2.14/2.29 (~(op(e2, e2) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[515, 17784])).
% 2.14/2.29 tff(17786,plain,
% 2.14/2.29 (op(e2, e2) = e1),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[524, 5548, 17, 17785])).
% 2.14/2.29 tff(17787,plain,
% 2.14/2.29 (op(e2, op(e2, e1)) = op(e2, e2)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[10381])).
% 2.14/2.29 tff(17788,plain,
% 2.14/2.29 (op(e2, op(e2, e1)) = e1),
% 2.14/2.29 inference(transitivity,[status(thm)],[17787, 307])).
% 2.14/2.29 tff(17789,plain,
% 2.14/2.29 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[2560])).
% 2.14/2.29 tff(17790,plain,
% 2.14/2.29 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17789])).
% 2.14/2.29 tff(17791,plain,
% 2.14/2.29 (~(op(e0, e3) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[1321, 17790])).
% 2.14/2.29 tff(17792,plain,
% 2.14/2.29 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[3071])).
% 2.14/2.29 tff(17793,plain,
% 2.14/2.29 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17792])).
% 2.14/2.29 tff(17794,plain,
% 2.14/2.29 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.14/2.29 inference(symmetry,[status(thm)],[3071])).
% 2.14/2.29 tff(17795,plain,
% 2.14/2.29 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17794, 6779])).
% 2.14/2.29 tff(17796,plain,
% 2.14/2.29 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17795])).
% 2.14/2.29 tff(17797,plain,
% 2.14/2.29 (op(e3, e1) = e3),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[446, 82, 2826, 183])).
% 2.14/2.29 tff(17798,plain,
% 2.14/2.29 (op(e3, e1) = op(e2, e3)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17797, 6779])).
% 2.14/2.29 tff(17799,plain,
% 2.14/2.29 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17798])).
% 2.14/2.29 tff(17800,plain,
% 2.14/2.29 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.14/2.29 inference(transitivity,[status(thm)],[17799, 394])).
% 2.14/2.29 tff(17801,plain,
% 2.14/2.29 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17800, 17796, 17793])).
% 2.14/2.29 tff(17802,plain,
% 2.14/2.29 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17801])).
% 2.14/2.29 tff(17803,plain,
% 2.14/2.29 (~(op(e3, e2) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[3429, 17802])).
% 2.14/2.29 tff(17804,plain,
% 2.14/2.29 ((op(e2, e1) = e0) <=> (op(e0, e3) = e0)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[10382])).
% 2.14/2.29 tff(17805,plain,
% 2.14/2.29 ((op(e0, e3) = e0) <=> (op(e2, e1) = e0)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17804])).
% 2.14/2.29 tff(17806,plain,
% 2.14/2.29 ((~(op(e0, e3) = e0)) <=> (~(op(e2, e1) = e0))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17805])).
% 2.14/2.29 tff(17807,plain,
% 2.14/2.29 (~(op(e2, e1) = e0)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[2500, 17806])).
% 2.14/2.29 tff(17808,plain,
% 2.14/2.29 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e2, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[6779])).
% 2.14/2.29 tff(17809,plain,
% 2.14/2.29 ((op(e3, e3) = e3) <=> (op(e2, e3) = op(e3, e3))),
% 2.14/2.29 inference(transitivity,[status(thm)],[17808, 2820])).
% 2.14/2.29 tff(17810,plain,
% 2.14/2.29 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17809])).
% 2.14/2.29 tff(17811,plain,
% 2.14/2.29 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17810])).
% 2.14/2.29 tff(17812,plain,
% 2.14/2.29 (~(op(e3, e3) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[368, 17811])).
% 2.14/2.29 tff(17813,plain,
% 2.14/2.29 (op(e3, e0) = e2),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[15971, 82, 2386])).
% 2.14/2.29 tff(17814,plain,
% 2.14/2.29 (op(e3, e0) = op(e0, e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[17813, 10370])).
% 2.14/2.29 tff(17815,plain,
% 2.14/2.29 (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[2656, 17814, 1219, 2, 17812, 1304, 1358, 17807, 75, 17803, 17084, 17791])).
% 2.14/2.29 tff(17816,plain,
% 2.14/2.29 ($false),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[1355, 17815, 17788])).
% 2.14/2.29 tff(17817,plain,((op(e3, e1) = e2) | (~(op(e1, e3) = e0)) | (~(op(e0, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (op(e1, e2) = e3) | (~(op(e2, e3) = e3)) | (~(op(e2, e2) = e1)) | (op(e3, e2) = e2) | (op(e3, e1) = e1) | (op(e3, e1) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.29 tff(17818,plain,
% 2.14/2.29 (op(e3, e1) = e2),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[17817, 183, 2, 1304, 1358, 75, 17772, 17786, 2386, 17781, 1219, 68])).
% 2.14/2.29 tff(17819,plain,
% 2.14/2.29 (op(e3, e1) = op(e0, e3)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17818, 2560])).
% 2.14/2.29 tff(17820,plain,
% 2.14/2.29 ((op(e3, e1) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17819, 17773])).
% 2.14/2.29 tff(17821,plain,
% 2.14/2.29 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e1) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17820])).
% 2.14/2.29 tff(17822,plain,
% 2.14/2.29 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17821])).
% 2.14/2.29 tff(17823,plain,
% 2.14/2.29 (~(op(e3, e1) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[964, 17822])).
% 2.14/2.29 tff(17824,plain,
% 2.14/2.29 (~(op(e3, e2) = e0)),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[6787, 17818, 17772, 17778])).
% 2.14/2.29 tff(17825,plain,
% 2.14/2.29 (op(e0, e2) = e0),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[973, 17824, 17, 17087])).
% 2.14/2.29 tff(17826,plain,
% 2.14/2.29 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17825])).
% 2.14/2.29 tff(17827,plain,
% 2.14/2.29 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17826])).
% 2.14/2.29 tff(17828,plain,
% 2.14/2.29 (~(op(e0, e1) = e0)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[2102, 17827])).
% 2.14/2.29 tff(17829,plain,
% 2.14/2.29 (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[17713, 17828, 2, 1304, 1358, 1357, 5548, 76, 17772, 2386, 17084, 17, 17087, 17778, 2639, 183, 17823])).
% 2.14/2.29 tff(17830,plain,
% 2.14/2.29 (op(op(e0, e1), e0) = e1),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[1461, 17829])).
% 2.14/2.29 tff(17831,plain,
% 2.14/2.29 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17773])).
% 2.14/2.29 tff(17832,plain,
% 2.14/2.29 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17831])).
% 2.14/2.29 tff(17833,plain,
% 2.14/2.29 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17832])).
% 2.14/2.29 tff(17834,plain,
% 2.14/2.29 (~(op(e2, e1) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[197, 17833])).
% 2.14/2.29 tff(17835,plain,
% 2.14/2.29 (op(e0, e1) = e3),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[1730, 17823, 17834, 1291])).
% 2.14/2.29 tff(17836,plain,
% 2.14/2.29 (e3 = op(e0, e1)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17835])).
% 2.14/2.29 tff(17837,plain,
% 2.14/2.29 (op(e3, e0) = op(op(e0, e1), e0)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17836])).
% 2.14/2.29 tff(17838,plain,
% 2.14/2.29 (op(e3, e0) = e0),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[1916, 17824, 17084, 183])).
% 2.14/2.29 tff(17839,plain,
% 2.14/2.29 (e0 = op(e3, e0)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17838])).
% 2.14/2.29 tff(17840,plain,
% 2.14/2.29 (e0 = e1),
% 2.14/2.29 inference(transitivity,[status(thm)],[17839, 17837, 17830])).
% 2.14/2.29 tff(17841,plain,
% 2.14/2.29 ($false),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[26, 17840])).
% 2.14/2.29 tff(17842,plain,((op(e3, e1) = e0) | (~(op(e0, e3) = e2)) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (op(e2, e2) = e2) | (op(e2, e3) = e1) | (op(e3, e2) = e2) | (op(e2, e2) = e0) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (~(op(e1, e3) = e0)) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.29 tff(17843,plain,
% 2.14/2.29 (op(e3, e1) = e0),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[17842, 17557, 17771, 17766, 17762, 17759, 76, 17755, 17, 17744, 75, 17053, 68])).
% 2.14/2.29 tff(17844,plain,
% 2.14/2.29 (op(e3, op(e3, e1)) = op(e3, e0)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17843])).
% 2.14/2.29 tff(17845,plain,
% 2.14/2.29 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17719, 17844])).
% 2.14/2.29 tff(17846,plain,
% 2.14/2.29 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e0, e3) = op(e3, e0))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17558, 17845])).
% 2.14/2.29 tff(17847,plain,
% 2.14/2.29 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = op(e0, e3))),
% 2.14/2.29 inference(transitivity,[status(thm)],[17846, 452])).
% 2.14/2.29 tff(17848,plain,
% 2.14/2.29 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17847, 17560])).
% 2.14/2.29 tff(17849,plain,
% 2.14/2.29 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17848])).
% 2.14/2.29 tff(17850,plain,
% 2.14/2.29 (e0 = op(e3, op(e3, e3))),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[17843, 17728])).
% 2.14/2.29 tff(17851,plain,
% 2.14/2.29 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[5397, 17850, 17725])).
% 2.14/2.29 tff(17852,plain,
% 2.14/2.29 (~(op(e3, e0) = e2)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[17851, 17849])).
% 2.14/2.29 tff(17853,plain,
% 2.14/2.29 ((op(e3, e1) = e2) <=> (e0 = op(e0, e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17843, 17558])).
% 2.14/2.29 tff(17854,plain,
% 2.14/2.29 ((op(e3, e1) = e2) <=> (op(e0, e3) = e0)),
% 2.14/2.29 inference(transitivity,[status(thm)],[17853, 1079])).
% 2.14/2.29 tff(17855,plain,
% 2.14/2.29 ((op(e0, e3) = e0) <=> (op(e3, e1) = e2)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17854])).
% 2.14/2.29 tff(17856,plain,
% 2.14/2.29 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e1) = e2))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17855])).
% 2.14/2.29 tff(17857,plain,
% 2.14/2.29 (~(op(e3, e1) = e2)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[17231, 17856])).
% 2.14/2.29 tff(17858,plain,
% 2.14/2.29 (op(e3, e0) = e2),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[15971, 17857, 17755])).
% 2.14/2.29 tff(17859,plain,
% 2.14/2.29 ($false),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[17858, 17852])).
% 2.14/2.29 tff(17860,plain,((op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e2) = e3) | (op(e1, e1) = e2) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.29 tff(17861,plain,
% 2.14/2.29 (op(e2, e3) = e1),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[17860, 75, 17, 68, 72])).
% 2.14/2.29 tff(17862,plain,
% 2.14/2.29 (op(op(e2, e3), e2) = op(e1, e2)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17861])).
% 2.14/2.29 tff(17863,plain,
% 2.14/2.29 ((op(op(e2, e3), e2) = e3) <=> (op(e1, e2) = e3)),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17862])).
% 2.14/2.29 tff(17864,plain,
% 2.14/2.29 ((op(e1, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 2.14/2.29 inference(symmetry,[status(thm)],[17863])).
% 2.14/2.29 tff(17865,plain,
% 2.14/2.29 ((~(op(e1, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.14/2.29 inference(monotonicity,[status(thm)],[17864])).
% 2.14/2.29 tff(17866,plain,
% 2.14/2.29 (~(op(op(e2, e3), e2) = e3)),
% 2.14/2.29 inference(modus_ponens,[status(thm)],[75, 17865])).
% 2.14/2.29 tff(17867,plain,
% 2.14/2.29 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.14/2.29 inference(unit_resolution,[status(thm)],[1934, 17866])).
% 2.14/2.29 tff(17868,plain,
% 2.19/2.29 ((op(e2, e3) = e2) <=> (e1 = e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[2684])).
% 2.19/2.29 tff(17869,plain,
% 2.19/2.29 ((e1 = e2) <=> (op(e2, e3) = e2)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17868])).
% 2.19/2.29 tff(17870,plain,
% 2.19/2.29 ((~(e1 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17869])).
% 2.19/2.29 tff(17871,plain,
% 2.19/2.29 (~(op(e2, e3) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[708, 17870])).
% 2.19/2.29 tff(17872,plain,
% 2.19/2.29 (op(e0, e3) = e2),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[15003, 17871, 72])).
% 2.19/2.29 tff(17873,plain,
% 2.19/2.29 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.29 tff(17874,plain,
% 2.19/2.29 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17873, 1])).
% 2.19/2.29 tff(17875,plain,
% 2.19/2.29 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17874])).
% 2.19/2.29 tff(17876,plain,
% 2.19/2.29 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17875])).
% 2.19/2.29 tff(17877,plain,
% 2.19/2.29 (~(op(e0, e3) = e0)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[14, 17876])).
% 2.19/2.29 tff(17878,plain,
% 2.19/2.29 (op(e3, e3) = e0),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[1098, 80, 13736, 17877])).
% 2.19/2.29 tff(17879,plain,
% 2.19/2.29 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.29 tff(17880,plain,
% 2.19/2.29 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17879])).
% 2.19/2.29 tff(17881,plain,
% 2.19/2.29 (~(op(e0, e1) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[818, 17880])).
% 2.19/2.29 tff(17882,plain,
% 2.19/2.29 (op(e2, e1) = e2),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[1993, 82, 68, 17881])).
% 2.19/2.29 tff(17883,plain,
% 2.19/2.29 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17882])).
% 2.19/2.29 tff(17884,plain,
% 2.19/2.29 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17883])).
% 2.19/2.29 tff(17885,plain,
% 2.19/2.29 (~(op(e2, e0) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[1966, 17884])).
% 2.19/2.29 tff(17886,plain,
% 2.19/2.29 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.29 tff(17887,plain,
% 2.19/2.29 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17886])).
% 2.19/2.29 tff(17888,plain,
% 2.19/2.29 (~(op(e0, e0) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[3414, 17887])).
% 2.19/2.29 tff(17889,plain,
% 2.19/2.29 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.29 tff(17890,plain,
% 2.19/2.29 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17889])).
% 2.19/2.29 tff(17891,plain,
% 2.19/2.29 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.29 tff(17892,plain,
% 2.19/2.29 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17891])).
% 2.19/2.29 tff(17893,plain,
% 2.19/2.29 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17892])).
% 2.19/2.29 tff(17894,plain,
% 2.19/2.29 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17882])).
% 2.19/2.29 tff(17895,plain,
% 2.19/2.29 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17894, 81])).
% 2.19/2.29 tff(17896,plain,
% 2.19/2.29 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17895])).
% 2.19/2.29 tff(17897,plain,
% 2.19/2.29 (~(op(e2, e2) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[508, 17896])).
% 2.19/2.29 tff(17898,plain,
% 2.19/2.29 (op(e2, e2) = e3),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[524, 17897, 17, 13500])).
% 2.19/2.29 tff(17899,plain,
% 2.19/2.29 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17898])).
% 2.19/2.29 tff(17900,plain,
% 2.19/2.29 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17899, 3423])).
% 2.19/2.29 tff(17901,plain,
% 2.19/2.29 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17900, 17893])).
% 2.19/2.29 tff(17902,plain,
% 2.19/2.29 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17901])).
% 2.19/2.29 tff(17903,plain,
% 2.19/2.29 (~(op(e3, op(e0, e3)) = e3)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[1546, 17902])).
% 2.19/2.29 tff(17904,plain,
% 2.19/2.29 (~(op(e3, e0) = op(e0, e3))),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[3102, 17903, 17872, 17878])).
% 2.19/2.29 tff(17905,plain,
% 2.19/2.29 (~(op(e3, e0) = e2)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[17904, 17890])).
% 2.19/2.29 tff(17906,plain,
% 2.19/2.29 (op(e1, e0) = e2),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[589, 17905, 17888, 17885])).
% 2.19/2.29 tff(17907,plain,
% 2.19/2.29 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17906])).
% 2.19/2.29 tff(17908,plain,
% 2.19/2.29 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17907, 69])).
% 2.19/2.29 tff(17909,plain,
% 2.19/2.29 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17908])).
% 2.19/2.29 tff(17910,plain,
% 2.19/2.29 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17909])).
% 2.19/2.29 tff(17911,plain,
% 2.19/2.29 (~(op(e1, e0) = e1)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[708, 17910])).
% 2.19/2.29 tff(17912,plain,
% 2.19/2.29 ((op(e2, e1) = e0) <=> (e2 = e0)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17882])).
% 2.19/2.29 tff(17913,plain,
% 2.19/2.29 ((op(e2, e1) = e0) <=> (e0 = e2)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17912, 1])).
% 2.19/2.29 tff(17914,plain,
% 2.19/2.29 ((e0 = e2) <=> (op(e2, e1) = e0)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17913])).
% 2.19/2.29 tff(17915,plain,
% 2.19/2.29 ((~(e0 = e2)) <=> (~(op(e2, e1) = e0))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17914])).
% 2.19/2.29 tff(17916,plain,
% 2.19/2.29 (~(op(e2, e1) = e0)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[14, 17915])).
% 2.19/2.29 tff(17917,plain,
% 2.19/2.29 (op(e2, e0) = e0),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[2311, 17916, 17, 13736])).
% 2.19/2.29 tff(17918,plain,
% 2.19/2.29 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17917])).
% 2.19/2.29 tff(17919,plain,
% 2.19/2.29 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17918])).
% 2.19/2.29 tff(17920,plain,
% 2.19/2.29 (~(op(e1, e0) = e0)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[756, 17919])).
% 2.19/2.29 tff(17921,plain,
% 2.19/2.29 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17878])).
% 2.19/2.29 tff(17922,plain,
% 2.19/2.29 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17921])).
% 2.19/2.29 tff(17923,plain,
% 2.19/2.29 (~(op(e3, e1) = e0)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[437, 17922])).
% 2.19/2.29 tff(17924,plain,
% 2.19/2.29 (op(e3, e2) = e2),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[15971, 17905, 82])).
% 2.19/2.29 tff(17925,plain,
% 2.19/2.29 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17924])).
% 2.19/2.29 tff(17926,plain,
% 2.19/2.29 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17925, 69])).
% 2.19/2.29 tff(17927,plain,
% 2.19/2.29 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17926])).
% 2.19/2.29 tff(17928,plain,
% 2.19/2.29 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17927])).
% 2.19/2.29 tff(17929,plain,
% 2.19/2.29 (~(op(e3, e2) = e1)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[708, 17928])).
% 2.19/2.29 tff(17930,plain,
% 2.19/2.29 (op(e1, e3) = e3),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[104, 80, 72, 13757])).
% 2.19/2.29 tff(17931,plain,
% 2.19/2.29 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17898])).
% 2.19/2.29 tff(17932,plain,
% 2.19/2.29 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17931])).
% 2.19/2.29 tff(17933,plain,
% 2.19/2.29 (~(op(e0, e2) = e3)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[2736, 17932])).
% 2.19/2.29 tff(17934,plain,
% 2.19/2.29 (op(e0, e1) = e0),
% 2.19/2.29 inference(unit_resolution,[status(thm)],[292, 84, 183, 2559])).
% 2.19/2.29 tff(17935,plain,
% 2.19/2.29 ((op(e0, e1) = e3) <=> (e0 = op(e1, e3))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17934, 11135])).
% 2.19/2.29 tff(17936,plain,
% 2.19/2.29 ((op(e0, e1) = e3) <=> (op(e1, e3) = e0)),
% 2.19/2.29 inference(transitivity,[status(thm)],[17935, 6095])).
% 2.19/2.29 tff(17937,plain,
% 2.19/2.29 ((op(e1, e3) = e0) <=> (op(e0, e1) = e3)),
% 2.19/2.29 inference(symmetry,[status(thm)],[17936])).
% 2.19/2.29 tff(17938,plain,
% 2.19/2.29 ((~(op(e1, e3) = e0)) <=> (~(op(e0, e1) = e3))),
% 2.19/2.29 inference(monotonicity,[status(thm)],[17937])).
% 2.19/2.29 tff(17939,plain,
% 2.19/2.29 (~(op(e0, e1) = e3)),
% 2.19/2.29 inference(modus_ponens,[status(thm)],[80, 17938])).
% 2.19/2.30 tff(17940,plain,
% 2.19/2.30 (op(e0, e0) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1495, 17939, 16740, 4412])).
% 2.19/2.30 tff(17941,plain,
% 2.19/2.30 (e3 = op(e0, e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[17940, 71])).
% 2.19/2.30 tff(17942,plain,
% 2.19/2.30 (op(e0, e0) = op(e1, e3)),
% 2.19/2.30 inference(transitivity,[status(thm)],[17940, 11135])).
% 2.19/2.30 tff(17943,plain,
% 2.19/2.30 (op(e0, op(e0, e0)) = op(e0, op(e1, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17942])).
% 2.19/2.30 tff(17944,plain,
% 2.19/2.30 (op(e0, op(e1, e3)) = op(e0, op(e0, e0))),
% 2.19/2.30 inference(symmetry,[status(thm)],[17943])).
% 2.19/2.30 tff(17945,plain,
% 2.19/2.30 (op(e0, e3) = op(e0, op(e1, e3))),
% 2.19/2.30 inference(symmetry,[status(thm)],[11343])).
% 2.19/2.30 tff(17946,plain,
% 2.19/2.30 (e2 = op(e0, op(e0, e0))),
% 2.19/2.30 inference(transitivity,[status(thm)],[2560, 17945, 17944])).
% 2.19/2.30 tff(17947,plain,
% 2.19/2.30 (op(e0, op(e0, e0)) = e2),
% 2.19/2.30 inference(transitivity,[status(thm)],[17943, 11343, 2])).
% 2.19/2.30 tff(17948,plain,
% 2.19/2.30 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17947])).
% 2.19/2.30 tff(17949,plain,
% 2.19/2.30 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.30 inference(symmetry,[status(thm)],[17948])).
% 2.19/2.30 tff(17950,plain,
% 2.19/2.30 (op(e1, e2) = e0),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1830, 84, 80, 2167])).
% 2.19/2.30 tff(17951,plain,
% 2.19/2.30 ((op(e1, e2) = e1) <=> (e0 = e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17950])).
% 2.19/2.30 tff(17952,plain,
% 2.19/2.30 ((e0 = e1) <=> (op(e1, e2) = e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17951])).
% 2.19/2.30 tff(17953,plain,
% 2.19/2.30 ((~(e0 = e1)) <=> (~(op(e1, e2) = e1))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17952])).
% 2.19/2.30 tff(17954,plain,
% 2.19/2.30 (~(op(e1, e2) = e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[26, 17953])).
% 2.19/2.30 tff(17955,plain,
% 2.19/2.30 (op(e0, e2) = e1),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1613, 17954, 1348, 930])).
% 2.19/2.30 tff(17956,plain,
% 2.19/2.30 (e1 = op(e0, e2)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17955])).
% 2.19/2.30 tff(17957,plain,
% 2.19/2.30 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.30 inference(transitivity,[status(thm)],[17956, 17949])).
% 2.19/2.30 tff(17958,plain,
% 2.19/2.30 ($false),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2760, 17957, 17946, 17941])).
% 2.19/2.30 tff(17959,plain,((op(e1, e1) = e0) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e3)) | (op(e0, e2) = e3) | (op(e2, e2) = e1) | (op(e3, e2) = e1) | (op(e1, e3) = e0) | (op(e3, e1) = e0) | (op(e2, e1) = e0) | (op(e1, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.30 tff(17960,plain,
% 2.19/2.30 (op(e1, e1) = e0),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[17959, 17933, 17930, 17872, 13500, 17929, 80, 17923, 17916, 17920])).
% 2.19/2.30 tff(17961,plain,
% 2.19/2.30 ((op(e1, e1) = e1) <=> (e0 = e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17960])).
% 2.19/2.30 tff(17962,plain,
% 2.19/2.30 ((e0 = e1) <=> (op(e1, e1) = e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17961])).
% 2.19/2.30 tff(17963,plain,
% 2.19/2.30 ((~(e0 = e1)) <=> (~(op(e1, e1) = e1))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17962])).
% 2.19/2.30 tff(17964,plain,
% 2.19/2.30 (~(op(e1, e1) = e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[26, 17963])).
% 2.19/2.30 tff(17965,plain,
% 2.19/2.30 (op(e1, e2) = e1),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[954, 17964, 17911, 13757])).
% 2.19/2.30 tff(17966,plain,
% 2.19/2.30 (e1 = op(e1, e2)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17965])).
% 2.19/2.30 tff(17967,plain,
% 2.19/2.30 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17966])).
% 2.19/2.30 tff(17968,plain,
% 2.19/2.30 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17967])).
% 2.19/2.30 tff(17969,plain,
% 2.19/2.30 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17968])).
% 2.19/2.30 tff(17970,plain,
% 2.19/2.30 (~(op(e0, e2) = e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[6205, 17969])).
% 2.19/2.30 tff(17971,plain,
% 2.19/2.30 (e3 = op(e1, e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17930])).
% 2.19/2.30 tff(17972,plain,
% 2.19/2.30 ((op(e2, e1) = e3) <=> (e2 = op(e1, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17882, 17971])).
% 2.19/2.30 tff(17973,plain,
% 2.19/2.30 ((op(e2, e1) = e3) <=> (op(e1, e3) = e2)),
% 2.19/2.30 inference(transitivity,[status(thm)],[17972, 66])).
% 2.19/2.30 tff(17974,plain,
% 2.19/2.30 ((op(e1, e3) = e2) <=> (op(e2, e1) = e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17973])).
% 2.19/2.30 tff(17975,plain,
% 2.19/2.30 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e1) = e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17974])).
% 2.19/2.30 tff(17976,plain,
% 2.19/2.30 (~(op(e2, e1) = e3)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[72, 17975])).
% 2.19/2.30 tff(17977,plain,
% 2.19/2.30 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17960])).
% 2.19/2.30 tff(17978,plain,
% 2.19/2.30 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e0))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17977])).
% 2.19/2.30 tff(17979,plain,
% 2.19/2.30 (~(op(e0, e1) = e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[792, 17978])).
% 2.19/2.30 tff(17980,plain,
% 2.19/2.30 ((e1 = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.19/2.30 inference(transitivity,[status(thm)],[17927, 14325])).
% 2.19/2.30 tff(17981,plain,
% 2.19/2.30 ((~(e1 = e2)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17980])).
% 2.19/2.30 tff(17982,plain,
% 2.19/2.30 (~(op(e3, e2) = op(e2, e3))),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[708, 17981])).
% 2.19/2.30 tff(17983,plain,
% 2.19/2.30 (op(op(e2, e1), e1) = op(e2, e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17882])).
% 2.19/2.30 tff(17984,plain,
% 2.19/2.30 (op(op(e2, e1), e1) = e2),
% 2.19/2.30 inference(transitivity,[status(thm)],[17983, 17882])).
% 2.19/2.30 tff(17985,plain,
% 2.19/2.30 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2371, 17984])).
% 2.19/2.30 tff(17986,plain,
% 2.19/2.30 (op(op(e1, e0), e1) = op(e2, e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17906])).
% 2.19/2.30 tff(17987,plain,
% 2.19/2.30 (op(op(e1, e0), e1) = e2),
% 2.19/2.30 inference(transitivity,[status(thm)],[17986, 17882])).
% 2.19/2.30 tff(17988,plain,
% 2.19/2.30 ((op(op(e1, e0), e1) = e0) <=> (e2 = e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17987])).
% 2.19/2.30 tff(17989,plain,
% 2.19/2.30 ((op(op(e1, e0), e1) = e0) <=> (e0 = e2)),
% 2.19/2.30 inference(transitivity,[status(thm)],[17988, 1])).
% 2.19/2.30 tff(17990,plain,
% 2.19/2.30 ((e0 = e2) <=> (op(op(e1, e0), e1) = e0)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17989])).
% 2.19/2.30 tff(17991,plain,
% 2.19/2.30 ((~(e0 = e2)) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17990])).
% 2.19/2.30 tff(17992,plain,
% 2.19/2.30 (~(op(op(e1, e0), e1) = e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[14, 17991])).
% 2.19/2.30 tff(17993,plain,
% 2.19/2.30 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1302, 17992])).
% 2.19/2.30 tff(17994,plain,
% 2.19/2.30 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17924])).
% 2.19/2.30 tff(17995,plain,
% 2.19/2.30 (op(e3, op(e3, e2)) = e2),
% 2.19/2.30 inference(transitivity,[status(thm)],[17994, 17924])).
% 2.19/2.30 tff(17996,plain,
% 2.19/2.30 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1904, 17995])).
% 2.19/2.30 tff(17997,plain,
% 2.19/2.30 (op(e2, op(e2, e0)) = op(e2, e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17917])).
% 2.19/2.30 tff(17998,plain,
% 2.19/2.30 (op(e2, op(e2, e0)) = e0),
% 2.19/2.30 inference(transitivity,[status(thm)],[17997, 17917])).
% 2.19/2.30 tff(17999,plain,
% 2.19/2.30 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2653, 17998])).
% 2.19/2.30 tff(18000,plain,
% 2.19/2.30 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17917])).
% 2.19/2.30 tff(18001,plain,
% 2.19/2.30 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18000])).
% 2.19/2.30 tff(18002,plain,
% 2.19/2.30 (~(op(e0, e0) = e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[359, 18001])).
% 2.19/2.30 tff(18003,plain,
% 2.19/2.30 (op(e0, e2) = e0),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[3976, 17979, 18002, 17877])).
% 2.19/2.30 tff(18004,plain,
% 2.19/2.30 (op(op(e0, e2), e2) = op(e0, e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18003])).
% 2.19/2.30 tff(18005,plain,
% 2.19/2.30 (op(op(e0, e2), e2) = e0),
% 2.19/2.30 inference(transitivity,[status(thm)],[18004, 18003])).
% 2.19/2.30 tff(18006,plain,
% 2.19/2.30 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1956, 18005])).
% 2.19/2.30 tff(18007,plain,
% 2.19/2.30 (op(op(e0, e3), e0) = op(e2, e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.30 tff(18008,plain,
% 2.19/2.30 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18007])).
% 2.19/2.30 tff(18009,plain,
% 2.19/2.30 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18008])).
% 2.19/2.30 tff(18010,plain,
% 2.19/2.30 ((op(e2, e0) = e3) <=> (e0 = op(e1, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17917, 17971])).
% 2.19/2.30 tff(18011,plain,
% 2.19/2.30 ((op(e2, e0) = e3) <=> (op(e1, e3) = e0)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18010, 6095])).
% 2.19/2.30 tff(18012,plain,
% 2.19/2.30 ((op(e1, e3) = e0) <=> (op(e2, e0) = e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18011])).
% 2.19/2.30 tff(18013,plain,
% 2.19/2.30 ((op(e1, e3) = e0) <=> (op(op(e0, e3), e0) = e3)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18012, 18009])).
% 2.19/2.30 tff(18014,plain,
% 2.19/2.30 ((~(op(e1, e3) = e0)) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18013])).
% 2.19/2.30 tff(18015,plain,
% 2.19/2.30 (~(op(op(e0, e3), e0) = e3)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[80, 18014])).
% 2.19/2.30 tff(18016,plain,
% 2.19/2.30 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2635, 18015])).
% 2.19/2.30 tff(18017,plain,
% 2.19/2.30 (op(op(e1, e2), e2) = op(e1, e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[6683])).
% 2.19/2.30 tff(18018,plain,
% 2.19/2.30 (op(op(e1, e2), e2) = e1),
% 2.19/2.30 inference(transitivity,[status(thm)],[18017, 6683])).
% 2.19/2.30 tff(18019,plain,
% 2.19/2.30 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1335, 18018])).
% 2.19/2.30 tff(18020,plain,
% 2.19/2.30 (op(e0, e1) = e1),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[829, 2527, 5828, 3849])).
% 2.19/2.30 tff(18021,plain,
% 2.19/2.30 (op(e0, op(e1, e2)) = op(e0, e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[6683])).
% 2.19/2.30 tff(18022,plain,
% 2.19/2.30 (e1 = op(e1, e2)),
% 2.19/2.30 inference(symmetry,[status(thm)],[6683])).
% 2.19/2.30 tff(18023,plain,
% 2.19/2.30 (op(e0, e1) = op(e1, e2)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18020, 18022])).
% 2.19/2.30 tff(18024,plain,
% 2.19/2.30 (op(e0, op(e0, e1)) = op(e0, op(e1, e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18023])).
% 2.19/2.30 tff(18025,plain,
% 2.19/2.30 (op(e0, op(e0, e1)) = e1),
% 2.19/2.30 inference(transitivity,[status(thm)],[18024, 18021, 18020])).
% 2.19/2.30 tff(18026,plain,
% 2.19/2.30 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2449, 18025])).
% 2.19/2.30 tff(18027,plain,
% 2.19/2.30 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e1, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[11135])).
% 2.19/2.30 tff(18028,plain,
% 2.19/2.30 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18027])).
% 2.19/2.30 tff(18029,plain,
% 2.19/2.30 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18028])).
% 2.19/2.30 tff(18030,plain,
% 2.19/2.30 (~(op(e1, e1) = e3)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[619, 18029])).
% 2.19/2.30 tff(18031,plain,
% 2.19/2.30 (op(e3, e1) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1730, 2527, 3271, 18030])).
% 2.19/2.30 tff(18032,plain,
% 2.19/2.30 (op(e3, op(e1, e2)) = op(op(e1, e3), e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[11135, 6683])).
% 2.19/2.30 tff(18033,plain,
% 2.19/2.30 (op(op(e3, e1), e1) = op(e3, op(e1, e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18031, 18022])).
% 2.19/2.30 tff(18034,plain,
% 2.19/2.30 (op(op(e3, e1), e1) = e3),
% 2.19/2.30 inference(transitivity,[status(thm)],[18033, 18032, 11165, 18031])).
% 2.19/2.30 tff(18035,plain,
% 2.19/2.30 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2416, 18034])).
% 2.19/2.30 tff(18036,plain,
% 2.19/2.30 (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1459, 18035, 3342, 18026, 1347, 1304, 1363, 18019, 2421, 3341, 1357, 1936])).
% 2.19/2.30 tff(18037,plain,
% 2.19/2.30 (op(op(e3, e0), e3) = e0),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1764, 18036])).
% 2.19/2.30 tff(18038,plain,
% 2.19/2.30 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[2684])).
% 2.19/2.30 tff(18039,plain,
% 2.19/2.30 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18038, 657])).
% 2.19/2.30 tff(18040,plain,
% 2.19/2.30 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18039])).
% 2.19/2.30 tff(18041,plain,
% 2.19/2.30 (~(op(e3, e3) = e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[368, 18040])).
% 2.19/2.30 tff(18042,plain,
% 2.19/2.30 ((op(e3, e1) = e3) <=> (op(e1, e3) = op(e3, e1))),
% 2.19/2.30 inference(transitivity,[status(thm)],[11299, 6290])).
% 2.19/2.30 tff(18043,plain,
% 2.19/2.30 (op(e1, e3) = op(e3, e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[18031, 18042])).
% 2.19/2.30 tff(18044,plain,
% 2.19/2.30 (op(e3, e0) = e1),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[7757, 18043, 2684, 18041, 7754])).
% 2.19/2.30 tff(18045,plain,
% 2.19/2.30 (e1 = op(e3, e0)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18044])).
% 2.19/2.30 tff(18046,plain,
% 2.19/2.30 (op(e1, op(e1, e3)) = op(op(e3, e0), e3)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18045, 164])).
% 2.19/2.30 tff(18047,plain,
% 2.19/2.30 (e3 = op(e1, op(e1, e3))),
% 2.19/2.30 inference(symmetry,[status(thm)],[11204])).
% 2.19/2.30 tff(18048,plain,
% 2.19/2.30 (op(e1, e3) = e0),
% 2.19/2.30 inference(transitivity,[status(thm)],[164, 18047, 18046, 18037])).
% 2.19/2.30 tff(18049,plain,
% 2.19/2.30 ($false),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[80, 18048])).
% 2.19/2.30 tff(18050,plain,((op(e0, e1) = e3) | (op(e1, e3) = e0) | (~(op(e1, e3) = e3)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e2, e3) = e1)) | (op(e3, e2) = op(e2, e3)) | (~(op(e1, e2) = e1)) | (op(e0, e1) = e2) | (op(e0, e1) = e0) | (op(e2, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.30 tff(18051,plain,
% 2.19/2.30 (op(e0, e1) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[18050, 18016, 17930, 80, 1347, 16411, 18006, 17999, 17996, 17993, 17985, 2684, 17982, 17965, 17881, 17979, 17976])).
% 2.19/2.30 tff(18052,plain,
% 2.19/2.30 (op(e0, e1) = op(e1, e3)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18051, 17971])).
% 2.19/2.30 tff(18053,plain,
% 2.19/2.30 ((op(e0, e1) = e1) <=> (op(e1, e3) = op(e1, e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18052, 17966])).
% 2.19/2.30 tff(18054,plain,
% 2.19/2.30 ((op(e0, e1) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 2.19/2.30 inference(transitivity,[status(thm)],[18053, 125])).
% 2.19/2.30 tff(18055,plain,
% 2.19/2.30 ((op(e1, e2) = op(e1, e3)) <=> (op(e0, e1) = e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18054])).
% 2.19/2.30 tff(18056,plain,
% 2.19/2.30 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e0, e1) = e1))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18055])).
% 2.19/2.30 tff(18057,plain,
% 2.19/2.30 (~(op(e0, e1) = e1)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[1850, 18056])).
% 2.19/2.30 tff(18058,plain,
% 2.19/2.30 (op(e0, e0) = e1),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[384, 18057, 13718, 17970])).
% 2.19/2.30 tff(18059,plain,
% 2.19/2.30 (e1 = op(e0, e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[18058, 74])).
% 2.19/2.30 tff(18060,plain,
% 2.19/2.30 (op(e0, e0) = op(e1, e2)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18058, 17966])).
% 2.19/2.30 tff(18061,plain,
% 2.19/2.30 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18060])).
% 2.19/2.30 tff(18062,plain,
% 2.19/2.30 (op(e0, op(e1, e2)) = op(e0, op(e0, e0))),
% 2.19/2.30 inference(symmetry,[status(thm)],[18061])).
% 2.19/2.30 tff(18063,plain,
% 2.19/2.30 (op(e0, op(e1, e2)) = op(e0, e1)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17965])).
% 2.19/2.30 tff(18064,plain,
% 2.19/2.30 (op(e0, e1) = op(e0, op(e1, e2))),
% 2.19/2.30 inference(symmetry,[status(thm)],[18063])).
% 2.19/2.30 tff(18065,plain,
% 2.19/2.30 (e3 = op(e0, e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18051])).
% 2.19/2.30 tff(18066,plain,
% 2.19/2.30 (e3 = op(e0, op(e0, e0))),
% 2.19/2.30 inference(transitivity,[status(thm)],[18065, 18064, 18062])).
% 2.19/2.30 tff(18067,plain,
% 2.19/2.30 (op(e0, op(e0, e0)) = op(e1, e3)),
% 2.19/2.30 inference(transitivity,[status(thm)],[18061, 18063, 18051, 17971])).
% 2.19/2.30 tff(18068,plain,
% 2.19/2.30 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18067])).
% 2.19/2.30 tff(18069,plain,
% 2.19/2.30 (op(e0, op(e1, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.30 inference(symmetry,[status(thm)],[18068])).
% 2.19/2.30 tff(18070,plain,
% 2.19/2.30 (op(e0, op(e1, e3)) = op(e0, e3)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17930])).
% 2.19/2.30 tff(18071,plain,
% 2.19/2.30 (op(e0, e3) = op(e0, op(e1, e3))),
% 2.19/2.30 inference(symmetry,[status(thm)],[18070])).
% 2.19/2.30 tff(18072,plain,
% 2.19/2.30 (e2 = op(e0, e3)),
% 2.19/2.30 inference(symmetry,[status(thm)],[17872])).
% 2.19/2.30 tff(18073,plain,
% 2.19/2.30 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.30 inference(transitivity,[status(thm)],[18072, 18071, 18069])).
% 2.19/2.30 tff(18074,plain,
% 2.19/2.30 ($false),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[16194, 18073, 18066, 18059])).
% 2.19/2.30 tff(18075,plain,((op(e3, e1) = e2) | (op(e1, e3) = e0) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e2, e3) = e1)) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.30 tff(18076,plain,
% 2.19/2.30 (op(e3, e1) = e2),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[18075, 80, 1347, 2684, 17, 72, 68])).
% 2.19/2.30 tff(18077,plain,
% 2.19/2.30 (~(op(e3, e0) = e1)),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[8647, 18076, 17878])).
% 2.19/2.30 tff(18078,plain,
% 2.19/2.30 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[17878])).
% 2.19/2.30 tff(18079,plain,
% 2.19/2.30 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18078])).
% 2.19/2.30 tff(18080,plain,
% 2.19/2.30 (~(op(e3, e0) = e0)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[157, 18079])).
% 2.19/2.30 tff(18081,plain,
% 2.19/2.30 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18076])).
% 2.19/2.30 tff(18082,plain,
% 2.19/2.30 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18081])).
% 2.19/2.30 tff(18083,plain,
% 2.19/2.30 (~(op(e3, e0) = e2)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[580, 18082])).
% 2.19/2.30 tff(18084,plain,
% 2.19/2.30 (op(e3, e0) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[5422, 18083, 18080, 18077])).
% 2.19/2.30 tff(18085,plain,
% 2.19/2.30 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e3)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18084])).
% 2.19/2.30 tff(18086,plain,
% 2.19/2.30 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e3))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18085])).
% 2.19/2.30 tff(18087,plain,
% 2.19/2.30 (~(op(e2, e0) = e3)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[747, 18086])).
% 2.19/2.30 tff(18088,plain,
% 2.19/2.30 (~(op(e2, e2) = e3)),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[6638, 3508, 2684])).
% 2.19/2.30 tff(18089,plain,
% 2.19/2.30 (op(e2, e1) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[1559, 18088, 13775, 3272])).
% 2.19/2.30 tff(18090,plain,
% 2.19/2.30 (e3 = op(e2, e1)),
% 2.19/2.30 inference(symmetry,[status(thm)],[18089])).
% 2.19/2.30 tff(18091,plain,
% 2.19/2.30 (op(e1, e3) = e0),
% 2.19/2.30 inference(transitivity,[status(thm)],[164, 18090, 3508])).
% 2.19/2.30 tff(18092,plain,
% 2.19/2.30 ($false),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[80, 18091])).
% 2.19/2.30 tff(18093,plain,((~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (~(op(e1, e3) = e3)) | (op(e2, e0) = e3) | (~(op(e2, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.19/2.30 tff(18094,plain,
% 2.19/2.30 (~(op(e2, e1) = e0)),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[18093, 80, 17930, 18087, 2684])).
% 2.19/2.30 tff(18095,plain,
% 2.19/2.30 (op(e2, e0) = e0),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2311, 18094, 17, 13736])).
% 2.19/2.30 tff(18096,plain,
% 2.19/2.30 (op(e3, op(e2, e0)) = op(e3, e0)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18095])).
% 2.19/2.30 tff(18097,plain,
% 2.19/2.30 (op(e3, op(e2, e0)) = e3),
% 2.19/2.30 inference(transitivity,[status(thm)],[18096, 18084])).
% 2.19/2.30 tff(18098,plain,
% 2.19/2.30 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[10697, 18097])).
% 2.19/2.30 tff(18099,plain,
% 2.19/2.30 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18076])).
% 2.19/2.30 tff(18100,plain,
% 2.19/2.30 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.19/2.30 inference(monotonicity,[status(thm)],[18099])).
% 2.19/2.30 tff(18101,plain,
% 2.19/2.30 (~(op(e2, e1) = e2)),
% 2.19/2.30 inference(modus_ponens,[status(thm)],[402, 18100])).
% 2.19/2.30 tff(18102,plain,
% 2.19/2.30 (op(e2, e1) = e3),
% 2.19/2.30 inference(unit_resolution,[status(thm)],[2367, 18094, 18101, 14333])).
% 2.19/2.30 tff(18103,plain,
% 2.19/2.30 (op(e2, e1) = op(e1, e3)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18102, 17971])).
% 2.19/2.31 tff(18104,plain,
% 2.19/2.31 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e3) = op(e1, e2))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18103])).
% 2.19/2.31 tff(18105,plain,
% 2.19/2.31 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = op(e1, e3))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18104, 125])).
% 2.19/2.31 tff(18106,plain,
% 2.19/2.31 ((op(e1, e2) = op(e1, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18105])).
% 2.19/2.31 tff(18107,plain,
% 2.19/2.31 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18106])).
% 2.19/2.31 tff(18108,plain,
% 2.19/2.31 (~(op(e2, e1) = op(e1, e2))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[1850, 18107])).
% 2.19/2.31 tff(18109,plain,
% 2.19/2.31 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[557, 18108])).
% 2.19/2.31 tff(18110,plain,
% 2.19/2.31 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[17878])).
% 2.19/2.31 tff(18111,plain,
% 2.19/2.31 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e0) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18110])).
% 2.19/2.31 tff(18112,plain,
% 2.19/2.31 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18111])).
% 2.19/2.31 tff(18113,plain,
% 2.19/2.31 (op(e3, op(e3, e3)) = e3),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[18084, 18112])).
% 2.19/2.31 tff(18114,plain,
% 2.19/2.31 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[6277, 18113])).
% 2.19/2.31 tff(18115,plain,
% 2.19/2.31 ((op(e2, e0) = e2) <=> (e0 = e2)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18095])).
% 2.19/2.31 tff(18116,plain,
% 2.19/2.31 ((e0 = e2) <=> (op(e2, e0) = e2)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18115])).
% 2.19/2.31 tff(18117,plain,
% 2.19/2.31 ((~(e0 = e2)) <=> (~(op(e2, e0) = e2))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18116])).
% 2.19/2.31 tff(18118,plain,
% 2.19/2.31 (~(op(e2, e0) = e2)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[14, 18117])).
% 2.19/2.31 tff(18119,plain,
% 2.19/2.31 (op(e1, e0) = e2),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[589, 18118, 17888, 18083])).
% 2.19/2.31 tff(18120,plain,
% 2.19/2.31 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18119])).
% 2.19/2.31 tff(18121,plain,
% 2.19/2.31 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18120, 4838])).
% 2.19/2.31 tff(18122,plain,
% 2.19/2.31 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18121])).
% 2.19/2.31 tff(18123,plain,
% 2.19/2.31 ((op(e0, e1) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18122, 596])).
% 2.19/2.31 tff(18124,plain,
% 2.19/2.31 ((~(op(e0, e1) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18123])).
% 2.19/2.31 tff(18125,plain,
% 2.19/2.31 (~(op(e0, e1) = op(e1, e0))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[17881, 18124])).
% 2.19/2.31 tff(18126,plain,
% 2.19/2.31 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[609, 18125])).
% 2.19/2.31 tff(18127,plain,
% 2.19/2.31 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18076])).
% 2.19/2.31 tff(18128,plain,
% 2.19/2.31 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18127, 69])).
% 2.19/2.31 tff(18129,plain,
% 2.19/2.31 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18128])).
% 2.19/2.31 tff(18130,plain,
% 2.19/2.31 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18129])).
% 2.19/2.31 tff(18131,plain,
% 2.19/2.31 (~(op(e3, e1) = e1)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[708, 18130])).
% 2.19/2.31 tff(18132,plain,
% 2.19/2.31 (op(e3, e2) = e1),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[939, 18131, 18041, 18077])).
% 2.19/2.31 tff(18133,plain,
% 2.19/2.31 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18132])).
% 2.19/2.31 tff(18134,plain,
% 2.19/2.31 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18133])).
% 2.19/2.31 tff(18135,plain,
% 2.19/2.31 (~(op(e1, e2) = e1)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[2292, 18134])).
% 2.19/2.31 tff(18136,plain,
% 2.19/2.31 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18119])).
% 2.19/2.31 tff(18137,plain,
% 2.19/2.31 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18136, 69])).
% 2.19/2.31 tff(18138,plain,
% 2.19/2.31 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18137])).
% 2.19/2.31 tff(18139,plain,
% 2.19/2.31 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18138])).
% 2.19/2.31 tff(18140,plain,
% 2.19/2.31 (~(op(e1, e0) = e1)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[708, 18139])).
% 2.19/2.31 tff(18141,plain,
% 2.19/2.31 (op(e1, e1) = e1),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[954, 18140, 18135, 13757])).
% 2.19/2.31 tff(18142,plain,
% 2.19/2.31 (op(e1, op(e2, e3)) = e1),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[18141, 14802])).
% 2.19/2.31 tff(18143,plain,
% 2.19/2.31 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[10724, 18142])).
% 2.19/2.31 tff(18144,plain,
% 2.19/2.31 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18106, 531])).
% 2.19/2.31 tff(18145,plain,
% 2.19/2.31 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18144])).
% 2.19/2.31 tff(18146,plain,
% 2.19/2.31 (~(op(e1, e2) = op(e2, e1))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[1850, 18145])).
% 2.19/2.31 tff(18147,plain,
% 2.19/2.31 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[539, 18146])).
% 2.19/2.31 tff(18148,plain,
% 2.19/2.31 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18102])).
% 2.19/2.31 tff(18149,plain,
% 2.19/2.31 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18148])).
% 2.19/2.31 tff(18150,plain,
% 2.19/2.31 (~(op(e0, e1) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[606, 18149])).
% 2.19/2.31 tff(18151,plain,
% 2.19/2.31 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18084])).
% 2.19/2.31 tff(18152,plain,
% 2.19/2.31 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18151])).
% 2.19/2.31 tff(18153,plain,
% 2.19/2.31 (~(op(e0, e0) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[6384, 18152])).
% 2.19/2.31 tff(18154,plain,
% 2.19/2.31 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18095])).
% 2.19/2.31 tff(18155,plain,
% 2.19/2.31 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18154])).
% 2.19/2.31 tff(18156,plain,
% 2.19/2.31 (~(op(e0, e0) = e0)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[359, 18155])).
% 2.19/2.31 tff(18157,plain,
% 2.19/2.31 (op(e0, e0) = e1),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[3612, 18156, 17888, 18153])).
% 2.19/2.31 tff(18158,plain,
% 2.19/2.31 ((op(e0, e0) = op(e0, e1)) <=> (e1 = op(e0, e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18157])).
% 2.19/2.31 tff(18159,plain,
% 2.19/2.31 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18158, 7013])).
% 2.19/2.31 tff(18160,plain,
% 2.19/2.31 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e1))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18159])).
% 2.19/2.31 tff(18161,plain,
% 2.19/2.31 (~(op(e0, e1) = e1)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[811, 18160])).
% 2.19/2.31 tff(18162,plain,
% 2.19/2.31 (op(e0, e1) = e0),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[829, 18161, 17881, 18150])).
% 2.19/2.31 tff(18163,plain,
% 2.19/2.31 (op(e0, op(e1, e1)) = op(e0, e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18141])).
% 2.19/2.31 tff(18164,plain,
% 2.19/2.31 (op(e0, op(e1, e1)) = e0),
% 2.19/2.31 inference(transitivity,[status(thm)],[18163, 18162])).
% 2.19/2.31 tff(18165,plain,
% 2.19/2.31 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[635, 18164])).
% 2.19/2.31 tff(18166,plain,
% 2.19/2.31 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18076])).
% 2.19/2.31 tff(18167,plain,
% 2.19/2.31 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18166, 66])).
% 2.19/2.31 tff(18168,plain,
% 2.19/2.31 ((op(e1, e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18167])).
% 2.19/2.31 tff(18169,plain,
% 2.19/2.31 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18168])).
% 2.19/2.31 tff(18170,plain,
% 2.19/2.31 (~(op(e3, e1) = op(e1, e3))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[72, 18169])).
% 2.19/2.31 tff(18171,plain,
% 2.19/2.31 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[6362, 18170])).
% 2.19/2.31 tff(18172,plain,
% 2.19/2.31 ((~(op(e0, e1) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18122])).
% 2.19/2.31 tff(18173,plain,
% 2.19/2.31 (~(op(e1, e0) = op(e0, e1))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[17881, 18172])).
% 2.19/2.31 tff(18174,plain,
% 2.19/2.31 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[613, 18173])).
% 2.19/2.31 tff(18175,plain,
% 2.19/2.31 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.19/2.31 inference(symmetry,[status(thm)],[17889])).
% 2.19/2.31 tff(18176,plain,
% 2.19/2.31 ((op(e3, e0) = op(e3, e1)) <=> (op(e0, e3) = op(e3, e0))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18081, 18175, 453])).
% 2.19/2.31 tff(18177,plain,
% 2.19/2.31 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18176])).
% 2.19/2.31 tff(18178,plain,
% 2.19/2.31 (~(op(e0, e3) = op(e3, e0))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[580, 18177])).
% 2.19/2.31 tff(18179,plain,
% 2.19/2.31 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[496, 18178])).
% 2.19/2.31 tff(18180,plain,
% 2.19/2.31 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18168, 6290])).
% 2.19/2.31 tff(18181,plain,
% 2.19/2.31 ((~(op(e1, e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18180])).
% 2.19/2.31 tff(18182,plain,
% 2.19/2.31 (~(op(e1, e3) = op(e3, e1))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[72, 18181])).
% 2.19/2.31 tff(18183,plain,
% 2.19/2.31 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[6307, 18182])).
% 2.19/2.31 tff(18184,plain,
% 2.19/2.31 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18095])).
% 2.19/2.31 tff(18185,plain,
% 2.19/2.31 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18184, 10200])).
% 2.19/2.31 tff(18186,plain,
% 2.19/2.31 ((op(e0, e2) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18185])).
% 2.19/2.31 tff(18187,plain,
% 2.19/2.31 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[17872])).
% 2.19/2.31 tff(18188,plain,
% 2.19/2.31 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18187])).
% 2.19/2.31 tff(18189,plain,
% 2.19/2.31 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18188])).
% 2.19/2.31 tff(18190,plain,
% 2.19/2.31 (~(op(e0, e3) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[1321, 18189])).
% 2.19/2.31 tff(18191,plain,
% 2.19/2.31 (op(e0, e2) = e3),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[1495, 18150, 18190, 18153])).
% 2.19/2.31 tff(18192,plain,
% 2.19/2.31 (op(e0, e2) = op(e1, e3)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18191, 17971])).
% 2.19/2.31 tff(18193,plain,
% 2.19/2.31 ((op(e0, e2) = e0) <=> (op(e1, e3) = e0)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18192])).
% 2.19/2.31 tff(18194,plain,
% 2.19/2.31 ((op(e1, e3) = e0) <=> (op(e0, e2) = e0)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18193])).
% 2.19/2.31 tff(18195,plain,
% 2.19/2.31 ((op(e1, e3) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18194, 18186])).
% 2.19/2.31 tff(18196,plain,
% 2.19/2.31 ((~(op(e1, e3) = e0)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18195])).
% 2.19/2.31 tff(18197,plain,
% 2.19/2.31 (~(op(e2, e0) = op(e0, e2))),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[80, 18196])).
% 2.19/2.31 tff(18198,plain,
% 2.19/2.31 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[6358, 18197])).
% 2.19/2.31 tff(18199,plain,
% 2.19/2.31 (op(e2, e2) = e2),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[2088, 18118, 17871, 18101])).
% 2.19/2.31 tff(18200,plain,
% 2.19/2.31 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18199])).
% 2.19/2.31 tff(18201,plain,
% 2.19/2.31 (op(e2, op(e2, e2)) = e2),
% 2.19/2.31 inference(transitivity,[status(thm)],[18200, 18199])).
% 2.19/2.31 tff(18202,plain,
% 2.19/2.31 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[528, 18201])).
% 2.19/2.31 tff(18203,plain,
% 2.19/2.31 (op(e1, op(e0, e0)) = op(e1, e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18157])).
% 2.19/2.31 tff(18204,plain,
% 2.19/2.31 ((op(e1, op(e0, e0)) = e1) <=> (op(e1, e1) = e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18203])).
% 2.19/2.31 tff(18205,plain,
% 2.19/2.31 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18204])).
% 2.19/2.31 tff(18206,plain,
% 2.19/2.31 (op(e1, op(e0, e0)) = e1),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[18141, 18205])).
% 2.19/2.31 tff(18207,plain,
% 2.19/2.31 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[6717, 18206])).
% 2.19/2.31 tff(18208,plain,
% 2.19/2.31 (op(e1, op(e3, e2)) = op(e1, e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18132])).
% 2.19/2.31 tff(18209,plain,
% 2.19/2.31 ((op(e1, op(e3, e2)) = e1) <=> (op(e1, e1) = e1)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18208])).
% 2.19/2.31 tff(18210,plain,
% 2.19/2.31 ((op(e1, e1) = e1) <=> (op(e1, op(e3, e2)) = e1)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18209])).
% 2.19/2.31 tff(18211,plain,
% 2.19/2.31 (op(e1, op(e3, e2)) = e1),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[18141, 18210])).
% 2.19/2.31 tff(18212,plain,
% 2.19/2.31 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[12544, 18211])).
% 2.19/2.31 tff(18213,plain,
% 2.19/2.31 ($false),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[5367, 18212, 18207, 18202, 18198, 18183, 18179, 18174, 18171, 18165, 18147, 18143, 18126, 18114, 18109, 18098])).
% 2.19/2.31 tff(18214,plain,((op(e1, e3) = e0) | (~(op(e2, e3) = e1)) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.31 tff(18215,plain,
% 2.19/2.31 (op(e1, e3) = e0),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[18214, 17861, 17, 72, 17867, 68])).
% 2.19/2.31 tff(18216,plain,
% 2.19/2.31 (e0 = op(e1, e3)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18215])).
% 2.19/2.31 tff(18217,plain,
% 2.19/2.31 ((op(e2, e3) = e2) <=> (e1 = e2)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.31 tff(18218,plain,
% 2.19/2.31 ((e1 = e2) <=> (op(e2, e3) = e2)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18217])).
% 2.19/2.31 tff(18219,plain,
% 2.19/2.31 ((~(e1 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18218])).
% 2.19/2.31 tff(18220,plain,
% 2.19/2.31 (~(op(e2, e3) = e2)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[708, 18219])).
% 2.19/2.31 tff(18221,plain,
% 2.19/2.31 (op(e0, e3) = e2),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[15003, 18220, 72])).
% 2.19/2.31 tff(18222,plain,
% 2.19/2.31 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18221])).
% 2.19/2.31 tff(18223,plain,
% 2.19/2.31 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18222, 1])).
% 2.19/2.31 tff(18224,plain,
% 2.19/2.31 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18223])).
% 2.19/2.31 tff(18225,plain,
% 2.19/2.31 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18224])).
% 2.19/2.31 tff(18226,plain,
% 2.19/2.31 (~(op(e0, e3) = e0)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[14, 18225])).
% 2.19/2.31 tff(18227,plain,
% 2.19/2.31 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.31 tff(18228,plain,
% 2.19/2.31 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 2.19/2.31 inference(transitivity,[status(thm)],[18227, 18])).
% 2.19/2.31 tff(18229,plain,
% 2.19/2.31 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18228])).
% 2.19/2.31 tff(18230,plain,
% 2.19/2.31 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18229])).
% 2.19/2.31 tff(18231,plain,
% 2.19/2.31 (~(op(e2, e3) = e0)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[26, 18230])).
% 2.19/2.31 tff(18232,plain,
% 2.19/2.31 (op(e2, e1) = op(e1, e3)),
% 2.19/2.31 inference(transitivity,[status(thm)],[3508, 2909])).
% 2.19/2.31 tff(18233,plain,
% 2.19/2.31 ((op(e2, e1) = e3) <=> (op(e1, e3) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18232])).
% 2.19/2.31 tff(18234,plain,
% 2.19/2.31 ((op(e1, e3) = e3) <=> (op(e2, e1) = e3)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18233])).
% 2.19/2.31 tff(18235,plain,
% 2.19/2.31 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e1) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18234])).
% 2.19/2.31 tff(18236,plain,
% 2.19/2.31 (~(op(e2, e1) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[4782, 18235])).
% 2.19/2.31 tff(18237,plain,
% 2.19/2.31 (op(e3, e3) = e3),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[15018, 17084, 18041])).
% 2.19/2.31 tff(18238,plain,
% 2.19/2.31 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18237])).
% 2.19/2.31 tff(18239,plain,
% 2.19/2.31 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18238])).
% 2.19/2.31 tff(18240,plain,
% 2.19/2.31 (~(op(e3, e1) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[437, 18239])).
% 2.19/2.31 tff(18241,plain,
% 2.19/2.31 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18237])).
% 2.19/2.31 tff(18242,plain,
% 2.19/2.31 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18241])).
% 2.19/2.31 tff(18243,plain,
% 2.19/2.31 (~(op(e3, e2) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[1888, 18242])).
% 2.19/2.31 tff(18244,plain,
% 2.19/2.31 (op(e0, e2) = e3),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[2111, 18088, 75, 18243])).
% 2.19/2.31 tff(18245,plain,
% 2.19/2.31 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18244])).
% 2.19/2.31 tff(18246,plain,
% 2.19/2.31 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18245])).
% 2.19/2.31 tff(18247,plain,
% 2.19/2.31 (~(op(e0, e1) = e3)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[2102, 18246])).
% 2.19/2.31 tff(18248,plain,
% 2.19/2.31 (op(e1, e1) = e3),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[1730, 18247, 18240, 18236])).
% 2.19/2.31 tff(18249,plain,
% 2.19/2.31 (e3 = op(e1, e1)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[18248, 1740])).
% 2.19/2.31 tff(18250,plain,
% 2.19/2.31 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18248])).
% 2.19/2.31 tff(18251,plain,
% 2.19/2.31 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18250])).
% 2.19/2.31 tff(18252,plain,
% 2.19/2.31 (e0 = op(e1, op(e1, e1))),
% 2.19/2.31 inference(transitivity,[status(thm)],[2909, 18251])).
% 2.19/2.31 tff(18253,plain,
% 2.19/2.31 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18250])).
% 2.19/2.31 tff(18254,plain,
% 2.19/2.31 (op(e1, op(e1, e3)) = op(e1, op(e1, op(e1, e1)))),
% 2.19/2.31 inference(symmetry,[status(thm)],[18253])).
% 2.19/2.31 tff(18255,plain,
% 2.19/2.31 (op(e1, e0) = op(e1, op(e1, e3))),
% 2.19/2.31 inference(symmetry,[status(thm)],[11579])).
% 2.19/2.31 tff(18256,plain,
% 2.19/2.31 (op(e2, e2) = e2),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[7007, 18088, 13775, 3508])).
% 2.19/2.31 tff(18257,plain,
% 2.19/2.31 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18256])).
% 2.19/2.31 tff(18258,plain,
% 2.19/2.31 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 2.19/2.31 inference(monotonicity,[status(thm)],[18257])).
% 2.19/2.31 tff(18259,plain,
% 2.19/2.31 (~(op(e1, e2) = e2)),
% 2.19/2.31 inference(modus_ponens,[status(thm)],[1273, 18258])).
% 2.19/2.31 tff(18260,plain,
% 2.19/2.31 (op(e1, e0) = e2),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[2285, 18259, 68, 72])).
% 2.19/2.31 tff(18261,plain,
% 2.19/2.31 (e2 = op(e1, e0)),
% 2.19/2.31 inference(symmetry,[status(thm)],[18260])).
% 2.19/2.31 tff(18262,plain,
% 2.19/2.31 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.19/2.31 inference(transitivity,[status(thm)],[18261, 18255, 18254])).
% 2.19/2.31 tff(18263,plain,
% 2.19/2.31 ($false),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[3009, 18262, 18252, 18249])).
% 2.19/2.31 tff(18264,plain,((~(op(e2, e1) = e0)) | (~(op(e1, e3) = e0)) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e1, e2) = e3) | (~(op(e2, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.19/2.31 tff(18265,plain,
% 2.19/2.31 (~(op(e2, e1) = e0)),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[18264, 18215, 68, 72, 75, 17861])).
% 2.19/2.31 tff(18266,plain,
% 2.19/2.31 (op(e2, e0) = e0),
% 2.19/2.31 inference(unit_resolution,[status(thm)],[2311, 18265, 17, 18231])).
% 2.19/2.32 tff(18267,plain,
% 2.19/2.32 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18266])).
% 2.19/2.32 tff(18268,plain,
% 2.19/2.32 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18267])).
% 2.19/2.32 tff(18269,plain,
% 2.19/2.32 (~(op(e0, e0) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[359, 18268])).
% 2.19/2.32 tff(18270,plain,
% 2.19/2.32 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.32 tff(18271,plain,
% 2.19/2.32 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18270, 657])).
% 2.19/2.32 tff(18272,plain,
% 2.19/2.32 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18271])).
% 2.19/2.32 tff(18273,plain,
% 2.19/2.32 (~(op(e3, e3) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[368, 18272])).
% 2.19/2.32 tff(18274,plain,
% 2.19/2.32 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18215])).
% 2.19/2.32 tff(18275,plain,
% 2.19/2.32 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18274, 3077])).
% 2.19/2.32 tff(18276,plain,
% 2.19/2.32 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18275])).
% 2.19/2.32 tff(18277,plain,
% 2.19/2.32 (~(op(e3, e3) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[571, 18276])).
% 2.19/2.32 tff(18278,plain,
% 2.19/2.32 (op(e3, e3) = e3),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[15018, 18277, 18273])).
% 2.19/2.32 tff(18279,plain,
% 2.19/2.32 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18278])).
% 2.19/2.32 tff(18280,plain,
% 2.19/2.32 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18279])).
% 2.19/2.32 tff(18281,plain,
% 2.19/2.32 (~(op(e3, e1) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[437, 18280])).
% 2.19/2.32 tff(18282,plain,
% 2.19/2.32 (op(e3, e0) = op(e3, op(e1, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18216])).
% 2.19/2.32 tff(18283,plain,
% 2.19/2.32 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18282])).
% 2.19/2.32 tff(18284,plain,
% 2.19/2.32 ((op(e3, op(e1, e3)) = e3) <=> (op(e3, e0) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18283])).
% 2.19/2.32 tff(18285,plain,
% 2.19/2.32 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, op(e1, e3)) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18282, 18278])).
% 2.19/2.32 tff(18286,plain,
% 2.19/2.32 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18285, 18284])).
% 2.19/2.32 tff(18287,plain,
% 2.19/2.32 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18286])).
% 2.19/2.32 tff(18288,plain,
% 2.19/2.32 (~(op(e3, e0) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[157, 18287])).
% 2.19/2.32 tff(18289,plain,
% 2.19/2.32 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18221])).
% 2.19/2.32 tff(18290,plain,
% 2.19/2.32 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18289])).
% 2.19/2.32 tff(18291,plain,
% 2.19/2.32 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18290])).
% 2.19/2.32 tff(18292,plain,
% 2.19/2.32 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18278])).
% 2.19/2.32 tff(18293,plain,
% 2.19/2.32 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18292, 18291])).
% 2.19/2.32 tff(18294,plain,
% 2.19/2.32 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18293])).
% 2.19/2.32 tff(18295,plain,
% 2.19/2.32 (~(op(e3, op(e0, e3)) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[1888, 18294])).
% 2.19/2.32 tff(18296,plain,
% 2.19/2.32 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.32 tff(18297,plain,
% 2.19/2.32 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18296])).
% 2.19/2.32 tff(18298,plain,
% 2.19/2.32 (~(op(e0, e3) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[964, 18297])).
% 2.19/2.32 tff(18299,plain,
% 2.19/2.32 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.32 tff(18300,plain,
% 2.19/2.32 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18299])).
% 2.19/2.32 tff(18301,plain,
% 2.19/2.32 (~(op(e2, e1) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[197, 18300])).
% 2.19/2.32 tff(18302,plain,
% 2.19/2.32 (op(e2, e0) = op(e1, e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18266, 18216])).
% 2.19/2.32 tff(18303,plain,
% 2.19/2.32 ((op(e2, e0) = e2) <=> (op(e1, e3) = e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18302])).
% 2.19/2.32 tff(18304,plain,
% 2.19/2.32 ((op(e1, e3) = e2) <=> (op(e2, e0) = e2)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18303])).
% 2.19/2.32 tff(18305,plain,
% 2.19/2.32 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18304])).
% 2.19/2.32 tff(18306,plain,
% 2.19/2.32 (~(op(e2, e0) = e2)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[72, 18305])).
% 2.19/2.32 tff(18307,plain,
% 2.19/2.32 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18221])).
% 2.19/2.32 tff(18308,plain,
% 2.19/2.32 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18307])).
% 2.19/2.32 tff(18309,plain,
% 2.19/2.32 (~(op(e0, e0) = e2)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[3414, 18308])).
% 2.19/2.32 tff(18310,plain,
% 2.19/2.32 (op(e2, e1) = e3),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2367, 16808, 2559, 4530])).
% 2.19/2.32 tff(18311,plain,
% 2.19/2.32 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18310])).
% 2.19/2.32 tff(18312,plain,
% 2.19/2.32 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18311])).
% 2.19/2.32 tff(18313,plain,
% 2.19/2.32 (~(op(e1, e1) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[225, 18312])).
% 2.19/2.32 tff(18314,plain,
% 2.19/2.32 ((op(e1, e0) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18255])).
% 2.19/2.32 tff(18315,plain,
% 2.19/2.32 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e0) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18314])).
% 2.19/2.32 tff(18316,plain,
% 2.19/2.32 (op(e1, e0) = e2),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[589, 6692, 12721, 982])).
% 2.19/2.32 tff(18317,plain,
% 2.19/2.32 (op(e1, op(e1, e3)) = e2),
% 2.19/2.32 inference(transitivity,[status(thm)],[11579, 18316])).
% 2.19/2.32 tff(18318,plain,
% 2.19/2.32 ((op(e1, op(e1, e3)) = e3) <=> (e2 = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18317])).
% 2.19/2.32 tff(18319,plain,
% 2.19/2.32 ((e2 = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18318])).
% 2.19/2.32 tff(18320,plain,
% 2.19/2.32 ((e2 = e3) <=> (op(e1, e0) = e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18319, 18315])).
% 2.19/2.32 tff(18321,plain,
% 2.19/2.32 ((~(e2 = e3)) <=> (~(op(e1, e0) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18320])).
% 2.19/2.32 tff(18322,plain,
% 2.19/2.32 (~(op(e1, e0) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[1321, 18321])).
% 2.19/2.32 tff(18323,plain,
% 2.19/2.32 ($false),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[247, 18322, 18313, 75, 4782])).
% 2.19/2.32 tff(18324,plain,((~(op(e3, e1) = e2)) | (op(e1, e2) = e3) | (~(op(e1, e3) = e0)) | (op(e0, e0) = e2) | (op(e2, e0) = e2) | (op(e2, e1) = e0) | (op(e2, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.32 tff(18325,plain,
% 2.19/2.32 (~(op(e3, e1) = e2)),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[18324, 75, 18215, 18309, 18306, 18265, 18301])).
% 2.19/2.32 tff(18326,plain,
% 2.19/2.32 (op(e3, e1) = e1),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[446, 82, 2839, 183])).
% 2.19/2.32 tff(18327,plain,
% 2.19/2.32 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18326])).
% 2.19/2.32 tff(18328,plain,
% 2.19/2.32 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18327])).
% 2.19/2.32 tff(18329,plain,
% 2.19/2.32 (~(op(e3, e0) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[580, 18328])).
% 2.19/2.32 tff(18330,plain,
% 2.19/2.32 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[2])).
% 2.19/2.32 tff(18331,plain,
% 2.19/2.32 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18330])).
% 2.19/2.32 tff(18332,plain,
% 2.19/2.32 (~(op(e0, e1) = e2)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[818, 18331])).
% 2.19/2.32 tff(18333,plain,
% 2.19/2.32 (op(e2, e1) = e2),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[1993, 82, 68, 18332])).
% 2.19/2.32 tff(18334,plain,
% 2.19/2.32 ((op(e2, e1) = e0) <=> (e2 = op(e1, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18333, 2909])).
% 2.19/2.32 tff(18335,plain,
% 2.19/2.32 ((op(e2, e1) = e0) <=> (op(e1, e3) = e2)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18334, 66])).
% 2.19/2.32 tff(18336,plain,
% 2.19/2.32 ((op(e1, e3) = e2) <=> (op(e2, e1) = e0)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18335])).
% 2.19/2.32 tff(18337,plain,
% 2.19/2.32 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e1) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18336])).
% 2.19/2.32 tff(18338,plain,
% 2.19/2.32 (~(op(e2, e1) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[72, 18337])).
% 2.19/2.32 tff(18339,plain,
% 2.19/2.32 (op(e2, e0) = e0),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2311, 18338, 17, 1063])).
% 2.19/2.32 tff(18340,plain,
% 2.19/2.32 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18339])).
% 2.19/2.32 tff(18341,plain,
% 2.19/2.32 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18340, 8115])).
% 2.19/2.32 tff(18342,plain,
% 2.19/2.32 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18341])).
% 2.19/2.32 tff(18343,plain,
% 2.19/2.32 (~(op(e3, e0) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[747, 18342])).
% 2.19/2.32 tff(18344,plain,
% 2.19/2.32 (op(e3, e0) = e2),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[5422, 18343, 2410, 18329])).
% 2.19/2.32 tff(18345,plain,
% 2.19/2.32 (op(e3, e0) = op(e0, e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[18344, 10370])).
% 2.19/2.32 tff(18346,plain,
% 2.19/2.32 (op(e2, op(e0, e3)) = op(e2, e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[2])).
% 2.19/2.32 tff(18347,plain,
% 2.19/2.32 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e2) = e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18346])).
% 2.19/2.32 tff(18348,plain,
% 2.19/2.32 ((op(e2, e2) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18347])).
% 2.19/2.32 tff(18349,plain,
% 2.19/2.32 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18333])).
% 2.19/2.32 tff(18350,plain,
% 2.19/2.32 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18349, 81])).
% 2.19/2.32 tff(18351,plain,
% 2.19/2.32 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, op(e0, e3)) = e2)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18350, 18348])).
% 2.19/2.32 tff(18352,plain,
% 2.19/2.32 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18351])).
% 2.19/2.32 tff(18353,plain,
% 2.19/2.32 (~(op(e2, op(e0, e3)) = e2)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[508, 18352])).
% 2.19/2.32 tff(18354,plain,
% 2.19/2.32 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[1219])).
% 2.19/2.32 tff(18355,plain,
% 2.19/2.32 ((op(op(e1, e3), e1) = e3) <=> (op(e0, e1) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18354])).
% 2.19/2.32 tff(18356,plain,
% 2.19/2.32 ((op(e0, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18355])).
% 2.19/2.32 tff(18357,plain,
% 2.19/2.32 ((op(e1, e1) = e0) <=> (op(e1, e1) = op(e1, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[2909])).
% 2.19/2.32 tff(18358,plain,
% 2.19/2.32 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e0)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18357])).
% 2.19/2.32 tff(18359,plain,
% 2.19/2.32 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18358])).
% 2.19/2.32 tff(18360,plain,
% 2.19/2.32 (~(op(e1, e1) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[619, 18359])).
% 2.19/2.32 tff(18361,plain,
% 2.19/2.32 (op(e0, e1) = e0),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[292, 18338, 18360, 183])).
% 2.19/2.32 tff(18362,plain,
% 2.19/2.32 (op(e0, e1) = op(e1, e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18361, 2909])).
% 2.19/2.32 tff(18363,plain,
% 2.19/2.32 ((op(e0, e1) = e3) <=> (op(e1, e3) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18362])).
% 2.19/2.32 tff(18364,plain,
% 2.19/2.32 ((op(e1, e3) = e3) <=> (op(e0, e1) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18363])).
% 2.19/2.32 tff(18365,plain,
% 2.19/2.32 ((op(e1, e3) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18364, 18356])).
% 2.19/2.32 tff(18366,plain,
% 2.19/2.32 ((~(op(e1, e3) = e3)) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18365])).
% 2.19/2.32 tff(18367,plain,
% 2.19/2.32 (~(op(op(e1, e3), e1) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[4782, 18366])).
% 2.19/2.32 tff(18368,plain,
% 2.19/2.32 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[160, 18367])).
% 2.19/2.32 tff(18369,plain,
% 2.19/2.32 ((~(op(e1, e3) = e3)) <=> (~(op(e0, e1) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18364])).
% 2.19/2.32 tff(18370,plain,
% 2.19/2.32 (~(op(e0, e1) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[4782, 18369])).
% 2.19/2.32 tff(18371,plain,
% 2.19/2.32 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e2) = e0)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[17663])).
% 2.19/2.32 tff(18372,plain,
% 2.19/2.32 ((op(e0, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18371])).
% 2.19/2.32 tff(18373,plain,
% 2.19/2.32 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18361])).
% 2.19/2.32 tff(18374,plain,
% 2.19/2.32 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18373, 10200])).
% 2.19/2.32 tff(18375,plain,
% 2.19/2.32 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, op(e0, e3)) = e0)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18374, 18372])).
% 2.19/2.32 tff(18376,plain,
% 2.19/2.32 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18375])).
% 2.19/2.32 tff(18377,plain,
% 2.19/2.32 (~(op(e0, op(e0, e3)) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[2102, 18376])).
% 2.19/2.32 tff(18378,plain,
% 2.19/2.32 (~(op(e3, e0) = op(e0, e3))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2763, 18377, 1219, 121, 16740, 18370, 17084, 18368, 18353, 650])).
% 2.19/2.32 tff(18379,plain,
% 2.19/2.32 ($false),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[18378, 18345])).
% 2.19/2.32 tff(18380,plain,((op(e3, e1) = e2) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e0)) | (op(e0, e3) = e1) | (op(e3, op(e0, e3)) = e3) | (op(e3, e0) = e3) | (op(e3, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0) | (op(e1, e3) = e2) | (op(e3, e1) = e3) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.32 tff(18381,plain,
% 2.19/2.32 (op(e3, e1) = e0),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[18380, 18325, 18215, 18298, 18295, 18288, 18221, 17, 18231, 72, 18281, 68])).
% 2.19/2.32 tff(18382,plain,
% 2.19/2.32 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e0)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18381])).
% 2.19/2.32 tff(18383,plain,
% 2.19/2.32 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e0))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18382])).
% 2.19/2.32 tff(18384,plain,
% 2.19/2.32 (~(op(e0, e1) = e0)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[3046, 18383])).
% 2.19/2.32 tff(18385,plain,
% 2.19/2.32 (op(e0, e2) = e0),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[3976, 18384, 18269, 18226])).
% 2.19/2.32 tff(18386,plain,
% 2.19/2.32 (op(e0, e2) = op(e1, e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18385, 18216])).
% 2.19/2.32 tff(18387,plain,
% 2.19/2.32 ((op(e0, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18386])).
% 2.19/2.32 tff(18388,plain,
% 2.19/2.32 ((op(e1, e3) = e1) <=> (op(e0, e2) = e1)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18387])).
% 2.19/2.32 tff(18389,plain,
% 2.19/2.32 ((~(op(e1, e3) = e1)) <=> (~(op(e0, e2) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18388])).
% 2.19/2.32 tff(18390,plain,
% 2.19/2.32 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[17861])).
% 2.19/2.32 tff(18391,plain,
% 2.19/2.32 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18390])).
% 2.19/2.32 tff(18392,plain,
% 2.19/2.32 (~(op(e1, e3) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[118, 18391])).
% 2.19/2.32 tff(18393,plain,
% 2.19/2.32 (~(op(e0, e2) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[18392, 18389])).
% 2.19/2.32 tff(18394,plain,
% 2.19/2.32 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18221])).
% 2.19/2.32 tff(18395,plain,
% 2.19/2.32 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18394])).
% 2.19/2.32 tff(18396,plain,
% 2.19/2.32 (~(op(e0, e1) = e2)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[818, 18395])).
% 2.19/2.32 tff(18397,plain,
% 2.19/2.32 (op(e2, e1) = e2),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[1993, 18325, 68, 18396])).
% 2.19/2.32 tff(18398,plain,
% 2.19/2.32 ((op(e2, e1) = e3) <=> (e2 = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18397])).
% 2.19/2.32 tff(18399,plain,
% 2.19/2.32 ((e2 = e3) <=> (op(e2, e1) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18398])).
% 2.19/2.32 tff(18400,plain,
% 2.19/2.32 ((~(e2 = e3)) <=> (~(op(e2, e1) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18399])).
% 2.19/2.32 tff(18401,plain,
% 2.19/2.32 (~(op(e2, e1) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[1321, 18400])).
% 2.19/2.32 tff(18402,plain,
% 2.19/2.32 (op(op(e2, e1), e1) = op(e2, e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18397])).
% 2.19/2.32 tff(18403,plain,
% 2.19/2.32 (op(op(e2, e1), e1) = e2),
% 2.19/2.32 inference(transitivity,[status(thm)],[18402, 18397])).
% 2.19/2.32 tff(18404,plain,
% 2.19/2.32 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2371, 18403])).
% 2.19/2.32 tff(18405,plain,
% 2.19/2.32 (op(e2, op(e1, e3)) = op(e2, e0)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18215])).
% 2.19/2.32 tff(18406,plain,
% 2.19/2.32 (op(e2, op(e2, e0)) = op(e2, op(e1, e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18302])).
% 2.19/2.32 tff(18407,plain,
% 2.19/2.32 (op(e2, op(e2, e0)) = e0),
% 2.19/2.32 inference(transitivity,[status(thm)],[18406, 18405, 18266])).
% 2.19/2.32 tff(18408,plain,
% 2.19/2.32 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2653, 18407])).
% 2.19/2.32 tff(18409,plain,
% 2.19/2.32 (op(op(e0, e2), e2) = op(e0, e2)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18385])).
% 2.19/2.32 tff(18410,plain,
% 2.19/2.32 (op(op(e0, e2), e2) = e0),
% 2.19/2.32 inference(transitivity,[status(thm)],[18409, 18385])).
% 2.19/2.32 tff(18411,plain,
% 2.19/2.32 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[1956, 18410])).
% 2.19/2.32 tff(18412,plain,
% 2.19/2.32 (op(op(e1, e3), e3) = op(e0, e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18215])).
% 2.19/2.32 tff(18413,plain,
% 2.19/2.32 (op(e3, e1) = op(e1, e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18381, 18216])).
% 2.19/2.32 tff(18414,plain,
% 2.19/2.32 (op(op(e3, e1), e3) = op(op(e1, e3), e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18413])).
% 2.19/2.32 tff(18415,plain,
% 2.19/2.32 (op(op(e3, e1), e3) = e2),
% 2.19/2.32 inference(transitivity,[status(thm)],[18414, 18412, 18221])).
% 2.19/2.32 tff(18416,plain,
% 2.19/2.32 ((op(op(e3, e1), e3) = e1) <=> (e2 = e1)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18415])).
% 2.19/2.32 tff(18417,plain,
% 2.19/2.32 ((op(op(e3, e1), e3) = e1) <=> (e1 = e2)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18416, 69])).
% 2.19/2.32 tff(18418,plain,
% 2.19/2.32 ((e1 = e2) <=> (op(op(e3, e1), e3) = e1)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18417])).
% 2.19/2.32 tff(18419,plain,
% 2.19/2.32 ((~(e1 = e2)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18418])).
% 2.19/2.32 tff(18420,plain,
% 2.19/2.32 (~(op(op(e3, e1), e3) = e1)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[708, 18419])).
% 2.19/2.32 tff(18421,plain,
% 2.19/2.32 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[1050, 18420])).
% 2.19/2.32 tff(18422,plain,
% 2.19/2.32 (op(op(e0, e3), e0) = op(e2, e0)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18221])).
% 2.19/2.32 tff(18423,plain,
% 2.19/2.32 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18422])).
% 2.19/2.32 tff(18424,plain,
% 2.19/2.32 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18423])).
% 2.19/2.32 tff(18425,plain,
% 2.19/2.32 ((op(e2, e0) = e3) <=> (op(e1, e3) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18302])).
% 2.19/2.32 tff(18426,plain,
% 2.19/2.32 ((op(e1, e3) = e3) <=> (op(e2, e0) = e3)),
% 2.19/2.32 inference(symmetry,[status(thm)],[18425])).
% 2.19/2.32 tff(18427,plain,
% 2.19/2.32 ((op(e1, e3) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.19/2.32 inference(transitivity,[status(thm)],[18426, 18424])).
% 2.19/2.32 tff(18428,plain,
% 2.19/2.32 ((~(op(e1, e3) = e3)) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18427])).
% 2.19/2.32 tff(18429,plain,
% 2.19/2.32 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18216])).
% 2.19/2.32 tff(18430,plain,
% 2.19/2.32 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18429])).
% 2.19/2.32 tff(18431,plain,
% 2.19/2.32 (~(op(e1, e3) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[181, 18430])).
% 2.19/2.32 tff(18432,plain,
% 2.19/2.32 (~(op(op(e0, e3), e0) = e3)),
% 2.19/2.32 inference(modus_ponens,[status(thm)],[18431, 18428])).
% 2.19/2.32 tff(18433,plain,
% 2.19/2.32 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[2635, 18432])).
% 2.19/2.32 tff(18434,plain,
% 2.19/2.32 (op(e1, e1) = e3),
% 2.19/2.32 inference(unit_resolution,[status(thm)],[1730, 2527, 18240, 3271])).
% 2.19/2.32 tff(18435,plain,
% 2.19/2.32 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, op(e1, e3)) = e3)),
% 2.19/2.32 inference(monotonicity,[status(thm)],[18255, 18434])).
% 2.19/2.33 tff(18436,plain,
% 2.19/2.33 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18435, 18315])).
% 2.19/2.33 tff(18437,plain,
% 2.19/2.33 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18436])).
% 2.19/2.33 tff(18438,plain,
% 2.19/2.33 (~(op(e1, e0) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[737, 18437])).
% 2.19/2.33 tff(18439,plain,
% 2.19/2.33 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[2909])).
% 2.19/2.33 tff(18440,plain,
% 2.19/2.33 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18439])).
% 2.19/2.33 tff(18441,plain,
% 2.19/2.33 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18440])).
% 2.19/2.33 tff(18442,plain,
% 2.19/2.33 (~(op(e1, e0) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[110, 18441])).
% 2.19/2.33 tff(18443,plain,
% 2.19/2.33 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18434])).
% 2.19/2.33 tff(18444,plain,
% 2.19/2.33 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18443])).
% 2.19/2.33 tff(18445,plain,
% 2.19/2.33 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18444, 11579])).
% 2.19/2.33 tff(18446,plain,
% 2.19/2.33 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18445])).
% 2.19/2.33 tff(18447,plain,
% 2.19/2.33 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18446, 2154])).
% 2.19/2.33 tff(18448,plain,
% 2.19/2.33 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18447])).
% 2.19/2.33 tff(18449,plain,
% 2.19/2.33 (e3 = op(e1, e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[18434, 1740])).
% 2.19/2.33 tff(18450,plain,
% 2.19/2.33 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.19/2.33 inference(symmetry,[status(thm)],[18443])).
% 2.19/2.33 tff(18451,plain,
% 2.19/2.33 (e0 = op(e1, op(e1, e1))),
% 2.19/2.33 inference(transitivity,[status(thm)],[2909, 18450])).
% 2.19/2.33 tff(18452,plain,
% 2.19/2.33 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[3009, 18451, 18449])).
% 2.19/2.33 tff(18453,plain,
% 2.19/2.33 (~(op(e1, e0) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[18452, 18448])).
% 2.19/2.33 tff(18454,plain,
% 2.19/2.33 (op(e1, e0) = e1),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[728, 18453, 18442, 18438])).
% 2.19/2.33 tff(18455,plain,
% 2.19/2.33 (op(op(e1, e0), e0) = op(e1, op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18454, 2909])).
% 2.19/2.33 tff(18456,plain,
% 2.19/2.33 (op(op(e1, e0), e0) = e1),
% 2.19/2.33 inference(transitivity,[status(thm)],[18455, 11579, 18454])).
% 2.19/2.33 tff(18457,plain,
% 2.19/2.33 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[3015, 18456])).
% 2.19/2.33 tff(18458,plain,
% 2.19/2.33 (op(e1, e2) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2285, 18453, 68, 72])).
% 2.19/2.33 tff(18459,plain,
% 2.19/2.33 (op(e1, op(e1, e2)) = op(e1, e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18458])).
% 2.19/2.33 tff(18460,plain,
% 2.19/2.33 (op(e1, op(e1, e2)) = e2),
% 2.19/2.33 inference(transitivity,[status(thm)],[18459, 18458])).
% 2.19/2.33 tff(18461,plain,
% 2.19/2.33 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2377, 18460])).
% 2.19/2.33 tff(18462,plain,
% 2.19/2.33 (op(e0, e1) = e1),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[829, 2527, 17881, 3849])).
% 2.19/2.33 tff(18463,plain,
% 2.19/2.33 (op(e0, op(e0, e1)) = op(op(e1, e3), e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[2909, 18462])).
% 2.19/2.33 tff(18464,plain,
% 2.19/2.33 (op(e0, op(e0, e1)) = e1),
% 2.19/2.33 inference(transitivity,[status(thm)],[18463, 18354, 18462])).
% 2.19/2.33 tff(18465,plain,
% 2.19/2.33 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2449, 18464])).
% 2.19/2.33 tff(18466,plain,
% 2.19/2.33 ((~(op(e0, e1) = e3)) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18356])).
% 2.19/2.33 tff(18467,plain,
% 2.19/2.33 (~(op(op(e1, e3), e1) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[2527, 18466])).
% 2.19/2.33 tff(18468,plain,
% 2.19/2.33 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[160, 18467])).
% 2.19/2.33 tff(18469,plain,
% 2.19/2.33 (op(e3, e0) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[589, 18453, 17888, 982])).
% 2.19/2.33 tff(18470,plain,
% 2.19/2.33 (op(op(e3, e0), e3) = op(e2, e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18469])).
% 2.19/2.33 tff(18471,plain,
% 2.19/2.33 (op(op(e3, e0), e3) = e1),
% 2.19/2.33 inference(transitivity,[status(thm)],[18470, 2684])).
% 2.19/2.33 tff(18472,plain,
% 2.19/2.33 ((op(op(e3, e0), e3) = e0) <=> (e1 = op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18471, 2909])).
% 2.19/2.33 tff(18473,plain,
% 2.19/2.33 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e3) = e1)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18472, 28])).
% 2.19/2.33 tff(18474,plain,
% 2.19/2.33 ((op(e1, e3) = e1) <=> (op(op(e3, e0), e3) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18473])).
% 2.19/2.33 tff(18475,plain,
% 2.19/2.33 ((~(op(e1, e3) = e1)) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18474])).
% 2.19/2.33 tff(18476,plain,
% 2.19/2.33 (~(op(op(e3, e0), e3) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[13757, 18475])).
% 2.19/2.33 tff(18477,plain,
% 2.19/2.33 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1764, 18476])).
% 2.19/2.33 tff(18478,plain,
% 2.19/2.33 (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1459, 18477, 3342, 1275, 1347, 18468, 18465, 1363, 2421, 18461, 18457, 1936])).
% 2.19/2.33 tff(18479,plain,
% 2.19/2.33 (op(op(e3, e2), e3) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2408, 18478])).
% 2.19/2.33 tff(18480,plain,
% 2.19/2.33 ((op(e1, e2) = e1) <=> (e2 = e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18458])).
% 2.19/2.33 tff(18481,plain,
% 2.19/2.33 ((op(e1, e2) = e1) <=> (e1 = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18480, 69])).
% 2.19/2.33 tff(18482,plain,
% 2.19/2.33 ((e1 = e2) <=> (op(e1, e2) = e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18481])).
% 2.19/2.33 tff(18483,plain,
% 2.19/2.33 ((~(e1 = e2)) <=> (~(op(e1, e2) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18482])).
% 2.19/2.33 tff(18484,plain,
% 2.19/2.33 (~(op(e1, e2) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[708, 18483])).
% 2.19/2.33 tff(18485,plain,
% 2.19/2.33 (op(e3, e2) = e1),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1613, 18484, 13500, 4484])).
% 2.19/2.33 tff(18486,plain,
% 2.19/2.33 (e1 = op(e3, e2)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18485])).
% 2.19/2.33 tff(18487,plain,
% 2.19/2.33 (op(e1, e3) = op(op(e3, e2), e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18486])).
% 2.19/2.33 tff(18488,plain,
% 2.19/2.33 (op(e1, e3) = e2),
% 2.19/2.33 inference(transitivity,[status(thm)],[18487, 18479])).
% 2.19/2.33 tff(18489,plain,
% 2.19/2.33 ($false),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[72, 18488])).
% 2.19/2.33 tff(18490,plain,((op(e0, e1) = e3) | (op(e1, e3) = e2) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (op(e0, e2) = e1) | (~(op(e1, e3) = e0)) | (~(op(e2, e3) = e1)) | (op(e2, e0) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e3) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.33 tff(18491,plain,
% 2.19/2.33 (op(e0, e1) = e3),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[18490, 18433, 72, 18421, 17867, 18411, 18408, 18404, 18393, 18215, 17861, 18306, 68, 18401, 18384])).
% 2.19/2.33 tff(18492,plain,
% 2.19/2.33 ((op(e0, e1) = e1) <=> (e3 = e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18491])).
% 2.19/2.33 tff(18493,plain,
% 2.19/2.33 ((op(e0, e1) = e1) <=> (e1 = e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18492, 128])).
% 2.19/2.33 tff(18494,plain,
% 2.19/2.33 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18493])).
% 2.19/2.33 tff(18495,plain,
% 2.19/2.33 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18494])).
% 2.19/2.33 tff(18496,plain,
% 2.19/2.33 (~(op(e0, e1) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[303, 18495])).
% 2.19/2.33 tff(18497,plain,
% 2.19/2.33 (op(e0, e0) = e1),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[384, 18496, 18298, 18393])).
% 2.19/2.33 tff(18498,plain,
% 2.19/2.33 (e1 = op(e0, e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[18497, 74])).
% 2.19/2.33 tff(18499,plain,
% 2.19/2.33 (op(e0, op(e0, e0)) = op(op(e1, e3), e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18216, 18497])).
% 2.19/2.33 tff(18500,plain,
% 2.19/2.33 (op(op(e1, e3), e1) = op(e0, op(e0, e0))),
% 2.19/2.33 inference(symmetry,[status(thm)],[18499])).
% 2.19/2.33 tff(18501,plain,
% 2.19/2.33 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18215])).
% 2.19/2.33 tff(18502,plain,
% 2.19/2.33 (op(e0, e1) = op(op(e1, e3), e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18501])).
% 2.19/2.33 tff(18503,plain,
% 2.19/2.33 (e3 = op(e0, e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18491])).
% 2.19/2.33 tff(18504,plain,
% 2.19/2.33 (e3 = op(e0, op(e0, e0))),
% 2.19/2.33 inference(transitivity,[status(thm)],[18503, 18502, 18500])).
% 2.19/2.33 tff(18505,plain,
% 2.19/2.33 (op(e0, op(e0, e0)) = e3),
% 2.19/2.33 inference(transitivity,[status(thm)],[18499, 18501, 18491])).
% 2.19/2.33 tff(18506,plain,
% 2.19/2.33 (op(e0, op(e0, op(e0, e0))) = op(op(e1, e3), e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18216, 18505])).
% 2.19/2.33 tff(18507,plain,
% 2.19/2.33 (op(op(e1, e3), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.33 inference(symmetry,[status(thm)],[18506])).
% 2.19/2.33 tff(18508,plain,
% 2.19/2.33 (op(e0, e3) = op(op(e1, e3), e3)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18412])).
% 2.19/2.33 tff(18509,plain,
% 2.19/2.33 (e2 = op(e0, e3)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18221])).
% 2.19/2.33 tff(18510,plain,
% 2.19/2.33 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.33 inference(transitivity,[status(thm)],[18509, 18508, 18507])).
% 2.19/2.33 tff(18511,plain,
% 2.19/2.33 ($false),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[16194, 18510, 18504, 18498])).
% 2.19/2.33 tff(18512,plain,((op(e1, e2) = e3) | (op(e1, e3) = e2) | (op(e1, e1) = e2) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.33 tff(18513,plain,
% 2.19/2.33 (op(e1, e2) = e3),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[18512, 72, 68, 17])).
% 2.19/2.33 tff(18514,plain,
% 2.19/2.33 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18513])).
% 2.19/2.33 tff(18515,plain,
% 2.19/2.33 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18514])).
% 2.19/2.33 tff(18516,plain,
% 2.19/2.33 (~(op(e0, e2) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[6205, 18515])).
% 2.19/2.33 tff(18517,plain,
% 2.19/2.33 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18513])).
% 2.19/2.33 tff(18518,plain,
% 2.19/2.33 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18517, 1314])).
% 2.19/2.33 tff(18519,plain,
% 2.19/2.33 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18518])).
% 2.19/2.33 tff(18520,plain,
% 2.19/2.33 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18519])).
% 2.19/2.33 tff(18521,plain,
% 2.19/2.33 (~(op(e1, e2) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[1321, 18520])).
% 2.19/2.33 tff(18522,plain,
% 2.19/2.33 (op(e1, e0) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2285, 18521, 68, 72])).
% 2.19/2.33 tff(18523,plain,
% 2.19/2.33 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18522])).
% 2.19/2.33 tff(18524,plain,
% 2.19/2.33 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18523])).
% 2.19/2.33 tff(18525,plain,
% 2.19/2.33 (~(op(e0, e0) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[2471, 18524])).
% 2.19/2.33 tff(18526,plain,
% 2.19/2.33 ((op(e1, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18522])).
% 2.19/2.33 tff(18527,plain,
% 2.19/2.33 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18526, 9812])).
% 2.19/2.33 tff(18528,plain,
% 2.19/2.33 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18527])).
% 2.19/2.33 tff(18529,plain,
% 2.19/2.33 (~(op(e2, e0) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[756, 18528])).
% 2.19/2.33 tff(18530,plain,
% 2.19/2.33 (~(op(e1, e1) = e0)),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[14511, 18513, 72])).
% 2.19/2.33 tff(18531,plain,
% 2.19/2.33 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18513])).
% 2.19/2.33 tff(18532,plain,
% 2.19/2.33 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18531])).
% 2.19/2.33 tff(18533,plain,
% 2.19/2.33 (~(op(e1, e1) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[1604, 18532])).
% 2.19/2.33 tff(18534,plain,
% 2.19/2.33 (op(e1, e1) = e1),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[630, 18533, 68, 18530])).
% 2.19/2.33 tff(18535,plain,
% 2.19/2.33 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18534])).
% 2.19/2.33 tff(18536,plain,
% 2.19/2.33 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18535, 2355])).
% 2.19/2.33 tff(18537,plain,
% 2.19/2.33 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18536])).
% 2.19/2.33 tff(18538,plain,
% 2.19/2.33 (~(op(e2, e1) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[225, 18537])).
% 2.19/2.33 tff(18539,plain,
% 2.19/2.33 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18534])).
% 2.19/2.33 tff(18540,plain,
% 2.19/2.33 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18539, 28])).
% 2.19/2.33 tff(18541,plain,
% 2.19/2.33 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18540])).
% 2.19/2.33 tff(18542,plain,
% 2.19/2.33 (~(op(e1, e3) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[619, 18541])).
% 2.19/2.33 tff(18543,plain,
% 2.19/2.33 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18534])).
% 2.19/2.33 tff(18544,plain,
% 2.19/2.33 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18543])).
% 2.19/2.33 tff(18545,plain,
% 2.19/2.33 (~(op(e0, e1) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[792, 18544])).
% 2.19/2.33 tff(18546,plain,
% 2.19/2.33 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[2899])).
% 2.19/2.33 tff(18547,plain,
% 2.19/2.33 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18546, 159])).
% 2.19/2.33 tff(18548,plain,
% 2.19/2.33 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18547])).
% 2.19/2.33 tff(18549,plain,
% 2.19/2.33 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18548])).
% 2.19/2.33 tff(18550,plain,
% 2.19/2.33 (~(op(e1, e2) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[181, 18549])).
% 2.19/2.33 tff(18551,plain,
% 2.19/2.33 (~(op(e1, e1) = e0)),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[14511, 2899, 72])).
% 2.19/2.33 tff(18552,plain,
% 2.19/2.33 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[920])).
% 2.19/2.33 tff(18553,plain,
% 2.19/2.33 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18552, 1])).
% 2.19/2.33 tff(18554,plain,
% 2.19/2.33 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18553])).
% 2.19/2.33 tff(18555,plain,
% 2.19/2.33 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18554])).
% 2.19/2.33 tff(18556,plain,
% 2.19/2.33 (~(op(e1, e0) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[14, 18555])).
% 2.19/2.33 tff(18557,plain,
% 2.19/2.33 (op(e1, e3) = e0),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1830, 18556, 18551, 18550])).
% 2.19/2.33 tff(18558,plain,
% 2.19/2.33 (e0 = op(e1, e3)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18557])).
% 2.19/2.33 tff(18559,plain,
% 2.19/2.33 ((op(e1, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[920])).
% 2.19/2.33 tff(18560,plain,
% 2.19/2.33 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18559, 5377])).
% 2.19/2.33 tff(18561,plain,
% 2.19/2.33 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18560])).
% 2.19/2.33 tff(18562,plain,
% 2.19/2.33 (~(op(e3, e0) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[410, 18561])).
% 2.19/2.33 tff(18563,plain,
% 2.19/2.33 (op(e3, e2) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[15971, 82, 18562])).
% 2.19/2.33 tff(18564,plain,
% 2.19/2.33 ((op(e3, e2) = e0) <=> (e2 = op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18563, 18558])).
% 2.19/2.33 tff(18565,plain,
% 2.19/2.33 ((op(e3, e2) = e0) <=> (op(e1, e3) = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18564, 66])).
% 2.19/2.33 tff(18566,plain,
% 2.19/2.33 ((op(e1, e3) = e2) <=> (op(e3, e2) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18565])).
% 2.19/2.33 tff(18567,plain,
% 2.19/2.33 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e2) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18566])).
% 2.19/2.33 tff(18568,plain,
% 2.19/2.33 (~(op(e3, e2) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[72, 18567])).
% 2.19/2.33 tff(18569,plain,
% 2.19/2.33 (op(e0, e2) = e0),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[973, 18568, 17, 18550])).
% 2.19/2.33 tff(18570,plain,
% 2.19/2.33 (op(e0, e2) = op(e1, e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18569, 18558])).
% 2.19/2.33 tff(18571,plain,
% 2.19/2.33 ((op(e0, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18570])).
% 2.19/2.33 tff(18572,plain,
% 2.19/2.33 ((op(e1, e3) = e1) <=> (op(e0, e2) = e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18571])).
% 2.19/2.33 tff(18573,plain,
% 2.19/2.33 ((~(op(e1, e3) = e1)) <=> (~(op(e0, e2) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18572])).
% 2.19/2.33 tff(18574,plain,
% 2.19/2.33 (~(op(e0, e2) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[87, 18573])).
% 2.19/2.33 tff(18575,plain,
% 2.19/2.33 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[2899])).
% 2.19/2.33 tff(18576,plain,
% 2.19/2.33 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18575])).
% 2.19/2.33 tff(18577,plain,
% 2.19/2.33 (~(op(e0, e2) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[6205, 18576])).
% 2.19/2.33 tff(18578,plain,
% 2.19/2.33 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18569])).
% 2.19/2.33 tff(18579,plain,
% 2.19/2.33 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18578])).
% 2.19/2.33 tff(18580,plain,
% 2.19/2.33 (~(op(e0, e1) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[2102, 18579])).
% 2.19/2.33 tff(18581,plain,
% 2.19/2.33 (~(op(op(e1, e2), e1) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[82, 10257])).
% 2.19/2.33 tff(18582,plain,
% 2.19/2.33 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[5959, 18581])).
% 2.19/2.33 tff(18583,plain,
% 2.19/2.33 (op(op(e0, e2), e2) = op(e0, e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18569])).
% 2.19/2.33 tff(18584,plain,
% 2.19/2.33 (op(op(e0, e2), e2) = e0),
% 2.19/2.33 inference(transitivity,[status(thm)],[18583, 18569])).
% 2.19/2.33 tff(18585,plain,
% 2.19/2.33 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1956, 18584])).
% 2.19/2.33 tff(18586,plain,
% 2.19/2.33 ((op(e0, e3) = e0) <=> (op(e0, e3) = op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[2909])).
% 2.19/2.33 tff(18587,plain,
% 2.19/2.33 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18586])).
% 2.19/2.33 tff(18588,plain,
% 2.19/2.33 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18587])).
% 2.19/2.33 tff(18589,plain,
% 2.19/2.33 (~(op(e0, e3) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[64, 18588])).
% 2.19/2.33 tff(18590,plain,
% 2.19/2.33 (op(e0, e1) = e2),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[3652, 79, 3781, 8958])).
% 2.19/2.33 tff(18591,plain,
% 2.19/2.33 ((op(e0, e1) = e3) <=> (e2 = e3)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18590])).
% 2.19/2.33 tff(18592,plain,
% 2.19/2.33 ((e2 = e3) <=> (op(e0, e1) = e3)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18591])).
% 2.19/2.33 tff(18593,plain,
% 2.19/2.33 ((~(e2 = e3)) <=> (~(op(e0, e1) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18592])).
% 2.19/2.33 tff(18594,plain,
% 2.19/2.33 (~(op(e0, e1) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[1321, 18593])).
% 2.19/2.33 tff(18595,plain,
% 2.19/2.33 (~(op(e0, e3) = e1)),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[5000, 18594, 4412, 3849])).
% 2.19/2.33 tff(18596,plain,
% 2.19/2.33 (op(e0, e3) = e3),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[687, 18595, 79, 18589])).
% 2.19/2.33 tff(18597,plain,
% 2.19/2.33 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[8955])).
% 2.19/2.33 tff(18598,plain,
% 2.19/2.33 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18597])).
% 2.19/2.33 tff(18599,plain,
% 2.19/2.33 (~(op(e2, e2) = e2)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[1546, 18598])).
% 2.19/2.33 tff(18600,plain,
% 2.19/2.33 (~(op(e2, e1) = e0)),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[7007, 16119, 2431, 18599])).
% 2.19/2.33 tff(18601,plain,
% 2.19/2.33 (op(e2, e1) = e3),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2367, 16124, 18600, 4530])).
% 2.19/2.33 tff(18602,plain,
% 2.19/2.33 ((op(e2, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18601])).
% 2.19/2.33 tff(18603,plain,
% 2.19/2.33 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18602, 396])).
% 2.19/2.33 tff(18604,plain,
% 2.19/2.33 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18603])).
% 2.19/2.33 tff(18605,plain,
% 2.19/2.33 (~(op(e3, e1) = e3)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[402, 18604])).
% 2.19/2.33 tff(18606,plain,
% 2.19/2.33 (op(e3, e0) = op(e0, e3)),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[6055, 18605, 18596, 1890])).
% 2.19/2.33 tff(18607,plain,
% 2.19/2.33 (op(e3, op(e1, e3)) = op(e3, e0)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[1219])).
% 2.19/2.33 tff(18608,plain,
% 2.19/2.33 (op(e3, e0) = e3),
% 2.19/2.33 inference(transitivity,[status(thm)],[18606, 18596])).
% 2.19/2.33 tff(18609,plain,
% 2.19/2.33 (op(op(e3, e0), e0) = op(e3, op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18608, 2909])).
% 2.19/2.33 tff(18610,plain,
% 2.19/2.33 (op(op(e3, e0), e0) = e3),
% 2.19/2.33 inference(transitivity,[status(thm)],[18609, 18607, 18606, 18596])).
% 2.19/2.33 tff(18611,plain,
% 2.19/2.33 (op(op(e2, e1), e2) = op(e3, e2)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18601])).
% 2.19/2.33 tff(18612,plain,
% 2.19/2.33 (op(op(e2, e1), e2) = e2),
% 2.19/2.33 inference(transitivity,[status(thm)],[18611, 8955])).
% 2.19/2.33 tff(18613,plain,
% 2.19/2.33 ((op(op(e2, e1), e2) = e1) <=> (e2 = e1)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18612])).
% 2.19/2.33 tff(18614,plain,
% 2.19/2.33 ((op(op(e2, e1), e2) = e1) <=> (e1 = e2)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18613, 69])).
% 2.19/2.33 tff(18615,plain,
% 2.19/2.33 ((e1 = e2) <=> (op(op(e2, e1), e2) = e1)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18614])).
% 2.19/2.33 tff(18616,plain,
% 2.19/2.33 ((~(e1 = e2)) <=> (~(op(op(e2, e1), e2) = e1))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18615])).
% 2.19/2.33 tff(18617,plain,
% 2.19/2.33 (~(op(op(e2, e1), e2) = e1)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[708, 18616])).
% 2.19/2.33 tff(18618,plain,
% 2.19/2.33 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[5808, 18617])).
% 2.19/2.33 tff(18619,plain,
% 2.19/2.33 ((op(op(e1, e0), e1) = e0) <=> (op(e2, e1) = e0)),
% 2.19/2.33 inference(monotonicity,[status(thm)],[1351])).
% 2.19/2.33 tff(18620,plain,
% 2.19/2.33 ((op(e2, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 2.19/2.33 inference(symmetry,[status(thm)],[18619])).
% 2.19/2.33 tff(18621,plain,
% 2.19/2.33 ((~(op(e2, e1) = e0)) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18620])).
% 2.19/2.33 tff(18622,plain,
% 2.19/2.33 (~(op(op(e1, e0), e1) = e0)),
% 2.19/2.33 inference(modus_ponens,[status(thm)],[18600, 18621])).
% 2.19/2.33 tff(18623,plain,
% 2.19/2.33 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[1302, 18622])).
% 2.19/2.33 tff(18624,plain,
% 2.19/2.33 (op(e2, e0) = e0),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2311, 18600, 17, 4891])).
% 2.19/2.33 tff(18625,plain,
% 2.19/2.33 (op(e3, e1) = e0),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[292, 18600, 84, 3849])).
% 2.19/2.33 tff(18626,plain,
% 2.19/2.33 (op(e2, op(e2, e0)) = e0),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[4926, 18625, 1219, 18624])).
% 2.19/2.33 tff(18627,plain,
% 2.19/2.33 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.19/2.33 inference(unit_resolution,[status(thm)],[2653, 18626])).
% 2.19/2.33 tff(18628,plain,
% 2.19/2.33 (op(op(e0, e1), e0) = op(e2, op(e1, e3))),
% 2.19/2.33 inference(monotonicity,[status(thm)],[18590, 2909])).
% 2.19/2.33 tff(18629,plain,
% 2.19/2.33 (op(op(e0, e1), e0) = op(e2, e0)),
% 2.19/2.33 inference(transitivity,[status(thm)],[18628, 4893])).
% 2.19/2.33 tff(18630,plain,
% 2.19/2.34 ((op(op(e0, e1), e0) = e1) <=> (op(e2, e0) = e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18629])).
% 2.19/2.34 tff(18631,plain,
% 2.19/2.34 ((op(e2, e0) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18630])).
% 2.19/2.34 tff(18632,plain,
% 2.19/2.34 ((~(op(e2, e0) = e1)) <=> (~(op(op(e0, e1), e0) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18631])).
% 2.19/2.34 tff(18633,plain,
% 2.19/2.34 (op(e2, e2) = e1),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[524, 18599, 17, 2431])).
% 2.19/2.34 tff(18634,plain,
% 2.19/2.34 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18633])).
% 2.19/2.34 tff(18635,plain,
% 2.19/2.34 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18634])).
% 2.19/2.34 tff(18636,plain,
% 2.19/2.34 (~(op(e2, e0) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[2228, 18635])).
% 2.19/2.34 tff(18637,plain,
% 2.19/2.34 (~(op(op(e0, e1), e0) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[18636, 18632])).
% 2.19/2.34 tff(18638,plain,
% 2.19/2.34 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1461, 18637])).
% 2.19/2.34 tff(18639,plain,
% 2.19/2.34 ((op(e3, e3) = e0) <=> (op(e3, e3) = op(e1, e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[2909])).
% 2.19/2.34 tff(18640,plain,
% 2.19/2.34 ((op(e3, e3) = e0) <=> (op(e1, e3) = op(e3, e3))),
% 2.19/2.34 inference(transitivity,[status(thm)],[18639, 1659])).
% 2.19/2.34 tff(18641,plain,
% 2.19/2.34 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18640])).
% 2.19/2.34 tff(18642,plain,
% 2.19/2.34 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18641])).
% 2.19/2.34 tff(18643,plain,
% 2.19/2.34 (~(op(e3, e3) = e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[571, 18642])).
% 2.19/2.34 tff(18644,plain,
% 2.19/2.34 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[10603, 79, 18643, 72])).
% 2.19/2.34 tff(18645,plain,
% 2.19/2.34 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[5468, 18595, 79])).
% 2.19/2.34 tff(18646,plain,
% 2.19/2.34 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[8955])).
% 2.19/2.34 tff(18647,plain,
% 2.19/2.34 (op(e3, op(e3, e2)) = e2),
% 2.19/2.34 inference(transitivity,[status(thm)],[18646, 8955])).
% 2.19/2.34 tff(18648,plain,
% 2.19/2.34 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1904, 18647])).
% 2.19/2.34 tff(18649,plain,
% 2.19/2.34 (op(e3, e1) = op(e1, e3)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18625, 2909])).
% 2.19/2.34 tff(18650,plain,
% 2.19/2.34 (op(op(e3, e1), e3) = op(op(e1, e3), e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18649])).
% 2.19/2.34 tff(18651,plain,
% 2.19/2.34 (op(op(e3, e1), e3) = e3),
% 2.19/2.34 inference(transitivity,[status(thm)],[18650, 1220, 18596])).
% 2.19/2.34 tff(18652,plain,
% 2.19/2.34 ((op(op(e3, e1), e3) = e1) <=> (e3 = e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18651])).
% 2.19/2.34 tff(18653,plain,
% 2.19/2.34 ((op(op(e3, e1), e3) = e1) <=> (e1 = e3)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18652, 128])).
% 2.19/2.34 tff(18654,plain,
% 2.19/2.34 ((e1 = e3) <=> (op(op(e3, e1), e3) = e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18653])).
% 2.19/2.34 tff(18655,plain,
% 2.19/2.34 ((~(e1 = e3)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18654])).
% 2.19/2.34 tff(18656,plain,
% 2.19/2.34 (~(op(op(e3, e1), e3) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[303, 18655])).
% 2.19/2.34 tff(18657,plain,
% 2.19/2.34 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1050, 18656])).
% 2.19/2.34 tff(18658,plain,
% 2.19/2.34 (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1459, 18657, 18648, 18645, 16414, 18644, 18638, 1363, 18627, 1358, 18623, 18618])).
% 2.19/2.34 tff(18659,plain,
% 2.19/2.34 (~(op(op(e3, e0), e0) = e3)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[4026, 18658])).
% 2.19/2.34 tff(18660,plain,
% 2.19/2.34 ($false),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[18659, 18610])).
% 2.19/2.34 tff(18661,plain,((op(e0, e3) = e2) | (~(op(e1, e3) = e0)) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (op(e3, e2) = e3) | (~(op(e3, e2) = e2)) | (~(op(e1, e0) = e2)) | (op(e1, e1) = e0) | (op(e0, e1) = e0) | (op(e2, e2) = e0) | (op(e0, e2) = e3) | (op(e2, e1) = e1) | (op(e2, e2) = e3) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.34 tff(18662,plain,
% 2.19/2.34 (op(e0, e3) = e2),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[18661, 18585, 18557, 18582, 10204, 18563, 920, 18551, 18580, 17, 18577, 4530, 9271, 72])).
% 2.19/2.34 tff(18663,plain,
% 2.19/2.34 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18662])).
% 2.19/2.34 tff(18664,plain,
% 2.19/2.34 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18663, 69])).
% 2.19/2.34 tff(18665,plain,
% 2.19/2.34 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18664])).
% 2.19/2.34 tff(18666,plain,
% 2.19/2.34 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18665])).
% 2.19/2.34 tff(18667,plain,
% 2.19/2.34 (~(op(e0, e3) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[708, 18666])).
% 2.19/2.34 tff(18668,plain,
% 2.19/2.34 (op(e0, e0) = e1),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[384, 18667, 3528, 18574])).
% 2.19/2.34 tff(18669,plain,
% 2.19/2.34 (e1 = op(e0, e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[18668, 74])).
% 2.19/2.34 tff(18670,plain,
% 2.19/2.34 (op(e0, op(e0, e0)) = op(op(e1, e3), e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18558, 18668])).
% 2.19/2.34 tff(18671,plain,
% 2.19/2.34 (op(op(e1, e3), e1) = op(e0, op(e0, e0))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18670])).
% 2.19/2.34 tff(18672,plain,
% 2.19/2.34 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18557])).
% 2.19/2.34 tff(18673,plain,
% 2.19/2.34 (op(e0, e1) = op(op(e1, e3), e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18672])).
% 2.19/2.34 tff(18674,plain,
% 2.19/2.34 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18662])).
% 2.19/2.34 tff(18675,plain,
% 2.19/2.34 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18674])).
% 2.19/2.34 tff(18676,plain,
% 2.19/2.34 (~(op(e0, e1) = e2)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[818, 18675])).
% 2.19/2.34 tff(18677,plain,
% 2.19/2.34 (op(e0, e1) = e3),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[829, 18676, 3528, 18580])).
% 2.19/2.34 tff(18678,plain,
% 2.19/2.34 (e3 = op(e0, e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18677])).
% 2.19/2.34 tff(18679,plain,
% 2.19/2.34 (e3 = op(e0, op(e0, e0))),
% 2.19/2.34 inference(transitivity,[status(thm)],[18678, 18673, 18671])).
% 2.19/2.34 tff(18680,plain,
% 2.19/2.34 (op(e0, op(e0, e0)) = e3),
% 2.19/2.34 inference(transitivity,[status(thm)],[18670, 18672, 18677])).
% 2.19/2.34 tff(18681,plain,
% 2.19/2.34 (op(e0, op(e0, op(e0, e0))) = op(op(e1, e3), e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18558, 18680])).
% 2.19/2.34 tff(18682,plain,
% 2.19/2.34 (op(op(e1, e3), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18681])).
% 2.19/2.34 tff(18683,plain,
% 2.19/2.34 (op(op(e1, e3), e3) = op(e0, e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18557])).
% 2.19/2.34 tff(18684,plain,
% 2.19/2.34 (op(e0, e3) = op(op(e1, e3), e3)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18683])).
% 2.19/2.34 tff(18685,plain,
% 2.19/2.34 (e2 = op(e0, e3)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18662])).
% 2.19/2.34 tff(18686,plain,
% 2.19/2.34 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.19/2.34 inference(transitivity,[status(thm)],[18685, 18684, 18682])).
% 2.19/2.34 tff(18687,plain,
% 2.19/2.34 ($false),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[16194, 18686, 18679, 18669])).
% 2.19/2.34 tff(18688,plain,((op(e3, e1) = e2) | (op(e0, e1) = e1) | (~(op(e1, e0) = e2)) | (op(e2, e2) = e0) | (op(e2, e1) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e1) | (~(op(e1, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.19/2.34 tff(18689,plain,
% 2.19/2.34 (op(e3, e1) = e2),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[18688, 18545, 18522, 17, 18538, 72, 18542, 18513])).
% 2.19/2.34 tff(18690,plain,
% 2.19/2.34 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18534])).
% 2.19/2.34 tff(18691,plain,
% 2.19/2.34 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18690, 7793])).
% 2.19/2.34 tff(18692,plain,
% 2.19/2.34 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18691])).
% 2.19/2.34 tff(18693,plain,
% 2.19/2.34 (~(op(e3, e1) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[945, 18692])).
% 2.19/2.34 tff(18694,plain,
% 2.19/2.34 ((op(e1, e2) = e0) <=> (e3 = e0)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18513])).
% 2.19/2.34 tff(18695,plain,
% 2.19/2.34 ((op(e1, e2) = e0) <=> (e0 = e3)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18694, 159])).
% 2.19/2.34 tff(18696,plain,
% 2.19/2.34 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18695])).
% 2.19/2.34 tff(18697,plain,
% 2.19/2.34 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18696])).
% 2.19/2.34 tff(18698,plain,
% 2.19/2.34 (~(op(e1, e2) = e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[181, 18697])).
% 2.19/2.34 tff(18699,plain,
% 2.19/2.34 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18522])).
% 2.19/2.34 tff(18700,plain,
% 2.19/2.34 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18699, 1])).
% 2.19/2.34 tff(18701,plain,
% 2.19/2.34 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18700])).
% 2.19/2.34 tff(18702,plain,
% 2.19/2.34 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18701])).
% 2.19/2.34 tff(18703,plain,
% 2.19/2.34 (~(op(e1, e0) = e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[14, 18702])).
% 2.19/2.34 tff(18704,plain,
% 2.19/2.34 (op(e1, e3) = e0),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1830, 18703, 18530, 18698])).
% 2.19/2.34 tff(18705,plain,
% 2.19/2.34 ((op(e1, e0) = op(e0, e1)) <=> (e2 = op(e0, e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18522])).
% 2.19/2.34 tff(18706,plain,
% 2.19/2.34 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18705, 4838])).
% 2.19/2.34 tff(18707,plain,
% 2.19/2.34 ((op(e0, e1) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18706])).
% 2.19/2.34 tff(18708,plain,
% 2.19/2.34 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18689])).
% 2.19/2.34 tff(18709,plain,
% 2.19/2.34 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = op(e1, e0))),
% 2.19/2.34 inference(transitivity,[status(thm)],[18708, 18707, 596])).
% 2.19/2.34 tff(18710,plain,
% 2.19/2.34 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18709])).
% 2.19/2.34 tff(18711,plain,
% 2.19/2.34 (~(op(e0, e1) = op(e1, e0))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[3046, 18710])).
% 2.19/2.34 tff(18712,plain,
% 2.19/2.34 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[609, 18711])).
% 2.19/2.34 tff(18713,plain,
% 2.19/2.34 (op(e1, op(e1, e1)) = op(e1, e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18534])).
% 2.19/2.34 tff(18714,plain,
% 2.19/2.34 (op(e1, op(e1, e1)) = e1),
% 2.19/2.34 inference(transitivity,[status(thm)],[18713, 18534])).
% 2.19/2.34 tff(18715,plain,
% 2.19/2.34 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[5678, 18714])).
% 2.19/2.34 tff(18716,plain,
% 2.19/2.34 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e0) = op(e0, e1))),
% 2.19/2.34 inference(transitivity,[status(thm)],[18708, 18707])).
% 2.19/2.34 tff(18717,plain,
% 2.19/2.34 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18716])).
% 2.19/2.34 tff(18718,plain,
% 2.19/2.34 (~(op(e1, e0) = op(e0, e1))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[3046, 18717])).
% 2.19/2.34 tff(18719,plain,
% 2.19/2.34 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[613, 18718])).
% 2.19/2.34 tff(18720,plain,
% 2.19/2.34 (op(e0, e2) = e2),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[3652, 79, 12721, 17329])).
% 2.19/2.34 tff(18721,plain,
% 2.19/2.34 ((op(e0, e2) = e0) <=> (e2 = op(e1, e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18720, 2909])).
% 2.19/2.34 tff(18722,plain,
% 2.19/2.34 ((op(e0, e2) = e0) <=> (op(e1, e3) = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18721, 66])).
% 2.19/2.34 tff(18723,plain,
% 2.19/2.34 ((op(e1, e3) = e2) <=> (op(e0, e2) = e0)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18722])).
% 2.19/2.34 tff(18724,plain,
% 2.19/2.34 ((~(op(e1, e3) = e2)) <=> (~(op(e0, e2) = e0))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18723])).
% 2.19/2.34 tff(18725,plain,
% 2.19/2.34 (~(op(e0, e2) = e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[72, 18724])).
% 2.19/2.34 tff(18726,plain,
% 2.19/2.34 (op(e3, e2) = e0),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[973, 18725, 17, 18550])).
% 2.19/2.34 tff(18727,plain,
% 2.19/2.34 (e0 = op(e3, e2)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18726])).
% 2.19/2.34 tff(18728,plain,
% 2.19/2.34 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[2909])).
% 2.19/2.34 tff(18729,plain,
% 2.19/2.34 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e0)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18728])).
% 2.19/2.34 tff(18730,plain,
% 2.19/2.34 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[6684])).
% 2.19/2.34 tff(18731,plain,
% 2.19/2.34 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18730, 66])).
% 2.19/2.34 tff(18732,plain,
% 2.19/2.34 ((op(e1, e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18731])).
% 2.19/2.34 tff(18733,plain,
% 2.19/2.34 ((op(e1, e3) = e2) <=> (op(e3, e1) = e0)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18732, 18729])).
% 2.19/2.34 tff(18734,plain,
% 2.19/2.34 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = e0))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18733])).
% 2.19/2.34 tff(18735,plain,
% 2.19/2.34 (~(op(e3, e1) = e0)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[72, 18734])).
% 2.19/2.34 tff(18736,plain,
% 2.19/2.34 (~(op(e2, e1) = e0)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[7007, 16119, 9271, 17191])).
% 2.19/2.34 tff(18737,plain,
% 2.19/2.34 (op(e0, e1) = e0),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[292, 18736, 18551, 18735])).
% 2.19/2.34 tff(18738,plain,
% 2.19/2.34 (op(e0, e1) = op(e3, e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18737, 18727])).
% 2.19/2.34 tff(18739,plain,
% 2.19/2.34 ((op(e0, e1) = e3) <=> (op(e3, e2) = e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18738])).
% 2.19/2.34 tff(18740,plain,
% 2.19/2.34 ((op(e3, e2) = e3) <=> (op(e0, e1) = e3)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18739])).
% 2.19/2.34 tff(18741,plain,
% 2.19/2.34 ((~(op(e3, e2) = e3)) <=> (~(op(e0, e1) = e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18740])).
% 2.19/2.34 tff(18742,plain,
% 2.19/2.34 (~(op(e0, e1) = e3)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[10204, 18741])).
% 2.19/2.34 tff(18743,plain,
% 2.19/2.34 (op(e2, e2) = e1),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[524, 17191, 17, 9271])).
% 2.19/2.34 tff(18744,plain,
% 2.19/2.34 (e1 = op(e2, e2)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18743])).
% 2.19/2.34 tff(18745,plain,
% 2.19/2.34 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[16115])).
% 2.19/2.34 tff(18746,plain,
% 2.19/2.34 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18745, 69])).
% 2.19/2.34 tff(18747,plain,
% 2.19/2.34 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18746])).
% 2.19/2.34 tff(18748,plain,
% 2.19/2.34 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18747])).
% 2.19/2.34 tff(18749,plain,
% 2.19/2.34 (~(op(e2, e3) = e1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[708, 18748])).
% 2.19/2.34 tff(18750,plain,
% 2.19/2.34 (e1 = op(e2, e2)),
% 2.19/2.34 inference(symmetry,[status(thm)],[307])).
% 2.19/2.34 tff(18751,plain,
% 2.19/2.34 (op(e3, e3) = op(e2, e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[305, 18750])).
% 2.19/2.34 tff(18752,plain,
% 2.19/2.34 (op(e3, op(e3, e3)) = op(e3, op(e2, e2))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18751])).
% 2.19/2.34 tff(18753,plain,
% 2.19/2.34 (op(e3, op(e2, e2)) = op(e3, op(e3, e3))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18752])).
% 2.19/2.34 tff(18754,plain,
% 2.19/2.34 (op(e3, op(e2, e2)) = op(e3, e1)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[307])).
% 2.19/2.34 tff(18755,plain,
% 2.19/2.34 (op(e3, e1) = op(e3, op(e2, e2))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18754])).
% 2.19/2.34 tff(18756,plain,
% 2.19/2.34 (e2 = op(e3, op(e3, e3))),
% 2.19/2.34 inference(transitivity,[status(thm)],[8644, 18755, 18753])).
% 2.19/2.34 tff(18757,plain,
% 2.19/2.34 (op(e3, op(e3, e3)) = e2),
% 2.19/2.34 inference(transitivity,[status(thm)],[18752, 18754, 6684])).
% 2.19/2.34 tff(18758,plain,
% 2.19/2.34 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18757])).
% 2.19/2.34 tff(18759,plain,
% 2.19/2.34 (op(e3, e2) = op(e3, op(e3, op(e3, e3)))),
% 2.19/2.34 inference(symmetry,[status(thm)],[18758])).
% 2.19/2.34 tff(18760,plain,
% 2.19/2.34 (e0 = op(e3, op(e3, op(e3, e3)))),
% 2.19/2.34 inference(transitivity,[status(thm)],[6784, 18759])).
% 2.19/2.34 tff(18761,plain,
% 2.19/2.34 ($false),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[2034, 18760, 18756, 6771])).
% 2.19/2.34 tff(18762,plain,((~(op(e3, e3) = e1)) | (~(op(e3, e2) = e0)) | (~(op(e3, e1) = e2)) | (~(op(e2, e2) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.19/2.34 tff(18763,plain,
% 2.19/2.34 (~(op(e3, e3) = e1)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[18762, 18726, 6684, 18743])).
% 2.19/2.34 tff(18764,plain,
% 2.19/2.34 (op(e0, e3) = e1),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[151, 18763, 18749, 87])).
% 2.19/2.34 tff(18765,plain,
% 2.19/2.34 (op(e0, e3) = op(e2, e2)),
% 2.19/2.34 inference(transitivity,[status(thm)],[18764, 18744])).
% 2.19/2.34 tff(18766,plain,
% 2.19/2.34 ((op(e0, e3) = e3) <=> (op(e2, e2) = e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18765])).
% 2.19/2.34 tff(18767,plain,
% 2.19/2.34 ((op(e2, e2) = e3) <=> (op(e0, e3) = e3)),
% 2.19/2.34 inference(symmetry,[status(thm)],[18766])).
% 2.19/2.34 tff(18768,plain,
% 2.19/2.34 ((~(op(e2, e2) = e3)) <=> (~(op(e0, e3) = e3))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18767])).
% 2.19/2.34 tff(18769,plain,
% 2.19/2.34 (~(op(e0, e3) = e3)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[9271, 18768])).
% 2.19/2.34 tff(18770,plain,
% 2.19/2.34 (op(e0, e0) = e3),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[1495, 18769, 18742, 18577])).
% 2.19/2.34 tff(18771,plain,
% 2.19/2.34 (op(e2, op(e0, e0)) = op(e2, e3)),
% 2.19/2.34 inference(monotonicity,[status(thm)],[18770])).
% 2.19/2.34 tff(18772,plain,
% 2.19/2.35 (op(e2, op(e0, e0)) = e2),
% 2.19/2.35 inference(transitivity,[status(thm)],[18771, 16115])).
% 2.19/2.35 tff(18773,plain,
% 2.19/2.35 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e2)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18720])).
% 2.19/2.35 tff(18774,plain,
% 2.19/2.35 ((op(e2, e0) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.19/2.35 inference(symmetry,[status(thm)],[18773])).
% 2.19/2.35 tff(18775,plain,
% 2.19/2.35 ((op(e2, e0) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.19/2.35 inference(transitivity,[status(thm)],[18774, 6337])).
% 2.19/2.35 tff(18776,plain,
% 2.19/2.35 ((~(op(e2, e0) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18775])).
% 2.19/2.35 tff(18777,plain,
% 2.19/2.35 (~(op(e0, e2) = op(e2, e0))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[982, 18776])).
% 2.19/2.35 tff(18778,plain,
% 2.19/2.35 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[6347, 18777])).
% 2.19/2.35 tff(18779,plain,
% 2.19/2.35 ((op(e2, op(e1, e2)) = e2) <=> (op(e2, e3) = e2)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[9377])).
% 2.19/2.35 tff(18780,plain,
% 2.19/2.35 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e2)) = e2)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18779])).
% 2.19/2.35 tff(18781,plain,
% 2.19/2.35 (op(e2, op(e1, e2)) = e2),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[16115, 18780])).
% 2.19/2.35 tff(18782,plain,
% 2.19/2.35 (((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)) | (~(op(e2, op(e1, e2)) = e2))),
% 2.19/2.35 inference(tautology,[status(thm)],[])).
% 2.19/2.35 tff(18783,plain,
% 2.19/2.35 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[18782, 18781])).
% 2.19/2.35 tff(18784,plain,
% 2.19/2.35 (op(e3, e3) = e3),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[15018, 18763, 18643])).
% 2.19/2.35 tff(18785,plain,
% 2.19/2.35 (op(e2, op(e3, e3)) = op(e2, e3)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18784])).
% 2.19/2.35 tff(18786,plain,
% 2.19/2.35 (op(e2, op(e3, e3)) = e2),
% 2.19/2.35 inference(transitivity,[status(thm)],[18785, 16115])).
% 2.19/2.35 tff(18787,plain,
% 2.19/2.35 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[14770, 18786])).
% 2.19/2.35 tff(18788,plain,
% 2.19/2.35 ((~(op(e3, e2) = e2)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[17206])).
% 2.19/2.35 tff(18789,plain,
% 2.19/2.35 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[6684])).
% 2.19/2.35 tff(18790,plain,
% 2.19/2.35 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.19/2.35 inference(transitivity,[status(thm)],[18789, 2234])).
% 2.19/2.35 tff(18791,plain,
% 2.19/2.35 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18790])).
% 2.19/2.35 tff(18792,plain,
% 2.19/2.35 (~(op(e3, e2) = e2)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[3429, 18791])).
% 2.19/2.35 tff(18793,plain,
% 2.19/2.35 (~(op(e3, e2) = op(e2, e3))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[18792, 18788])).
% 2.19/2.35 tff(18794,plain,
% 2.19/2.35 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[500, 18793])).
% 2.19/2.35 tff(18795,plain,
% 2.19/2.35 (op(e2, e1) = e3),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[2367, 18736, 16808, 4530])).
% 2.19/2.35 tff(18796,plain,
% 2.19/2.35 (op(e2, op(e2, e1)) = op(e2, e3)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18795])).
% 2.19/2.35 tff(18797,plain,
% 2.19/2.35 (op(e2, op(e2, e1)) = e2),
% 2.19/2.35 inference(transitivity,[status(thm)],[18796, 16115])).
% 2.19/2.35 tff(18798,plain,
% 2.19/2.35 (((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)) | (~(op(e2, op(e2, e1)) = e2))),
% 2.19/2.35 inference(tautology,[status(thm)],[])).
% 2.19/2.35 tff(18799,plain,
% 2.19/2.35 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[18798, 18797])).
% 2.19/2.35 tff(18800,plain,
% 2.19/2.35 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18732])).
% 2.19/2.35 tff(18801,plain,
% 2.19/2.35 (~(op(e3, e1) = op(e1, e3))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[72, 18800])).
% 2.19/2.35 tff(18802,plain,
% 2.19/2.35 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[6362, 18801])).
% 2.19/2.35 tff(18803,plain,
% 2.19/2.35 ((~(op(e2, e0) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18774])).
% 2.19/2.35 tff(18804,plain,
% 2.19/2.35 (~(op(e2, e0) = op(e0, e2))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[982, 18803])).
% 2.19/2.35 tff(18805,plain,
% 2.19/2.35 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[6358, 18804])).
% 2.19/2.35 tff(18806,plain,
% 2.19/2.35 (op(e0, op(e2, e2)) = op(op(e1, e3), e1)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[2909, 18743])).
% 2.19/2.35 tff(18807,plain,
% 2.19/2.35 (op(e0, op(e2, e2)) = e0),
% 2.19/2.35 inference(transitivity,[status(thm)],[18806, 18354, 18737])).
% 2.19/2.35 tff(18808,plain,
% 2.19/2.35 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[5619, 18807])).
% 2.19/2.35 tff(18809,plain,
% 2.19/2.35 ((op(e3, e2) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.19/2.35 inference(transitivity,[status(thm)],[17206, 395])).
% 2.19/2.35 tff(18810,plain,
% 2.19/2.35 ((~(op(e3, e2) = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18809])).
% 2.19/2.35 tff(18811,plain,
% 2.19/2.35 (~(op(e2, e3) = op(e3, e2))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[18792, 18810])).
% 2.19/2.35 tff(18812,plain,
% 2.19/2.35 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[430, 18811])).
% 2.19/2.35 tff(18813,plain,
% 2.19/2.35 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.19/2.35 inference(transitivity,[status(thm)],[18732, 6290])).
% 2.19/2.35 tff(18814,plain,
% 2.19/2.35 ((~(op(e1, e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18813])).
% 2.19/2.35 tff(18815,plain,
% 2.19/2.35 (~(op(e1, e3) = op(e3, e1))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[72, 18814])).
% 2.19/2.35 tff(18816,plain,
% 2.19/2.35 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[6307, 18815])).
% 2.19/2.35 tff(18817,plain,
% 2.19/2.35 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18744])).
% 2.19/2.35 tff(18818,plain,
% 2.19/2.35 ((op(e3, e2) = e1) <=> (op(e2, e2) = op(e3, e2))),
% 2.19/2.35 inference(transitivity,[status(thm)],[18817, 9346])).
% 2.19/2.35 tff(18819,plain,
% 2.19/2.35 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18818])).
% 2.19/2.35 tff(18820,plain,
% 2.19/2.35 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18819])).
% 2.19/2.35 tff(18821,plain,
% 2.19/2.35 (~(op(e3, e2) = e1)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[1546, 18820])).
% 2.19/2.35 tff(18822,plain,
% 2.19/2.35 (op(e3, e0) = e1),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[939, 18763, 18821, 2826])).
% 2.19/2.35 tff(18823,plain,
% 2.19/2.35 (op(e3, e0) = op(e2, e2)),
% 2.19/2.35 inference(transitivity,[status(thm)],[18822, 18744])).
% 2.19/2.35 tff(18824,plain,
% 2.19/2.35 (op(e0, op(e3, e0)) = op(e0, op(e2, e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18823])).
% 2.19/2.35 tff(18825,plain,
% 2.19/2.35 (op(e0, op(e3, e0)) = e0),
% 2.19/2.35 inference(transitivity,[status(thm)],[18824, 18806, 18354, 18737])).
% 2.19/2.35 tff(18826,plain,
% 2.19/2.35 (((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)) | (~(op(e0, op(e3, e0)) = e0))),
% 2.19/2.35 inference(tautology,[status(thm)],[])).
% 2.19/2.35 tff(18827,plain,
% 2.19/2.35 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[18826, 18825])).
% 2.19/2.35 tff(18828,plain,
% 2.19/2.35 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[5367, 18827, 18816, 18812, 18808, 18805, 5675, 18802, 6689, 18799, 18794, 5681, 18787, 18783, 18778])).
% 2.19/2.35 tff(18829,plain,
% 2.19/2.35 (~(op(e2, op(e0, e0)) = e2)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[593, 18828])).
% 2.19/2.35 tff(18830,plain,
% 2.19/2.35 ($false),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[18829, 18772])).
% 2.19/2.35 tff(18831,plain,((op(e0, e3) = e2) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~(op(e1, e3) = e0)) | (op(e3, e1) = e1) | (op(e1, e3) = e1) | (~(op(e3, e1) = e2)) | (op(e2, e1) = e1) | (op(e2, e2) = e0) | (op(e2, e0) = e2) | (op(e1, e3) = e2) | (~(op(e1, e2) = e3)) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.35 tff(18832,plain,
% 2.19/2.35 (op(e0, e3) = e2),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[18831, 18719, 18715, 18712, 18704, 18693, 18542, 18689, 18538, 17, 18529, 72, 18513, 18525])).
% 2.19/2.35 tff(18833,plain,
% 2.19/2.35 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18832])).
% 2.19/2.35 tff(18834,plain,
% 2.19/2.35 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18833])).
% 2.19/2.35 tff(18835,plain,
% 2.19/2.35 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18834])).
% 2.19/2.35 tff(18836,plain,
% 2.19/2.35 (~(op(e0, e3) = e3)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[1321, 18835])).
% 2.19/2.35 tff(18837,plain,
% 2.19/2.35 (e0 = op(e1, e3)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18704])).
% 2.19/2.35 tff(18838,plain,
% 2.19/2.35 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18708])).
% 2.19/2.35 tff(18839,plain,
% 2.19/2.35 (~(op(e0, e1) = e2)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[3046, 18838])).
% 2.19/2.35 tff(18840,plain,
% 2.19/2.35 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18689])).
% 2.19/2.35 tff(18841,plain,
% 2.19/2.35 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.19/2.35 inference(transitivity,[status(thm)],[18840, 2234])).
% 2.19/2.35 tff(18842,plain,
% 2.19/2.35 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18841])).
% 2.19/2.35 tff(18843,plain,
% 2.19/2.35 (~(op(e3, e2) = e2)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[3429, 18842])).
% 2.19/2.35 tff(18844,plain,
% 2.19/2.35 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18832])).
% 2.19/2.35 tff(18845,plain,
% 2.19/2.35 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 2.19/2.35 inference(transitivity,[status(thm)],[18844, 69])).
% 2.19/2.35 tff(18846,plain,
% 2.19/2.35 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18845])).
% 2.19/2.35 tff(18847,plain,
% 2.19/2.35 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18846])).
% 2.19/2.35 tff(18848,plain,
% 2.19/2.35 (~(op(e0, e3) = e1)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[708, 18847])).
% 2.19/2.35 tff(18849,plain,
% 2.19/2.35 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e1, e3))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18837])).
% 2.19/2.35 tff(18850,plain,
% 2.19/2.35 ((op(e2, e3) = e0) <=> (op(e1, e3) = op(e2, e3))),
% 2.19/2.35 inference(transitivity,[status(thm)],[18849, 1687])).
% 2.19/2.35 tff(18851,plain,
% 2.19/2.35 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 2.19/2.35 inference(symmetry,[status(thm)],[18850])).
% 2.19/2.35 tff(18852,plain,
% 2.19/2.35 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18851])).
% 2.19/2.35 tff(18853,plain,
% 2.19/2.35 (~(op(e2, e3) = e0)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[118, 18852])).
% 2.19/2.35 tff(18854,plain,
% 2.19/2.35 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18832])).
% 2.19/2.35 tff(18855,plain,
% 2.19/2.35 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.19/2.35 inference(transitivity,[status(thm)],[18854, 120])).
% 2.19/2.35 tff(18856,plain,
% 2.19/2.35 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[18855])).
% 2.19/2.35 tff(18857,plain,
% 2.19/2.35 (~(op(e2, e3) = e2)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[964, 18856])).
% 2.25/2.35 tff(18858,plain,
% 2.25/2.35 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18513])).
% 2.25/2.35 tff(18859,plain,
% 2.25/2.35 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.25/2.35 inference(transitivity,[status(thm)],[18858, 3423])).
% 2.25/2.35 tff(18860,plain,
% 2.25/2.35 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18859])).
% 2.25/2.35 tff(18861,plain,
% 2.25/2.35 (~(op(e3, e2) = e3)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[2292, 18860])).
% 2.25/2.35 tff(18862,plain,
% 2.25/2.35 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[5682])).
% 2.25/2.35 tff(18863,plain,
% 2.25/2.35 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.25/2.35 inference(symmetry,[status(thm)],[18862])).
% 2.25/2.35 tff(18864,plain,
% 2.25/2.35 (op(e2, e3) = e3),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[206, 76, 4382, 1063])).
% 2.25/2.35 tff(18865,plain,
% 2.25/2.35 (~(op(e3, e2) = e0)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[6787, 18864, 6684, 5682])).
% 2.25/2.35 tff(18866,plain,
% 2.25/2.35 (op(e3, e2) = e1),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[1898, 18865, 18792, 1890])).
% 2.25/2.35 tff(18867,plain,
% 2.25/2.35 (op(e3, e2) = op(e3, e3)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[18866, 18863])).
% 2.25/2.35 tff(18868,plain,
% 2.25/2.35 ($false),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[1888, 18867])).
% 2.25/2.35 tff(18869,plain,((op(e2, e3) = e1) | (op(e3, e2) = e3) | (~(op(e3, e1) = e2)) | (op(e2, e3) = e2) | (op(e2, e3) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.25/2.35 tff(18870,plain,
% 2.25/2.35 (op(e2, e3) = e1),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[18869, 18861, 18689, 18857, 18853, 18848, 18542])).
% 2.25/2.35 tff(18871,plain,
% 2.25/2.35 (op(e3, op(e1, e2)) = op(e3, e3)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18513])).
% 2.25/2.35 tff(18872,plain,
% 2.25/2.35 ((op(e3, op(e1, e2)) = e3) <=> (op(e3, e3) = e3)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18871])).
% 2.25/2.35 tff(18873,plain,
% 2.25/2.35 ((op(e3, e3) = e3) <=> (op(e3, op(e1, e2)) = e3)),
% 2.25/2.35 inference(symmetry,[status(thm)],[18872])).
% 2.25/2.35 tff(18874,plain,
% 2.25/2.35 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18513])).
% 2.25/2.35 tff(18875,plain,
% 2.25/2.35 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.25/2.35 inference(transitivity,[status(thm)],[18874, 3230])).
% 2.25/2.35 tff(18876,plain,
% 2.25/2.35 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18875])).
% 2.25/2.35 tff(18877,plain,
% 2.25/2.35 (~(op(e1, e3) = e3)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[1850, 18876])).
% 2.25/2.35 tff(18878,plain,
% 2.25/2.35 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18870])).
% 2.25/2.35 tff(18879,plain,
% 2.25/2.35 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 2.25/2.35 inference(symmetry,[status(thm)],[18878])).
% 2.25/2.35 tff(18880,plain,
% 2.25/2.35 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18879])).
% 2.25/2.35 tff(18881,plain,
% 2.25/2.35 (~(op(e2, e3) = e3)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[303, 18880])).
% 2.25/2.35 tff(18882,plain,
% 2.25/2.35 (op(e3, e3) = e3),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[480, 18881, 18877, 18836])).
% 2.25/2.35 tff(18883,plain,
% 2.25/2.35 (op(e3, op(e1, e2)) = e3),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[18882, 18873])).
% 2.25/2.35 tff(18884,plain,
% 2.25/2.35 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[11442, 18883])).
% 2.25/2.35 tff(18885,plain,
% 2.25/2.35 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18882])).
% 2.25/2.35 tff(18886,plain,
% 2.25/2.35 (op(e3, op(e3, e3)) = e3),
% 2.25/2.35 inference(transitivity,[status(thm)],[18885, 18882])).
% 2.25/2.35 tff(18887,plain,
% 2.25/2.35 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[6277, 18886])).
% 2.25/2.35 tff(18888,plain,
% 2.25/2.35 ((op(e3, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18689])).
% 2.25/2.35 tff(18889,plain,
% 2.25/2.35 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.25/2.35 inference(transitivity,[status(thm)],[18888, 66])).
% 2.25/2.35 tff(18890,plain,
% 2.25/2.35 ((op(e1, e3) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.25/2.35 inference(symmetry,[status(thm)],[18889])).
% 2.25/2.35 tff(18891,plain,
% 2.25/2.35 ((~(op(e1, e3) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18890])).
% 2.25/2.35 tff(18892,plain,
% 2.25/2.35 (~(op(e3, e1) = op(e1, e3))),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[72, 18891])).
% 2.25/2.35 tff(18893,plain,
% 2.25/2.35 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[6362, 18892])).
% 2.25/2.35 tff(18894,plain,
% 2.25/2.35 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18689])).
% 2.25/2.35 tff(18895,plain,
% 2.25/2.35 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18894])).
% 2.25/2.35 tff(18896,plain,
% 2.25/2.35 (~(op(e2, e1) = e2)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[402, 18895])).
% 2.25/2.35 tff(18897,plain,
% 2.25/2.35 (op(e2, e2) = e2),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[2088, 18857, 18896, 18529])).
% 2.25/2.35 tff(18898,plain,
% 2.25/2.35 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18897])).
% 2.25/2.35 tff(18899,plain,
% 2.25/2.35 (op(e2, op(e2, e2)) = e2),
% 2.25/2.35 inference(transitivity,[status(thm)],[18898, 18897])).
% 2.25/2.35 tff(18900,plain,
% 2.25/2.35 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[528, 18899])).
% 2.25/2.35 tff(18901,plain,
% 2.25/2.35 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18832])).
% 2.25/2.35 tff(18902,plain,
% 2.25/2.35 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.25/2.35 inference(symmetry,[status(thm)],[18901])).
% 2.25/2.35 tff(18903,plain,
% 2.25/2.35 ((op(e3, e0) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.25/2.35 inference(transitivity,[status(thm)],[18902, 453])).
% 2.25/2.35 tff(18904,plain,
% 2.25/2.35 ((~(op(e3, e0) = e2)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18903])).
% 2.25/2.35 tff(18905,plain,
% 2.25/2.35 ((op(e1, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18522])).
% 2.25/2.35 tff(18906,plain,
% 2.25/2.35 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.25/2.35 inference(transitivity,[status(thm)],[18905, 5377])).
% 2.25/2.35 tff(18907,plain,
% 2.25/2.35 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18906])).
% 2.25/2.35 tff(18908,plain,
% 2.25/2.35 (~(op(e3, e0) = e2)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[410, 18907])).
% 2.25/2.35 tff(18909,plain,
% 2.25/2.35 (~(op(e0, e3) = op(e3, e0))),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[18908, 18904])).
% 2.25/2.35 tff(18910,plain,
% 2.25/2.35 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[496, 18909])).
% 2.25/2.35 tff(18911,plain,
% 2.25/2.35 ((op(e1, e3) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.25/2.35 inference(transitivity,[status(thm)],[18890, 6290])).
% 2.25/2.35 tff(18912,plain,
% 2.25/2.35 ((~(op(e1, e3) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18911])).
% 2.25/2.35 tff(18913,plain,
% 2.25/2.35 (~(op(e1, e3) = op(e3, e1))),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[72, 18912])).
% 2.25/2.35 tff(18914,plain,
% 2.25/2.35 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[6307, 18913])).
% 2.25/2.35 tff(18915,plain,
% 2.25/2.35 (op(e0, e1) = e3),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[829, 3849, 14782, 5828])).
% 2.25/2.35 tff(18916,plain,
% 2.25/2.35 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18915])).
% 2.25/2.35 tff(18917,plain,
% 2.25/2.35 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.25/2.35 inference(transitivity,[status(thm)],[18916, 1262])).
% 2.25/2.35 tff(18918,plain,
% 2.25/2.35 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18917])).
% 2.25/2.35 tff(18919,plain,
% 2.25/2.35 (~(op(e2, e1) = e3)),
% 2.25/2.35 inference(modus_ponens,[status(thm)],[606, 18918])).
% 2.25/2.35 tff(18920,plain,
% 2.25/2.35 (op(e2, e0) = e3),
% 2.25/2.35 inference(unit_resolution,[status(thm)],[1559, 18919, 9271, 13775])).
% 2.25/2.35 tff(18921,plain,
% 2.25/2.35 ((op(e2, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.25/2.35 inference(monotonicity,[status(thm)],[18920])).
% 2.26/2.36 tff(18922,plain,
% 2.26/2.36 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.26/2.36 inference(transitivity,[status(thm)],[18921, 4221])).
% 2.26/2.36 tff(18923,plain,
% 2.26/2.36 ((op(e0, e2) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.26/2.36 inference(symmetry,[status(thm)],[18922])).
% 2.26/2.36 tff(18924,plain,
% 2.26/2.36 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.26/2.36 inference(transitivity,[status(thm)],[18923, 6337])).
% 2.26/2.36 tff(18925,plain,
% 2.26/2.36 ((~(op(e0, e2) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18924])).
% 2.26/2.36 tff(18926,plain,
% 2.26/2.36 (~(op(e0, e2) = op(e2, e0))),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[18577, 18925])).
% 2.26/2.36 tff(18927,plain,
% 2.26/2.36 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[6347, 18926])).
% 2.26/2.36 tff(18928,plain,
% 2.26/2.36 (op(e1, op(e2, e3)) = e1),
% 2.26/2.36 inference(transitivity,[status(thm)],[14800, 5523])).
% 2.26/2.36 tff(18929,plain,
% 2.26/2.36 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[10724, 18928])).
% 2.26/2.36 tff(18930,plain,
% 2.26/2.36 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e3)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[2899])).
% 2.26/2.36 tff(18931,plain,
% 2.26/2.36 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 2.26/2.36 inference(symmetry,[status(thm)],[18930])).
% 2.26/2.36 tff(18932,plain,
% 2.26/2.36 ((op(e0, e1) = op(e2, e1)) <=> (op(e1, e2) = op(e2, e1))),
% 2.26/2.36 inference(transitivity,[status(thm)],[18917, 18931, 531])).
% 2.26/2.36 tff(18933,plain,
% 2.26/2.36 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18932])).
% 2.26/2.36 tff(18934,plain,
% 2.26/2.36 (~(op(e1, e2) = op(e2, e1))),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[606, 18933])).
% 2.26/2.36 tff(18935,plain,
% 2.26/2.36 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[539, 18934])).
% 2.26/2.36 tff(18936,plain,
% 2.26/2.36 ((~(op(e0, e2) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18923])).
% 2.26/2.36 tff(18937,plain,
% 2.26/2.36 (~(op(e2, e0) = op(e0, e2))),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[18577, 18936])).
% 2.26/2.36 tff(18938,plain,
% 2.26/2.36 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[6358, 18937])).
% 2.26/2.36 tff(18939,plain,
% 2.26/2.36 (op(e0, e2) = op(e1, e3)),
% 2.26/2.36 inference(transitivity,[status(thm)],[10155, 2909])).
% 2.26/2.36 tff(18940,plain,
% 2.26/2.36 ((op(e0, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18939])).
% 2.26/2.36 tff(18941,plain,
% 2.26/2.36 ((op(e1, e3) = e1) <=> (op(e0, e2) = e1)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18940])).
% 2.26/2.36 tff(18942,plain,
% 2.26/2.36 ((~(op(e1, e3) = e1)) <=> (~(op(e0, e2) = e1))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18941])).
% 2.26/2.36 tff(18943,plain,
% 2.26/2.36 (~(op(e0, e2) = e1)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[10908, 18942])).
% 2.26/2.36 tff(18944,plain,
% 2.26/2.36 (op(e0, e0) = e1),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[384, 18943, 14782, 121])).
% 2.26/2.36 tff(18945,plain,
% 2.26/2.36 (op(e1, op(e0, e0)) = op(e1, e1)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18944])).
% 2.26/2.36 tff(18946,plain,
% 2.26/2.36 (op(e1, op(e0, e0)) = e1),
% 2.26/2.36 inference(transitivity,[status(thm)],[18945, 5523])).
% 2.26/2.36 tff(18947,plain,
% 2.26/2.36 (op(e3, e2) = e1),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[1898, 85, 2386, 1890])).
% 2.26/2.36 tff(18948,plain,
% 2.26/2.36 (op(e1, op(e3, e2)) = op(e1, e1)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18947])).
% 2.26/2.36 tff(18949,plain,
% 2.26/2.36 (op(e1, op(e3, e2)) = e1),
% 2.26/2.36 inference(transitivity,[status(thm)],[18948, 5523])).
% 2.26/2.36 tff(18950,plain,
% 2.26/2.36 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[12544, 18949])).
% 2.26/2.36 tff(18951,plain,
% 2.26/2.36 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[5367, 18950, 5669, 5670, 5672, 5674, 5675, 5511, 5679, 5673, 5671, 5681, 6688, 5680, 9846])).
% 2.26/2.36 tff(18952,plain,
% 2.26/2.36 (~(op(e1, op(e0, e0)) = e1)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[6717, 18951])).
% 2.26/2.36 tff(18953,plain,
% 2.26/2.36 ($false),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[18952, 18946])).
% 2.26/2.36 tff(18954,plain,((op(e3, e2) = e0) | (~(op(e1, e1) = e1)) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (op(e0, e3) = e1) | (~(op(e1, e3) = e0)) | (op(e3, e2) = e2) | (op(e3, e2) = e3) | (op(e2, e2) = e0) | (op(e1, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.36 tff(18955,plain,
% 2.26/2.36 (op(e3, e2) = e0),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[18954, 18938, 5669, 5670, 5672, 5523, 5675, 5511, 18935, 18929, 5681, 6688, 5680, 18927, 121, 1219, 2386, 10204, 17, 18550])).
% 2.26/2.36 tff(18956,plain,
% 2.26/2.36 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e0)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18955])).
% 2.26/2.36 tff(18957,plain,
% 2.26/2.36 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e0))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18956])).
% 2.26/2.36 tff(18958,plain,
% 2.26/2.36 (~(op(e0, e2) = e0)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[1467, 18957])).
% 2.26/2.36 tff(18959,plain,
% 2.26/2.36 (op(e0, e0) = e0),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[3976, 18958, 3849, 18589])).
% 2.26/2.36 tff(18960,plain,
% 2.26/2.36 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18959])).
% 2.26/2.36 tff(18961,plain,
% 2.26/2.36 (op(e0, op(e0, e0)) = e0),
% 2.26/2.36 inference(transitivity,[status(thm)],[18960, 18959])).
% 2.26/2.36 tff(18962,plain,
% 2.26/2.36 (op(e3, e2) = op(e1, e3)),
% 2.26/2.36 inference(transitivity,[status(thm)],[18955, 2909])).
% 2.26/2.36 tff(18963,plain,
% 2.26/2.36 ((op(e3, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18962])).
% 2.26/2.36 tff(18964,plain,
% 2.26/2.36 ((op(e1, e3) = e1) <=> (op(e3, e2) = e1)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18963])).
% 2.26/2.36 tff(18965,plain,
% 2.26/2.36 ((op(e1, e3) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 2.26/2.36 inference(transitivity,[status(thm)],[18964, 14325, 395])).
% 2.26/2.36 tff(18966,plain,
% 2.26/2.36 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18965])).
% 2.26/2.36 tff(18967,plain,
% 2.26/2.36 (~(op(e2, e3) = op(e3, e2))),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[10908, 18966])).
% 2.26/2.36 tff(18968,plain,
% 2.26/2.36 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[430, 18967])).
% 2.26/2.36 tff(18969,plain,
% 2.26/2.36 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[5367, 18968, 5669, 5670, 5672, 18938, 5675, 5511, 5679, 18935, 18929, 5681, 6688, 5680, 18927])).
% 2.26/2.36 tff(18970,plain,
% 2.26/2.36 (~(op(e0, op(e0, e0)) = e0)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[5598, 18969])).
% 2.26/2.36 tff(18971,plain,
% 2.26/2.36 ($false),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[18970, 18961])).
% 2.26/2.36 tff(18972,plain,((op(e0, e1) = e0) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~(op(e1, e3) = e0)) | (~(op(e2, e3) = e1)) | (~(op(e1, e1) = e1)) | (op(e0, e3) = e1) | (op(e3, e2) = e2) | (op(e2, e2) = e0) | (~(op(e1, e2) = e3)) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.36 tff(18973,plain,
% 2.26/2.36 (op(e0, e1) = e0),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[18972, 18914, 18910, 18900, 18719, 18893, 18712, 18887, 18884, 18704, 18870, 18534, 18848, 18843, 17, 18513, 18839])).
% 2.26/2.36 tff(18974,plain,
% 2.26/2.36 (op(e0, e1) = op(e1, e3)),
% 2.26/2.36 inference(transitivity,[status(thm)],[18973, 18837])).
% 2.26/2.36 tff(18975,plain,
% 2.26/2.36 ((op(e0, e1) = e3) <=> (op(e1, e3) = e3)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18974])).
% 2.26/2.36 tff(18976,plain,
% 2.26/2.36 ((op(e1, e3) = e3) <=> (op(e0, e1) = e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18975])).
% 2.26/2.36 tff(18977,plain,
% 2.26/2.36 ((~(op(e1, e3) = e3)) <=> (~(op(e0, e1) = e3))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18976])).
% 2.26/2.36 tff(18978,plain,
% 2.26/2.36 (~(op(e0, e1) = e3)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[18877, 18977])).
% 2.26/2.36 tff(18979,plain,
% 2.26/2.36 (op(e0, e0) = e3),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[1495, 18978, 18836, 18516])).
% 2.26/2.36 tff(18980,plain,
% 2.26/2.36 (e3 = op(e0, e0)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[18979, 71])).
% 2.26/2.36 tff(18981,plain,
% 2.26/2.36 (op(e0, op(e0, e0)) = op(op(e1, e3), e3)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18837, 18979])).
% 2.26/2.36 tff(18982,plain,
% 2.26/2.36 (op(op(e1, e3), e3) = op(e0, op(e0, e0))),
% 2.26/2.36 inference(symmetry,[status(thm)],[18981])).
% 2.26/2.36 tff(18983,plain,
% 2.26/2.36 (op(op(e1, e3), e3) = op(e0, e3)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18704])).
% 2.26/2.36 tff(18984,plain,
% 2.26/2.36 (op(e0, e3) = op(op(e1, e3), e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18983])).
% 2.26/2.36 tff(18985,plain,
% 2.26/2.36 (e2 = op(e0, e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18832])).
% 2.26/2.36 tff(18986,plain,
% 2.26/2.36 (e2 = op(e0, op(e0, e0))),
% 2.26/2.36 inference(transitivity,[status(thm)],[18985, 18984, 18982])).
% 2.26/2.36 tff(18987,plain,
% 2.26/2.36 (op(e0, op(e0, e0)) = e2),
% 2.26/2.36 inference(transitivity,[status(thm)],[18981, 18983, 18832])).
% 2.26/2.36 tff(18988,plain,
% 2.26/2.36 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18987])).
% 2.26/2.36 tff(18989,plain,
% 2.26/2.36 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 2.26/2.36 inference(symmetry,[status(thm)],[18988])).
% 2.26/2.36 tff(18990,plain,
% 2.26/2.36 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18832])).
% 2.26/2.36 tff(18991,plain,
% 2.26/2.36 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18990])).
% 2.26/2.36 tff(18992,plain,
% 2.26/2.36 (~(op(e0, e2) = e2)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[918, 18991])).
% 2.26/2.36 tff(18993,plain,
% 2.26/2.36 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18973])).
% 2.26/2.36 tff(18994,plain,
% 2.26/2.36 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.26/2.36 inference(transitivity,[status(thm)],[18993, 10200])).
% 2.26/2.36 tff(18995,plain,
% 2.26/2.36 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[18994])).
% 2.26/2.36 tff(18996,plain,
% 2.26/2.36 (~(op(e0, e2) = e0)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[2102, 18995])).
% 2.26/2.36 tff(18997,plain,
% 2.26/2.36 (op(e0, e2) = e1),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[2745, 18996, 18992, 18516])).
% 2.26/2.36 tff(18998,plain,
% 2.26/2.36 (e1 = op(e0, e2)),
% 2.26/2.36 inference(symmetry,[status(thm)],[18997])).
% 2.26/2.36 tff(18999,plain,
% 2.26/2.36 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.26/2.36 inference(transitivity,[status(thm)],[18998, 18989])).
% 2.26/2.36 tff(19000,plain,
% 2.26/2.36 ($false),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[2760, 18999, 18986, 18980])).
% 2.26/2.36 tff(19001,plain,((op(e1, e3) = e2) | (op(e2, e2) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.36 tff(19002,plain,
% 2.26/2.36 (op(e1, e3) = e2),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[19001, 68, 17])).
% 2.26/2.36 tff(19003,plain,
% 2.26/2.36 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.36 tff(19004,plain,
% 2.26/2.36 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 2.26/2.36 inference(transitivity,[status(thm)],[19003, 69])).
% 2.26/2.36 tff(19005,plain,
% 2.26/2.36 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 2.26/2.36 inference(symmetry,[status(thm)],[19004])).
% 2.26/2.36 tff(19006,plain,
% 2.26/2.36 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19005])).
% 2.26/2.36 tff(19007,plain,
% 2.26/2.36 (~(op(e1, e3) = e1)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[708, 19006])).
% 2.26/2.36 tff(19008,plain,
% 2.26/2.36 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.36 tff(19009,plain,
% 2.26/2.36 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 2.26/2.36 inference(transitivity,[status(thm)],[19008, 1])).
% 2.26/2.36 tff(19010,plain,
% 2.26/2.36 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 2.26/2.36 inference(symmetry,[status(thm)],[19009])).
% 2.26/2.36 tff(19011,plain,
% 2.26/2.36 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19010])).
% 2.26/2.36 tff(19012,plain,
% 2.26/2.36 (~(op(e1, e3) = e0)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[14, 19011])).
% 2.26/2.36 tff(19013,plain,
% 2.26/2.36 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e2)),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.36 tff(19014,plain,
% 2.26/2.36 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e2))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19013])).
% 2.26/2.36 tff(19015,plain,
% 2.26/2.36 (~(op(e0, e3) = e2)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[64, 19014])).
% 2.26/2.36 tff(19016,plain,
% 2.26/2.36 (op(e2, e3) = e3),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[12598, 121, 19012, 19015, 76])).
% 2.26/2.36 tff(19017,plain,
% 2.26/2.36 (e3 = op(e2, e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[19016])).
% 2.26/2.36 tff(19018,plain,
% 2.26/2.36 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19017])).
% 2.26/2.36 tff(19019,plain,
% 2.26/2.36 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[19018])).
% 2.26/2.36 tff(19020,plain,
% 2.26/2.36 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19019])).
% 2.26/2.36 tff(19021,plain,
% 2.26/2.36 (~(op(e0, e3) = e3)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[964, 19020])).
% 2.26/2.36 tff(19022,plain,
% 2.26/2.36 (op(e0, e3) = e0),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[687, 19021, 19015, 121])).
% 2.26/2.36 tff(19023,plain,
% 2.26/2.36 (e0 = op(e0, e3)),
% 2.26/2.36 inference(symmetry,[status(thm)],[19022])).
% 2.26/2.36 tff(19024,plain,
% 2.26/2.36 (~(op(e2, e1) = e0)),
% 2.26/2.36 inference(unit_resolution,[status(thm)],[7790, 121, 19015, 19012])).
% 2.26/2.36 tff(19025,plain,
% 2.26/2.36 ((e0 = e3) <=> (e0 = op(e2, e3))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19017])).
% 2.26/2.36 tff(19026,plain,
% 2.26/2.36 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 2.26/2.36 inference(transitivity,[status(thm)],[19025, 86])).
% 2.26/2.36 tff(19027,plain,
% 2.26/2.36 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 2.26/2.36 inference(monotonicity,[status(thm)],[19026])).
% 2.26/2.36 tff(19028,plain,
% 2.26/2.36 (~(op(e2, e3) = e0)),
% 2.26/2.36 inference(modus_ponens,[status(thm)],[181, 19027])).
% 2.26/2.36 tff(19029,plain,
% 2.26/2.37 (op(e2, e0) = e0),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[2311, 19028, 17, 19024])).
% 2.26/2.37 tff(19030,plain,
% 2.26/2.37 (op(e2, e0) = op(e0, e3)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19029, 19023])).
% 2.26/2.37 tff(19031,plain,
% 2.26/2.37 ((op(e2, e0) = e2) <=> (op(e0, e3) = e2)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19030])).
% 2.26/2.37 tff(19032,plain,
% 2.26/2.37 ((op(e0, e3) = e2) <=> (op(e2, e0) = e2)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19031])).
% 2.26/2.37 tff(19033,plain,
% 2.26/2.37 ((~(op(e0, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19032])).
% 2.26/2.37 tff(19034,plain,
% 2.26/2.37 (~(op(e2, e0) = e2)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[19015, 19033])).
% 2.26/2.37 tff(19035,plain,
% 2.26/2.37 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.37 tff(19036,plain,
% 2.26/2.37 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19035, 120])).
% 2.26/2.37 tff(19037,plain,
% 2.26/2.37 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19036])).
% 2.26/2.37 tff(19038,plain,
% 2.26/2.37 (~(op(e2, e3) = e2)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[118, 19037])).
% 2.26/2.37 tff(19039,plain,
% 2.26/2.37 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19017])).
% 2.26/2.37 tff(19040,plain,
% 2.26/2.37 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19039])).
% 2.26/2.37 tff(19041,plain,
% 2.26/2.37 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19040])).
% 2.26/2.37 tff(19042,plain,
% 2.26/2.37 (~(op(e2, e2) = e3)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[515, 19041])).
% 2.26/2.37 tff(19043,plain,
% 2.26/2.37 ((op(e2, e0) = e1) <=> (op(e0, e3) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19030])).
% 2.26/2.37 tff(19044,plain,
% 2.26/2.37 ((op(e0, e3) = e1) <=> (op(e2, e0) = e1)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19043])).
% 2.26/2.37 tff(19045,plain,
% 2.26/2.37 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19044])).
% 2.26/2.37 tff(19046,plain,
% 2.26/2.37 (~(op(e2, e0) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[121, 19045])).
% 2.26/2.37 tff(19047,plain,
% 2.26/2.37 (op(e3, e3) = e1),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[151, 121, 76, 19007])).
% 2.26/2.37 tff(19048,plain,
% 2.26/2.37 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19047])).
% 2.26/2.37 tff(19049,plain,
% 2.26/2.37 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19048])).
% 2.26/2.37 tff(19050,plain,
% 2.26/2.37 (~(op(e3, e0) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[157, 19049])).
% 2.26/2.37 tff(19051,plain,
% 2.26/2.37 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19029])).
% 2.26/2.37 tff(19052,plain,
% 2.26/2.37 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19051])).
% 2.26/2.37 tff(19053,plain,
% 2.26/2.37 (~(op(e1, e0) = e0)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[756, 19052])).
% 2.26/2.37 tff(19054,plain,
% 2.26/2.37 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[264])).
% 2.26/2.37 tff(19055,plain,
% 2.26/2.37 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19054, 1])).
% 2.26/2.37 tff(19056,plain,
% 2.26/2.37 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19055])).
% 2.26/2.37 tff(19057,plain,
% 2.26/2.37 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19056])).
% 2.26/2.37 tff(19058,plain,
% 2.26/2.37 (~(op(e1, e3) = e0)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[14, 19057])).
% 2.26/2.37 tff(19059,plain,
% 2.26/2.37 (op(e1, e1) = op(e0, e3)),
% 2.26/2.37 inference(transitivity,[status(thm)],[249, 772])).
% 2.26/2.37 tff(19060,plain,
% 2.26/2.37 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19059])).
% 2.26/2.37 tff(19061,plain,
% 2.26/2.37 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19060, 2179])).
% 2.26/2.37 tff(19062,plain,
% 2.26/2.37 ((e3 = op(e1, op(e1, e1))) <=> (e3 = op(e1, e0))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19061])).
% 2.26/2.37 tff(19063,plain,
% 2.26/2.37 ((e3 = op(e1, op(e1, e1))) <=> (op(e1, e0) = e3)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19062, 3497])).
% 2.26/2.37 tff(19064,plain,
% 2.26/2.37 ((op(e1, e0) = e3) <=> (e3 = op(e1, op(e1, e1)))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19063])).
% 2.26/2.37 tff(19065,plain,
% 2.26/2.37 ((op(e1, e1) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19059, 6779])).
% 2.26/2.37 tff(19066,plain,
% 2.26/2.37 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e1) = e3)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19065])).
% 2.26/2.37 tff(19067,plain,
% 2.26/2.37 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e1) = e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19066])).
% 2.26/2.37 tff(19068,plain,
% 2.26/2.37 (~(op(e1, e1) = e3)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[964, 19067])).
% 2.26/2.37 tff(19069,plain,
% 2.26/2.37 (op(e1, e0) = e3),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[247, 19068, 75, 6613])).
% 2.26/2.37 tff(19070,plain,
% 2.26/2.37 (e3 = op(e1, op(e1, e1))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[19069, 19064])).
% 2.26/2.37 tff(19071,plain,
% 2.26/2.37 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e0))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19061])).
% 2.26/2.37 tff(19072,plain,
% 2.26/2.37 (op(e1, op(e1, e0)) = op(e1, op(e1, op(e1, e1)))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19071])).
% 2.26/2.37 tff(19073,plain,
% 2.26/2.37 (op(e1, e0) = op(e2, e3)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19069, 6779])).
% 2.26/2.37 tff(19074,plain,
% 2.26/2.37 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19073])).
% 2.26/2.37 tff(19075,plain,
% 2.26/2.37 (op(e1, op(e2, e3)) = op(e1, op(e1, e0))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19074])).
% 2.26/2.37 tff(19076,plain,
% 2.26/2.37 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.26/2.37 inference(transitivity,[status(thm)],[265, 6911, 19075, 19072])).
% 2.26/2.37 tff(19077,plain,
% 2.26/2.37 ($false),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[276, 19076, 19070, 250])).
% 2.26/2.37 tff(19078,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e3) = e2)) | (~(op(e2, e3) = e3)) | (~(op(e0, e3) = e0)) | (op(e1, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.37 tff(19079,plain,
% 2.26/2.37 (~(op(e1, e1) = e0)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[19078, 75, 6778, 771, 264])).
% 2.26/2.37 tff(19080,plain,
% 2.26/2.37 (op(e1, e2) = e0),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[1830, 19079, 19058, 2167])).
% 2.26/2.37 tff(19081,plain,
% 2.26/2.37 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[6779])).
% 2.26/2.37 tff(19082,plain,
% 2.26/2.37 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19081])).
% 2.26/2.37 tff(19083,plain,
% 2.26/2.37 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19082])).
% 2.26/2.37 tff(19084,plain,
% 2.26/2.37 (~(op(e2, e1) = e3)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[197, 19083])).
% 2.26/2.37 tff(19085,plain,
% 2.26/2.37 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[264])).
% 2.26/2.37 tff(19086,plain,
% 2.26/2.37 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19085])).
% 2.26/2.37 tff(19087,plain,
% 2.26/2.37 (~(op(e1, e2) = e2)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[1850, 19086])).
% 2.26/2.37 tff(19088,plain,
% 2.26/2.37 (op(e2, e1) = e2),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[1993, 5828, 68, 82])).
% 2.26/2.37 tff(19089,plain,
% 2.26/2.37 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19088])).
% 2.26/2.37 tff(19090,plain,
% 2.26/2.37 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19089, 69])).
% 2.26/2.37 tff(19091,plain,
% 2.26/2.37 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19090])).
% 2.26/2.37 tff(19092,plain,
% 2.26/2.37 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19091])).
% 2.26/2.37 tff(19093,plain,
% 2.26/2.37 (~(op(e2, e1) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[708, 19092])).
% 2.26/2.37 tff(19094,plain,
% 2.26/2.37 (op(e2, e2) = e1),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[345, 19093, 76, 1349])).
% 2.26/2.37 tff(19095,plain,
% 2.26/2.37 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19094])).
% 2.26/2.37 tff(19096,plain,
% 2.26/2.37 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19095])).
% 2.26/2.37 tff(19097,plain,
% 2.26/2.37 (~(op(e1, e2) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[1273, 19096])).
% 2.26/2.37 tff(19098,plain,
% 2.26/2.37 (op(e1, e2) = e0),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[1859, 19097, 19087, 75])).
% 2.26/2.37 tff(19099,plain,
% 2.26/2.37 (op(e0, e1) = e1),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[829, 5828, 3849, 2527])).
% 2.26/2.37 tff(19100,plain,
% 2.26/2.37 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19099])).
% 2.26/2.37 tff(19101,plain,
% 2.26/2.37 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19100])).
% 2.26/2.37 tff(19102,plain,
% 2.26/2.37 (~(op(e0, e0) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[811, 19101])).
% 2.26/2.37 tff(19103,plain,
% 2.26/2.37 (op(e1, e0) = e1),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[1480, 19102, 931, 1349])).
% 2.26/2.37 tff(19104,plain,
% 2.26/2.37 ((op(e1, e0) = e3) <=> (e1 = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19103, 6779])).
% 2.26/2.37 tff(19105,plain,
% 2.26/2.37 ((op(e1, e0) = e3) <=> (op(e2, e3) = e1)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19104, 5574])).
% 2.26/2.37 tff(19106,plain,
% 2.26/2.37 ((op(e2, e3) = e1) <=> (op(e1, e0) = e3)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19105])).
% 2.26/2.37 tff(19107,plain,
% 2.26/2.37 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e0) = e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19106])).
% 2.26/2.37 tff(19108,plain,
% 2.26/2.37 (~(op(e1, e0) = e3)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[76, 19107])).
% 2.26/2.37 tff(19109,plain,
% 2.26/2.37 (op(e1, e1) = e3),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[247, 19108, 75, 6613])).
% 2.26/2.37 tff(19110,plain,
% 2.26/2.37 ($false),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[6918, 19109, 19098, 264, 6778])).
% 2.26/2.37 tff(19111,plain,((op(e0, e1) = e2) | (~(op(e1, e3) = e2)) | (~(op(e2, e3) = e3)) | (op(e1, e2) = e3) | (op(e2, e3) = e1) | (op(e3, e0) = e1) | (op(e2, e0) = e1) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.37 tff(19112,plain,
% 2.26/2.37 (op(e0, e1) = e2),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[19111, 75, 6778, 264, 76, 931, 1349, 3849, 2527, 68, 82])).
% 2.26/2.37 tff(19113,plain,
% 2.26/2.37 ((op(e0, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19112])).
% 2.26/2.37 tff(19114,plain,
% 2.26/2.37 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19113, 1960])).
% 2.26/2.37 tff(19115,plain,
% 2.26/2.37 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19114])).
% 2.26/2.37 tff(19116,plain,
% 2.26/2.37 (~(op(e2, e1) = e2)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[606, 19115])).
% 2.26/2.37 tff(19117,plain,
% 2.26/2.37 (op(e2, e1) = e1),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[2367, 19116, 2559, 19084])).
% 2.26/2.37 tff(19118,plain,
% 2.26/2.37 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19117])).
% 2.26/2.37 tff(19119,plain,
% 2.26/2.37 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19118])).
% 2.26/2.37 tff(19120,plain,
% 2.26/2.37 (~(op(e1, e1) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[225, 19119])).
% 2.26/2.37 tff(19121,plain,
% 2.26/2.37 (op(e1, e1) = e3),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[630, 19079, 68, 19120])).
% 2.26/2.37 tff(19122,plain,
% 2.26/2.37 ($false),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[6918, 19121, 19080, 264, 6778])).
% 2.26/2.37 tff(19123,plain,((op(e1, e2) = e3) | (~(op(e1, e3) = e2)) | (~(op(e2, e3) = e3)) | (op(e1, e1) = e2) | (op(e1, e0) = e0) | (~(op(e0, e3) = e0)) | (op(e2, e1) = e0) | (op(e2, e3) = e1) | (op(e3, e0) = e1) | (op(e2, e0) = e1) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.37 tff(19124,plain,
% 2.26/2.37 (op(e1, e2) = e3),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[19123, 19016, 19002, 68, 19053, 19022, 19024, 76, 19050, 19046, 3849, 2527, 82])).
% 2.26/2.37 tff(19125,plain,
% 2.26/2.37 (op(e1, e2) = op(e2, e3)),
% 2.26/2.37 inference(transitivity,[status(thm)],[19124, 19017])).
% 2.26/2.37 tff(19126,plain,
% 2.26/2.37 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = op(e2, e3))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19125])).
% 2.26/2.37 tff(19127,plain,
% 2.26/2.37 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19126])).
% 2.26/2.37 tff(19128,plain,
% 2.26/2.37 ((op(e2, e1) = op(e2, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.26/2.37 inference(transitivity,[status(thm)],[19127, 531])).
% 2.26/2.37 tff(19129,plain,
% 2.26/2.37 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19128])).
% 2.26/2.37 tff(19130,plain,
% 2.26/2.37 (~(op(e1, e2) = op(e2, e1))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[197, 19129])).
% 2.26/2.37 tff(19131,plain,
% 2.26/2.37 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[539, 19130])).
% 2.26/2.37 tff(19132,plain,
% 2.26/2.37 ((op(e1, e2) = e1) <=> (op(e2, e3) = e1)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19125])).
% 2.26/2.37 tff(19133,plain,
% 2.26/2.37 ((op(e2, e3) = e1) <=> (op(e1, e2) = e1)),
% 2.26/2.37 inference(symmetry,[status(thm)],[19132])).
% 2.26/2.37 tff(19134,plain,
% 2.26/2.37 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e2) = e1))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19133])).
% 2.26/2.37 tff(19135,plain,
% 2.26/2.37 (~(op(e1, e2) = e1)),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[76, 19134])).
% 2.26/2.37 tff(19136,plain,
% 2.26/2.37 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19127])).
% 2.26/2.37 tff(19137,plain,
% 2.26/2.37 (~(op(e2, e1) = op(e1, e2))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[197, 19136])).
% 2.26/2.37 tff(19138,plain,
% 2.26/2.37 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[557, 19137])).
% 2.26/2.37 tff(19139,plain,
% 2.26/2.37 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19030])).
% 2.26/2.37 tff(19140,plain,
% 2.26/2.37 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 2.26/2.37 inference(transitivity,[status(thm)],[19139, 7797])).
% 2.26/2.37 tff(19141,plain,
% 2.26/2.37 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19140])).
% 2.26/2.37 tff(19142,plain,
% 2.26/2.37 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 2.26/2.37 inference(transitivity,[status(thm)],[19141, 6337])).
% 2.26/2.37 tff(19143,plain,
% 2.26/2.37 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19142])).
% 2.26/2.37 tff(19144,plain,
% 2.26/2.37 (~(op(e0, e2) = op(e2, e0))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[918, 19143])).
% 2.26/2.37 tff(19145,plain,
% 2.26/2.37 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[6347, 19144])).
% 2.26/2.37 tff(19146,plain,
% 2.26/2.37 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19125])).
% 2.26/2.37 tff(19147,plain,
% 2.26/2.37 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.26/2.37 inference(transitivity,[status(thm)],[19146, 394])).
% 2.26/2.37 tff(19148,plain,
% 2.26/2.37 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.26/2.37 inference(transitivity,[status(thm)],[19147, 395])).
% 2.26/2.37 tff(19149,plain,
% 2.26/2.37 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19148])).
% 2.26/2.37 tff(19150,plain,
% 2.26/2.37 (~(op(e2, e3) = op(e3, e2))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[2292, 19149])).
% 2.26/2.37 tff(19151,plain,
% 2.26/2.37 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[430, 19150])).
% 2.26/2.37 tff(19152,plain,
% 2.26/2.37 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19141])).
% 2.26/2.37 tff(19153,plain,
% 2.26/2.37 (~(op(e2, e0) = op(e0, e2))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[918, 19152])).
% 2.26/2.37 tff(19154,plain,
% 2.26/2.37 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.26/2.37 inference(unit_resolution,[status(thm)],[6358, 19153])).
% 2.26/2.37 tff(19155,plain,
% 2.26/2.37 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.37 tff(19156,plain,
% 2.26/2.37 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.26/2.37 inference(symmetry,[status(thm)],[19155])).
% 2.26/2.37 tff(19157,plain,
% 2.26/2.37 ((~(op(e3, e1) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.26/2.37 inference(monotonicity,[status(thm)],[19156])).
% 2.26/2.37 tff(19158,plain,
% 2.26/2.37 (~(op(e3, e1) = op(e1, e3))),
% 2.26/2.37 inference(modus_ponens,[status(thm)],[82, 19157])).
% 2.26/2.37 tff(19159,plain,
% 2.26/2.37 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[6362, 19158])).
% 2.26/2.38 tff(19160,plain,
% 2.26/2.38 (op(e0, e3) = op(e0, op(e2, e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19017])).
% 2.26/2.38 tff(19161,plain,
% 2.26/2.38 ((op(e0, e3) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19160])).
% 2.26/2.38 tff(19162,plain,
% 2.26/2.38 (op(e0, op(e2, e3)) = e0),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[19022, 19161])).
% 2.26/2.38 tff(19163,plain,
% 2.26/2.38 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[13359, 19162])).
% 2.26/2.38 tff(19164,plain,
% 2.26/2.38 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19030])).
% 2.26/2.38 tff(19165,plain,
% 2.26/2.38 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19164, 452])).
% 2.26/2.38 tff(19166,plain,
% 2.26/2.38 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19165, 453])).
% 2.26/2.38 tff(19167,plain,
% 2.26/2.38 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19166])).
% 2.26/2.38 tff(19168,plain,
% 2.26/2.38 (~(op(e0, e3) = op(e3, e0))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[747, 19167])).
% 2.26/2.38 tff(19169,plain,
% 2.26/2.38 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[496, 19168])).
% 2.26/2.38 tff(19170,plain,
% 2.26/2.38 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19017])).
% 2.26/2.38 tff(19171,plain,
% 2.26/2.38 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19170])).
% 2.26/2.38 tff(19172,plain,
% 2.26/2.38 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19171])).
% 2.26/2.38 tff(19173,plain,
% 2.26/2.38 (~(op(e2, e1) = e3)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[197, 19172])).
% 2.26/2.38 tff(19174,plain,
% 2.26/2.38 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19124])).
% 2.26/2.38 tff(19175,plain,
% 2.26/2.38 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19174])).
% 2.26/2.38 tff(19176,plain,
% 2.26/2.38 (~(op(e1, e1) = e3)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[1604, 19175])).
% 2.26/2.38 tff(19177,plain,
% 2.26/2.38 (op(e3, e1) = e3),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[1730, 19176, 2527, 19173])).
% 2.26/2.38 tff(19178,plain,
% 2.26/2.38 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19002])).
% 2.26/2.38 tff(19179,plain,
% 2.26/2.38 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19178])).
% 2.26/2.38 tff(19180,plain,
% 2.26/2.38 (~(op(e1, e0) = e2)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[110, 19179])).
% 2.26/2.38 tff(19181,plain,
% 2.26/2.38 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19124])).
% 2.26/2.38 tff(19182,plain,
% 2.26/2.38 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19181])).
% 2.26/2.38 tff(19183,plain,
% 2.26/2.38 (~(op(e1, e0) = e3)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[1312, 19182])).
% 2.26/2.38 tff(19184,plain,
% 2.26/2.38 (op(e1, e0) = e1),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[728, 19183, 19180, 19053])).
% 2.26/2.38 tff(19185,plain,
% 2.26/2.38 (op(e3, op(e1, e0)) = op(e3, e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19184])).
% 2.26/2.38 tff(19186,plain,
% 2.26/2.38 (op(e3, op(e1, e0)) = e3),
% 2.26/2.38 inference(transitivity,[status(thm)],[19185, 19177])).
% 2.26/2.38 tff(19187,plain,
% 2.26/2.38 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[9792, 19186])).
% 2.26/2.38 tff(19188,plain,
% 2.26/2.38 (op(e1, op(e0, e3)) = op(e1, e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19022])).
% 2.26/2.38 tff(19189,plain,
% 2.26/2.38 ((op(e1, e2) = e0) <=> (op(e2, e3) = op(e0, e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19125, 19023])).
% 2.26/2.38 tff(19190,plain,
% 2.26/2.38 ((op(e1, e2) = e0) <=> (op(e0, e3) = op(e2, e3))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19189, 925])).
% 2.26/2.38 tff(19191,plain,
% 2.26/2.38 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e2) = e0)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19190])).
% 2.26/2.38 tff(19192,plain,
% 2.26/2.38 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e2) = e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19191])).
% 2.26/2.38 tff(19193,plain,
% 2.26/2.38 (~(op(e1, e2) = e0)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[964, 19192])).
% 2.26/2.38 tff(19194,plain,
% 2.26/2.38 (op(e1, e1) = e0),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[1830, 19193, 19012, 19053])).
% 2.26/2.38 tff(19195,plain,
% 2.26/2.38 (op(e1, e1) = op(e0, e3)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19194, 19023])).
% 2.26/2.38 tff(19196,plain,
% 2.26/2.38 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19195])).
% 2.26/2.38 tff(19197,plain,
% 2.26/2.38 (op(e1, op(e1, e1)) = e1),
% 2.26/2.38 inference(transitivity,[status(thm)],[19196, 19188, 19184])).
% 2.26/2.38 tff(19198,plain,
% 2.26/2.38 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5678, 19197])).
% 2.26/2.38 tff(19199,plain,
% 2.26/2.38 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19047])).
% 2.26/2.38 tff(19200,plain,
% 2.26/2.38 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19199])).
% 2.26/2.38 tff(19201,plain,
% 2.26/2.38 (~(op(e3, e2) = e1)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[1888, 19200])).
% 2.26/2.38 tff(19202,plain,
% 2.26/2.38 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19047])).
% 2.26/2.38 tff(19203,plain,
% 2.26/2.38 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19202])).
% 2.26/2.38 tff(19204,plain,
% 2.26/2.38 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19203])).
% 2.26/2.38 tff(19205,plain,
% 2.26/2.38 (op(e3, op(e3, e3)) = e3),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[19177, 19204])).
% 2.26/2.38 tff(19206,plain,
% 2.26/2.38 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[6277, 19205])).
% 2.26/2.38 tff(19207,plain,
% 2.26/2.38 ((op(e3, e1) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19156, 6290])).
% 2.26/2.38 tff(19208,plain,
% 2.26/2.38 ((~(op(e3, e1) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19207])).
% 2.26/2.38 tff(19209,plain,
% 2.26/2.38 (~(op(e1, e3) = op(e3, e1))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[82, 19208])).
% 2.26/2.38 tff(19210,plain,
% 2.26/2.38 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[6307, 19209])).
% 2.26/2.38 tff(19211,plain,
% 2.26/2.38 (op(op(e0, e3), e3) = e0),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5461, 19022])).
% 2.26/2.38 tff(19212,plain,
% 2.26/2.38 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19124])).
% 2.26/2.38 tff(19213,plain,
% 2.26/2.38 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19212])).
% 2.26/2.38 tff(19214,plain,
% 2.26/2.38 (~(op(e0, e2) = e3)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[6205, 19213])).
% 2.26/2.38 tff(19215,plain,
% 2.26/2.38 (op(e0, e0) = e3),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[1495, 19214, 2527, 19021])).
% 2.26/2.38 tff(19216,plain,
% 2.26/2.38 (op(e0, op(e0, e0)) = op(op(e0, e3), e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19023, 19215])).
% 2.26/2.38 tff(19217,plain,
% 2.26/2.38 (op(e0, op(e0, e0)) = e0),
% 2.26/2.38 inference(transitivity,[status(thm)],[19216, 19211])).
% 2.26/2.38 tff(19218,plain,
% 2.26/2.38 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5598, 19217])).
% 2.26/2.38 tff(19219,plain,
% 2.26/2.38 (op(e2, e2) = e1),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[12575, 19218, 19210, 19184, 19206, 19201, 19198, 19187, 19169, 19163, 19159, 19154, 19151, 19145, 19138, 19135, 19131, 17, 19042])).
% 2.26/2.38 tff(19220,plain,
% 2.26/2.38 ((op(e2, e2) = e2) <=> (e1 = e2)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19219])).
% 2.26/2.38 tff(19221,plain,
% 2.26/2.38 ((e1 = e2) <=> (op(e2, e2) = e2)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19220])).
% 2.26/2.38 tff(19222,plain,
% 2.26/2.38 ((~(e1 = e2)) <=> (~(op(e2, e2) = e2))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19221])).
% 2.26/2.38 tff(19223,plain,
% 2.26/2.38 (~(op(e2, e2) = e2)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[708, 19222])).
% 2.26/2.38 tff(19224,plain,
% 2.26/2.38 (op(e2, e1) = e2),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[2088, 19223, 19038, 19034])).
% 2.26/2.38 tff(19225,plain,
% 2.26/2.38 (op(e0, e0) = op(e2, e3)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19215, 19017])).
% 2.26/2.38 tff(19226,plain,
% 2.26/2.38 ((op(e0, e0) = e1) <=> (op(e2, e3) = e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19225])).
% 2.26/2.38 tff(19227,plain,
% 2.26/2.38 ((op(e2, e3) = e1) <=> (op(e0, e0) = e1)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19226])).
% 2.26/2.38 tff(19228,plain,
% 2.26/2.38 ((~(op(e2, e3) = e1)) <=> (~(op(e0, e0) = e1))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19227])).
% 2.26/2.38 tff(19229,plain,
% 2.26/2.38 (~(op(e0, e0) = e1)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[76, 19228])).
% 2.26/2.38 tff(19230,plain,
% 2.26/2.38 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19219])).
% 2.26/2.38 tff(19231,plain,
% 2.26/2.38 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e1))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19230])).
% 2.26/2.38 tff(19232,plain,
% 2.26/2.38 (~(op(e0, e2) = e1)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[2736, 19231])).
% 2.26/2.38 tff(19233,plain,
% 2.26/2.38 (op(e0, e1) = e1),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[384, 19232, 19229, 121])).
% 2.26/2.38 tff(19234,plain,
% 2.26/2.38 (op(e2, op(e0, e1)) = op(e2, e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19233])).
% 2.26/2.38 tff(19235,plain,
% 2.26/2.38 (op(e2, op(e0, e1)) = e2),
% 2.26/2.38 inference(transitivity,[status(thm)],[19234, 19224])).
% 2.26/2.38 tff(19236,plain,
% 2.26/2.38 (op(e3, op(e2, e2)) = op(e3, e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19219])).
% 2.26/2.38 tff(19237,plain,
% 2.26/2.38 (op(e3, op(e2, e2)) = e3),
% 2.26/2.38 inference(transitivity,[status(thm)],[19236, 19177])).
% 2.26/2.38 tff(19238,plain,
% 2.26/2.38 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[12593, 19237])).
% 2.26/2.38 tff(19239,plain,
% 2.26/2.38 (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5367, 19238, 19210, 19169, 19198, 19154, 19218, 19159, 19151, 19131, 19163, 19187, 19206, 19138, 19145])).
% 2.26/2.38 tff(19240,plain,
% 2.26/2.38 (~(op(e2, op(e0, e1)) = e2)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[9902, 19239])).
% 2.26/2.38 tff(19241,plain,
% 2.26/2.38 ($false),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[19240, 19235])).
% 2.26/2.38 tff(19242,plain,((op(e0, e3) = e1) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e0, e1) = e0) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.38 tff(19243,plain,
% 2.26/2.38 (op(e0, e3) = e1),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[19242, 2527, 76, 17, 68, 3849, 82])).
% 2.26/2.38 tff(19244,plain,
% 2.26/2.38 (op(e0, e2) = e3),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5000, 19243, 3849, 2527])).
% 2.26/2.38 tff(19245,plain,
% 2.26/2.38 (e3 = op(e0, e2)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19244])).
% 2.26/2.38 tff(19246,plain,
% 2.26/2.38 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19243])).
% 2.26/2.38 tff(19247,plain,
% 2.26/2.38 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19246, 18])).
% 2.26/2.38 tff(19248,plain,
% 2.26/2.38 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19247])).
% 2.26/2.38 tff(19249,plain,
% 2.26/2.38 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19248])).
% 2.26/2.38 tff(19250,plain,
% 2.26/2.38 (~(op(e0, e3) = e0)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[26, 19249])).
% 2.26/2.38 tff(19251,plain,
% 2.26/2.38 ((e0 = e3) <=> (e0 = op(e0, e2))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19245])).
% 2.26/2.38 tff(19252,plain,
% 2.26/2.38 ((e0 = e3) <=> (op(e0, e2) = e0)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19251, 10200])).
% 2.26/2.38 tff(19253,plain,
% 2.26/2.38 ((~(e0 = e3)) <=> (~(op(e0, e2) = e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19252])).
% 2.26/2.38 tff(19254,plain,
% 2.26/2.38 (~(op(e0, e2) = e0)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[181, 19253])).
% 2.26/2.38 tff(19255,plain,
% 2.26/2.38 (op(e0, e0) = e0),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[3976, 19254, 3849, 19250])).
% 2.26/2.38 tff(19256,plain,
% 2.26/2.38 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19243])).
% 2.26/2.38 tff(19257,plain,
% 2.26/2.38 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19256])).
% 2.26/2.38 tff(19258,plain,
% 2.26/2.38 (~(op(e0, e1) = e1)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[818, 19257])).
% 2.26/2.38 tff(19259,plain,
% 2.26/2.38 (op(e0, e1) = e2),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[829, 19258, 3849, 2527])).
% 2.26/2.38 tff(19260,plain,
% 2.26/2.38 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19259])).
% 2.26/2.38 tff(19261,plain,
% 2.26/2.38 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.26/2.38 inference(symmetry,[status(thm)],[19260])).
% 2.26/2.38 tff(19262,plain,
% 2.26/2.38 ((op(e1, e0) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19261, 596])).
% 2.26/2.38 tff(19263,plain,
% 2.26/2.38 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19262])).
% 2.26/2.38 tff(19264,plain,
% 2.26/2.38 (~(op(e0, e1) = op(e1, e0))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[19180, 19263])).
% 2.26/2.38 tff(19265,plain,
% 2.26/2.38 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[609, 19264])).
% 2.26/2.38 tff(19266,plain,
% 2.26/2.38 ((~(op(e1, e0) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19261])).
% 2.26/2.38 tff(19267,plain,
% 2.26/2.38 (~(op(e1, e0) = op(e0, e1))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[19180, 19266])).
% 2.26/2.38 tff(19268,plain,
% 2.26/2.38 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[613, 19267])).
% 2.26/2.38 tff(19269,assumption,(op(e0, e0) = e0), introduced(assumption)).
% 2.26/2.38 tff(19270,plain,
% 2.26/2.38 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19269])).
% 2.26/2.38 tff(19271,plain,
% 2.26/2.38 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19270, 16741])).
% 2.26/2.38 tff(19272,plain,
% 2.26/2.38 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19271])).
% 2.26/2.38 tff(19273,plain,
% 2.26/2.38 (~(op(e1, e0) = e0)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[2471, 19272])).
% 2.26/2.38 tff(19274,plain,
% 2.26/2.38 (op(e3, e3) = e3),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[480, 124, 6613, 11546])).
% 2.26/2.38 tff(19275,plain,
% 2.26/2.38 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19274])).
% 2.26/2.38 tff(19276,plain,
% 2.26/2.38 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19275])).
% 2.26/2.38 tff(19277,plain,
% 2.26/2.38 (~(op(e3, e1) = e3)),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[437, 19276])).
% 2.26/2.38 tff(19278,plain,
% 2.26/2.38 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19274])).
% 2.26/2.38 tff(19279,plain,
% 2.26/2.38 (op(e3, op(e3, e3)) = e3),
% 2.26/2.38 inference(transitivity,[status(thm)],[19278, 19274])).
% 2.26/2.38 tff(19280,plain,
% 2.26/2.38 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[6277, 19279])).
% 2.26/2.38 tff(19281,plain,
% 2.26/2.38 (op(e2, e3) = e0),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[206, 124, 6598, 76])).
% 2.26/2.38 tff(19282,plain,
% 2.26/2.38 (op(e0, op(e2, e3)) = op(e0, e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19281])).
% 2.26/2.38 tff(19283,plain,
% 2.26/2.38 (op(e0, op(e2, e3)) = e0),
% 2.26/2.38 inference(transitivity,[status(thm)],[19282, 19269])).
% 2.26/2.38 tff(19284,plain,
% 2.26/2.38 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[13359, 19283])).
% 2.26/2.38 tff(19285,plain,
% 2.26/2.38 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19269])).
% 2.26/2.38 tff(19286,plain,
% 2.26/2.38 (op(e0, op(e0, e0)) = e0),
% 2.26/2.38 inference(transitivity,[status(thm)],[19285, 19269])).
% 2.26/2.38 tff(19287,plain,
% 2.26/2.38 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5598, 19286])).
% 2.26/2.38 tff(19288,plain,
% 2.26/2.38 (op(e3, op(e0, e2)) = op(e3, e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[7826])).
% 2.26/2.38 tff(19289,plain,
% 2.26/2.38 ((op(e3, op(e0, e2)) = e3) <=> (op(e3, e3) = e3)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19288])).
% 2.26/2.38 tff(19290,plain,
% 2.26/2.38 ((op(e3, e3) = e3) <=> (op(e3, op(e0, e2)) = e3)),
% 2.26/2.38 inference(symmetry,[status(thm)],[19289])).
% 2.26/2.38 tff(19291,plain,
% 2.26/2.38 (op(e3, op(e0, e2)) = e3),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[19274, 19290])).
% 2.26/2.38 tff(19292,plain,
% 2.26/2.38 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[5635, 19291])).
% 2.26/2.38 tff(19293,plain,
% 2.26/2.38 (op(e1, e2) = e0),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[1830, 84, 19058, 2167])).
% 2.26/2.38 tff(19294,plain,
% 2.26/2.38 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e0)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19293])).
% 2.26/2.38 tff(19295,plain,
% 2.26/2.38 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 2.26/2.38 inference(symmetry,[status(thm)],[19294])).
% 2.26/2.38 tff(19296,plain,
% 2.26/2.38 ((~(op(e2, e1) = e0)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19295])).
% 2.26/2.38 tff(19297,plain,
% 2.26/2.38 (~(op(e2, e1) = op(e1, e2))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[11150, 19296])).
% 2.26/2.38 tff(19298,plain,
% 2.26/2.38 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[557, 19297])).
% 2.26/2.38 tff(19299,plain,
% 2.26/2.38 ((op(e2, e1) = e0) <=> (op(e1, e2) = op(e2, e1))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19295, 531])).
% 2.26/2.38 tff(19300,plain,
% 2.26/2.38 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19299])).
% 2.26/2.38 tff(19301,plain,
% 2.26/2.38 (~(op(e1, e2) = op(e2, e1))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[11150, 19300])).
% 2.26/2.38 tff(19302,plain,
% 2.26/2.38 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[539, 19301])).
% 2.26/2.38 tff(19303,plain,
% 2.26/2.38 ((op(e1, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19293])).
% 2.26/2.38 tff(19304,plain,
% 2.26/2.38 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 2.26/2.38 inference(transitivity,[status(thm)],[19303, 4959])).
% 2.26/2.38 tff(19305,plain,
% 2.26/2.38 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19304, 9730, 395])).
% 2.26/2.38 tff(19306,plain,
% 2.26/2.38 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19305])).
% 2.26/2.38 tff(19307,plain,
% 2.26/2.38 (~(op(e2, e3) = op(e3, e2))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[2292, 19306])).
% 2.26/2.38 tff(19308,plain,
% 2.26/2.38 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[430, 19307])).
% 2.26/2.38 tff(19309,plain,
% 2.26/2.38 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 2.26/2.38 inference(monotonicity,[status(thm)],[264])).
% 2.26/2.38 tff(19310,plain,
% 2.26/2.38 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.26/2.38 inference(symmetry,[status(thm)],[19309])).
% 2.26/2.38 tff(19311,plain,
% 2.26/2.38 ((~(op(e3, e1) = e2)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19310])).
% 2.26/2.38 tff(19312,plain,
% 2.26/2.38 (~(op(e3, e1) = op(e1, e3))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[82, 19311])).
% 2.26/2.38 tff(19313,plain,
% 2.26/2.38 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.26/2.38 inference(unit_resolution,[status(thm)],[6362, 19312])).
% 2.26/2.38 tff(19314,plain,
% 2.26/2.38 ((op(e3, e1) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.26/2.38 inference(transitivity,[status(thm)],[19310, 6290])).
% 2.26/2.38 tff(19315,plain,
% 2.26/2.38 ((~(op(e3, e1) = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.26/2.38 inference(monotonicity,[status(thm)],[19314])).
% 2.26/2.38 tff(19316,plain,
% 2.26/2.38 (~(op(e1, e3) = op(e3, e1))),
% 2.26/2.38 inference(modus_ponens,[status(thm)],[82, 19315])).
% 2.26/2.38 tff(19317,plain,
% 2.26/2.39 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[6307, 19316])).
% 2.26/2.39 tff(19318,plain,
% 2.26/2.39 ((op(e1, e2) = e1) <=> (e0 = e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19293])).
% 2.26/2.39 tff(19319,plain,
% 2.26/2.39 ((e0 = e1) <=> (op(e1, e2) = e1)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19318])).
% 2.26/2.39 tff(19320,plain,
% 2.26/2.39 ((~(e0 = e1)) <=> (~(op(e1, e2) = e1))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19319])).
% 2.26/2.39 tff(19321,plain,
% 2.26/2.39 (~(op(e1, e2) = e1)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[26, 19320])).
% 2.26/2.39 tff(19322,plain,
% 2.26/2.39 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[7826])).
% 2.26/2.39 tff(19323,plain,
% 2.26/2.39 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19322, 1314])).
% 2.26/2.39 tff(19324,plain,
% 2.26/2.39 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19323])).
% 2.26/2.39 tff(19325,plain,
% 2.26/2.39 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19324])).
% 2.26/2.39 tff(19326,plain,
% 2.26/2.39 (~(op(e0, e2) = e2)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[1321, 19325])).
% 2.26/2.39 tff(19327,plain,
% 2.26/2.39 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e0, e2))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[7827])).
% 2.26/2.39 tff(19328,plain,
% 2.26/2.39 ((op(e1, e2) = e3) <=> (op(e0, e2) = op(e1, e2))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19327, 8060])).
% 2.26/2.39 tff(19329,plain,
% 2.26/2.39 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19328])).
% 2.26/2.39 tff(19330,plain,
% 2.26/2.39 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19329])).
% 2.26/2.39 tff(19331,plain,
% 2.26/2.39 (~(op(e1, e2) = e3)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[6205, 19330])).
% 2.26/2.39 tff(19332,plain,
% 2.26/2.39 (op(e1, e0) = e3),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[247, 1291, 19331, 1080])).
% 2.26/2.39 tff(19333,plain,
% 2.26/2.39 (op(e1, e0) = op(e0, e2)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19332, 7827])).
% 2.26/2.39 tff(19334,plain,
% 2.26/2.39 ((op(e1, e0) = op(e2, e0)) <=> (op(e0, e2) = op(e2, e0))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19333])).
% 2.26/2.39 tff(19335,plain,
% 2.26/2.39 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = op(e0, e2))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19334, 6336])).
% 2.26/2.39 tff(19336,plain,
% 2.26/2.39 ((op(e1, e0) = op(e2, e0)) <=> (op(e0, e2) = op(e2, e0))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19335, 6337])).
% 2.26/2.39 tff(19337,plain,
% 2.26/2.39 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19336])).
% 2.26/2.39 tff(19338,plain,
% 2.26/2.39 (~(op(e0, e2) = op(e2, e0))),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[756, 19337])).
% 2.26/2.39 tff(19339,plain,
% 2.26/2.39 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[6347, 19338])).
% 2.26/2.39 tff(19340,plain,
% 2.26/2.39 (op(e1, e1) = e1),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[630, 1291, 68, 84])).
% 2.26/2.39 tff(19341,plain,
% 2.26/2.39 (op(e1, op(e1, e1)) = op(e1, e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19340])).
% 2.26/2.39 tff(19342,plain,
% 2.26/2.39 (op(e1, op(e1, e1)) = e1),
% 2.26/2.39 inference(transitivity,[status(thm)],[19341, 19340])).
% 2.26/2.39 tff(19343,plain,
% 2.26/2.39 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[5678, 19342])).
% 2.26/2.39 tff(19344,plain,
% 2.26/2.39 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19])).
% 2.26/2.39 tff(19345,plain,
% 2.26/2.39 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19344])).
% 2.26/2.39 tff(19346,plain,
% 2.26/2.39 (op(e3, e0) = e2),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[15971, 2386, 82])).
% 2.26/2.39 tff(19347,plain,
% 2.26/2.39 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19346])).
% 2.26/2.39 tff(19348,plain,
% 2.26/2.39 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19347, 69])).
% 2.26/2.39 tff(19349,plain,
% 2.26/2.39 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19348])).
% 2.26/2.39 tff(19350,plain,
% 2.26/2.39 ((e1 = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19349, 19345, 453])).
% 2.26/2.39 tff(19351,plain,
% 2.26/2.39 ((~(e1 = e2)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19350])).
% 2.26/2.39 tff(19352,plain,
% 2.26/2.39 (~(op(e0, e3) = op(e3, e0))),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[708, 19351])).
% 2.26/2.39 tff(19353,plain,
% 2.26/2.39 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[496, 19352])).
% 2.26/2.39 tff(19354,plain,
% 2.26/2.39 (op(e2, e2) = e2),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[1151, 2386, 3785, 6229])).
% 2.26/2.39 tff(19355,plain,
% 2.26/2.39 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19354])).
% 2.26/2.39 tff(19356,plain,
% 2.26/2.39 (op(e2, op(e2, e2)) = e2),
% 2.26/2.39 inference(transitivity,[status(thm)],[19355, 19354])).
% 2.26/2.39 tff(19357,plain,
% 2.26/2.39 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[528, 19356])).
% 2.26/2.39 tff(19358,plain,
% 2.26/2.39 ($false),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[5367, 19357, 19353, 5669, 5675, 6689, 5674, 5667, 5511, 5668, 5673, 5671, 5681, 6688, 5680, 9846])).
% 2.26/2.39 tff(19359,plain,((op(e3, e2) = e2) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e0, e3) = e1)) | (op(e1, e2) = e2) | (op(e0, e2) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.39 tff(19360,plain,
% 2.26/2.39 (op(e3, e2) = e2),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[19359, 19343, 5675, 5669, 5674, 5667, 5511, 5668, 5673, 5671, 5681, 6688, 5680, 19339, 19, 3785, 19326, 82])).
% 2.26/2.39 tff(19361,plain,
% 2.26/2.39 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19360])).
% 2.26/2.39 tff(19362,plain,
% 2.26/2.39 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19361, 69])).
% 2.26/2.39 tff(19363,plain,
% 2.26/2.39 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19362])).
% 2.26/2.39 tff(19364,plain,
% 2.26/2.39 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19363])).
% 2.26/2.39 tff(19365,plain,
% 2.26/2.39 (~(op(e3, e2) = e1)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[708, 19364])).
% 2.26/2.39 tff(19366,plain,
% 2.26/2.39 (op(e2, e2) = e1),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[1613, 19365, 11315, 4515])).
% 2.26/2.39 tff(19367,plain,
% 2.26/2.39 (e1 = op(e2, e2)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[19366, 317])).
% 2.26/2.39 tff(19368,plain,
% 2.26/2.39 (op(e2, op(e2, e2)) = op(e2, e1)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19366])).
% 2.26/2.39 tff(19369,plain,
% 2.26/2.39 (op(e2, e1) = op(e2, op(e2, e2))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19368])).
% 2.26/2.39 tff(19370,plain,
% 2.26/2.39 (op(e2, e1) = e3),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[1730, 1291, 2527, 2839])).
% 2.26/2.39 tff(19371,plain,
% 2.26/2.39 (e3 = op(e2, e1)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19370])).
% 2.26/2.39 tff(19372,plain,
% 2.26/2.39 (e3 = op(e2, op(e2, e2))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19371, 19369])).
% 2.26/2.39 tff(19373,plain,
% 2.26/2.39 (op(e2, op(e2, e2)) = op(e0, e2)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19368, 19370, 7827])).
% 2.26/2.39 tff(19374,plain,
% 2.26/2.39 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e0, e2))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19373])).
% 2.26/2.39 tff(19375,plain,
% 2.26/2.39 (op(e2, op(e0, e2)) = op(e2, op(e2, op(e2, e2)))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19374])).
% 2.26/2.39 tff(19376,plain,
% 2.26/2.39 (op(e2, op(e0, e2)) = op(e2, e3)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[7826])).
% 2.26/2.39 tff(19377,plain,
% 2.26/2.39 (op(e2, e3) = op(e2, op(e0, e2))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19376])).
% 2.26/2.39 tff(19378,plain,
% 2.26/2.39 (e0 = op(e2, op(e2, op(e2, e2)))),
% 2.26/2.39 inference(transitivity,[status(thm)],[252, 19377, 19375])).
% 2.26/2.39 tff(19379,plain,
% 2.26/2.39 ($false),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[334, 19378, 19372, 19367])).
% 2.26/2.39 tff(19380,plain,((op(e1, e1) = e3) | (~(op(e2, e3) = e0)) | (~(op(e0, e2) = e3)) | (op(e1, e2) = e1) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~(op(e0, e3) = e1)) | (op(e1, e2) = e2) | (op(e3, e1) = e2) | (op(e0, e1) = e3) | (op(e3, e1) = e3) | (op(e1, e1) = e2) | (op(e1, e1) = e0) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.39 tff(19381,plain,
% 2.26/2.39 (op(e1, e1) = e3),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[19380, 19321, 7826, 251, 5675, 19317, 5674, 5667, 19313, 19308, 19302, 5671, 5681, 6688, 19298, 19, 19087, 82, 2527, 2839, 68, 84, 6613])).
% 2.26/2.39 tff(19382,plain,
% 2.26/2.39 (e3 = op(e1, e1)),
% 2.26/2.39 inference(modus_ponens,[status(thm)],[19381, 1740])).
% 2.26/2.39 tff(19383,plain,
% 2.26/2.39 (op(e1, e1) = op(e0, e2)),
% 2.26/2.39 inference(transitivity,[status(thm)],[19381, 7827])).
% 2.26/2.39 tff(19384,plain,
% 2.26/2.39 (op(e1, op(e1, e1)) = op(e1, op(e0, e2))),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19383])).
% 2.26/2.39 tff(19385,plain,
% 2.26/2.39 (op(e1, op(e0, e2)) = op(e1, op(e1, e1))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19384])).
% 2.26/2.39 tff(19386,plain,
% 2.26/2.39 (op(e1, op(e0, e2)) = op(e1, e3)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[7826])).
% 2.26/2.39 tff(19387,plain,
% 2.26/2.39 (op(e1, e3) = op(e1, op(e0, e2))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19386])).
% 2.26/2.39 tff(19388,plain,
% 2.26/2.39 (e2 = op(e1, op(e1, e1))),
% 2.26/2.39 inference(transitivity,[status(thm)],[265, 19387, 19385])).
% 2.26/2.39 tff(19389,plain,
% 2.26/2.39 (op(e1, op(e1, e1)) = e2),
% 2.26/2.39 inference(transitivity,[status(thm)],[19384, 19386, 264])).
% 2.26/2.39 tff(19390,plain,
% 2.26/2.39 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 2.26/2.39 inference(monotonicity,[status(thm)],[19389])).
% 2.26/2.39 tff(19391,plain,
% 2.26/2.39 (op(e1, e2) = op(e1, op(e1, op(e1, e1)))),
% 2.26/2.39 inference(symmetry,[status(thm)],[19390])).
% 2.26/2.39 tff(19392,plain,
% 2.26/2.39 (e0 = op(e1, e2)),
% 2.26/2.39 inference(symmetry,[status(thm)],[19293])).
% 2.26/2.39 tff(19393,plain,
% 2.26/2.39 (e0 = op(e1, op(e1, op(e1, e1)))),
% 2.26/2.39 inference(transitivity,[status(thm)],[19392, 19391])).
% 2.26/2.39 tff(19394,plain,
% 2.26/2.39 ($false),
% 2.26/2.39 inference(unit_resolution,[status(thm)],[1753, 19393, 19388, 19382])).
% 2.26/2.39 tff(19395,plain,((op(e1, e1) = e0) | (~(op(e1, e3) = e2)) | (~(op(e0, e2) = e3)) | (~(op(e2, e3) = e0)) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~(op(e0, e3) = e1)) | (op(e3, e1) = e2) | (op(e0, e1) = e3) | (op(e3, e1) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.40 tff(19396,plain,
% 2.26/2.40 (op(e1, e1) = e0),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[19395, 19281, 7826, 264, 5675, 19292, 19287, 19284, 5681, 19280, 19, 82, 2527, 19277, 68, 19273])).
% 2.26/2.40 tff(19397,plain,
% 2.26/2.40 ((op(e0, e2) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[7826])).
% 2.26/2.40 tff(19398,plain,
% 2.26/2.40 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.26/2.40 inference(transitivity,[status(thm)],[19397, 532])).
% 2.26/2.40 tff(19399,plain,
% 2.26/2.40 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19398])).
% 2.26/2.40 tff(19400,plain,
% 2.26/2.40 (~(op(e1, e2) = e3)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[6205, 19399])).
% 2.26/2.40 tff(19401,plain,
% 2.26/2.40 (~(op(e1, e0) = e3)),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[278, 19396, 264, 19281])).
% 2.26/2.40 tff(19402,plain,
% 2.26/2.40 (op(e1, e1) = e3),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[247, 19401, 19400, 6613])).
% 2.26/2.40 tff(19403,plain,
% 2.26/2.40 (e3 = op(e1, e1)),
% 2.26/2.40 inference(symmetry,[status(thm)],[19402])).
% 2.26/2.40 tff(19404,plain,
% 2.26/2.40 (op(e0, e2) = e0),
% 2.26/2.40 inference(transitivity,[status(thm)],[7826, 19403, 19396])).
% 2.26/2.40 tff(19405,plain,
% 2.26/2.40 ((e0 = e3) <=> (e0 = op(e0, e2))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[7827])).
% 2.26/2.40 tff(19406,plain,
% 2.26/2.40 ((e0 = e3) <=> (op(e0, e2) = e0)),
% 2.26/2.40 inference(transitivity,[status(thm)],[19405, 10200])).
% 2.26/2.40 tff(19407,plain,
% 2.26/2.40 ((~(e0 = e3)) <=> (~(op(e0, e2) = e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19406])).
% 2.26/2.40 tff(19408,plain,
% 2.26/2.40 (~(op(e0, e2) = e0)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[181, 19407])).
% 2.26/2.40 tff(19409,plain,
% 2.26/2.40 ($false),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[19408, 19404])).
% 2.26/2.40 tff(19410,plain,((op(e2, e3) = e3) | (~(op(e0, e2) = e3)) | (~(op(e1, e3) = e2)) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~(op(e0, e3) = e1)) | (op(e3, e1) = e2) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (~(op(e0, e0) = e0)) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.26/2.40 tff(19411,plain,
% 2.26/2.40 (op(e2, e3) = e3),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[19410, 19244, 19002, 19268, 19265, 19243, 82, 2527, 68, 19255, 76])).
% 2.26/2.40 tff(19412,plain,
% 2.26/2.40 (op(e2, e3) = op(e0, e2)),
% 2.26/2.40 inference(transitivity,[status(thm)],[19411, 19245])).
% 2.26/2.40 tff(19413,plain,
% 2.26/2.40 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19412])).
% 2.26/2.40 tff(19414,plain,
% 2.26/2.40 ((op(e2, e0) = op(e2, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 2.26/2.40 inference(transitivity,[status(thm)],[19413, 6337])).
% 2.26/2.40 tff(19415,plain,
% 2.26/2.40 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19414])).
% 2.26/2.40 tff(19416,plain,
% 2.26/2.40 (~(op(e0, e2) = op(e2, e0))),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[989, 19415])).
% 2.26/2.40 tff(19417,plain,
% 2.26/2.40 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[6347, 19416])).
% 2.26/2.40 tff(19418,plain,
% 2.26/2.40 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19255])).
% 2.26/2.40 tff(19419,plain,
% 2.26/2.40 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 2.26/2.40 inference(transitivity,[status(thm)],[19418, 16741])).
% 2.26/2.40 tff(19420,plain,
% 2.26/2.40 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19419])).
% 2.26/2.40 tff(19421,plain,
% 2.26/2.40 (~(op(e1, e0) = e0)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[2471, 19420])).
% 2.26/2.40 tff(19422,plain,
% 2.26/2.40 ((op(e0, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19255])).
% 2.26/2.40 tff(19423,plain,
% 2.26/2.40 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 2.26/2.40 inference(transitivity,[status(thm)],[19422, 4499])).
% 2.26/2.40 tff(19424,plain,
% 2.26/2.40 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19423])).
% 2.26/2.40 tff(19425,plain,
% 2.26/2.40 (~(op(e2, e0) = e0)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[359, 19424])).
% 2.26/2.40 tff(19426,plain,
% 2.26/2.40 ((op(e2, e3) = e0) <=> (op(e0, e2) = e0)),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19412])).
% 2.26/2.40 tff(19427,plain,
% 2.26/2.40 ((op(e0, e2) = e0) <=> (op(e2, e3) = e0)),
% 2.26/2.40 inference(symmetry,[status(thm)],[19426])).
% 2.26/2.40 tff(19428,plain,
% 2.26/2.40 ((~(op(e0, e2) = e0)) <=> (~(op(e2, e3) = e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19427])).
% 2.26/2.40 tff(19429,plain,
% 2.26/2.40 (~(op(e2, e3) = e0)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[19254, 19428])).
% 2.26/2.40 tff(19430,plain,
% 2.26/2.40 (op(e2, e1) = e0),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[2311, 19429, 17, 19425])).
% 2.26/2.40 tff(19431,plain,
% 2.26/2.40 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e0)),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19430])).
% 2.26/2.40 tff(19432,plain,
% 2.26/2.40 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e0))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19431])).
% 2.26/2.40 tff(19433,plain,
% 2.26/2.40 (~(op(e1, e1) = e0)),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[225, 19432])).
% 2.26/2.40 tff(19434,plain,
% 2.26/2.40 (op(e1, e2) = e0),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[1830, 19433, 19012, 19421])).
% 2.26/2.40 tff(19435,plain,
% 2.26/2.40 (op(e0, op(e1, e2)) = op(e0, e0)),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19434])).
% 2.26/2.40 tff(19436,plain,
% 2.26/2.40 (op(e0, op(e1, e2)) = e0),
% 2.26/2.40 inference(transitivity,[status(thm)],[19435, 19255])).
% 2.26/2.40 tff(19437,plain,
% 2.26/2.40 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[6398, 19436])).
% 2.26/2.40 tff(19438,plain,
% 2.26/2.40 (op(e3, e3) = e0),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[1098, 19429, 19012, 19250])).
% 2.26/2.40 tff(19439,plain,
% 2.26/2.40 (op(e0, op(e3, e3)) = op(e0, e0)),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19438])).
% 2.26/2.40 tff(19440,plain,
% 2.26/2.40 (op(e0, op(e3, e3)) = e0),
% 2.26/2.40 inference(transitivity,[status(thm)],[19439, 19255])).
% 2.26/2.40 tff(19441,plain,
% 2.26/2.40 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[392, 19440])).
% 2.26/2.40 tff(19442,plain,
% 2.26/2.40 ((op(e3, e2) = op(e0, e2)) <=> (op(e0, e2) = op(e3, e2))),
% 2.26/2.40 inference(commutativity,[status(thm)],[])).
% 2.26/2.40 tff(19443,plain,
% 2.26/2.40 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = op(e0, e2))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19412])).
% 2.26/2.40 tff(19444,plain,
% 2.26/2.40 ((op(e3, e2) = op(e2, e3)) <=> (op(e0, e2) = op(e3, e2))),
% 2.26/2.40 inference(transitivity,[status(thm)],[19443, 19442])).
% 2.26/2.40 tff(19445,plain,
% 2.26/2.40 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.26/2.40 inference(symmetry,[status(thm)],[19444])).
% 2.26/2.40 tff(19446,plain,
% 2.26/2.40 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19445])).
% 2.26/2.40 tff(19447,plain,
% 2.26/2.40 (~(op(e3, e2) = op(e2, e3))),
% 2.26/2.40 inference(modus_ponens,[status(thm)],[1467, 19446])).
% 2.26/2.40 tff(19448,plain,
% 2.26/2.40 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.26/2.40 inference(unit_resolution,[status(thm)],[500, 19447])).
% 2.26/2.40 tff(19449,plain,
% 2.26/2.40 (op(e0, op(e2, e1)) = op(e0, e0)),
% 2.26/2.40 inference(monotonicity,[status(thm)],[19430])).
% 2.26/2.40 tff(19450,plain,
% 2.26/2.40 (op(e0, op(e2, e1)) = e0),
% 2.26/2.40 inference(transitivity,[status(thm)],[19449, 19255])).
% 2.30/2.40 tff(19451,plain,
% 2.30/2.40 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[13223, 19450])).
% 2.30/2.40 tff(19452,plain,
% 2.30/2.40 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.30/2.40 inference(transitivity,[status(thm)],[19445, 395])).
% 2.30/2.40 tff(19453,plain,
% 2.30/2.40 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19452])).
% 2.30/2.40 tff(19454,plain,
% 2.30/2.40 (~(op(e2, e3) = op(e3, e2))),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[1467, 19453])).
% 2.30/2.40 tff(19455,plain,
% 2.30/2.40 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[430, 19454])).
% 2.30/2.40 tff(19456,plain,
% 2.30/2.40 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19255])).
% 2.30/2.40 tff(19457,plain,
% 2.30/2.40 (op(e0, op(e0, e0)) = e0),
% 2.30/2.40 inference(transitivity,[status(thm)],[19456, 19255])).
% 2.30/2.40 tff(19458,plain,
% 2.30/2.40 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[5598, 19457])).
% 2.30/2.40 tff(19459,plain,
% 2.30/2.40 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19413])).
% 2.30/2.40 tff(19460,plain,
% 2.30/2.40 (~(op(e2, e0) = op(e0, e2))),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[989, 19459])).
% 2.30/2.40 tff(19461,plain,
% 2.30/2.40 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[6358, 19460])).
% 2.30/2.40 tff(19462,plain,
% 2.30/2.40 (~(op(e1, e1) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[6918, 19434, 19002, 19411])).
% 2.30/2.40 tff(19463,plain,
% 2.30/2.40 (op(e1, e1) = e1),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[630, 19462, 68, 19433])).
% 2.30/2.40 tff(19464,plain,
% 2.30/2.40 (op(e1, op(e1, e1)) = op(e1, e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19463])).
% 2.30/2.40 tff(19465,plain,
% 2.30/2.40 (op(e1, op(e1, e1)) = e1),
% 2.30/2.40 inference(transitivity,[status(thm)],[19464, 19463])).
% 2.30/2.40 tff(19466,plain,
% 2.30/2.40 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[5678, 19465])).
% 2.30/2.40 tff(19467,plain,
% 2.30/2.40 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19411])).
% 2.30/2.40 tff(19468,plain,
% 2.30/2.40 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19467])).
% 2.30/2.40 tff(19469,plain,
% 2.30/2.40 (~(op(e2, e1) = e3)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[197, 19468])).
% 2.30/2.40 tff(19470,plain,
% 2.30/2.40 (op(e3, e1) = e3),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[1730, 19462, 2527, 19469])).
% 2.30/2.40 tff(19471,plain,
% 2.30/2.40 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19463])).
% 2.30/2.40 tff(19472,plain,
% 2.30/2.40 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19471, 7793])).
% 2.30/2.40 tff(19473,plain,
% 2.30/2.40 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19472])).
% 2.30/2.40 tff(19474,plain,
% 2.30/2.40 (~(op(e3, e1) = e1)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[945, 19473])).
% 2.30/2.40 tff(19475,plain,
% 2.30/2.40 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19243])).
% 2.30/2.40 tff(19476,plain,
% 2.30/2.40 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19475, 657])).
% 2.30/2.40 tff(19477,plain,
% 2.30/2.40 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19476])).
% 2.30/2.40 tff(19478,plain,
% 2.30/2.40 (~(op(e3, e3) = e1)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[1077, 19477])).
% 2.30/2.40 tff(19479,plain,
% 2.30/2.40 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19244])).
% 2.30/2.40 tff(19480,plain,
% 2.30/2.40 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19479, 1314])).
% 2.30/2.40 tff(19481,plain,
% 2.30/2.40 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 2.30/2.40 inference(symmetry,[status(thm)],[19480])).
% 2.30/2.40 tff(19482,plain,
% 2.30/2.40 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19481])).
% 2.30/2.40 tff(19483,plain,
% 2.30/2.40 (~(op(e0, e2) = e2)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[1321, 19482])).
% 2.30/2.40 tff(19484,plain,
% 2.30/2.40 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19002])).
% 2.30/2.40 tff(19485,plain,
% 2.30/2.40 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19484])).
% 2.30/2.40 tff(19486,plain,
% 2.30/2.40 (~(op(e1, e2) = e2)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[1850, 19485])).
% 2.30/2.40 tff(19487,plain,
% 2.30/2.40 (op(e3, e2) = e2),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[19359, 19466, 19268, 19210, 19461, 19458, 19159, 19455, 19451, 19448, 19265, 19441, 19437, 19417, 19243, 19486, 19483, 82])).
% 2.30/2.40 tff(19488,plain,
% 2.30/2.40 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19487])).
% 2.30/2.40 tff(19489,plain,
% 2.30/2.40 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19488, 69])).
% 2.30/2.40 tff(19490,plain,
% 2.30/2.40 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 2.30/2.40 inference(symmetry,[status(thm)],[19489])).
% 2.30/2.40 tff(19491,plain,
% 2.30/2.40 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19490])).
% 2.30/2.40 tff(19492,plain,
% 2.30/2.40 (~(op(e3, e2) = e1)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[708, 19491])).
% 2.30/2.40 tff(19493,plain,
% 2.30/2.40 (op(e3, e0) = e1),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[939, 19492, 19478, 19474])).
% 2.30/2.40 tff(19494,plain,
% 2.30/2.40 (op(e3, op(e3, e0)) = op(e3, e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19493])).
% 2.30/2.40 tff(19495,plain,
% 2.30/2.40 (op(e3, op(e3, e0)) = e3),
% 2.30/2.40 inference(transitivity,[status(thm)],[19494, 19470])).
% 2.30/2.40 tff(19496,plain,
% 2.30/2.40 (((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)) | (~(op(e3, op(e3, e0)) = e3))),
% 2.30/2.40 inference(tautology,[status(thm)],[])).
% 2.30/2.40 tff(19497,plain,
% 2.30/2.40 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[19496, 19495])).
% 2.30/2.40 tff(19498,plain,
% 2.30/2.40 ((op(e1, e2) = e1) <=> (e0 = e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19434])).
% 2.30/2.40 tff(19499,plain,
% 2.30/2.40 ((e0 = e1) <=> (op(e1, e2) = e1)),
% 2.30/2.40 inference(symmetry,[status(thm)],[19498])).
% 2.30/2.40 tff(19500,plain,
% 2.30/2.40 ((~(e0 = e1)) <=> (~(op(e1, e2) = e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19499])).
% 2.30/2.40 tff(19501,plain,
% 2.30/2.40 (~(op(e1, e2) = e1)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[26, 19500])).
% 2.30/2.40 tff(19502,plain,
% 2.30/2.40 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19243])).
% 2.30/2.40 tff(19503,plain,
% 2.30/2.40 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19502])).
% 2.30/2.40 tff(19504,plain,
% 2.30/2.40 (~(op(e0, e2) = e1)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[918, 19503])).
% 2.30/2.40 tff(19505,plain,
% 2.30/2.40 (op(e2, e2) = e1),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[1613, 19492, 19504, 19501])).
% 2.30/2.40 tff(19506,plain,
% 2.30/2.40 (op(e1, op(e2, e2)) = op(e1, e1)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19505])).
% 2.30/2.40 tff(19507,plain,
% 2.30/2.40 (op(e1, op(e2, e2)) = e1),
% 2.30/2.40 inference(transitivity,[status(thm)],[19506, 19463])).
% 2.30/2.40 tff(19508,plain,
% 2.30/2.40 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[6714, 19507])).
% 2.30/2.40 tff(19509,plain,
% 2.30/2.40 ($false),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[5367, 19508, 19497, 19210, 19268, 19466, 19461, 19458, 19159, 19455, 19451, 19448, 19265, 19441, 19437, 19417])).
% 2.30/2.40 tff(19510,plain,((op(e0, e1) = e3) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.40 tff(19511,plain,
% 2.30/2.40 (op(e0, e1) = e3),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[19510, 3849, 68, 17, 76, 82])).
% 2.30/2.40 tff(19512,plain,
% 2.30/2.40 ((op(e0, e1) = e2) <=> (e3 = e2)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.40 tff(19513,plain,
% 2.30/2.40 ((op(e0, e1) = e2) <=> (e2 = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19512, 1314])).
% 2.30/2.40 tff(19514,plain,
% 2.30/2.40 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 2.30/2.40 inference(symmetry,[status(thm)],[19513])).
% 2.30/2.40 tff(19515,plain,
% 2.30/2.40 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19514])).
% 2.30/2.40 tff(19516,plain,
% 2.30/2.40 (~(op(e0, e1) = e2)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[1321, 19515])).
% 2.30/2.40 tff(19517,plain,
% 2.30/2.40 (op(e2, e1) = e2),
% 2.30/2.40 inference(unit_resolution,[status(thm)],[1993, 19516, 68, 82])).
% 2.30/2.40 tff(19518,plain,
% 2.30/2.40 ((op(e2, e1) = e0) <=> (e2 = e0)),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.40 tff(19519,plain,
% 2.30/2.40 ((op(e2, e1) = e0) <=> (e0 = e2)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19518, 1])).
% 2.30/2.40 tff(19520,plain,
% 2.30/2.40 ((e0 = e2) <=> (op(e2, e1) = e0)),
% 2.30/2.40 inference(symmetry,[status(thm)],[19519])).
% 2.30/2.40 tff(19521,plain,
% 2.30/2.40 ((~(e0 = e2)) <=> (~(op(e2, e1) = e0))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19520])).
% 2.30/2.40 tff(19522,plain,
% 2.30/2.40 (~(op(e2, e1) = e0)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[14, 19521])).
% 2.30/2.40 tff(19523,plain,
% 2.30/2.40 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.40 tff(19524,plain,
% 2.30/2.40 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19523, 396])).
% 2.30/2.40 tff(19525,plain,
% 2.30/2.40 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19524])).
% 2.30/2.40 tff(19526,plain,
% 2.30/2.40 (~(op(e3, e1) = e3)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[3046, 19525])).
% 2.30/2.40 tff(19527,plain,
% 2.30/2.40 ((op(e0, e1) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.40 tff(19528,plain,
% 2.30/2.40 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19527, 4221])).
% 2.30/2.40 tff(19529,plain,
% 2.30/2.40 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19528])).
% 2.30/2.40 tff(19530,plain,
% 2.30/2.40 (~(op(e0, e2) = e3)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[2102, 19529])).
% 2.30/2.40 tff(19531,plain,
% 2.30/2.40 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.40 tff(19532,plain,
% 2.30/2.40 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19531, 1262])).
% 2.30/2.40 tff(19533,plain,
% 2.30/2.40 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19532])).
% 2.30/2.40 tff(19534,plain,
% 2.30/2.40 (~(op(e2, e1) = e3)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[606, 19533])).
% 2.30/2.40 tff(19535,plain,
% 2.30/2.40 ((op(e0, e1) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.40 tff(19536,plain,
% 2.30/2.40 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.30/2.40 inference(transitivity,[status(thm)],[19535, 1364])).
% 2.30/2.40 tff(19537,plain,
% 2.30/2.40 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.30/2.40 inference(monotonicity,[status(thm)],[19536])).
% 2.30/2.40 tff(19538,plain,
% 2.30/2.40 (~(op(e0, e3) = e3)),
% 2.30/2.40 inference(modus_ponens,[status(thm)],[818, 19537])).
% 2.30/2.40 tff(19539,plain,
% 2.30/2.40 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.41 tff(19540,plain,
% 2.30/2.41 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19539, 1112])).
% 2.30/2.41 tff(19541,plain,
% 2.30/2.41 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19540])).
% 2.30/2.41 tff(19542,plain,
% 2.30/2.41 (~(op(e1, e1) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[792, 19541])).
% 2.30/2.41 tff(19543,plain,
% 2.30/2.41 (op(e0, e3) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[687, 121, 79, 661])).
% 2.30/2.41 tff(19544,plain,
% 2.30/2.41 (op(e3, op(e0, e3)) = op(e3, e0)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19543])).
% 2.30/2.41 tff(19545,plain,
% 2.30/2.41 (e0 = op(e0, e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19543])).
% 2.30/2.41 tff(19546,plain,
% 2.30/2.41 (e1 = op(e3, e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[10347])).
% 2.30/2.41 tff(19547,plain,
% 2.30/2.41 ((op(e3, e1) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19546])).
% 2.30/2.41 tff(19548,plain,
% 2.30/2.41 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19547])).
% 2.30/2.41 tff(19549,plain,
% 2.30/2.41 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19548])).
% 2.30/2.41 tff(19550,plain,
% 2.30/2.41 (~(op(e3, e1) = e1)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[437, 19549])).
% 2.30/2.41 tff(19551,plain,
% 2.30/2.41 (op(e3, e1) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[446, 19550, 82, 2839])).
% 2.30/2.41 tff(19552,plain,
% 2.30/2.41 (op(e3, e1) = op(e0, e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19551, 19545])).
% 2.30/2.41 tff(19553,plain,
% 2.30/2.41 (op(e3, op(e3, e1)) = op(e3, op(e0, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19552])).
% 2.30/2.41 tff(19554,plain,
% 2.30/2.41 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[10347])).
% 2.30/2.41 tff(19555,plain,
% 2.30/2.41 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19554])).
% 2.30/2.41 tff(19556,plain,
% 2.30/2.41 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19555, 19553, 19544])).
% 2.30/2.41 tff(19557,plain,
% 2.30/2.41 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19556])).
% 2.30/2.41 tff(19558,plain,
% 2.30/2.41 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19557, 5377])).
% 2.30/2.41 tff(19559,plain,
% 2.30/2.41 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19558])).
% 2.30/2.41 tff(19560,plain,
% 2.30/2.41 (e1 = op(e3, e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[10347, 658])).
% 2.30/2.41 tff(19561,plain,
% 2.30/2.41 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19554])).
% 2.30/2.41 tff(19562,plain,
% 2.30/2.41 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19561, 5470])).
% 2.30/2.41 tff(19563,plain,
% 2.30/2.41 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.30/2.41 inference(symmetry,[status(thm)],[19562])).
% 2.30/2.41 tff(19564,plain,
% 2.30/2.41 (e0 = op(e3, op(e3, e3))),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19551, 19563])).
% 2.30/2.41 tff(19565,plain,
% 2.30/2.41 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[5397, 19564, 19560])).
% 2.30/2.41 tff(19566,plain,
% 2.30/2.41 (~(op(e3, e0) = e2)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19565, 19559])).
% 2.30/2.41 tff(19567,plain,
% 2.30/2.41 (op(e2, e3) = e3),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[12598, 121, 80, 79, 76])).
% 2.30/2.41 tff(19568,plain,
% 2.30/2.41 (e3 = op(e2, e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19567])).
% 2.30/2.41 tff(19569,plain,
% 2.30/2.41 ((e0 = e3) <=> (e0 = op(e2, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19568])).
% 2.30/2.41 tff(19570,plain,
% 2.30/2.41 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19569, 86])).
% 2.30/2.41 tff(19571,plain,
% 2.30/2.41 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19570])).
% 2.30/2.41 tff(19572,plain,
% 2.30/2.41 (~(op(e2, e3) = e0)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[181, 19571])).
% 2.30/2.41 tff(19573,plain,
% 2.30/2.41 (op(e2, e0) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2311, 19572, 17, 2559])).
% 2.30/2.41 tff(19574,plain,
% 2.30/2.41 (op(e2, e0) = op(e0, e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19573, 19545])).
% 2.30/2.41 tff(19575,plain,
% 2.30/2.41 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19574])).
% 2.30/2.41 tff(19576,plain,
% 2.30/2.41 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.30/2.41 inference(transitivity,[status(thm)],[19575, 452])).
% 2.30/2.41 tff(19577,plain,
% 2.30/2.41 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = op(e0, e3)))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19576])).
% 2.30/2.41 tff(19578,plain,
% 2.30/2.41 (~(op(e3, e0) = op(e0, e3))),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[747, 19577])).
% 2.30/2.41 tff(19579,plain,
% 2.30/2.41 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19545])).
% 2.30/2.41 tff(19580,plain,
% 2.30/2.41 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19579])).
% 2.30/2.41 tff(19581,plain,
% 2.30/2.41 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19576, 19580])).
% 2.30/2.41 tff(19582,plain,
% 2.30/2.41 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19581])).
% 2.30/2.41 tff(19583,plain,
% 2.30/2.41 (~(op(e3, e0) = e0)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[747, 19582])).
% 2.30/2.41 tff(19584,plain,
% 2.30/2.41 (~(op(e3, e2) = e2)),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[8994, 19583, 1291, 19543, 661, 3271, 10347, 4412, 19578, 79])).
% 2.30/2.41 tff(19585,plain,
% 2.30/2.41 (op(e3, e0) = e2),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[15971, 19584, 82])).
% 2.30/2.41 tff(19586,plain,
% 2.30/2.41 ($false),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[19585, 19566])).
% 2.30/2.41 tff(19587,plain,((op(e0, e3) = e1) | (op(e3, e1) = e2) | (op(e1, e1) = e3) | (op(e0, e3) = e3) | (op(e2, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e2) | (op(e3, e1) = e3) | (op(e2, e2) = e0) | (op(e2, e1) = e0) | (op(e2, e3) = e1) | (op(e1, e3) = e1) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.41 tff(19588,plain,
% 2.30/2.41 (op(e0, e3) = e1),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[19587, 19542, 82, 19538, 19534, 19530, 19015, 19526, 17, 19522, 76, 19007, 19012])).
% 2.30/2.41 tff(19589,plain,
% 2.30/2.41 (e1 = op(e0, e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19588])).
% 2.30/2.41 tff(19590,plain,
% 2.30/2.41 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19589])).
% 2.30/2.41 tff(19591,plain,
% 2.30/2.41 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19590])).
% 2.30/2.41 tff(19592,plain,
% 2.30/2.41 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19591])).
% 2.30/2.41 tff(19593,plain,
% 2.30/2.41 (~(op(e0, e2) = e1)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[918, 19592])).
% 2.30/2.41 tff(19594,plain,
% 2.30/2.41 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.41 tff(19595,plain,
% 2.30/2.41 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19594, 81])).
% 2.30/2.41 tff(19596,plain,
% 2.30/2.41 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19595])).
% 2.30/2.41 tff(19597,plain,
% 2.30/2.41 (~(op(e2, e2) = e2)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[508, 19596])).
% 2.30/2.41 tff(19598,plain,
% 2.30/2.41 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19002])).
% 2.30/2.41 tff(19599,plain,
% 2.30/2.41 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19598])).
% 2.30/2.41 tff(19600,plain,
% 2.30/2.41 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19599])).
% 2.30/2.41 tff(19601,plain,
% 2.30/2.41 (~(op(e1, e3) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[1321, 19600])).
% 2.30/2.41 tff(19602,plain,
% 2.30/2.41 (op(e3, e3) = e3),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[480, 124, 19601, 19538])).
% 2.30/2.41 tff(19603,plain,
% 2.30/2.41 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19602])).
% 2.30/2.41 tff(19604,plain,
% 2.30/2.41 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19603])).
% 2.30/2.41 tff(19605,plain,
% 2.30/2.41 (~(op(e3, e2) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[1888, 19604])).
% 2.30/2.41 tff(19606,plain,
% 2.30/2.41 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.41 tff(19607,plain,
% 2.30/2.41 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19606])).
% 2.30/2.41 tff(19608,plain,
% 2.30/2.41 (~(op(e2, e0) = e2)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[1966, 19607])).
% 2.30/2.41 tff(19609,plain,
% 2.30/2.41 (op(e2, e3) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[206, 124, 19038, 76])).
% 2.30/2.41 tff(19610,plain,
% 2.30/2.41 (op(e2, e2) = e3),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2111, 75, 4412, 1890])).
% 2.30/2.41 tff(19611,plain,
% 2.30/2.41 (op(e2, op(e2, e2)) = op(e2, e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19610])).
% 2.30/2.41 tff(19612,plain,
% 2.30/2.41 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19611])).
% 2.30/2.41 tff(19613,plain,
% 2.30/2.41 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19612, 1942])).
% 2.30/2.41 tff(19614,plain,
% 2.30/2.41 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (e1 = op(e2, e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19613])).
% 2.30/2.41 tff(19615,plain,
% 2.30/2.41 ((e1 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e0) = e1)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19614, 16])).
% 2.30/2.41 tff(19616,plain,
% 2.30/2.41 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, op(e2, e2))))),
% 2.30/2.41 inference(symmetry,[status(thm)],[19615])).
% 2.30/2.41 tff(19617,plain,
% 2.30/2.41 ((op(e2, e0) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[1941])).
% 2.30/2.41 tff(19618,plain,
% 2.30/2.41 ((op(e2, op(e2, e3)) = e3) <=> (op(e2, e0) = e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19617])).
% 2.30/2.41 tff(19619,plain,
% 2.30/2.41 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, op(e2, e3)))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[7131, 1941])).
% 2.30/2.41 tff(19620,plain,
% 2.30/2.41 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, op(e2, e3)) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19619, 2881])).
% 2.30/2.41 tff(19621,plain,
% 2.30/2.41 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19620, 19618])).
% 2.30/2.41 tff(19622,plain,
% 2.30/2.41 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19621])).
% 2.30/2.41 tff(19623,plain,
% 2.30/2.41 (~(op(e2, e0) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[756, 19622])).
% 2.30/2.41 tff(19624,plain,
% 2.30/2.41 (op(e2, e0) = e1),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[765, 19623, 982, 3288])).
% 2.30/2.41 tff(19625,plain,
% 2.30/2.41 (e1 = op(e2, op(e2, op(e2, e2)))),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19624, 19616])).
% 2.30/2.41 tff(19626,plain,
% 2.30/2.41 (e3 = op(e2, e2)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19610, 1796])).
% 2.30/2.41 tff(19627,plain,
% 2.30/2.41 (op(e2, e3) = op(e2, op(e2, e2))),
% 2.30/2.41 inference(symmetry,[status(thm)],[19611])).
% 2.30/2.41 tff(19628,plain,
% 2.30/2.41 (e0 = op(e2, op(e2, e2))),
% 2.30/2.41 inference(transitivity,[status(thm)],[252, 19627])).
% 2.30/2.41 tff(19629,plain,
% 2.30/2.41 (~(e1 = op(e2, op(e2, op(e2, e2))))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1810, 19628, 19626])).
% 2.30/2.41 tff(19630,plain,
% 2.30/2.41 ($false),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[19629, 19625])).
% 2.30/2.41 tff(19631,plain,((op(e1, e2) = e3) | (~(op(e2, e3) = e0)) | (op(e2, e0) = e2) | (op(e0, e2) = e3) | (op(e3, e2) = e3) | (op(e1, e1) = e3) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.41 tff(19632,plain,
% 2.30/2.41 (op(e1, e2) = e3),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[19631, 19609, 19608, 19530, 19605, 19542, 19601])).
% 2.30/2.41 tff(19633,plain,
% 2.30/2.41 ((op(e1, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19632])).
% 2.30/2.41 tff(19634,plain,
% 2.30/2.41 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19633, 502])).
% 2.30/2.41 tff(19635,plain,
% 2.30/2.41 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19634])).
% 2.30/2.41 tff(19636,plain,
% 2.30/2.41 (~(op(e2, e2) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[1273, 19635])).
% 2.30/2.41 tff(19637,plain,
% 2.30/2.41 (op(e2, e2) = e1),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[524, 19636, 17, 19597])).
% 2.30/2.41 tff(19638,plain,
% 2.30/2.41 ((op(e2, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19637])).
% 2.30/2.41 tff(19639,plain,
% 2.30/2.41 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19638, 7171])).
% 2.30/2.41 tff(19640,plain,
% 2.30/2.41 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19639])).
% 2.30/2.41 tff(19641,plain,
% 2.30/2.41 (~(op(e3, e2) = e1)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[1546, 19640])).
% 2.30/2.41 tff(19642,plain,
% 2.30/2.41 (op(op(e2, e1), e1) = op(e2, e1)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.41 tff(19643,plain,
% 2.30/2.41 (op(op(e2, e1), e1) = e2),
% 2.30/2.41 inference(transitivity,[status(thm)],[19642, 19517])).
% 2.30/2.41 tff(19644,plain,
% 2.30/2.41 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2371, 19643])).
% 2.30/2.41 tff(19645,plain,
% 2.30/2.41 (e0 = op(e2, e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19609])).
% 2.30/2.41 tff(19646,plain,
% 2.30/2.41 ((op(e1, e2) = e0) <=> (e3 = op(e2, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19632, 19645])).
% 2.30/2.41 tff(19647,plain,
% 2.30/2.41 ((op(e1, e2) = e0) <=> (op(e2, e3) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19646, 112])).
% 2.30/2.41 tff(19648,plain,
% 2.30/2.41 ((op(e2, e3) = e3) <=> (op(e1, e2) = e0)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19647])).
% 2.30/2.41 tff(19649,plain,
% 2.30/2.41 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e2) = e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19648])).
% 2.30/2.41 tff(19650,plain,
% 2.30/2.41 (~(op(e1, e2) = e0)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[124, 19649])).
% 2.30/2.41 tff(19651,plain,
% 2.30/2.41 (op(e2, e0) = e3),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1559, 19636, 19534, 124])).
% 2.30/2.41 tff(19652,plain,
% 2.30/2.41 (op(e2, op(e2, e0)) = op(e2, e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19651])).
% 2.30/2.41 tff(19653,plain,
% 2.30/2.41 (op(e2, op(e2, e0)) = e0),
% 2.30/2.41 inference(transitivity,[status(thm)],[19652, 19609])).
% 2.30/2.41 tff(19654,plain,
% 2.30/2.41 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2653, 19653])).
% 2.30/2.41 tff(19655,plain,
% 2.30/2.41 (op(op(e0, e3), e3) = op(e1, e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19588])).
% 2.30/2.41 tff(19656,plain,
% 2.30/2.41 (op(e1, op(e1, e2)) = op(op(e0, e3), e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19589, 19632])).
% 2.30/2.41 tff(19657,plain,
% 2.30/2.41 (op(e1, op(e1, e2)) = e2),
% 2.30/2.41 inference(transitivity,[status(thm)],[19656, 19655, 19002])).
% 2.30/2.41 tff(19658,plain,
% 2.30/2.41 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2377, 19657])).
% 2.30/2.41 tff(19659,plain,
% 2.30/2.41 (op(e1, e0) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1830, 84, 19012, 1947])).
% 2.30/2.41 tff(19660,plain,
% 2.30/2.41 (op(e1, op(e2, e3)) = op(op(e0, e3), e0)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[4681, 251])).
% 2.30/2.41 tff(19661,plain,
% 2.30/2.41 (op(e1, e0) = op(e2, e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19659, 252])).
% 2.30/2.41 tff(19662,plain,
% 2.30/2.41 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19661])).
% 2.30/2.41 tff(19663,plain,
% 2.30/2.41 (op(e1, op(e1, e0)) = e0),
% 2.30/2.41 inference(transitivity,[status(thm)],[19662, 19660, 5069, 19659])).
% 2.30/2.41 tff(19664,plain,
% 2.30/2.41 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1836, 19663])).
% 2.30/2.41 tff(19665,plain,
% 2.30/2.41 ((op(e0, e1) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[4839])).
% 2.30/2.41 tff(19666,plain,
% 2.30/2.41 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19665, 4221])).
% 2.30/2.41 tff(19667,plain,
% 2.30/2.41 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19666])).
% 2.30/2.41 tff(19668,plain,
% 2.30/2.41 (~(op(e0, e2) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[2102, 19667])).
% 2.30/2.41 tff(19669,plain,
% 2.30/2.41 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[14938, 19, 19668])).
% 2.30/2.41 tff(19670,plain,
% 2.30/2.41 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[252])).
% 2.30/2.41 tff(19671,plain,
% 2.30/2.41 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e0)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19670])).
% 2.30/2.41 tff(19672,plain,
% 2.30/2.41 (op(e3, e1) = e0),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[292, 84, 3849, 2559])).
% 2.30/2.41 tff(19673,plain,
% 2.30/2.41 (op(e3, e1) = op(e2, e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19672, 252])).
% 2.30/2.41 tff(19674,plain,
% 2.30/2.41 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19673])).
% 2.30/2.41 tff(19675,plain,
% 2.30/2.41 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.30/2.41 inference(transitivity,[status(thm)],[19674, 394])).
% 2.30/2.41 tff(19676,plain,
% 2.30/2.41 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19675, 19671])).
% 2.30/2.41 tff(19677,plain,
% 2.30/2.41 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19676])).
% 2.30/2.41 tff(19678,plain,
% 2.30/2.41 (~(op(e3, e2) = e0)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[3429, 19677])).
% 2.30/2.41 tff(19679,plain,
% 2.30/2.41 (op(e3, e2) = e2),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1898, 19678, 1890, 930])).
% 2.30/2.41 tff(19680,plain,
% 2.30/2.41 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19679])).
% 2.30/2.41 tff(19681,plain,
% 2.30/2.41 (op(e3, op(e3, e2)) = e2),
% 2.30/2.41 inference(transitivity,[status(thm)],[19680, 19679])).
% 2.30/2.41 tff(19682,plain,
% 2.30/2.41 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1904, 19681])).
% 2.30/2.41 tff(19683,plain,
% 2.30/2.41 (op(op(e3, e1), e1) = op(e0, op(e0, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19672, 4681])).
% 2.30/2.41 tff(19684,plain,
% 2.30/2.41 (op(op(e3, e1), e1) = e3),
% 2.30/2.41 inference(transitivity,[status(thm)],[19683, 4972, 4839])).
% 2.30/2.41 tff(19685,plain,
% 2.30/2.41 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2416, 19684])).
% 2.30/2.41 tff(19686,plain,
% 2.30/2.41 (op(op(e1, e3), e1) = op(e2, e1)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19002])).
% 2.30/2.41 tff(19687,plain,
% 2.30/2.41 ((op(op(e1, e3), e1) = e3) <=> (op(e2, e1) = e3)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19686])).
% 2.30/2.41 tff(19688,plain,
% 2.30/2.41 ((op(e2, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19687])).
% 2.30/2.41 tff(19689,plain,
% 2.30/2.41 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[4839])).
% 2.30/2.41 tff(19690,plain,
% 2.30/2.41 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19689, 1262])).
% 2.30/2.41 tff(19691,plain,
% 2.30/2.41 ((op(e0, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.30/2.41 inference(transitivity,[status(thm)],[19690, 19688])).
% 2.30/2.41 tff(19692,plain,
% 2.30/2.41 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19691])).
% 2.30/2.41 tff(19693,plain,
% 2.30/2.41 (~(op(op(e1, e3), e1) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[606, 19692])).
% 2.30/2.41 tff(19694,plain,
% 2.30/2.41 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[160, 19693])).
% 2.30/2.41 tff(19695,plain,
% 2.30/2.41 ((op(e0, op(e0, e1)) = e1) <=> (op(e0, e3) = e1)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[7103])).
% 2.30/2.41 tff(19696,plain,
% 2.30/2.41 ((op(e0, e3) = e1) <=> (op(e0, op(e0, e1)) = e1)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19695])).
% 2.30/2.41 tff(19697,plain,
% 2.30/2.41 (op(e0, op(e0, e1)) = e1),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19, 19696])).
% 2.30/2.41 tff(19698,plain,
% 2.30/2.41 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[2449, 19697])).
% 2.30/2.41 tff(19699,plain,
% 2.30/2.41 ((~(op(e0, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[5090])).
% 2.30/2.41 tff(19700,plain,
% 2.30/2.41 (~(op(op(e2, e3), e2) = e3)),
% 2.30/2.41 inference(modus_ponens,[status(thm)],[19668, 19699])).
% 2.30/2.41 tff(19701,plain,
% 2.30/2.41 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.30/2.41 inference(unit_resolution,[status(thm)],[1934, 19700])).
% 2.30/2.41 tff(19702,plain,
% 2.30/2.41 (op(e3, op(e0, e3)) = op(e3, e1)),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19])).
% 2.30/2.41 tff(19703,plain,
% 2.30/2.41 ((op(e3, e3) = e1) <=> (op(e3, e3) = op(e0, e3))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[4681])).
% 2.30/2.41 tff(19704,plain,
% 2.30/2.41 ((op(e3, e3) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 2.30/2.41 inference(transitivity,[status(thm)],[19703, 659])).
% 2.30/2.41 tff(19705,plain,
% 2.30/2.41 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.30/2.41 inference(symmetry,[status(thm)],[19704])).
% 2.30/2.41 tff(19706,plain,
% 2.30/2.41 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.30/2.41 inference(monotonicity,[status(thm)],[19705])).
% 2.30/2.41 tff(19707,plain,
% 2.30/2.41 (~(op(e3, e3) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[1077, 19706])).
% 2.30/2.42 tff(19708,plain,
% 2.30/2.42 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[4839])).
% 2.30/2.42 tff(19709,plain,
% 2.30/2.42 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19708, 1112])).
% 2.30/2.42 tff(19710,plain,
% 2.30/2.42 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19709])).
% 2.30/2.42 tff(19711,plain,
% 2.30/2.42 (~(op(e1, e1) = e3)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[792, 19710])).
% 2.30/2.42 tff(19712,plain,
% 2.30/2.42 (op(e1, e1) = e1),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[630, 84, 68, 19711])).
% 2.30/2.42 tff(19713,plain,
% 2.30/2.42 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19712])).
% 2.30/2.42 tff(19714,plain,
% 2.30/2.42 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19713, 7793])).
% 2.30/2.42 tff(19715,plain,
% 2.30/2.42 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19714])).
% 2.30/2.42 tff(19716,plain,
% 2.30/2.42 (~(op(e3, e1) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[945, 19715])).
% 2.30/2.42 tff(19717,plain,
% 2.30/2.42 (op(e3, e0) = e1),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[939, 19716, 19707, 930])).
% 2.30/2.42 tff(19718,plain,
% 2.30/2.42 (op(e3, e0) = op(e0, e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19717, 4681])).
% 2.30/2.42 tff(19719,plain,
% 2.30/2.42 (op(e3, op(e3, e0)) = op(e3, op(e0, e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19718])).
% 2.30/2.42 tff(19720,plain,
% 2.30/2.42 (op(e3, op(e3, e0)) = e0),
% 2.30/2.42 inference(transitivity,[status(thm)],[19719, 19702, 19672])).
% 2.30/2.42 tff(19721,plain,
% 2.30/2.42 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1345, 19720])).
% 2.30/2.42 tff(19722,plain,
% 2.30/2.42 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[4839])).
% 2.30/2.42 tff(19723,plain,
% 2.30/2.42 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19722])).
% 2.30/2.42 tff(19724,plain,
% 2.30/2.42 (~(op(e0, e0) = e3)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[811, 19723])).
% 2.30/2.42 tff(19725,plain,
% 2.30/2.42 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19659])).
% 2.30/2.42 tff(19726,plain,
% 2.30/2.42 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19725])).
% 2.30/2.42 tff(19727,plain,
% 2.30/2.42 (~(op(e0, e0) = e0)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[2471, 19726])).
% 2.30/2.42 tff(19728,plain,
% 2.30/2.42 (op(e0, e0) = e2),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[3612, 19727, 5048, 19724])).
% 2.30/2.42 tff(19729,plain,
% 2.30/2.42 (op(e0, e2) = e0),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[973, 19678, 17, 1947])).
% 2.30/2.42 tff(19730,plain,
% 2.30/2.42 (op(e0, op(e0, e2)) = op(e0, e0)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19729])).
% 2.30/2.42 tff(19731,plain,
% 2.30/2.42 (op(e0, op(e0, e2)) = e2),
% 2.30/2.42 inference(transitivity,[status(thm)],[19730, 19728])).
% 2.30/2.42 tff(19732,plain,
% 2.30/2.42 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1331, 19731])).
% 2.30/2.42 tff(19733,plain,
% 2.30/2.42 ($false),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1459, 19732, 19721, 19701, 19698, 1358, 19694, 19685, 19682, 2421, 19669, 19664, 1936])).
% 2.30/2.42 tff(19734,plain,((op(e1, e1) = e0) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e0, e3) = e1)) | (op(e3, e2) = e3) | (op(e3, e2) = e1) | (op(e2, e2) = e0) | (op(e1, e2) = e0) | (~(op(e2, e3) = e0)) | (~(op(e0, e1) = e3)) | (op(e0, e1) = e0) | (op(e2, e1) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.42 tff(19735,plain,
% 2.30/2.42 (op(e1, e1) = e0),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[19734, 19658, 19654, 19644, 19588, 19605, 19641, 17, 19650, 19609, 19511, 3849, 19522, 68])).
% 2.30/2.42 tff(19736,plain,
% 2.30/2.42 ((op(e1, e2) = e1) <=> (e3 = op(e0, e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19632, 19589])).
% 2.30/2.42 tff(19737,plain,
% 2.30/2.42 ((op(e1, e2) = e1) <=> (op(e0, e3) = e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19736, 1364])).
% 2.30/2.42 tff(19738,plain,
% 2.30/2.42 ((op(e0, e3) = e3) <=> (op(e1, e2) = e1)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19737])).
% 2.30/2.42 tff(19739,plain,
% 2.30/2.42 ((~(op(e0, e3) = e3)) <=> (~(op(e1, e2) = e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19738])).
% 2.30/2.42 tff(19740,plain,
% 2.30/2.42 (~(op(e1, e2) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[19538, 19739])).
% 2.30/2.42 tff(19741,plain,
% 2.30/2.42 (op(e1, e1) = op(e2, e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19735, 19645])).
% 2.30/2.42 tff(19742,plain,
% 2.30/2.42 ((op(e1, e1) = e1) <=> (op(e2, e3) = op(e0, e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19741, 19589])).
% 2.30/2.42 tff(19743,plain,
% 2.30/2.42 ((op(e1, e1) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 2.30/2.42 inference(transitivity,[status(thm)],[19742, 925])).
% 2.30/2.42 tff(19744,plain,
% 2.30/2.42 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e1) = e1)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19743])).
% 2.30/2.42 tff(19745,plain,
% 2.30/2.42 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e1) = e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19744])).
% 2.30/2.42 tff(19746,plain,
% 2.30/2.42 (~(op(e1, e1) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[964, 19745])).
% 2.30/2.42 tff(19747,plain,
% 2.30/2.42 (op(e1, e0) = e1),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[954, 19746, 19740, 19007])).
% 2.30/2.42 tff(19748,plain,
% 2.30/2.42 (op(e1, op(e1, e0)) = op(e1, e1)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19747])).
% 2.30/2.42 tff(19749,plain,
% 2.30/2.42 (op(e1, op(e1, e0)) = e0),
% 2.30/2.42 inference(transitivity,[status(thm)],[19748, 19735])).
% 2.30/2.42 tff(19750,plain,
% 2.30/2.42 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1836, 19749])).
% 2.30/2.42 tff(19751,plain,
% 2.30/2.42 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[14938, 19588, 19530])).
% 2.30/2.42 tff(19752,plain,
% 2.30/2.42 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.42 tff(19753,plain,
% 2.30/2.42 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19752, 69])).
% 2.30/2.42 tff(19754,plain,
% 2.30/2.42 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19753])).
% 2.30/2.42 tff(19755,plain,
% 2.30/2.42 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19754])).
% 2.30/2.42 tff(19756,plain,
% 2.30/2.42 (~(op(e2, e1) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[708, 19755])).
% 2.30/2.42 tff(19757,plain,
% 2.30/2.42 ((op(e0, e1) = e1) <=> (e3 = e1)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.42 tff(19758,plain,
% 2.30/2.42 ((op(e0, e1) = e1) <=> (e1 = e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19757, 128])).
% 2.30/2.42 tff(19759,plain,
% 2.30/2.42 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19758])).
% 2.30/2.42 tff(19760,plain,
% 2.30/2.42 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19759])).
% 2.30/2.42 tff(19761,plain,
% 2.30/2.42 (~(op(e0, e1) = e1)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[303, 19760])).
% 2.30/2.42 tff(19762,plain,
% 2.30/2.42 (op(e3, e1) = e1),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1252, 19746, 19761, 19756])).
% 2.30/2.42 tff(19763,plain,
% 2.30/2.42 (op(e3, op(e0, e3)) = op(e3, e1)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19588])).
% 2.30/2.42 tff(19764,plain,
% 2.30/2.42 (op(e3, e1) = op(e0, e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19762, 19589])).
% 2.30/2.42 tff(19765,plain,
% 2.30/2.42 (op(e3, op(e3, e1)) = op(e3, op(e0, e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19764])).
% 2.30/2.42 tff(19766,plain,
% 2.30/2.42 (op(e3, op(e3, e1)) = e1),
% 2.30/2.42 inference(transitivity,[status(thm)],[19765, 19763, 19762])).
% 2.30/2.42 tff(19767,plain,
% 2.30/2.42 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[2594, 19766])).
% 2.30/2.42 tff(19768,plain,
% 2.30/2.42 ((op(e0, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19532, 19688])).
% 2.30/2.42 tff(19769,plain,
% 2.30/2.42 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19768])).
% 2.30/2.42 tff(19770,plain,
% 2.30/2.42 (~(op(op(e1, e3), e1) = e3)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[606, 19769])).
% 2.30/2.42 tff(19771,plain,
% 2.30/2.42 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[160, 19770])).
% 2.30/2.42 tff(19772,plain,
% 2.30/2.42 (op(e0, op(e0, e1)) = op(e0, e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.42 tff(19773,plain,
% 2.30/2.42 ((op(e0, op(e0, e1)) = e1) <=> (op(e0, e3) = e1)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19772])).
% 2.30/2.42 tff(19774,plain,
% 2.30/2.42 ((op(e0, e3) = e1) <=> (op(e0, op(e0, e1)) = e1)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19773])).
% 2.30/2.42 tff(19775,plain,
% 2.30/2.42 (op(e0, op(e0, e1)) = e1),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[19588, 19774])).
% 2.30/2.42 tff(19776,plain,
% 2.30/2.42 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[2449, 19775])).
% 2.30/2.42 tff(19777,plain,
% 2.30/2.42 (op(op(e2, e3), e2) = op(e0, e2)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19609])).
% 2.30/2.42 tff(19778,plain,
% 2.30/2.42 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e2) = e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19777])).
% 2.30/2.42 tff(19779,plain,
% 2.30/2.42 ((op(e0, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19778])).
% 2.30/2.42 tff(19780,plain,
% 2.30/2.42 ((~(op(e0, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19779])).
% 2.30/2.42 tff(19781,plain,
% 2.30/2.42 (~(op(op(e2, e3), e2) = e3)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[19530, 19780])).
% 2.30/2.42 tff(19782,plain,
% 2.30/2.42 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1934, 19781])).
% 2.30/2.42 tff(19783,plain,
% 2.30/2.42 (op(e3, e2) = e0),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1898, 2386, 1890, 930])).
% 2.30/2.42 tff(19784,plain,
% 2.30/2.42 (op(e3, e2) = op(e2, e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19783, 252])).
% 2.30/2.42 tff(19785,plain,
% 2.30/2.42 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19784])).
% 2.30/2.42 tff(19786,plain,
% 2.30/2.42 (op(e3, op(e3, e2)) = e2),
% 2.30/2.42 inference(transitivity,[status(thm)],[19785, 10439, 19346])).
% 2.30/2.42 tff(19787,plain,
% 2.30/2.42 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1904, 19786])).
% 2.30/2.42 tff(19788,plain,
% 2.30/2.42 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19346])).
% 2.30/2.42 tff(19789,plain,
% 2.30/2.42 (op(e3, op(e3, e0)) = e0),
% 2.30/2.42 inference(transitivity,[status(thm)],[19788, 19783])).
% 2.30/2.42 tff(19790,plain,
% 2.30/2.42 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1345, 19789])).
% 2.30/2.42 tff(19791,plain,
% 2.30/2.42 (op(e0, e2) = e2),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1151, 2386, 3785, 5548])).
% 2.30/2.42 tff(19792,plain,
% 2.30/2.42 (op(e0, op(e0, e2)) = op(op(e2, e3), e2)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[252, 19791])).
% 2.30/2.42 tff(19793,plain,
% 2.30/2.42 (op(e0, op(e0, e2)) = e2),
% 2.30/2.42 inference(transitivity,[status(thm)],[19792, 5088, 19791])).
% 2.30/2.42 tff(19794,plain,
% 2.30/2.42 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1331, 19793])).
% 2.30/2.42 tff(19795,plain,
% 2.30/2.42 ($false),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[1459, 19794, 19790, 1347, 4549, 1358, 1304, 1275, 19787, 2421, 3342, 1357, 1936])).
% 2.30/2.42 tff(19796,plain,((op(e3, e2) = e2) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e2, e3) = e0)) | (op(e3, e2) = e3) | (op(e3, e2) = e1) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.42 tff(19797,plain,
% 2.30/2.42 (op(e3, e2) = e2),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[19796, 19782, 19776, 19658, 19771, 19767, 19654, 19751, 19750, 19644, 19609, 19605, 19641, 19486, 19597, 82])).
% 2.30/2.42 tff(19798,plain,
% 2.30/2.42 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19797])).
% 2.30/2.42 tff(19799,plain,
% 2.30/2.42 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19798])).
% 2.30/2.42 tff(19800,plain,
% 2.30/2.42 (~(op(e0, e2) = e2)),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[1467, 19799])).
% 2.30/2.42 tff(19801,plain,
% 2.30/2.42 (op(e0, e2) = e0),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[2745, 19800, 19530, 19593])).
% 2.30/2.42 tff(19802,plain,
% 2.30/2.42 (op(e0, e0) = e2),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[3652, 19800, 19015, 19516])).
% 2.30/2.42 tff(19803,plain,
% 2.30/2.42 (op(e0, op(e0, e0)) = op(op(e2, e3), e2)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19645, 19802])).
% 2.30/2.42 tff(19804,plain,
% 2.30/2.42 (op(e0, op(e0, e0)) = e0),
% 2.30/2.42 inference(transitivity,[status(thm)],[19803, 19777, 19801])).
% 2.30/2.42 tff(19805,plain,
% 2.30/2.42 ((op(e2, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19651])).
% 2.30/2.42 tff(19806,plain,
% 2.30/2.42 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19805, 4221])).
% 2.30/2.42 tff(19807,plain,
% 2.30/2.42 ((op(e0, e2) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.30/2.42 inference(symmetry,[status(thm)],[19806])).
% 2.30/2.42 tff(19808,plain,
% 2.30/2.42 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.30/2.42 inference(transitivity,[status(thm)],[19807, 6337])).
% 2.30/2.42 tff(19809,plain,
% 2.30/2.42 ((~(op(e0, e2) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19808])).
% 2.30/2.42 tff(19810,plain,
% 2.30/2.42 (~(op(e0, e2) = op(e2, e0))),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[19530, 19809])).
% 2.30/2.42 tff(19811,plain,
% 2.30/2.42 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[6347, 19810])).
% 2.30/2.42 tff(19812,plain,
% 2.30/2.42 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19517])).
% 2.30/2.42 tff(19813,plain,
% 2.30/2.42 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.30/2.42 inference(transitivity,[status(thm)],[19812, 5762])).
% 2.30/2.42 tff(19814,plain,
% 2.30/2.42 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.30/2.42 inference(symmetry,[status(thm)],[19813])).
% 2.30/2.42 tff(19815,plain,
% 2.30/2.42 ((~(op(e1, e2) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19814])).
% 2.30/2.42 tff(19816,plain,
% 2.30/2.42 (~(op(e2, e1) = op(e1, e2))),
% 2.30/2.42 inference(modus_ponens,[status(thm)],[19486, 19815])).
% 2.30/2.42 tff(19817,plain,
% 2.30/2.42 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[557, 19816])).
% 2.30/2.42 tff(19818,plain,
% 2.30/2.42 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19602])).
% 2.30/2.42 tff(19819,plain,
% 2.30/2.42 (op(e3, op(e3, e3)) = e3),
% 2.30/2.42 inference(transitivity,[status(thm)],[19818, 19602])).
% 2.30/2.42 tff(19820,plain,
% 2.30/2.42 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.30/2.42 inference(unit_resolution,[status(thm)],[6277, 19819])).
% 2.30/2.42 tff(19821,plain,
% 2.30/2.42 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.42 tff(19822,plain,
% 2.30/2.42 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.30/2.42 inference(symmetry,[status(thm)],[19821])).
% 2.30/2.42 tff(19823,plain,
% 2.30/2.42 (op(op(e0, e3), e0) = op(e1, e0)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19588])).
% 2.30/2.42 tff(19824,plain,
% 2.30/2.42 (op(e1, e0) = op(op(e0, e3), e0)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19823])).
% 2.30/2.42 tff(19825,plain,
% 2.30/2.42 ((op(e1, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.30/2.42 inference(monotonicity,[status(thm)],[19824])).
% 2.30/2.42 tff(19826,plain,
% 2.30/2.42 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = e3)),
% 2.30/2.42 inference(symmetry,[status(thm)],[19825])).
% 2.30/2.42 tff(19827,plain,
% 2.30/2.42 ((op(e1, e0) = op(e1, e2)) <=> (op(op(e0, e3), e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19824, 19632])).
% 2.30/2.43 tff(19828,plain,
% 2.30/2.43 ((op(e1, e0) = op(e1, e2)) <=> (op(e0, e1) = op(e1, e0))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19827, 19826, 19822, 596])).
% 2.30/2.43 tff(19829,plain,
% 2.30/2.43 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19828])).
% 2.30/2.43 tff(19830,plain,
% 2.30/2.43 (~(op(e0, e1) = op(e1, e0))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[1312, 19829])).
% 2.30/2.43 tff(19831,plain,
% 2.30/2.43 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[609, 19830])).
% 2.30/2.43 tff(19832,plain,
% 2.30/2.43 (op(e1, op(e2, e3)) = op(op(e0, e3), e0)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19589, 19609])).
% 2.30/2.43 tff(19833,plain,
% 2.30/2.43 (op(e1, op(e2, e3)) = op(e1, e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19832, 19823])).
% 2.30/2.43 tff(19834,plain,
% 2.30/2.43 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19833])).
% 2.30/2.43 tff(19835,plain,
% 2.30/2.43 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19834])).
% 2.30/2.43 tff(19836,plain,
% 2.30/2.43 (op(e1, op(e2, e3)) = e1),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19747, 19835])).
% 2.30/2.43 tff(19837,plain,
% 2.30/2.43 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[10724, 19836])).
% 2.30/2.43 tff(19838,plain,
% 2.30/2.43 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19814, 531])).
% 2.30/2.43 tff(19839,plain,
% 2.30/2.43 ((~(op(e1, e2) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19838])).
% 2.30/2.43 tff(19840,plain,
% 2.30/2.43 (~(op(e1, e2) = op(e2, e1))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19486, 19839])).
% 2.30/2.43 tff(19841,plain,
% 2.30/2.43 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[539, 19840])).
% 2.30/2.43 tff(19842,plain,
% 2.30/2.43 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19741])).
% 2.30/2.43 tff(19843,plain,
% 2.30/2.43 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19842, 19832, 19823])).
% 2.30/2.43 tff(19844,plain,
% 2.30/2.43 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e0) = e1)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19843])).
% 2.30/2.43 tff(19845,plain,
% 2.30/2.43 ((op(e1, e0) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19844])).
% 2.30/2.43 tff(19846,plain,
% 2.30/2.43 (op(e1, op(e1, e1)) = e1),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19747, 19845])).
% 2.30/2.43 tff(19847,plain,
% 2.30/2.43 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5678, 19846])).
% 2.30/2.43 tff(19848,plain,
% 2.30/2.43 (op(e2, op(e0, e3)) = op(e2, e1)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19588])).
% 2.30/2.43 tff(19849,plain,
% 2.30/2.43 (op(e2, e2) = op(e0, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19637, 19589])).
% 2.30/2.43 tff(19850,plain,
% 2.30/2.43 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19849])).
% 2.30/2.43 tff(19851,plain,
% 2.30/2.43 (op(e2, op(e2, e2)) = e2),
% 2.30/2.43 inference(transitivity,[status(thm)],[19850, 19848, 19517])).
% 2.30/2.43 tff(19852,plain,
% 2.30/2.43 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[528, 19851])).
% 2.30/2.43 tff(19853,plain,
% 2.30/2.43 (op(e1, e0) = op(e0, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19747, 19589])).
% 2.30/2.43 tff(19854,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19853])).
% 2.30/2.43 tff(19855,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19854, 452])).
% 2.30/2.43 tff(19856,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19855, 453])).
% 2.30/2.43 tff(19857,plain,
% 2.30/2.43 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19856])).
% 2.30/2.43 tff(19858,plain,
% 2.30/2.43 (~(op(e0, e3) = op(e3, e0))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[410, 19857])).
% 2.30/2.43 tff(19859,plain,
% 2.30/2.43 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[496, 19858])).
% 2.30/2.43 tff(19860,plain,
% 2.30/2.43 ((~(op(e0, e2) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19807])).
% 2.30/2.43 tff(19861,plain,
% 2.30/2.43 (~(op(e2, e0) = op(e0, e2))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19530, 19860])).
% 2.30/2.43 tff(19862,plain,
% 2.30/2.43 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[6358, 19861])).
% 2.30/2.43 tff(19863,plain,
% 2.30/2.43 (op(e3, op(e0, e1)) = op(e3, e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.43 tff(19864,plain,
% 2.30/2.43 ((op(e3, op(e0, e1)) = e3) <=> (op(e3, e3) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19863])).
% 2.30/2.43 tff(19865,plain,
% 2.30/2.43 ((op(e3, e3) = e3) <=> (op(e3, op(e0, e1)) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19864])).
% 2.30/2.43 tff(19866,plain,
% 2.30/2.43 (op(e3, op(e0, e1)) = e3),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19602, 19865])).
% 2.30/2.43 tff(19867,plain,
% 2.30/2.43 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[12000, 19866])).
% 2.30/2.43 tff(19868,plain,
% 2.30/2.43 ((op(e3, e2) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19797])).
% 2.30/2.43 tff(19869,plain,
% 2.30/2.43 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19868, 120])).
% 2.30/2.43 tff(19870,plain,
% 2.30/2.43 ((op(e2, e3) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.30/2.43 inference(symmetry,[status(thm)],[19869])).
% 2.30/2.43 tff(19871,plain,
% 2.30/2.43 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19870, 395])).
% 2.30/2.43 tff(19872,plain,
% 2.30/2.43 ((~(op(e2, e3) = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19871])).
% 2.30/2.43 tff(19873,plain,
% 2.30/2.43 (~(op(e2, e3) = op(e3, e2))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19038, 19872])).
% 2.30/2.43 tff(19874,plain,
% 2.30/2.43 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[430, 19873])).
% 2.30/2.43 tff(19875,plain,
% 2.30/2.43 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5367, 19874, 19210, 19867, 19862, 19859, 19852, 19159, 19847, 19841, 19837, 19831, 19820, 19817, 19811])).
% 2.30/2.43 tff(19876,plain,
% 2.30/2.43 (~(op(e0, op(e0, e0)) = e0)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5598, 19875])).
% 2.30/2.43 tff(19877,plain,
% 2.30/2.43 ($false),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[19876, 19804])).
% 2.30/2.43 tff(19878,plain,((op(e2, e3) = e3) | (op(e3, e1) = e2) | (op(e2, e2) = e0) | (op(e0, e1) = e0) | (op(e1, e1) = e2) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.43 tff(19879,plain,
% 2.30/2.43 (op(e2, e3) = e3),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[19878, 3849, 17, 82, 68, 76])).
% 2.30/2.43 tff(19880,plain,
% 2.30/2.43 ((op(e2, e3) = e0) <=> (e3 = e0)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19879])).
% 2.30/2.43 tff(19881,plain,
% 2.30/2.43 ((op(e2, e3) = e0) <=> (e0 = e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19880, 159])).
% 2.30/2.43 tff(19882,plain,
% 2.30/2.43 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19881])).
% 2.30/2.43 tff(19883,plain,
% 2.30/2.43 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19882])).
% 2.30/2.43 tff(19884,plain,
% 2.30/2.43 (~(op(e2, e3) = e0)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[181, 19883])).
% 2.30/2.43 tff(19885,plain,
% 2.30/2.43 (op(e2, e0) = e0),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[2311, 19884, 17, 19522])).
% 2.30/2.43 tff(19886,plain,
% 2.30/2.43 (op(e3, op(e2, e0)) = op(e3, e0)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19885])).
% 2.30/2.43 tff(19887,plain,
% 2.30/2.43 ((op(e3, op(e2, e0)) = e3) <=> (op(e3, e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19886])).
% 2.30/2.43 tff(19888,plain,
% 2.30/2.43 ((op(e3, e0) = e3) <=> (op(e3, op(e2, e0)) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19887])).
% 2.30/2.43 tff(19889,plain,
% 2.30/2.43 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19589])).
% 2.30/2.43 tff(19890,plain,
% 2.30/2.43 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e1)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19889])).
% 2.30/2.43 tff(19891,plain,
% 2.30/2.43 ((e0 = e1) <=> (e0 = op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19589])).
% 2.30/2.43 tff(19892,plain,
% 2.30/2.43 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19891, 1079])).
% 2.30/2.43 tff(19893,plain,
% 2.30/2.43 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19892])).
% 2.30/2.43 tff(19894,plain,
% 2.30/2.43 (~(op(e0, e3) = e0)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[26, 19893])).
% 2.30/2.43 tff(19895,plain,
% 2.30/2.43 (op(e3, e3) = e0),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[1098, 19884, 19012, 19894])).
% 2.30/2.43 tff(19896,plain,
% 2.30/2.43 (e0 = op(e3, e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19895])).
% 2.30/2.43 tff(19897,plain,
% 2.30/2.43 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e3, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19896])).
% 2.30/2.43 tff(19898,plain,
% 2.30/2.43 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19897])).
% 2.30/2.43 tff(19899,plain,
% 2.30/2.43 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19898])).
% 2.30/2.43 tff(19900,plain,
% 2.30/2.43 (~(op(e3, e1) = e0)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[437, 19899])).
% 2.30/2.43 tff(19901,plain,
% 2.30/2.43 (op(e3, e1) = e1),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[446, 19900, 82, 19526])).
% 2.30/2.43 tff(19902,plain,
% 2.30/2.43 (op(e3, e1) = op(e0, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19901, 19589])).
% 2.30/2.43 tff(19903,plain,
% 2.30/2.43 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19902])).
% 2.30/2.43 tff(19904,plain,
% 2.30/2.43 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19903, 19890])).
% 2.30/2.43 tff(19905,plain,
% 2.30/2.43 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19904])).
% 2.30/2.43 tff(19906,plain,
% 2.30/2.43 (~(op(e3, e0) = e1)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[580, 19905])).
% 2.30/2.43 tff(19907,plain,
% 2.30/2.43 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19885])).
% 2.30/2.43 tff(19908,plain,
% 2.30/2.43 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19907, 8115])).
% 2.30/2.43 tff(19909,plain,
% 2.30/2.43 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19908])).
% 2.30/2.43 tff(19910,plain,
% 2.30/2.43 (~(op(e3, e0) = e0)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[747, 19909])).
% 2.30/2.43 tff(19911,plain,
% 2.30/2.43 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19511])).
% 2.30/2.43 tff(19912,plain,
% 2.30/2.43 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19911])).
% 2.30/2.43 tff(19913,plain,
% 2.30/2.43 (~(op(e0, e0) = e3)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[811, 19912])).
% 2.30/2.43 tff(19914,plain,
% 2.30/2.43 ((op(e0, e0) = e1) <=> (op(e0, e0) = op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19589])).
% 2.30/2.43 tff(19915,plain,
% 2.30/2.43 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19914])).
% 2.30/2.43 tff(19916,plain,
% 2.30/2.43 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19915])).
% 2.30/2.43 tff(19917,plain,
% 2.30/2.43 (~(op(e0, e0) = e1)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[3414, 19916])).
% 2.30/2.43 tff(19918,plain,
% 2.30/2.43 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19885])).
% 2.30/2.43 tff(19919,plain,
% 2.30/2.43 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19918])).
% 2.30/2.43 tff(19920,plain,
% 2.30/2.43 (~(op(e0, e0) = e0)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[359, 19919])).
% 2.30/2.43 tff(19921,plain,
% 2.30/2.43 (op(e0, e0) = e2),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[3612, 19920, 19917, 19913])).
% 2.30/2.43 tff(19922,plain,
% 2.30/2.43 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19921])).
% 2.30/2.43 tff(19923,plain,
% 2.30/2.43 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19922, 5377])).
% 2.30/2.43 tff(19924,plain,
% 2.30/2.43 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19923])).
% 2.30/2.43 tff(19925,plain,
% 2.30/2.43 (~(op(e3, e0) = e2)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[6384, 19924])).
% 2.30/2.43 tff(19926,plain,
% 2.30/2.43 (op(e3, e0) = e3),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5422, 19925, 19910, 19906])).
% 2.30/2.43 tff(19927,plain,
% 2.30/2.43 (op(e3, op(e2, e0)) = e3),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19926, 19888])).
% 2.30/2.43 tff(19928,plain,
% 2.30/2.43 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[10697, 19927])).
% 2.30/2.43 tff(19929,plain,
% 2.30/2.43 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19895])).
% 2.30/2.43 tff(19930,plain,
% 2.30/2.43 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19929])).
% 2.30/2.43 tff(19931,plain,
% 2.30/2.43 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19930])).
% 2.30/2.43 tff(19932,plain,
% 2.30/2.43 (op(e3, op(e3, e3)) = e3),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19926, 19931])).
% 2.30/2.43 tff(19933,plain,
% 2.30/2.43 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[6277, 19932])).
% 2.30/2.43 tff(19934,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(op(e0, e3), e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19824, 19926])).
% 2.30/2.43 tff(19935,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e1) = op(e1, e0))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19934, 19826, 19822, 596])).
% 2.30/2.43 tff(19936,plain,
% 2.30/2.43 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19935])).
% 2.30/2.43 tff(19937,plain,
% 2.30/2.43 (~(op(e0, e1) = op(e1, e0))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[410, 19936])).
% 2.30/2.43 tff(19938,plain,
% 2.30/2.43 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[609, 19937])).
% 2.30/2.43 tff(19939,plain,
% 2.30/2.43 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19879])).
% 2.30/2.43 tff(19940,plain,
% 2.30/2.43 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.30/2.43 inference(symmetry,[status(thm)],[19939])).
% 2.30/2.43 tff(19941,plain,
% 2.30/2.43 (op(e3, e2) = e2),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[15971, 19925, 82])).
% 2.30/2.43 tff(19942,plain,
% 2.30/2.43 ((op(e3, e2) = e3) <=> (e2 = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19941])).
% 2.30/2.43 tff(19943,plain,
% 2.30/2.43 ((e2 = e3) <=> (op(e3, e2) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19942])).
% 2.30/2.43 tff(19944,plain,
% 2.30/2.43 ((e2 = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19943, 19940])).
% 2.30/2.43 tff(19945,plain,
% 2.30/2.43 ((~(e2 = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19944])).
% 2.30/2.43 tff(19946,plain,
% 2.30/2.43 (~(op(e3, e2) = op(e2, e3))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[1321, 19945])).
% 2.30/2.43 tff(19947,plain,
% 2.30/2.43 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[500, 19946])).
% 2.30/2.43 tff(19948,plain,
% 2.30/2.43 (op(e1, e1) = e0),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[292, 19900, 3849, 19522])).
% 2.30/2.43 tff(19949,plain,
% 2.30/2.43 (op(e1, e1) = op(e3, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19948, 19896])).
% 2.30/2.43 tff(19950,plain,
% 2.30/2.43 (op(e3, op(e1, e1)) = op(e3, op(e3, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19949])).
% 2.30/2.43 tff(19951,plain,
% 2.30/2.43 (op(e3, op(e1, e1)) = op(e3, e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19950, 19929])).
% 2.30/2.43 tff(19952,plain,
% 2.30/2.43 ((op(e3, op(e1, e1)) = e3) <=> (op(e3, e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19951])).
% 2.30/2.43 tff(19953,plain,
% 2.30/2.43 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e1)) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19952])).
% 2.30/2.43 tff(19954,plain,
% 2.30/2.43 (op(e3, op(e1, e1)) = e3),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19926, 19953])).
% 2.30/2.43 tff(19955,plain,
% 2.30/2.43 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[14029, 19954])).
% 2.30/2.43 tff(19956,plain,
% 2.30/2.43 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19879])).
% 2.30/2.43 tff(19957,plain,
% 2.30/2.43 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19956])).
% 2.30/2.43 tff(19958,plain,
% 2.30/2.43 (~(op(e2, e2) = e3)),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[515, 19957])).
% 2.30/2.43 tff(19959,plain,
% 2.30/2.43 (op(e2, e2) = e1),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[524, 19958, 17, 19597])).
% 2.30/2.43 tff(19960,plain,
% 2.30/2.43 (op(e2, e2) = op(e0, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19959, 19589])).
% 2.30/2.43 tff(19961,plain,
% 2.30/2.43 (op(e2, op(e2, e2)) = op(e2, op(e0, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19960])).
% 2.30/2.43 tff(19962,plain,
% 2.30/2.43 (op(e2, op(e2, e2)) = e2),
% 2.30/2.43 inference(transitivity,[status(thm)],[19961, 19848, 19517])).
% 2.30/2.43 tff(19963,plain,
% 2.30/2.43 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[528, 19962])).
% 2.30/2.43 tff(19964,plain,
% 2.30/2.43 ((op(e3, e0) = op(e3, e1)) <=> (op(e0, e3) = op(e3, e0))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19903, 453])).
% 2.30/2.43 tff(19965,plain,
% 2.30/2.43 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19964])).
% 2.30/2.43 tff(19966,plain,
% 2.30/2.43 (~(op(e0, e3) = op(e3, e0))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[580, 19965])).
% 2.30/2.43 tff(19967,plain,
% 2.30/2.43 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[496, 19966])).
% 2.30/2.43 tff(19968,plain,
% 2.30/2.43 (op(e0, e2) = e0),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[3976, 19920, 3849, 19894])).
% 2.30/2.43 tff(19969,plain,
% 2.30/2.43 (op(e0, e2) = op(e3, e3)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19968, 19896])).
% 2.30/2.43 tff(19970,plain,
% 2.30/2.43 (op(e3, op(e0, e2)) = op(e3, op(e3, e3))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19969])).
% 2.30/2.43 tff(19971,plain,
% 2.30/2.43 (op(e3, op(e0, e2)) = op(e3, e0)),
% 2.30/2.43 inference(transitivity,[status(thm)],[19970, 19929])).
% 2.30/2.43 tff(19972,plain,
% 2.30/2.43 ((op(e3, op(e0, e2)) = e3) <=> (op(e3, e0) = e3)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19971])).
% 2.30/2.43 tff(19973,plain,
% 2.30/2.43 ((op(e3, e0) = e3) <=> (op(e3, op(e0, e2)) = e3)),
% 2.30/2.43 inference(symmetry,[status(thm)],[19972])).
% 2.30/2.43 tff(19974,plain,
% 2.30/2.43 (op(e3, op(e0, e2)) = e3),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[19926, 19973])).
% 2.30/2.43 tff(19975,plain,
% 2.30/2.43 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5635, 19974])).
% 2.30/2.43 tff(19976,plain,
% 2.30/2.43 (op(e0, op(e0, e0)) = op(e0, e2)),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19921])).
% 2.30/2.43 tff(19977,plain,
% 2.30/2.43 (op(e0, op(e0, e0)) = e0),
% 2.30/2.43 inference(transitivity,[status(thm)],[19976, 19968])).
% 2.30/2.43 tff(19978,plain,
% 2.30/2.43 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[5598, 19977])).
% 2.30/2.43 tff(19979,plain,
% 2.30/2.43 ((e2 = e3) <=> (op(e2, e3) = op(e3, e2))),
% 2.30/2.43 inference(transitivity,[status(thm)],[19943, 19940, 395])).
% 2.30/2.43 tff(19980,plain,
% 2.30/2.43 ((~(e2 = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.30/2.43 inference(monotonicity,[status(thm)],[19979])).
% 2.30/2.43 tff(19981,plain,
% 2.30/2.43 (~(op(e2, e3) = op(e3, e2))),
% 2.30/2.43 inference(modus_ponens,[status(thm)],[1321, 19980])).
% 2.30/2.43 tff(19982,plain,
% 2.30/2.43 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.30/2.43 inference(unit_resolution,[status(thm)],[430, 19981])).
% 2.30/2.43 tff(19983,plain,
% 2.30/2.43 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 2.30/2.44 inference(transitivity,[status(thm)],[19934, 19826, 19822])).
% 2.30/2.44 tff(19984,plain,
% 2.30/2.44 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19983])).
% 2.30/2.44 tff(19985,plain,
% 2.30/2.44 (~(op(e1, e0) = op(e0, e1))),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[410, 19984])).
% 2.30/2.44 tff(19986,plain,
% 2.30/2.44 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[613, 19985])).
% 2.30/2.44 tff(19987,plain,
% 2.30/2.44 ($false),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[5367, 19986, 19982, 19210, 19978, 19975, 19967, 19963, 19159, 19955, 19841, 19947, 19938, 19933, 19817, 19928])).
% 2.30/2.44 tff(19988,plain,((op(e0, e1) = e0) | (op(e3, e1) = e2) | (op(e2, e2) = e0) | (op(e1, e1) = e2) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.44 tff(19989,plain,
% 2.30/2.44 (op(e0, e1) = e0),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[19988, 82, 17, 68, 76])).
% 2.30/2.44 tff(19990,plain,
% 2.30/2.44 ((op(e0, e1) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19989])).
% 2.30/2.44 tff(19991,plain,
% 2.30/2.44 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 2.30/2.44 inference(transitivity,[status(thm)],[19990, 1079])).
% 2.30/2.44 tff(19992,plain,
% 2.30/2.44 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19991])).
% 2.30/2.44 tff(19993,plain,
% 2.30/2.44 (~(op(e0, e3) = e0)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[818, 19992])).
% 2.30/2.44 tff(19994,plain,
% 2.30/2.44 (op(e0, e3) = e3),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[687, 121, 79, 1087])).
% 2.30/2.44 tff(19995,plain,
% 2.30/2.44 (op(e0, e3) = op(e2, e3)),
% 2.30/2.44 inference(transitivity,[status(thm)],[19994, 19568])).
% 2.30/2.44 tff(19996,plain,
% 2.30/2.44 ($false),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[964, 19995])).
% 2.30/2.44 tff(19997,plain,((op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.44 tff(19998,plain,
% 2.30/2.44 (op(e0, e3) = e1),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[19997, 19993, 19015, 19012, 76])).
% 2.30/2.44 tff(19999,plain,
% 2.30/2.44 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e1)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19998])).
% 2.30/2.44 tff(20000,plain,
% 2.30/2.44 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e1))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19999])).
% 2.30/2.44 tff(20001,plain,
% 2.30/2.44 (~(op(e0, e0) = e1)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[3414, 20000])).
% 2.30/2.44 tff(20002,plain,
% 2.30/2.44 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19989])).
% 2.30/2.44 tff(20003,plain,
% 2.30/2.44 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20002])).
% 2.30/2.44 tff(20004,plain,
% 2.30/2.44 (~(op(e0, e0) = e0)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[811, 20003])).
% 2.30/2.44 tff(20005,plain,
% 2.30/2.44 ((op(e0, e3) = e3) <=> (e1 = e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19998])).
% 2.30/2.44 tff(20006,plain,
% 2.30/2.44 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20005])).
% 2.30/2.44 tff(20007,plain,
% 2.30/2.44 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20006])).
% 2.30/2.44 tff(20008,plain,
% 2.30/2.44 (~(op(e0, e3) = e3)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[303, 20007])).
% 2.30/2.44 tff(20009,plain,
% 2.30/2.44 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19989])).
% 2.30/2.44 tff(20010,plain,
% 2.30/2.44 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20009])).
% 2.30/2.44 tff(20011,plain,
% 2.30/2.44 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20010])).
% 2.30/2.44 tff(20012,plain,
% 2.30/2.44 (~(op(e0, e1) = e2)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[14, 20011])).
% 2.30/2.44 tff(20013,plain,
% 2.30/2.44 (op(e2, e1) = e2),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[1993, 20012, 68, 82])).
% 2.30/2.44 tff(20014,plain,
% 2.30/2.44 ((op(e2, e1) = e3) <=> (e2 = e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20013])).
% 2.30/2.44 tff(20015,plain,
% 2.30/2.44 ((e2 = e3) <=> (op(e2, e1) = e3)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20014])).
% 2.30/2.44 tff(20016,plain,
% 2.30/2.44 ((~(e2 = e3)) <=> (~(op(e2, e1) = e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20015])).
% 2.30/2.44 tff(20017,plain,
% 2.30/2.44 (~(op(e2, e1) = e3)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[1321, 20016])).
% 2.30/2.44 tff(20018,plain,
% 2.30/2.44 ((op(e0, e1) = e3) <=> (e0 = e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19989])).
% 2.30/2.44 tff(20019,plain,
% 2.30/2.44 ((e0 = e3) <=> (op(e0, e1) = e3)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20018])).
% 2.30/2.44 tff(20020,plain,
% 2.30/2.44 ((~(e0 = e3)) <=> (~(op(e0, e1) = e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20019])).
% 2.30/2.44 tff(20021,plain,
% 2.30/2.44 (~(op(e0, e1) = e3)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[181, 20020])).
% 2.30/2.44 tff(20022,plain,
% 2.30/2.44 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20013])).
% 2.30/2.44 tff(20023,plain,
% 2.30/2.44 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20022, 81])).
% 2.30/2.44 tff(20024,plain,
% 2.30/2.44 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20023])).
% 2.30/2.44 tff(20025,plain,
% 2.30/2.44 (~(op(e2, e2) = e2)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[508, 20024])).
% 2.30/2.44 tff(20026,plain,
% 2.30/2.44 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20013])).
% 2.30/2.44 tff(20027,plain,
% 2.30/2.44 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20026, 69])).
% 2.30/2.44 tff(20028,plain,
% 2.30/2.44 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20027])).
% 2.30/2.44 tff(20029,plain,
% 2.30/2.44 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20028])).
% 2.30/2.44 tff(20030,plain,
% 2.30/2.44 (~(op(e2, e1) = e1)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[708, 20029])).
% 2.30/2.44 tff(20031,plain,
% 2.30/2.44 (op(e3, e3) = e3),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[480, 124, 6613, 661])).
% 2.30/2.44 tff(20032,plain,
% 2.30/2.44 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20031])).
% 2.30/2.44 tff(20033,plain,
% 2.30/2.44 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20032])).
% 2.30/2.44 tff(20034,plain,
% 2.30/2.44 (~(op(e3, e1) = e3)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[437, 20033])).
% 2.30/2.44 tff(20035,plain,
% 2.30/2.44 (op(e1, e1) = e3),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[1730, 20034, 2527, 3271])).
% 2.30/2.44 tff(20036,plain,
% 2.30/2.44 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20035])).
% 2.30/2.44 tff(20037,plain,
% 2.30/2.44 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20036, 532])).
% 2.30/2.44 tff(20038,plain,
% 2.30/2.44 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20037])).
% 2.30/2.44 tff(20039,plain,
% 2.30/2.44 (~(op(e1, e2) = e3)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[1604, 20038])).
% 2.30/2.44 tff(20040,plain,
% 2.30/2.44 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20035])).
% 2.30/2.44 tff(20041,plain,
% 2.30/2.44 (op(e1, op(e1, e1)) = e2),
% 2.30/2.44 inference(transitivity,[status(thm)],[20040, 264])).
% 2.30/2.44 tff(20042,plain,
% 2.30/2.44 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20041])).
% 2.30/2.44 tff(20043,plain,
% 2.30/2.44 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20042])).
% 2.30/2.44 tff(20044,plain,
% 2.30/2.44 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20043, 67])).
% 2.30/2.44 tff(20045,plain,
% 2.30/2.44 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20044])).
% 2.30/2.44 tff(20046,plain,
% 2.30/2.44 (e3 = op(e1, e1)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[20035, 1740])).
% 2.30/2.44 tff(20047,plain,
% 2.30/2.44 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.30/2.44 inference(symmetry,[status(thm)],[20040])).
% 2.30/2.44 tff(20048,plain,
% 2.30/2.44 (e2 = op(e1, op(e1, e1))),
% 2.30/2.44 inference(transitivity,[status(thm)],[265, 20047])).
% 2.30/2.44 tff(20049,plain,
% 2.30/2.44 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[1753, 20048, 20046])).
% 2.30/2.44 tff(20050,plain,
% 2.30/2.44 (~(op(e1, e2) = e0)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[20049, 20045])).
% 2.30/2.44 tff(20051,plain,
% 2.30/2.44 (op(e1, e2) = e1),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[1859, 20050, 19087, 20039])).
% 2.30/2.44 tff(20052,plain,
% 2.30/2.44 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20051])).
% 2.30/2.44 tff(20053,plain,
% 2.30/2.44 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20052, 316])).
% 2.30/2.44 tff(20054,plain,
% 2.30/2.44 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20053])).
% 2.30/2.44 tff(20055,plain,
% 2.30/2.44 (~(op(e2, e2) = e1)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[1273, 20054])).
% 2.30/2.44 tff(20056,plain,
% 2.30/2.44 (op(e2, e2) = e3),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[524, 20055, 17, 5548])).
% 2.30/2.44 tff(20057,plain,
% 2.30/2.44 (e3 = op(e2, e2)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[20056, 1796])).
% 2.30/2.44 tff(20058,plain,
% 2.30/2.44 (op(e2, op(e2, e2)) = op(e2, e3)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20056])).
% 2.30/2.44 tff(20059,plain,
% 2.30/2.44 (op(e2, e3) = op(e2, op(e2, e2))),
% 2.30/2.44 inference(symmetry,[status(thm)],[20058])).
% 2.30/2.44 tff(20060,plain,
% 2.30/2.44 (e0 = op(e2, e3)),
% 2.30/2.44 inference(symmetry,[status(thm)],[19281])).
% 2.30/2.44 tff(20061,plain,
% 2.30/2.44 (e0 = op(e2, op(e2, e2))),
% 2.30/2.44 inference(transitivity,[status(thm)],[20060, 20059])).
% 2.30/2.44 tff(20062,plain,
% 2.30/2.44 (op(e2, op(e2, e2)) = e0),
% 2.30/2.44 inference(transitivity,[status(thm)],[20058, 19281])).
% 2.30/2.44 tff(20063,plain,
% 2.30/2.44 (op(e2, op(e2, op(e2, e2))) = op(e2, e0)),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20062])).
% 2.30/2.44 tff(20064,plain,
% 2.30/2.44 (op(e2, e0) = op(e2, op(e2, op(e2, e2)))),
% 2.30/2.44 inference(symmetry,[status(thm)],[20063])).
% 2.30/2.44 tff(20065,plain,
% 2.30/2.44 (op(e2, e0) = e1),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[345, 20055, 76, 4530])).
% 2.30/2.44 tff(20066,plain,
% 2.30/2.44 (e1 = op(e2, e0)),
% 2.30/2.44 inference(symmetry,[status(thm)],[20065])).
% 2.30/2.44 tff(20067,plain,
% 2.30/2.44 (e1 = op(e2, op(e2, op(e2, e2)))),
% 2.30/2.44 inference(transitivity,[status(thm)],[20066, 20064])).
% 2.30/2.44 tff(20068,plain,
% 2.30/2.44 ($false),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[1810, 20067, 20061, 20057])).
% 2.30/2.44 tff(20069,plain,((op(e2, e3) = e3) | (op(e2, e3) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e0) | (op(e2, e2) = e2) | (~(op(e1, e3) = e2)) | (op(e0, e1) = e3) | (op(e2, e1) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.30/2.44 tff(20070,plain,
% 2.30/2.44 (op(e2, e3) = e3),
% 2.30/2.44 inference(unit_resolution,[status(thm)],[20069, 20030, 76, 17, 20025, 19002, 20021, 20017, 20008])).
% 2.30/2.44 tff(20071,plain,
% 2.30/2.44 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19989])).
% 2.30/2.44 tff(20072,plain,
% 2.30/2.44 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20071, 10200])).
% 2.30/2.44 tff(20073,plain,
% 2.30/2.44 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20072])).
% 2.30/2.44 tff(20074,plain,
% 2.30/2.44 (~(op(e0, e2) = e0)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[2102, 20073])).
% 2.30/2.44 tff(20075,plain,
% 2.30/2.44 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[19998])).
% 2.30/2.44 tff(20076,plain,
% 2.30/2.44 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.30/2.44 inference(transitivity,[status(thm)],[20075, 657])).
% 2.30/2.44 tff(20077,plain,
% 2.30/2.44 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.30/2.44 inference(monotonicity,[status(thm)],[20076])).
% 2.30/2.44 tff(20078,plain,
% 2.30/2.44 (~(op(e3, e3) = e1)),
% 2.30/2.44 inference(modus_ponens,[status(thm)],[1077, 20077])).
% 2.34/2.44 tff(20079,plain,
% 2.34/2.44 (e3 = op(e2, e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20070])).
% 2.34/2.44 tff(20080,plain,
% 2.34/2.44 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e2, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20079])).
% 2.34/2.44 tff(20081,plain,
% 2.34/2.44 ((op(e3, e3) = e3) <=> (op(e2, e3) = op(e3, e3))),
% 2.34/2.44 inference(transitivity,[status(thm)],[20080, 2820])).
% 2.34/2.44 tff(20082,plain,
% 2.34/2.44 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20081])).
% 2.34/2.44 tff(20083,plain,
% 2.34/2.44 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20082])).
% 2.34/2.44 tff(20084,plain,
% 2.34/2.44 (~(op(e3, e3) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[368, 20083])).
% 2.34/2.44 tff(20085,plain,
% 2.34/2.44 (op(e3, e3) = e0),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[15018, 20084, 20078])).
% 2.34/2.44 tff(20086,plain,
% 2.34/2.44 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20085])).
% 2.34/2.44 tff(20087,plain,
% 2.34/2.44 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20086])).
% 2.34/2.44 tff(20088,plain,
% 2.34/2.44 (~(op(e3, e2) = e0)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[1888, 20087])).
% 2.34/2.44 tff(20089,plain,
% 2.34/2.44 (op(e1, e2) = e0),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[973, 20088, 17, 20074])).
% 2.34/2.44 tff(20090,plain,
% 2.34/2.44 (~(op(e1, e1) = e3)),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[6918, 20089, 19002, 20070])).
% 2.34/2.44 tff(20091,plain,
% 2.34/2.44 ((op(e1, e2) = e3) <=> (e0 = op(e2, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20089, 20079])).
% 2.34/2.44 tff(20092,plain,
% 2.34/2.44 ((op(e1, e2) = e3) <=> (op(e2, e3) = e0)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20091, 86])).
% 2.34/2.44 tff(20093,plain,
% 2.34/2.44 ((op(e2, e3) = e0) <=> (op(e1, e2) = e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20092])).
% 2.34/2.44 tff(20094,plain,
% 2.34/2.44 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e2) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20093])).
% 2.34/2.44 tff(20095,plain,
% 2.34/2.44 ((op(e2, e3) = e0) <=> (e3 = e0)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20070])).
% 2.34/2.44 tff(20096,plain,
% 2.34/2.44 ((op(e2, e3) = e0) <=> (e0 = e3)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20095, 159])).
% 2.34/2.44 tff(20097,plain,
% 2.34/2.44 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20096])).
% 2.34/2.44 tff(20098,plain,
% 2.34/2.44 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20097])).
% 2.34/2.44 tff(20099,plain,
% 2.34/2.44 (~(op(e2, e3) = e0)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[181, 20098])).
% 2.34/2.44 tff(20100,plain,
% 2.34/2.44 (~(op(e1, e2) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[20099, 20094])).
% 2.34/2.44 tff(20101,plain,
% 2.34/2.44 (op(e1, e0) = e3),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[247, 20100, 20090, 19601])).
% 2.34/2.44 tff(20102,plain,
% 2.34/2.44 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20101])).
% 2.34/2.44 tff(20103,plain,
% 2.34/2.44 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20102])).
% 2.34/2.44 tff(20104,plain,
% 2.34/2.44 (~(op(e0, e0) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[2471, 20103])).
% 2.34/2.44 tff(20105,plain,
% 2.34/2.44 (op(e0, e0) = e2),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[3612, 20104, 20004, 20001])).
% 2.34/2.44 tff(20106,plain,
% 2.34/2.44 (e2 = op(e0, e0)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[20105, 78])).
% 2.34/2.44 tff(20107,plain,
% 2.34/2.44 (op(e0, op(e0, e0)) = op(e0, e2)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20105])).
% 2.34/2.44 tff(20108,plain,
% 2.34/2.44 (op(e0, e2) = op(e0, op(e0, e0))),
% 2.34/2.44 inference(symmetry,[status(thm)],[20107])).
% 2.34/2.44 tff(20109,plain,
% 2.34/2.44 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20079])).
% 2.34/2.44 tff(20110,plain,
% 2.34/2.44 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20109])).
% 2.34/2.44 tff(20111,plain,
% 2.34/2.44 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20110])).
% 2.34/2.44 tff(20112,plain,
% 2.34/2.44 (~(op(e2, e2) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[515, 20111])).
% 2.34/2.44 tff(20113,plain,
% 2.34/2.44 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20079])).
% 2.34/2.44 tff(20114,plain,
% 2.34/2.44 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20113])).
% 2.34/2.44 tff(20115,plain,
% 2.34/2.44 (op(e3, e1) = e3),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[1730, 20090, 20021, 20017])).
% 2.34/2.44 tff(20116,plain,
% 2.34/2.44 (op(e3, e1) = op(e2, e3)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20115, 20079])).
% 2.34/2.44 tff(20117,plain,
% 2.34/2.44 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20116])).
% 2.34/2.44 tff(20118,plain,
% 2.34/2.44 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.44 inference(transitivity,[status(thm)],[20117, 394])).
% 2.34/2.44 tff(20119,plain,
% 2.34/2.44 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20118, 20114])).
% 2.34/2.44 tff(20120,plain,
% 2.34/2.44 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20119])).
% 2.34/2.44 tff(20121,plain,
% 2.34/2.44 (~(op(e3, e2) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[3429, 20120])).
% 2.34/2.44 tff(20122,plain,
% 2.34/2.44 (op(e0, e2) = e3),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[2111, 20121, 20112, 20100])).
% 2.34/2.44 tff(20123,plain,
% 2.34/2.44 (e3 = op(e0, e2)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20122])).
% 2.34/2.44 tff(20124,plain,
% 2.34/2.44 (e3 = op(e0, op(e0, e0))),
% 2.34/2.44 inference(transitivity,[status(thm)],[20123, 20108])).
% 2.34/2.44 tff(20125,plain,
% 2.34/2.44 (op(e0, op(e0, e0)) = op(e2, e3)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20107, 20122, 20079])).
% 2.34/2.44 tff(20126,plain,
% 2.34/2.44 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e2, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20125])).
% 2.34/2.44 tff(20127,plain,
% 2.34/2.44 (op(e0, op(e2, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.44 inference(symmetry,[status(thm)],[20126])).
% 2.34/2.44 tff(20128,plain,
% 2.34/2.44 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20070])).
% 2.34/2.44 tff(20129,plain,
% 2.34/2.44 (op(e0, e3) = op(e0, op(e2, e3))),
% 2.34/2.44 inference(symmetry,[status(thm)],[20128])).
% 2.34/2.44 tff(20130,plain,
% 2.34/2.44 (e1 = op(e0, e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[19998])).
% 2.34/2.44 tff(20131,plain,
% 2.34/2.44 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.44 inference(transitivity,[status(thm)],[20130, 20129, 20127])).
% 2.34/2.44 tff(20132,plain,
% 2.34/2.44 ($false),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[10921, 20131, 20124, 20106])).
% 2.34/2.44 tff(20133,plain,((op(e3, e1) = e2) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.44 tff(20134,plain,
% 2.34/2.44 (op(e3, e1) = e2),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[20133, 76, 17, 68])).
% 2.34/2.44 tff(20135,plain,
% 2.34/2.44 (~(op(e2, e1) = e0)),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[7790, 121, 79, 80])).
% 2.34/2.44 tff(20136,plain,
% 2.34/2.44 (op(e0, e3) = e0),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[19997, 121, 79, 80, 76])).
% 2.34/2.44 tff(20137,plain,
% 2.34/2.44 (~(op(e3, e2) = e0)),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[6787, 19567, 6684, 10347])).
% 2.34/2.44 tff(20138,plain,
% 2.34/2.44 (op(e3, e0) = op(e0, e3)),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[5538, 20137, 8495, 20136])).
% 2.34/2.44 tff(20139,plain,
% 2.34/2.44 (op(e3, e0) = e0),
% 2.34/2.44 inference(transitivity,[status(thm)],[20138, 20136])).
% 2.34/2.44 tff(20140,plain,
% 2.34/2.44 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20139])).
% 2.34/2.44 tff(20141,plain,
% 2.34/2.44 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20140])).
% 2.34/2.44 tff(20142,plain,
% 2.34/2.44 (~(op(e2, e0) = e0)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[747, 20141])).
% 2.34/2.44 tff(20143,plain,
% 2.34/2.44 ($false),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[2311, 20142, 19572, 17, 20135])).
% 2.34/2.44 tff(20144,plain,((op(e0, e3) = e1) | (op(e2, e2) = e0) | (~(op(e3, e1) = e2)) | (op(e0, e3) = e2) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.44 tff(20145,plain,
% 2.34/2.44 (op(e0, e3) = e1),
% 2.34/2.44 inference(unit_resolution,[status(thm)],[20144, 20134, 17, 19015, 19012, 76, 19007])).
% 2.34/2.44 tff(20146,plain,
% 2.34/2.44 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.44 tff(20147,plain,
% 2.34/2.44 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20146, 657])).
% 2.34/2.44 tff(20148,plain,
% 2.34/2.44 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20147])).
% 2.34/2.44 tff(20149,plain,
% 2.34/2.44 (~(op(e3, e3) = e1)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[1077, 20148])).
% 2.34/2.44 tff(20150,plain,
% 2.34/2.44 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.44 tff(20151,plain,
% 2.34/2.44 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 2.34/2.44 inference(transitivity,[status(thm)],[20150, 69])).
% 2.34/2.44 tff(20152,plain,
% 2.34/2.44 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20151])).
% 2.34/2.44 tff(20153,plain,
% 2.34/2.44 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20152])).
% 2.34/2.44 tff(20154,plain,
% 2.34/2.44 (~(op(e3, e1) = e1)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[708, 20153])).
% 2.34/2.44 tff(20155,plain,
% 2.34/2.44 ((op(e0, e3) = e3) <=> (e1 = e3)),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.44 tff(20156,plain,
% 2.34/2.44 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 2.34/2.44 inference(symmetry,[status(thm)],[20155])).
% 2.34/2.44 tff(20157,plain,
% 2.34/2.44 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.34/2.44 inference(monotonicity,[status(thm)],[20156])).
% 2.34/2.44 tff(20158,plain,
% 2.34/2.44 (~(op(e0, e3) = e3)),
% 2.34/2.44 inference(modus_ponens,[status(thm)],[303, 20157])).
% 2.34/2.45 tff(20159,plain,
% 2.34/2.45 (op(e3, e3) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[480, 124, 19601, 20158])).
% 2.34/2.45 tff(20160,plain,
% 2.34/2.45 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20159])).
% 2.34/2.45 tff(20161,plain,
% 2.34/2.45 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20160])).
% 2.34/2.45 tff(20162,plain,
% 2.34/2.45 (~(op(e3, e0) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[157, 20161])).
% 2.34/2.45 tff(20163,plain,
% 2.34/2.45 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.45 tff(20164,plain,
% 2.34/2.45 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20163])).
% 2.34/2.45 tff(20165,plain,
% 2.34/2.45 (~(op(e0, e1) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[818, 20164])).
% 2.34/2.45 tff(20166,plain,
% 2.34/2.45 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.45 tff(20167,plain,
% 2.34/2.45 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20166])).
% 2.34/2.45 tff(20168,plain,
% 2.34/2.45 (~(op(e0, e1) = e2)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[3046, 20167])).
% 2.34/2.45 tff(20169,plain,
% 2.34/2.45 (op(e0, e1) = e0),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[829, 2527, 20168, 20165])).
% 2.34/2.45 tff(20170,plain,
% 2.34/2.45 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20169])).
% 2.34/2.45 tff(20171,plain,
% 2.34/2.45 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20170, 122])).
% 2.34/2.45 tff(20172,plain,
% 2.34/2.45 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20171])).
% 2.34/2.45 tff(20173,plain,
% 2.34/2.45 (~(op(e1, e1) = e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[792, 20172])).
% 2.34/2.45 tff(20174,plain,
% 2.34/2.45 (op(e1, e1) = e1),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[630, 1291, 68, 20173])).
% 2.34/2.45 tff(20175,plain,
% 2.34/2.45 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20174])).
% 2.34/2.45 tff(20176,plain,
% 2.34/2.45 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20175, 5522])).
% 2.34/2.45 tff(20177,plain,
% 2.34/2.45 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20176])).
% 2.34/2.45 tff(20178,plain,
% 2.34/2.45 (~(op(e1, e2) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[1604, 20177])).
% 2.34/2.45 tff(20179,plain,
% 2.34/2.45 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.45 tff(20180,plain,
% 2.34/2.45 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20179])).
% 2.34/2.45 tff(20181,plain,
% 2.34/2.45 (~(op(e0, e2) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[918, 20180])).
% 2.34/2.45 tff(20182,plain,
% 2.34/2.45 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20169])).
% 2.34/2.45 tff(20183,plain,
% 2.34/2.45 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20182, 10200])).
% 2.34/2.45 tff(20184,plain,
% 2.34/2.45 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20183])).
% 2.34/2.45 tff(20185,plain,
% 2.34/2.45 (~(op(e0, e2) = e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[2102, 20184])).
% 2.34/2.45 tff(20186,plain,
% 2.34/2.45 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20159])).
% 2.34/2.45 tff(20187,plain,
% 2.34/2.45 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20186])).
% 2.34/2.45 tff(20188,plain,
% 2.34/2.45 (~(op(e3, e2) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[1888, 20187])).
% 2.34/2.45 tff(20189,plain,
% 2.34/2.45 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20169])).
% 2.34/2.45 tff(20190,plain,
% 2.34/2.45 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20189])).
% 2.34/2.45 tff(20191,plain,
% 2.34/2.45 (~(op(e0, e0) = e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[811, 20190])).
% 2.34/2.45 tff(20192,plain,
% 2.34/2.45 ((op(e3, e1) = e3) <=> (e2 = e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.45 tff(20193,plain,
% 2.34/2.45 ((e2 = e3) <=> (op(e3, e1) = e3)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20192])).
% 2.34/2.45 tff(20194,plain,
% 2.34/2.45 ((~(e2 = e3)) <=> (~(op(e3, e1) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20193])).
% 2.34/2.45 tff(20195,plain,
% 2.34/2.45 (~(op(e3, e1) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[1321, 20194])).
% 2.34/2.45 tff(20196,plain,
% 2.34/2.45 (op(e2, e1) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1730, 1291, 20195, 2527])).
% 2.34/2.45 tff(20197,plain,
% 2.34/2.45 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20196])).
% 2.34/2.45 tff(20198,plain,
% 2.34/2.45 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20197, 502])).
% 2.34/2.45 tff(20199,plain,
% 2.34/2.45 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20198])).
% 2.34/2.45 tff(20200,plain,
% 2.34/2.45 (~(op(e2, e2) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[508, 20199])).
% 2.34/2.45 tff(20201,plain,
% 2.34/2.45 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[7131])).
% 2.34/2.45 tff(20202,plain,
% 2.34/2.45 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20201])).
% 2.34/2.45 tff(20203,plain,
% 2.34/2.45 (~(op(e0, e0) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[2471, 20202])).
% 2.34/2.45 tff(20204,plain,
% 2.34/2.45 (op(e0, e0) = e2),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[3612, 20203, 6213, 11527])).
% 2.34/2.45 tff(20205,plain,
% 2.34/2.45 (e2 = op(e0, e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[20204, 78])).
% 2.34/2.45 tff(20206,plain,
% 2.34/2.45 (op(e0, op(e0, e0)) = op(op(e2, e3), e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[252, 20204])).
% 2.34/2.45 tff(20207,plain,
% 2.34/2.45 (op(op(e2, e3), e2) = op(e0, op(e0, e0))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20206])).
% 2.34/2.45 tff(20208,plain,
% 2.34/2.45 (op(e0, e2) = op(op(e2, e3), e2)),
% 2.34/2.45 inference(symmetry,[status(thm)],[5088])).
% 2.34/2.45 tff(20209,plain,
% 2.34/2.45 (op(e0, e2) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[2111, 75, 1890, 2431])).
% 2.34/2.45 tff(20210,plain,
% 2.34/2.45 (e3 = op(e0, e2)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20209])).
% 2.34/2.45 tff(20211,plain,
% 2.34/2.45 (e3 = op(e0, op(e0, e0))),
% 2.34/2.45 inference(transitivity,[status(thm)],[20210, 20208, 20207])).
% 2.34/2.45 tff(20212,plain,
% 2.34/2.45 (op(e0, op(e0, e0)) = e3),
% 2.34/2.45 inference(transitivity,[status(thm)],[20206, 5088, 20209])).
% 2.34/2.45 tff(20213,plain,
% 2.34/2.45 (op(e0, op(e0, op(e0, e0))) = op(op(e2, e3), e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[252, 20212])).
% 2.34/2.45 tff(20214,plain,
% 2.34/2.45 (op(op(e2, e3), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20213])).
% 2.34/2.45 tff(20215,plain,
% 2.34/2.45 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.45 inference(transitivity,[status(thm)],[4681, 16755, 20214])).
% 2.34/2.45 tff(20216,plain,
% 2.34/2.45 ($false),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[10921, 20215, 20211, 20205])).
% 2.34/2.45 tff(20217,plain,((op(e1, e2) = e3) | (~(op(e0, e3) = e1)) | (~(op(e2, e3) = e0)) | (op(e0, e0) = e0) | (op(e3, e2) = e3) | (op(e2, e2) = e3) | (op(e1, e1) = e3) | (op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.45 tff(20218,plain,
% 2.34/2.45 (op(e1, e2) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[20217, 20200, 19609, 20191, 20188, 20145, 1291, 19601])).
% 2.34/2.45 tff(20219,plain,
% 2.34/2.45 ((op(e1, e2) = e0) <=> (e3 = op(e2, e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20218, 19645])).
% 2.34/2.45 tff(20220,plain,
% 2.34/2.45 ((op(e1, e2) = e0) <=> (op(e2, e3) = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20219, 112])).
% 2.34/2.45 tff(20221,plain,
% 2.34/2.45 ((op(e2, e3) = e3) <=> (op(e1, e2) = e0)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20220])).
% 2.34/2.45 tff(20222,plain,
% 2.34/2.45 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e2) = e0))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20221])).
% 2.34/2.45 tff(20223,plain,
% 2.34/2.45 (~(op(e1, e2) = e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[124, 20222])).
% 2.34/2.45 tff(20224,plain,
% 2.34/2.45 (op(e3, e2) = e0),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[973, 20223, 17, 20185])).
% 2.34/2.45 tff(20225,plain,
% 2.34/2.45 (op(e3, e2) = op(e2, e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20224, 19645])).
% 2.34/2.45 tff(20226,plain,
% 2.34/2.45 ((op(e3, e2) = e1) <=> (op(e2, e3) = e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20225])).
% 2.34/2.45 tff(20227,plain,
% 2.34/2.45 ((op(e2, e3) = e1) <=> (op(e3, e2) = e1)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20226])).
% 2.34/2.45 tff(20228,plain,
% 2.34/2.45 ((~(op(e2, e3) = e1)) <=> (~(op(e3, e2) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20227])).
% 2.34/2.45 tff(20229,plain,
% 2.34/2.45 (~(op(e3, e2) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[76, 20228])).
% 2.34/2.45 tff(20230,plain,
% 2.34/2.45 (op(e2, e2) = e1),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1613, 20229, 20181, 20178])).
% 2.34/2.45 tff(20231,plain,
% 2.34/2.45 (e1 = op(e2, e2)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[20230, 317])).
% 2.34/2.45 tff(20232,plain,
% 2.34/2.45 (op(e2, op(e2, e2)) = op(e2, e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20230])).
% 2.34/2.45 tff(20233,plain,
% 2.34/2.45 (op(e2, e1) = op(e2, op(e2, e2))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20232])).
% 2.34/2.45 tff(20234,plain,
% 2.34/2.45 (e3 = op(e2, e1)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20196])).
% 2.34/2.45 tff(20235,plain,
% 2.34/2.45 (e3 = op(e2, op(e2, e2))),
% 2.34/2.45 inference(transitivity,[status(thm)],[20234, 20233])).
% 2.34/2.45 tff(20236,plain,
% 2.34/2.45 (op(e2, op(e2, e2)) = e3),
% 2.34/2.45 inference(transitivity,[status(thm)],[20232, 20196])).
% 2.34/2.45 tff(20237,plain,
% 2.34/2.45 (op(e2, op(e2, op(e2, e2))) = op(e2, e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20236])).
% 2.34/2.45 tff(20238,plain,
% 2.34/2.45 (op(e2, e3) = op(e2, op(e2, op(e2, e2)))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20237])).
% 2.34/2.45 tff(20239,plain,
% 2.34/2.45 (e0 = op(e2, op(e2, op(e2, e2)))),
% 2.34/2.45 inference(transitivity,[status(thm)],[19645, 20238])).
% 2.34/2.45 tff(20240,plain,
% 2.34/2.45 ($false),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[334, 20239, 20235, 20231])).
% 2.34/2.45 tff(20241,plain,((op(e1, e1) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e2, e3) = e3) | (op(e1, e1) = e2) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.45 tff(20242,plain,
% 2.34/2.45 (op(e1, e1) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[20241, 2527, 17, 124, 68, 76])).
% 2.34/2.45 tff(20243,plain,
% 2.34/2.45 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20242])).
% 2.34/2.45 tff(20244,plain,
% 2.34/2.45 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20243, 532])).
% 2.34/2.45 tff(20245,plain,
% 2.34/2.45 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20244])).
% 2.34/2.45 tff(20246,plain,
% 2.34/2.45 (~(op(e1, e2) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[1604, 20245])).
% 2.34/2.45 tff(20247,plain,
% 2.34/2.45 (op(e1, op(e1, e1)) = op(e1, e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20242])).
% 2.34/2.45 tff(20248,plain,
% 2.34/2.45 (op(e1, op(e1, e1)) = e2),
% 2.34/2.45 inference(transitivity,[status(thm)],[20247, 19002])).
% 2.34/2.45 tff(20249,plain,
% 2.34/2.45 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20248])).
% 2.34/2.45 tff(20250,plain,
% 2.34/2.45 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20249])).
% 2.34/2.45 tff(20251,plain,
% 2.34/2.45 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20250, 67])).
% 2.34/2.45 tff(20252,plain,
% 2.34/2.45 ((~(e0 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e2) = e0))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20251])).
% 2.34/2.45 tff(20253,plain,
% 2.34/2.45 (e3 = op(e1, e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[20242, 1740])).
% 2.34/2.45 tff(20254,plain,
% 2.34/2.45 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20247])).
% 2.34/2.45 tff(20255,plain,
% 2.34/2.45 (e2 = op(e1, e3)),
% 2.34/2.45 inference(symmetry,[status(thm)],[19002])).
% 2.34/2.45 tff(20256,plain,
% 2.34/2.45 (e2 = op(e1, op(e1, e1))),
% 2.34/2.45 inference(transitivity,[status(thm)],[20255, 20254])).
% 2.34/2.45 tff(20257,plain,
% 2.34/2.45 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1753, 20256, 20253])).
% 2.34/2.45 tff(20258,plain,
% 2.34/2.45 (~(op(e1, e2) = e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[20257, 20252])).
% 2.34/2.45 tff(20259,plain,
% 2.34/2.45 (op(e1, e2) = e1),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1859, 20258, 19486, 20246])).
% 2.34/2.45 tff(20260,plain,
% 2.34/2.45 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20259])).
% 2.34/2.45 tff(20261,plain,
% 2.34/2.45 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20260, 7171])).
% 2.34/2.45 tff(20262,plain,
% 2.34/2.45 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20261])).
% 2.34/2.45 tff(20263,plain,
% 2.34/2.45 (~(op(e3, e2) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[2292, 20262])).
% 2.34/2.45 tff(20264,plain,
% 2.34/2.45 (op(e3, e0) = e1),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[939, 20263, 20154, 20149])).
% 2.34/2.45 tff(20265,plain,
% 2.34/2.45 (e1 = op(e3, e0)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20264])).
% 2.34/2.45 tff(20266,plain,
% 2.34/2.45 (op(e1, e3) = op(op(e3, e0), e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20265])).
% 2.34/2.45 tff(20267,plain,
% 2.34/2.45 (op(op(e3, e0), e3) = op(e1, e3)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20266])).
% 2.34/2.45 tff(20268,plain,
% 2.34/2.45 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.45 tff(20269,plain,
% 2.34/2.45 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20268])).
% 2.34/2.45 tff(20270,plain,
% 2.34/2.45 (~(op(e3, e0) = e2)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[580, 20269])).
% 2.34/2.45 tff(20271,plain,
% 2.34/2.45 ((op(e1, e1) = e1) <=> (e3 = e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20242])).
% 2.34/2.45 tff(20272,plain,
% 2.34/2.45 ((op(e1, e1) = e1) <=> (e1 = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20271, 128])).
% 2.34/2.45 tff(20273,plain,
% 2.34/2.45 ((e1 = e3) <=> (op(e1, e1) = e1)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20272])).
% 2.34/2.45 tff(20274,plain,
% 2.34/2.45 ((~(e1 = e3)) <=> (~(op(e1, e1) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20273])).
% 2.34/2.45 tff(20275,plain,
% 2.34/2.45 (~(op(e1, e1) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[303, 20274])).
% 2.34/2.45 tff(20276,plain,
% 2.34/2.45 (op(e2, e1) = e1),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1252, 20275, 20154, 20165])).
% 2.34/2.45 tff(20277,plain,
% 2.34/2.45 (op(e2, op(e2, e1)) = op(e2, e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20276])).
% 2.34/2.45 tff(20278,plain,
% 2.34/2.45 (op(e2, op(e2, e1)) = e1),
% 2.34/2.45 inference(transitivity,[status(thm)],[20277, 20276])).
% 2.34/2.45 tff(20279,plain,
% 2.34/2.45 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1355, 20278])).
% 2.34/2.45 tff(20280,plain,
% 2.34/2.45 (op(e1, e0) = e0),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1830, 20258, 19012, 20173])).
% 2.34/2.45 tff(20281,plain,
% 2.34/2.45 (op(e1, op(e2, e3)) = op(e1, e0)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[19609])).
% 2.34/2.45 tff(20282,plain,
% 2.34/2.45 (op(e1, e0) = op(e2, e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20280, 19645])).
% 2.34/2.45 tff(20283,plain,
% 2.34/2.45 (op(e1, op(e1, e0)) = op(e1, op(e2, e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20282])).
% 2.34/2.45 tff(20284,plain,
% 2.34/2.45 (op(e1, op(e1, e0)) = e0),
% 2.34/2.45 inference(transitivity,[status(thm)],[20283, 20281, 20280])).
% 2.34/2.45 tff(20285,plain,
% 2.34/2.45 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1836, 20284])).
% 2.34/2.45 tff(20286,plain,
% 2.34/2.45 (op(op(e2, e3), e3) = op(e0, e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[19609])).
% 2.34/2.45 tff(20287,plain,
% 2.34/2.45 (op(e3, e2) = e0),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[973, 20258, 17, 20185])).
% 2.34/2.45 tff(20288,plain,
% 2.34/2.45 (op(e3, e2) = op(e2, e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20287, 19645])).
% 2.34/2.45 tff(20289,plain,
% 2.34/2.45 (op(op(e3, e2), e3) = op(op(e2, e3), e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20288])).
% 2.34/2.45 tff(20290,plain,
% 2.34/2.45 (op(op(e3, e2), e3) = e1),
% 2.34/2.45 inference(transitivity,[status(thm)],[20289, 20286, 20145])).
% 2.34/2.45 tff(20291,plain,
% 2.34/2.45 ((op(op(e3, e2), e3) = e2) <=> (e1 = e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20290])).
% 2.34/2.45 tff(20292,plain,
% 2.34/2.45 ((e1 = e2) <=> (op(op(e3, e2), e3) = e2)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20291])).
% 2.34/2.45 tff(20293,plain,
% 2.34/2.45 ((~(e1 = e2)) <=> (~(op(op(e3, e2), e3) = e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20292])).
% 2.34/2.45 tff(20294,plain,
% 2.34/2.45 (~(op(op(e3, e2), e3) = e2)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[708, 20293])).
% 2.34/2.45 tff(20295,plain,
% 2.34/2.45 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[2408, 20294])).
% 2.34/2.45 tff(20296,plain,
% 2.34/2.45 (op(op(e0, e1), e1) = op(e0, e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20169])).
% 2.34/2.45 tff(20297,plain,
% 2.34/2.45 (op(op(e0, e1), e1) = e0),
% 2.34/2.45 inference(transitivity,[status(thm)],[20296, 20169])).
% 2.34/2.45 tff(20298,plain,
% 2.34/2.45 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[2650, 20297])).
% 2.34/2.45 tff(20299,plain,
% 2.34/2.45 (op(op(e3, e1), e3) = op(e2, e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.45 tff(20300,plain,
% 2.34/2.45 ((op(op(e3, e1), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20299])).
% 2.34/2.45 tff(20301,plain,
% 2.34/2.45 ((op(e2, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20300])).
% 2.34/2.45 tff(20302,plain,
% 2.34/2.45 ((~(op(e2, e3) = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20301])).
% 2.34/2.45 tff(20303,plain,
% 2.34/2.45 (~(op(op(e3, e1), e3) = e1)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[76, 20302])).
% 2.34/2.45 tff(20304,plain,
% 2.34/2.45 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1050, 20303])).
% 2.34/2.45 tff(20305,plain,
% 2.34/2.45 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20242])).
% 2.34/2.45 tff(20306,plain,
% 2.34/2.45 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20305, 1262])).
% 2.34/2.45 tff(20307,plain,
% 2.34/2.45 ((op(e1, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20306, 19688])).
% 2.34/2.45 tff(20308,plain,
% 2.34/2.45 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20307])).
% 2.34/2.45 tff(20309,plain,
% 2.34/2.45 (~(op(op(e1, e3), e1) = e3)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[225, 20308])).
% 2.34/2.45 tff(20310,plain,
% 2.34/2.45 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[160, 20309])).
% 2.34/2.45 tff(20311,plain,
% 2.34/2.45 (op(e0, e0) = e2),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[3652, 19326, 79, 5828])).
% 2.34/2.45 tff(20312,plain,
% 2.34/2.45 (e2 = op(e0, e0)),
% 2.34/2.45 inference(modus_ponens,[status(thm)],[20311, 78])).
% 2.34/2.45 tff(20313,plain,
% 2.34/2.45 (op(e0, op(e0, e0)) = op(op(e2, e3), e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[252, 20311])).
% 2.34/2.45 tff(20314,plain,
% 2.34/2.45 (op(op(e2, e3), e2) = op(e0, op(e0, e0))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20313])).
% 2.34/2.45 tff(20315,plain,
% 2.34/2.45 (e3 = op(e0, op(e0, e0))),
% 2.34/2.45 inference(transitivity,[status(thm)],[7827, 20208, 20314])).
% 2.34/2.45 tff(20316,plain,
% 2.34/2.45 (op(e0, op(e0, e0)) = e3),
% 2.34/2.45 inference(transitivity,[status(thm)],[20313, 5088, 7826])).
% 2.34/2.45 tff(20317,plain,
% 2.34/2.45 (op(e0, op(e0, op(e0, e0))) = op(op(e2, e3), e3)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[252, 20316])).
% 2.34/2.45 tff(20318,plain,
% 2.34/2.45 (op(op(e2, e3), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.45 inference(symmetry,[status(thm)],[20317])).
% 2.34/2.45 tff(20319,plain,
% 2.34/2.45 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.45 inference(transitivity,[status(thm)],[4681, 16755, 20318])).
% 2.34/2.45 tff(20320,plain,
% 2.34/2.45 ($false),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[10921, 20319, 20315, 20312])).
% 2.34/2.45 tff(20321,plain,((~(op(e0, e2) = e3)) | (~(op(e0, e3) = e1)) | (~(op(e2, e3) = e0)) | (op(e0, e3) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.45 tff(20322,plain,
% 2.34/2.45 (~(op(e0, e2) = e3)),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[20321, 19609, 20145, 19015, 20168])).
% 2.34/2.45 tff(20323,plain,
% 2.34/2.45 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[14938, 20322, 20145])).
% 2.34/2.45 tff(20324,plain,
% 2.34/2.45 (op(op(e1, e2), e2) = op(e1, e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20259])).
% 2.34/2.45 tff(20325,plain,
% 2.34/2.45 (op(op(e1, e2), e2) = e1),
% 2.34/2.45 inference(transitivity,[status(thm)],[20324, 20259])).
% 2.34/2.45 tff(20326,plain,
% 2.34/2.45 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1335, 20325])).
% 2.34/2.45 tff(20327,plain,
% 2.34/2.45 (op(e0, e0) = e3),
% 2.34/2.45 inference(unit_resolution,[status(thm)],[1495, 4412, 2527, 661])).
% 2.34/2.45 tff(20328,plain,
% 2.34/2.45 ((op(e0, e0) = e2) <=> (e3 = e2)),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20327])).
% 2.34/2.45 tff(20329,plain,
% 2.34/2.45 ((op(e0, e0) = e2) <=> (e2 = e3)),
% 2.34/2.45 inference(transitivity,[status(thm)],[20328, 1314])).
% 2.34/2.45 tff(20330,plain,
% 2.34/2.45 ((e2 = e3) <=> (op(e0, e0) = e2)),
% 2.34/2.45 inference(symmetry,[status(thm)],[20329])).
% 2.34/2.45 tff(20331,plain,
% 2.34/2.45 ((~(e2 = e3)) <=> (~(op(e0, e0) = e2))),
% 2.34/2.45 inference(monotonicity,[status(thm)],[20330])).
% 2.34/2.46 tff(20332,plain,
% 2.34/2.46 (~(op(e0, e0) = e2)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[1321, 20331])).
% 2.34/2.46 tff(20333,plain,
% 2.34/2.46 (op(e2, e0) = e2),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[589, 20332, 6687, 3786])).
% 2.34/2.46 tff(20334,plain,
% 2.34/2.46 (op(op(e2, e0), e0) = op(e2, op(e2, e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20333, 252])).
% 2.34/2.46 tff(20335,plain,
% 2.34/2.46 (op(op(e2, e0), e0) = e2),
% 2.34/2.46 inference(transitivity,[status(thm)],[20334, 11212, 20333])).
% 2.34/2.46 tff(20336,plain,
% 2.34/2.46 (op(e0, e2) = e2),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[2745, 4412, 7053, 4484])).
% 2.34/2.46 tff(20337,plain,
% 2.34/2.46 (op(e0, op(e0, e2)) = op(op(e2, e3), e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[252, 20336])).
% 2.34/2.46 tff(20338,plain,
% 2.34/2.46 (op(e0, op(e0, e2)) = e2),
% 2.34/2.46 inference(transitivity,[status(thm)],[20337, 5088, 20336])).
% 2.34/2.46 tff(20339,plain,
% 2.34/2.46 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[1331, 20338])).
% 2.34/2.46 tff(20340,plain,
% 2.34/2.46 (~(op(op(e2, e3), e2) = e3)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[4412, 19699])).
% 2.34/2.46 tff(20341,plain,
% 2.34/2.46 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[1934, 20340])).
% 2.34/2.46 tff(20342,plain,
% 2.34/2.46 (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[1459, 20341, 3342, 4549, 1358, 1304, 1275, 1926, 20339, 3341, 1357, 1936])).
% 2.34/2.46 tff(20343,plain,
% 2.34/2.46 (~(op(op(e2, e0), e0) = e2)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[1945, 20342])).
% 2.34/2.46 tff(20344,plain,
% 2.34/2.46 ($false),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[20343, 20335])).
% 2.34/2.46 tff(20345,plain,((op(e0, e2) = e3) | (~(op(e2, e3) = e0)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (op(e1, e0) = e2) | (op(e3, e0) = e2) | (op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e1) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.46 tff(20346,plain,
% 2.34/2.46 (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[20345, 20326, 19609, 20322, 20323, 20310, 20304, 20298, 20295, 20285, 20279, 19180, 20270, 20185, 20181, 2527, 20158])).
% 2.34/2.46 tff(20347,plain,
% 2.34/2.46 (op(op(e3, e0), e3) = e0),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[1764, 20346])).
% 2.34/2.46 tff(20348,plain,
% 2.34/2.46 (e0 = op(op(e3, e0), e3)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20347])).
% 2.34/2.46 tff(20349,plain,
% 2.34/2.46 (op(e2, e3) = e2),
% 2.34/2.46 inference(transitivity,[status(thm)],[19609, 20348, 20267, 19002])).
% 2.34/2.46 tff(20350,plain,
% 2.34/2.46 ($false),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[19038, 20349])).
% 2.34/2.46 tff(20351,plain,((op(e0, e1) = e3) | (op(e2, e2) = e0) | (op(e2, e3) = e3) | (op(e1, e1) = e2) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.46 tff(20352,plain,
% 2.34/2.46 (op(e0, e1) = e3),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[20351, 124, 17, 68, 76])).
% 2.34/2.46 tff(20353,plain,
% 2.34/2.46 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20352])).
% 2.34/2.46 tff(20354,plain,
% 2.34/2.46 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20353])).
% 2.34/2.46 tff(20355,plain,
% 2.34/2.46 (~(op(e0, e0) = e3)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[811, 20354])).
% 2.34/2.46 tff(20356,plain,
% 2.34/2.46 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e2, e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[19645])).
% 2.34/2.46 tff(20357,plain,
% 2.34/2.46 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e0)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20356])).
% 2.34/2.46 tff(20358,plain,
% 2.34/2.46 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e0))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20357])).
% 2.34/2.46 tff(20359,plain,
% 2.34/2.46 (~(op(e2, e1) = e0)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[197, 20358])).
% 2.34/2.46 tff(20360,plain,
% 2.34/2.46 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.46 tff(20361,plain,
% 2.34/2.46 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20360, 1])).
% 2.34/2.46 tff(20362,plain,
% 2.34/2.46 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20361])).
% 2.34/2.46 tff(20363,plain,
% 2.34/2.46 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20362])).
% 2.34/2.46 tff(20364,plain,
% 2.34/2.46 (~(op(e3, e1) = e0)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[14, 20363])).
% 2.34/2.46 tff(20365,plain,
% 2.34/2.46 ((op(e0, e1) = e0) <=> (e3 = op(e2, e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20352, 19645])).
% 2.34/2.46 tff(20366,plain,
% 2.34/2.46 ((op(e0, e1) = e0) <=> (op(e2, e3) = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20365, 112])).
% 2.34/2.46 tff(20367,plain,
% 2.34/2.46 ((op(e2, e3) = e3) <=> (op(e0, e1) = e0)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20366])).
% 2.34/2.46 tff(20368,plain,
% 2.34/2.46 ((~(op(e2, e3) = e3)) <=> (~(op(e0, e1) = e0))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20367])).
% 2.34/2.46 tff(20369,plain,
% 2.34/2.46 (~(op(e0, e1) = e0)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[124, 20368])).
% 2.34/2.46 tff(20370,plain,
% 2.34/2.46 (op(e1, e1) = e0),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[292, 20369, 20364, 20359])).
% 2.34/2.46 tff(20371,plain,
% 2.34/2.46 (~(op(e1, e0) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[278, 20370, 19002, 19609])).
% 2.34/2.46 tff(20372,plain,
% 2.34/2.46 (op(e2, e0) = e3),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[2713, 20371, 20355, 20162])).
% 2.34/2.46 tff(20373,plain,
% 2.34/2.46 ((op(e2, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20372])).
% 2.34/2.46 tff(20374,plain,
% 2.34/2.46 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20373, 4221])).
% 2.34/2.46 tff(20375,plain,
% 2.34/2.46 ((op(e0, e2) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.34/2.46 inference(symmetry,[status(thm)],[20374])).
% 2.34/2.46 tff(20376,plain,
% 2.34/2.46 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.34/2.46 inference(transitivity,[status(thm)],[20375, 6337])).
% 2.34/2.46 tff(20377,plain,
% 2.34/2.46 ((~(op(e0, e2) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20376])).
% 2.34/2.46 tff(20378,plain,
% 2.34/2.46 (~(op(e0, e2) = op(e2, e0))),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20322, 20377])).
% 2.34/2.46 tff(20379,plain,
% 2.34/2.46 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[6347, 20378])).
% 2.34/2.46 tff(20380,plain,
% 2.34/2.46 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.46 tff(20381,plain,
% 2.34/2.46 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20380])).
% 2.34/2.46 tff(20382,plain,
% 2.34/2.46 (~(op(e2, e1) = e2)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[402, 20381])).
% 2.34/2.46 tff(20383,plain,
% 2.34/2.46 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20352])).
% 2.34/2.46 tff(20384,plain,
% 2.34/2.46 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20383, 1262])).
% 2.34/2.46 tff(20385,plain,
% 2.34/2.46 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20384])).
% 2.34/2.46 tff(20386,plain,
% 2.34/2.46 (~(op(e2, e1) = e3)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[606, 20385])).
% 2.34/2.46 tff(20387,plain,
% 2.34/2.46 (op(e2, e1) = e1),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[2367, 20386, 20382, 20359])).
% 2.34/2.46 tff(20388,plain,
% 2.34/2.46 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20387])).
% 2.34/2.46 tff(20389,plain,
% 2.34/2.46 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20388, 5522])).
% 2.34/2.46 tff(20390,plain,
% 2.34/2.46 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.34/2.46 inference(symmetry,[status(thm)],[20389])).
% 2.34/2.46 tff(20391,plain,
% 2.34/2.46 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20352])).
% 2.34/2.46 tff(20392,plain,
% 2.34/2.46 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20391, 1112])).
% 2.34/2.46 tff(20393,plain,
% 2.34/2.46 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20392])).
% 2.34/2.46 tff(20394,plain,
% 2.34/2.46 (~(op(e1, e1) = e3)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[792, 20393])).
% 2.34/2.46 tff(20395,plain,
% 2.34/2.46 (op(e1, e2) = e3),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[247, 20371, 20394, 19601])).
% 2.34/2.46 tff(20396,plain,
% 2.34/2.46 ((op(e1, e2) = e1) <=> (e3 = e1)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20395])).
% 2.34/2.46 tff(20397,plain,
% 2.34/2.46 ((op(e1, e2) = e1) <=> (e1 = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20396, 128])).
% 2.34/2.46 tff(20398,plain,
% 2.34/2.46 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20397])).
% 2.34/2.46 tff(20399,plain,
% 2.34/2.46 ((e1 = e3) <=> (op(e2, e1) = op(e1, e2))),
% 2.34/2.46 inference(transitivity,[status(thm)],[20398, 20390])).
% 2.34/2.46 tff(20400,plain,
% 2.34/2.46 ((~(e1 = e3)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20399])).
% 2.34/2.46 tff(20401,plain,
% 2.34/2.46 (~(op(e2, e1) = op(e1, e2))),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[303, 20400])).
% 2.34/2.46 tff(20402,plain,
% 2.34/2.46 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[557, 20401])).
% 2.34/2.46 tff(20403,plain,
% 2.34/2.46 (op(e2, op(e3, e1)) = op(e2, e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20134])).
% 2.34/2.46 tff(20404,plain,
% 2.34/2.46 ((op(e2, op(e3, e1)) = e2) <=> (op(e2, e2) = e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20403])).
% 2.34/2.46 tff(20405,plain,
% 2.34/2.46 ((op(e2, e2) = e2) <=> (op(e2, op(e3, e1)) = e2)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20404])).
% 2.34/2.46 tff(20406,plain,
% 2.34/2.46 ((op(e2, e1) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20387])).
% 2.34/2.46 tff(20407,plain,
% 2.34/2.46 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20406, 316])).
% 2.34/2.46 tff(20408,plain,
% 2.34/2.46 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20407])).
% 2.34/2.46 tff(20409,plain,
% 2.34/2.46 (~(op(e2, e2) = e1)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[508, 20408])).
% 2.34/2.46 tff(20410,plain,
% 2.34/2.46 ((op(e1, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20395])).
% 2.34/2.46 tff(20411,plain,
% 2.34/2.46 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20410, 502])).
% 2.34/2.46 tff(20412,plain,
% 2.34/2.46 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20411])).
% 2.34/2.46 tff(20413,plain,
% 2.34/2.46 (~(op(e2, e2) = e3)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[1273, 20412])).
% 2.34/2.46 tff(20414,plain,
% 2.34/2.46 (op(e2, e2) = e2),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[524, 20413, 17, 20409])).
% 2.34/2.46 tff(20415,plain,
% 2.34/2.46 (op(e2, op(e3, e1)) = e2),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20414, 20405])).
% 2.34/2.46 tff(20416,plain,
% 2.34/2.46 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[14271, 20415])).
% 2.34/2.46 tff(20417,plain,
% 2.34/2.46 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e3)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20352])).
% 2.34/2.46 tff(20418,plain,
% 2.34/2.46 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.34/2.46 inference(symmetry,[status(thm)],[20417])).
% 2.34/2.46 tff(20419,plain,
% 2.34/2.46 ((op(e1, e0) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.34/2.46 inference(transitivity,[status(thm)],[20418, 596])).
% 2.34/2.46 tff(20420,plain,
% 2.34/2.46 ((~(op(e1, e0) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20419])).
% 2.34/2.46 tff(20421,plain,
% 2.34/2.46 (~(op(e0, e1) = op(e1, e0))),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20371, 20420])).
% 2.34/2.46 tff(20422,plain,
% 2.34/2.46 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[609, 20421])).
% 2.34/2.46 tff(20423,plain,
% 2.34/2.46 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20281])).
% 2.34/2.46 tff(20424,plain,
% 2.34/2.46 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20423])).
% 2.34/2.46 tff(20425,plain,
% 2.34/2.46 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e0)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20370])).
% 2.34/2.46 tff(20426,plain,
% 2.34/2.46 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e0))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20425])).
% 2.34/2.46 tff(20427,plain,
% 2.34/2.46 (~(op(e1, e0) = e0)),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[737, 20426])).
% 2.34/2.46 tff(20428,plain,
% 2.34/2.46 (op(e1, e0) = e1),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[728, 20427, 19180, 20371])).
% 2.34/2.46 tff(20429,plain,
% 2.34/2.46 (op(e1, op(e2, e3)) = e1),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20428, 20424])).
% 2.34/2.46 tff(20430,plain,
% 2.34/2.46 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[10724, 20429])).
% 2.34/2.46 tff(20431,plain,
% 2.34/2.46 ((e1 = e3) <=> (op(e1, e2) = op(e2, e1))),
% 2.34/2.46 inference(transitivity,[status(thm)],[20398, 20390, 531])).
% 2.34/2.46 tff(20432,plain,
% 2.34/2.46 ((~(e1 = e3)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20431])).
% 2.34/2.46 tff(20433,plain,
% 2.34/2.46 (~(op(e1, e2) = op(e2, e1))),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[303, 20432])).
% 2.34/2.46 tff(20434,plain,
% 2.34/2.46 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[539, 20433])).
% 2.34/2.46 tff(20435,plain,
% 2.34/2.46 (op(e1, e1) = op(e2, e3)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20370, 19645])).
% 2.34/2.46 tff(20436,plain,
% 2.34/2.46 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20435])).
% 2.34/2.46 tff(20437,plain,
% 2.34/2.46 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.34/2.46 inference(transitivity,[status(thm)],[20436, 20281])).
% 2.34/2.46 tff(20438,plain,
% 2.34/2.46 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e0) = e1)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20437])).
% 2.34/2.46 tff(20439,plain,
% 2.34/2.46 ((op(e1, e0) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20438])).
% 2.34/2.46 tff(20440,plain,
% 2.34/2.46 (op(e1, op(e1, e1)) = e1),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20428, 20439])).
% 2.34/2.46 tff(20441,plain,
% 2.34/2.46 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[5678, 20440])).
% 2.34/2.46 tff(20442,plain,
% 2.34/2.46 (op(e2, op(e1, e3)) = op(e2, e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[19002])).
% 2.34/2.46 tff(20443,plain,
% 2.34/2.46 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e2) = e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20442])).
% 2.34/2.46 tff(20444,plain,
% 2.34/2.46 ((op(e2, e2) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 2.34/2.46 inference(symmetry,[status(thm)],[20443])).
% 2.34/2.46 tff(20445,plain,
% 2.34/2.46 (op(e2, op(e1, e3)) = e2),
% 2.34/2.46 inference(modus_ponens,[status(thm)],[20414, 20444])).
% 2.34/2.46 tff(20446,plain,
% 2.34/2.46 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[9084, 20445])).
% 2.34/2.46 tff(20447,plain,
% 2.34/2.46 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20414])).
% 2.34/2.46 tff(20448,plain,
% 2.34/2.46 (op(e2, op(e2, e2)) = e2),
% 2.34/2.46 inference(transitivity,[status(thm)],[20447, 20414])).
% 2.34/2.46 tff(20449,plain,
% 2.34/2.46 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.34/2.46 inference(unit_resolution,[status(thm)],[528, 20448])).
% 2.34/2.46 tff(20450,plain,
% 2.34/2.46 (op(e2, op(e2, e3)) = op(e2, e0)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[19609])).
% 2.34/2.46 tff(20451,plain,
% 2.34/2.46 (op(e2, e0) = op(e2, op(e2, e3))),
% 2.34/2.46 inference(symmetry,[status(thm)],[20450])).
% 2.34/2.46 tff(20452,plain,
% 2.34/2.46 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.34/2.46 inference(monotonicity,[status(thm)],[20451])).
% 2.34/2.46 tff(20453,plain,
% 2.34/2.46 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e0) = e2)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20452])).
% 2.34/2.47 tff(20454,plain,
% 2.34/2.47 (op(e2, op(e2, e3)) = e3),
% 2.34/2.47 inference(transitivity,[status(thm)],[20450, 20372])).
% 2.34/2.47 tff(20455,plain,
% 2.34/2.47 ((op(e2, op(e2, e3)) = e2) <=> (e3 = e2)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20454])).
% 2.34/2.47 tff(20456,plain,
% 2.34/2.47 ((op(e2, op(e2, e3)) = e2) <=> (e2 = e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20455, 1314])).
% 2.34/2.47 tff(20457,plain,
% 2.34/2.47 ((e2 = e3) <=> (op(e2, op(e2, e3)) = e2)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20456])).
% 2.34/2.47 tff(20458,plain,
% 2.34/2.47 ((e2 = e3) <=> (op(e2, e0) = e2)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20457, 20453])).
% 2.34/2.47 tff(20459,plain,
% 2.34/2.47 ((~(e2 = e3)) <=> (~(op(e2, e0) = e2))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20458])).
% 2.34/2.47 tff(20460,plain,
% 2.34/2.47 (~(op(e2, e0) = e2)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[1321, 20459])).
% 2.34/2.47 tff(20461,plain,
% 2.34/2.47 (op(e0, e0) = e2),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[589, 20460, 19180, 20270])).
% 2.34/2.47 tff(20462,plain,
% 2.34/2.47 (op(e2, op(e0, e0)) = op(e2, e2)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20461])).
% 2.34/2.47 tff(20463,plain,
% 2.34/2.47 (op(e2, op(e0, e0)) = e2),
% 2.34/2.47 inference(transitivity,[status(thm)],[20462, 20414])).
% 2.34/2.47 tff(20464,plain,
% 2.34/2.47 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[593, 20463])).
% 2.34/2.47 tff(20465,plain,
% 2.34/2.47 ((~(op(e0, e2) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20375])).
% 2.34/2.47 tff(20466,plain,
% 2.34/2.47 (~(op(e2, e0) = op(e0, e2))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20322, 20465])).
% 2.34/2.47 tff(20467,plain,
% 2.34/2.47 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[6358, 20466])).
% 2.34/2.47 tff(20468,plain,
% 2.34/2.47 (op(e3, op(e0, e1)) = op(e3, e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20352])).
% 2.34/2.47 tff(20469,plain,
% 2.34/2.47 (op(e3, op(e0, e1)) = e3),
% 2.34/2.47 inference(transitivity,[status(thm)],[20468, 20159])).
% 2.34/2.47 tff(20470,plain,
% 2.34/2.47 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[12000, 20469])).
% 2.34/2.47 tff(20471,plain,
% 2.34/2.47 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20159])).
% 2.34/2.47 tff(20472,plain,
% 2.34/2.47 (op(e3, op(e3, e3)) = e3),
% 2.34/2.47 inference(transitivity,[status(thm)],[20471, 20159])).
% 2.34/2.47 tff(20473,plain,
% 2.34/2.47 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[6277, 20472])).
% 2.34/2.47 tff(20474,plain,
% 2.34/2.47 ((op(e0, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20384, 19688])).
% 2.34/2.47 tff(20475,plain,
% 2.34/2.47 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20474])).
% 2.34/2.47 tff(20476,plain,
% 2.34/2.47 (~(op(op(e1, e3), e1) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[606, 20475])).
% 2.34/2.47 tff(20477,plain,
% 2.34/2.47 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[160, 20476])).
% 2.34/2.47 tff(20478,plain,
% 2.34/2.47 ((op(e2, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[19609])).
% 2.34/2.47 tff(20479,plain,
% 2.34/2.47 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20478, 3077])).
% 2.34/2.47 tff(20480,plain,
% 2.34/2.47 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20479])).
% 2.34/2.47 tff(20481,plain,
% 2.34/2.47 (~(op(e3, e3) = e0)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[368, 20480])).
% 2.34/2.47 tff(20482,plain,
% 2.34/2.47 ((op(e1, e1) = e1) <=> (op(e2, e3) = e1)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20435])).
% 2.34/2.47 tff(20483,plain,
% 2.34/2.47 ((op(e2, e3) = e1) <=> (op(e1, e1) = e1)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20482])).
% 2.34/2.47 tff(20484,plain,
% 2.34/2.47 ((~(op(e2, e3) = e1)) <=> (~(op(e1, e1) = e1))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20483])).
% 2.34/2.47 tff(20485,plain,
% 2.34/2.47 (~(op(e1, e1) = e1)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[76, 20484])).
% 2.34/2.47 tff(20486,plain,
% 2.34/2.47 (~(op(e3, e0) = op(e0, e3))),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[5154, 20485, 19012, 20382, 20145, 20481, 20369, 20477, 20195])).
% 2.34/2.47 tff(20487,plain,
% 2.34/2.47 (~(op(e0, e3) = op(e3, e0))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20486, 454])).
% 2.34/2.47 tff(20488,plain,
% 2.34/2.47 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[496, 20487])).
% 2.34/2.47 tff(20489,plain,
% 2.34/2.47 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20398])).
% 2.34/2.47 tff(20490,plain,
% 2.34/2.47 (~(op(e1, e2) = e1)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[303, 20489])).
% 2.34/2.47 tff(20491,plain,
% 2.34/2.47 (op(e3, e2) = e1),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[1613, 20490, 20181, 20409])).
% 2.34/2.47 tff(20492,plain,
% 2.34/2.47 ((op(e3, e2) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20491])).
% 2.34/2.47 tff(20493,plain,
% 2.34/2.47 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20492, 5574])).
% 2.34/2.47 tff(20494,plain,
% 2.34/2.47 ((op(e2, e3) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.47 inference(symmetry,[status(thm)],[20493])).
% 2.34/2.47 tff(20495,plain,
% 2.34/2.47 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.47 inference(transitivity,[status(thm)],[20494, 395])).
% 2.34/2.47 tff(20496,plain,
% 2.34/2.47 ((~(op(e2, e3) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20495])).
% 2.34/2.47 tff(20497,plain,
% 2.34/2.47 (~(op(e2, e3) = op(e3, e2))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[76, 20496])).
% 2.34/2.47 tff(20498,plain,
% 2.34/2.47 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[430, 20497])).
% 2.34/2.47 tff(20499,plain,
% 2.34/2.47 ($false),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[5367, 20498, 20488, 20473, 20470, 20467, 20464, 20449, 20446, 20441, 20434, 20430, 20422, 20416, 20402, 20379])).
% 2.34/2.47 tff(20500,plain,((op(e2, e3) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.47 tff(20501,plain,
% 2.34/2.47 (op(e2, e3) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[20500, 76, 17, 68])).
% 2.34/2.47 tff(20502,plain,
% 2.34/2.47 (e3 = op(e2, e3)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20501])).
% 2.34/2.47 tff(20503,plain,
% 2.34/2.47 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e2, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20502])).
% 2.34/2.47 tff(20504,plain,
% 2.34/2.47 ((op(e3, e3) = e3) <=> (op(e2, e3) = op(e3, e3))),
% 2.34/2.47 inference(transitivity,[status(thm)],[20503, 2820])).
% 2.34/2.47 tff(20505,plain,
% 2.34/2.47 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20504])).
% 2.34/2.47 tff(20506,plain,
% 2.34/2.47 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20505])).
% 2.34/2.47 tff(20507,plain,
% 2.34/2.47 (~(op(e3, e3) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[368, 20506])).
% 2.34/2.47 tff(20508,plain,
% 2.34/2.47 (op(e3, e3) = e0),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[15018, 20507, 20149])).
% 2.34/2.47 tff(20509,plain,
% 2.34/2.47 (~(op(e3, e0) = e1)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[8647, 20508, 20134])).
% 2.34/2.47 tff(20510,plain,
% 2.34/2.47 (op(e3, e2) = e1),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[939, 20509, 20154, 20149])).
% 2.34/2.47 tff(20511,plain,
% 2.34/2.47 (e1 = op(e3, e2)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20510])).
% 2.34/2.47 tff(20512,plain,
% 2.34/2.47 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20511])).
% 2.34/2.47 tff(20513,plain,
% 2.34/2.47 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e1)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20512])).
% 2.34/2.47 tff(20514,plain,
% 2.34/2.47 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e1))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20513])).
% 2.34/2.47 tff(20515,plain,
% 2.34/2.47 (~(op(e1, e2) = e1)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[2292, 20514])).
% 2.34/2.47 tff(20516,plain,
% 2.34/2.47 (e0 = op(e3, e3)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20508])).
% 2.34/2.47 tff(20517,plain,
% 2.34/2.47 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20516])).
% 2.34/2.47 tff(20518,plain,
% 2.34/2.47 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20517])).
% 2.34/2.47 tff(20519,plain,
% 2.34/2.47 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20518])).
% 2.34/2.47 tff(20520,plain,
% 2.34/2.47 (~(op(e3, e0) = e0)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[157, 20519])).
% 2.34/2.47 tff(20521,plain,
% 2.34/2.47 (op(e3, e0) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[5422, 20520, 20270, 20509])).
% 2.34/2.47 tff(20522,plain,
% 2.34/2.47 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20521])).
% 2.34/2.47 tff(20523,plain,
% 2.34/2.47 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20522])).
% 2.34/2.47 tff(20524,plain,
% 2.34/2.47 (~(op(e0, e0) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[6384, 20523])).
% 2.34/2.47 tff(20525,plain,
% 2.34/2.47 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[6778])).
% 2.34/2.47 tff(20526,plain,
% 2.34/2.47 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20525])).
% 2.34/2.47 tff(20527,plain,
% 2.34/2.47 (~(op(e2, e1) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[197, 20526])).
% 2.34/2.47 tff(20528,plain,
% 2.34/2.47 (op(e1, e1) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[1730, 2527, 2839, 20527])).
% 2.34/2.47 tff(20529,plain,
% 2.34/2.47 (~(op(e1, e2) = e0)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[6918, 20528, 264, 6778])).
% 2.34/2.47 tff(20530,plain,
% 2.34/2.47 (op(e0, e2) = e0),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[973, 20529, 17, 4455])).
% 2.34/2.47 tff(20531,plain,
% 2.34/2.47 (op(e0, e2) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[1495, 2527, 10447, 661])).
% 2.34/2.47 tff(20532,plain,
% 2.34/2.47 (e3 = op(e0, e2)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20531])).
% 2.34/2.47 tff(20533,plain,
% 2.34/2.47 (op(e2, e3) = op(e3, e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[6778, 20532, 20530, 4451])).
% 2.34/2.47 tff(20534,plain,
% 2.34/2.47 ($false),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[368, 20533])).
% 2.34/2.47 tff(20535,plain,((op(e0, e1) = e3) | (~(op(e3, e3) = e0)) | (~(op(e2, e3) = e3)) | (op(e2, e2) = e0) | (~(op(e1, e3) = e2)) | (op(e3, e1) = e3) | (op(e0, e0) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.47 tff(20536,plain,
% 2.34/2.47 (op(e0, e1) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[20535, 20508, 20501, 17, 19002, 20195, 20524, 20158])).
% 2.34/2.47 tff(20537,plain,
% 2.34/2.47 (op(e0, e1) = op(e2, e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20536, 20502])).
% 2.34/2.47 tff(20538,plain,
% 2.34/2.47 ((op(e0, e1) = e0) <=> (op(e2, e3) = op(e3, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20537, 20516])).
% 2.34/2.47 tff(20539,plain,
% 2.34/2.47 ((op(e2, e3) = op(e3, e3)) <=> (op(e0, e1) = e0)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20538])).
% 2.34/2.47 tff(20540,plain,
% 2.34/2.47 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e0, e1) = e0))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20539])).
% 2.34/2.47 tff(20541,plain,
% 2.34/2.47 (~(op(e0, e1) = e0)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[368, 20540])).
% 2.34/2.47 tff(20542,plain,
% 2.34/2.47 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20536])).
% 2.34/2.47 tff(20543,plain,
% 2.34/2.47 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20542, 1112])).
% 2.34/2.47 tff(20544,plain,
% 2.34/2.47 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20543])).
% 2.34/2.47 tff(20545,plain,
% 2.34/2.47 (~(op(e1, e1) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[792, 20544])).
% 2.34/2.47 tff(20546,plain,
% 2.34/2.47 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.47 tff(20547,plain,
% 2.34/2.47 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20546, 18])).
% 2.34/2.47 tff(20548,plain,
% 2.34/2.47 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20547])).
% 2.34/2.47 tff(20549,plain,
% 2.34/2.47 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20548])).
% 2.34/2.47 tff(20550,plain,
% 2.34/2.47 (~(op(e0, e3) = e0)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[26, 20549])).
% 2.34/2.47 tff(20551,plain,
% 2.34/2.47 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e2, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20502])).
% 2.34/2.47 tff(20552,plain,
% 2.34/2.47 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20551])).
% 2.34/2.47 tff(20553,plain,
% 2.34/2.47 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20552])).
% 2.34/2.47 tff(20554,plain,
% 2.34/2.47 (~(op(e2, e2) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[515, 20553])).
% 2.34/2.47 tff(20555,plain,
% 2.34/2.47 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e3, e2))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20511])).
% 2.34/2.47 tff(20556,plain,
% 2.34/2.47 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e1)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20555])).
% 2.34/2.47 tff(20557,plain,
% 2.34/2.47 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e1))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20556])).
% 2.34/2.47 tff(20558,plain,
% 2.34/2.47 (~(op(e2, e2) = e1)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[1546, 20557])).
% 2.34/2.47 tff(20559,plain,
% 2.34/2.47 (op(e2, e2) = e2),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[524, 20558, 17, 20554])).
% 2.34/2.47 tff(20560,plain,
% 2.34/2.47 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20559])).
% 2.34/2.47 tff(20561,plain,
% 2.34/2.47 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20560])).
% 2.34/2.47 tff(20562,plain,
% 2.34/2.47 (~(op(e0, e2) = e2)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[2736, 20561])).
% 2.34/2.47 tff(20563,plain,
% 2.34/2.47 (op(e0, e0) = e2),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[3652, 20562, 19015, 20168])).
% 2.34/2.47 tff(20564,plain,
% 2.34/2.47 ((op(e0, e0) = e0) <=> (e2 = op(e3, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20563, 20516])).
% 2.34/2.47 tff(20565,plain,
% 2.34/2.47 ((op(e0, e0) = e0) <=> (op(e3, e3) = e2)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20564, 565])).
% 2.34/2.47 tff(20566,plain,
% 2.34/2.47 ((op(e3, e3) = e2) <=> (op(e0, e0) = e0)),
% 2.34/2.47 inference(symmetry,[status(thm)],[20565])).
% 2.34/2.47 tff(20567,plain,
% 2.34/2.47 ((~(op(e3, e3) = e2)) <=> (~(op(e0, e0) = e0))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20566])).
% 2.34/2.47 tff(20568,plain,
% 2.34/2.47 (~(op(e0, e0) = e0)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[15002, 20567])).
% 2.34/2.47 tff(20569,plain,
% 2.34/2.47 (op(e0, e2) = e0),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[3976, 20541, 20568, 20550])).
% 2.34/2.47 tff(20570,plain,
% 2.34/2.47 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20508])).
% 2.34/2.47 tff(20571,plain,
% 2.34/2.47 (op(e0, e2) = op(e3, e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20569, 20516])).
% 2.34/2.47 tff(20572,plain,
% 2.34/2.47 (op(e3, op(e0, e2)) = op(e3, op(e3, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20571])).
% 2.34/2.47 tff(20573,plain,
% 2.34/2.47 (op(e3, op(e0, e2)) = e3),
% 2.34/2.47 inference(transitivity,[status(thm)],[20572, 20570, 20521])).
% 2.34/2.47 tff(20574,plain,
% 2.34/2.47 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[5635, 20573])).
% 2.34/2.47 tff(20575,plain,
% 2.34/2.47 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20521])).
% 2.34/2.47 tff(20576,plain,
% 2.34/2.47 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20575])).
% 2.34/2.47 tff(20577,plain,
% 2.34/2.47 (~(op(e1, e0) = e3)),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[410, 20576])).
% 2.34/2.47 tff(20578,plain,
% 2.34/2.47 (op(e1, e2) = e3),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[247, 20545, 20577, 19601])).
% 2.34/2.47 tff(20579,plain,
% 2.34/2.47 (op(e1, e2) = op(e2, e3)),
% 2.34/2.47 inference(transitivity,[status(thm)],[20578, 20502])).
% 2.34/2.47 tff(20580,plain,
% 2.34/2.47 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = op(e2, e3))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20579])).
% 2.34/2.47 tff(20581,plain,
% 2.34/2.47 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.34/2.47 inference(symmetry,[status(thm)],[20580])).
% 2.34/2.47 tff(20582,plain,
% 2.34/2.47 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20581])).
% 2.34/2.47 tff(20583,plain,
% 2.34/2.47 (~(op(e2, e1) = op(e1, e2))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[197, 20582])).
% 2.34/2.47 tff(20584,plain,
% 2.34/2.47 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[557, 20583])).
% 2.34/2.47 tff(20585,plain,
% 2.34/2.47 (op(e2, op(e3, e1)) = e2),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20559, 20405])).
% 2.34/2.47 tff(20586,plain,
% 2.34/2.47 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[14271, 20585])).
% 2.34/2.47 tff(20587,plain,
% 2.34/2.47 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e3)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20536])).
% 2.34/2.47 tff(20588,plain,
% 2.34/2.47 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.34/2.47 inference(symmetry,[status(thm)],[20587])).
% 2.34/2.47 tff(20589,plain,
% 2.34/2.47 ((op(e1, e0) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.34/2.47 inference(transitivity,[status(thm)],[20588, 596])).
% 2.34/2.47 tff(20590,plain,
% 2.34/2.47 ((~(op(e1, e0) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20589])).
% 2.34/2.47 tff(20591,plain,
% 2.34/2.47 (~(op(e0, e1) = op(e1, e0))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20577, 20590])).
% 2.34/2.47 tff(20592,plain,
% 2.34/2.47 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[609, 20591])).
% 2.34/2.47 tff(20593,plain,
% 2.34/2.47 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20511])).
% 2.34/2.47 tff(20594,plain,
% 2.34/2.47 ((op(e2, e3) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.47 inference(transitivity,[status(thm)],[20593, 394])).
% 2.34/2.47 tff(20595,plain,
% 2.34/2.47 ((~(op(e2, e3) = e1)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20594])).
% 2.34/2.47 tff(20596,plain,
% 2.34/2.47 (~(op(e3, e2) = op(e2, e3))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[76, 20595])).
% 2.34/2.47 tff(20597,plain,
% 2.34/2.47 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[500, 20596])).
% 2.34/2.47 tff(20598,plain,
% 2.34/2.47 ((op(e2, e1) = op(e2, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.34/2.47 inference(transitivity,[status(thm)],[20581, 531])).
% 2.34/2.47 tff(20599,plain,
% 2.34/2.47 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20598])).
% 2.34/2.47 tff(20600,plain,
% 2.34/2.47 (~(op(e1, e2) = op(e2, e1))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[197, 20599])).
% 2.34/2.47 tff(20601,plain,
% 2.34/2.47 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[539, 20600])).
% 2.34/2.47 tff(20602,plain,
% 2.34/2.47 ((~(op(e1, e0) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20588])).
% 2.34/2.47 tff(20603,plain,
% 2.34/2.47 (~(op(e1, e0) = op(e0, e1))),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20577, 20602])).
% 2.34/2.47 tff(20604,plain,
% 2.34/2.47 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[613, 20603])).
% 2.34/2.47 tff(20605,plain,
% 2.34/2.47 (op(e2, op(e1, e3)) = e2),
% 2.34/2.47 inference(modus_ponens,[status(thm)],[20559, 20444])).
% 2.34/2.47 tff(20606,plain,
% 2.34/2.47 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[9084, 20605])).
% 2.34/2.47 tff(20607,plain,
% 2.34/2.47 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20559])).
% 2.34/2.47 tff(20608,plain,
% 2.34/2.47 (op(e2, op(e2, e2)) = e2),
% 2.34/2.47 inference(transitivity,[status(thm)],[20607, 20559])).
% 2.34/2.47 tff(20609,plain,
% 2.34/2.47 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[528, 20608])).
% 2.34/2.47 tff(20610,plain,
% 2.34/2.47 (op(e2, op(e0, e0)) = op(e2, e2)),
% 2.34/2.47 inference(monotonicity,[status(thm)],[20563])).
% 2.34/2.47 tff(20611,plain,
% 2.34/2.47 (op(e2, op(e0, e0)) = e2),
% 2.34/2.47 inference(transitivity,[status(thm)],[20610, 20559])).
% 2.34/2.47 tff(20612,plain,
% 2.34/2.47 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.34/2.47 inference(unit_resolution,[status(thm)],[593, 20611])).
% 2.34/2.47 tff(20613,plain,
% 2.34/2.47 (op(e3, e0) = op(e3, op(e3, e3))),
% 2.34/2.48 inference(symmetry,[status(thm)],[20570])).
% 2.34/2.48 tff(20614,plain,
% 2.34/2.48 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20613])).
% 2.34/2.48 tff(20615,plain,
% 2.34/2.48 (op(e3, op(e3, e3)) = e3),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[20521, 20614])).
% 2.34/2.48 tff(20616,plain,
% 2.34/2.48 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[6277, 20615])).
% 2.34/2.48 tff(20617,plain,
% 2.34/2.48 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20594, 395])).
% 2.34/2.48 tff(20618,plain,
% 2.34/2.48 ((~(op(e2, e3) = e1)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20617])).
% 2.34/2.48 tff(20619,plain,
% 2.34/2.48 (~(op(e2, e3) = op(e3, e2))),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[76, 20618])).
% 2.34/2.48 tff(20620,plain,
% 2.34/2.48 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[430, 20619])).
% 2.34/2.48 tff(20621,plain,
% 2.34/2.48 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e1)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20145])).
% 2.34/2.48 tff(20622,plain,
% 2.34/2.48 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e0, e3))),
% 2.34/2.48 inference(symmetry,[status(thm)],[20621])).
% 2.34/2.48 tff(20623,plain,
% 2.34/2.48 ((op(e3, e0) = e1) <=> (op(e0, e3) = op(e3, e0))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20622, 453])).
% 2.34/2.48 tff(20624,plain,
% 2.34/2.48 ((~(op(e3, e0) = e1)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20623])).
% 2.34/2.48 tff(20625,plain,
% 2.34/2.48 (~(op(e0, e3) = op(e3, e0))),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[20509, 20624])).
% 2.34/2.48 tff(20626,plain,
% 2.34/2.48 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[496, 20625])).
% 2.34/2.48 tff(20627,plain,
% 2.34/2.48 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[17119])).
% 2.34/2.48 tff(20628,plain,
% 2.34/2.48 (op(e2, e1) = e0),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[292, 84, 183, 3849])).
% 2.34/2.48 tff(20629,plain,
% 2.34/2.48 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e0)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20628])).
% 2.34/2.48 tff(20630,plain,
% 2.34/2.48 ((op(e2, e0) = op(e2, e1)) <=> (op(e0, e2) = op(e2, e0))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20629, 20627, 6337])).
% 2.34/2.48 tff(20631,plain,
% 2.34/2.48 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20630])).
% 2.34/2.48 tff(20632,plain,
% 2.34/2.48 (~(op(e0, e2) = op(e2, e0))),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[1966, 20631])).
% 2.34/2.48 tff(20633,plain,
% 2.34/2.48 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[6347, 20632])).
% 2.34/2.48 tff(20634,plain,
% 2.34/2.48 (op(e1, op(e1, e1)) = op(e1, e1)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[12395])).
% 2.34/2.48 tff(20635,plain,
% 2.34/2.48 (op(e1, op(e1, e1)) = e1),
% 2.34/2.48 inference(transitivity,[status(thm)],[20634, 12395])).
% 2.34/2.48 tff(20636,plain,
% 2.34/2.48 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[5678, 20635])).
% 2.34/2.48 tff(20637,plain,
% 2.34/2.48 ($false),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[5367, 20636, 20633, 5670, 5668, 6688, 5667, 5672, 5511, 5675, 5673, 5671, 5681, 5669, 5680, 5674])).
% 2.34/2.48 tff(20638,plain,((op(e1, e1) = e0) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~(op(e0, e2) = e0)) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e3, e1) = e0) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.48 tff(20639,plain,
% 2.34/2.48 (op(e1, e1) = e0),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[20638, 20626, 20620, 20616, 20612, 20609, 20606, 20604, 20601, 20597, 20592, 20586, 20584, 20574, 20569, 68, 20545, 20364, 20541])).
% 2.34/2.48 tff(20640,plain,
% 2.34/2.48 (op(e1, e1) = op(e3, e3)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20639, 20516])).
% 2.34/2.48 tff(20641,plain,
% 2.34/2.48 ((op(e1, e1) = e1) <=> (op(e3, e3) = op(e3, e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20640, 20511])).
% 2.34/2.48 tff(20642,plain,
% 2.34/2.48 ((op(e1, e1) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20641, 7805])).
% 2.34/2.48 tff(20643,plain,
% 2.34/2.48 ((op(e3, e2) = op(e3, e3)) <=> (op(e1, e1) = e1)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20642])).
% 2.34/2.48 tff(20644,plain,
% 2.34/2.48 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e1, e1) = e1))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20643])).
% 2.34/2.48 tff(20645,plain,
% 2.34/2.48 (~(op(e1, e1) = e1)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[1888, 20644])).
% 2.34/2.48 tff(20646,plain,
% 2.34/2.48 (op(e1, e0) = e1),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[954, 20645, 20515, 19007])).
% 2.34/2.48 tff(20647,plain,
% 2.34/2.48 (op(e1, op(e3, e3)) = op(e1, e0)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20508])).
% 2.34/2.48 tff(20648,plain,
% 2.34/2.48 ((e0 = e3) <=> (e0 = op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20502])).
% 2.34/2.48 tff(20649,plain,
% 2.34/2.48 ((e0 = e3) <=> (op(e2, e3) = e0)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20648, 86])).
% 2.34/2.48 tff(20650,plain,
% 2.34/2.48 ((~(e0 = e3)) <=> (~(op(e2, e3) = e0))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20649])).
% 2.34/2.48 tff(20651,plain,
% 2.34/2.48 (~(op(e2, e3) = e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[181, 20650])).
% 2.34/2.48 tff(20652,plain,
% 2.34/2.48 ((op(e1, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20639])).
% 2.34/2.48 tff(20653,plain,
% 2.34/2.48 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20652, 83])).
% 2.34/2.48 tff(20654,plain,
% 2.34/2.48 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20653])).
% 2.34/2.48 tff(20655,plain,
% 2.34/2.48 (~(op(e2, e1) = e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[225, 20654])).
% 2.34/2.48 tff(20656,plain,
% 2.34/2.48 (op(e2, e0) = e0),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[2311, 20655, 17, 20651])).
% 2.34/2.48 tff(20657,plain,
% 2.34/2.48 (op(e2, e0) = op(e3, e3)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20656, 20516])).
% 2.34/2.48 tff(20658,plain,
% 2.34/2.48 (op(e1, op(e2, e0)) = op(e1, op(e3, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20657])).
% 2.34/2.48 tff(20659,plain,
% 2.34/2.48 (op(e1, op(e2, e0)) = e1),
% 2.34/2.48 inference(transitivity,[status(thm)],[20658, 20647, 20646])).
% 2.34/2.48 tff(20660,plain,
% 2.34/2.48 (op(e3, op(e1, e1)) = op(e3, op(e3, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20640])).
% 2.34/2.48 tff(20661,plain,
% 2.34/2.48 (op(e3, op(e1, e1)) = e3),
% 2.34/2.48 inference(transitivity,[status(thm)],[20660, 20570, 20521])).
% 2.34/2.48 tff(20662,plain,
% 2.34/2.48 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[14029, 20661])).
% 2.34/2.48 tff(20663,plain,
% 2.34/2.48 (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[5367, 20662, 20626, 20620, 20616, 20612, 20609, 20606, 20604, 20601, 20597, 20592, 20586, 20584, 20574])).
% 2.34/2.48 tff(20664,plain,
% 2.34/2.48 (~(op(e1, op(e2, e0)) = e1)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[5690, 20663])).
% 2.34/2.48 tff(20665,plain,
% 2.34/2.48 ($false),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[20664, 20659])).
% 2.34/2.48 tff(20666,plain,((op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.48 tff(20667,plain,
% 2.34/2.48 (op(e2, e3) = e1),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[20666, 68, 17])).
% 2.34/2.48 tff(20668,plain,
% 2.34/2.48 (op(op(e2, e3), e2) = op(e1, e2)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20667])).
% 2.34/2.48 tff(20669,plain,
% 2.34/2.48 (op(op(e2, e3), e3) = op(e1, e3)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20667])).
% 2.34/2.48 tff(20670,plain,
% 2.34/2.48 (e1 = op(e2, e3)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20667])).
% 2.34/2.48 tff(20671,plain,
% 2.34/2.48 ((op(e0, e3) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20670])).
% 2.34/2.48 tff(20672,plain,
% 2.34/2.48 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e1)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20671])).
% 2.34/2.48 tff(20673,plain,
% 2.34/2.48 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e1))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20672])).
% 2.34/2.48 tff(20674,plain,
% 2.34/2.48 (~(op(e0, e3) = e1)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[964, 20673])).
% 2.34/2.48 tff(20675,plain,
% 2.34/2.48 (~(op(e2, e1) = e0)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[7790, 20674, 19015, 19012])).
% 2.34/2.48 tff(20676,plain,
% 2.34/2.48 ((e0 = e1) <=> (e0 = op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20670])).
% 2.34/2.48 tff(20677,plain,
% 2.34/2.48 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20676, 86])).
% 2.34/2.48 tff(20678,plain,
% 2.34/2.48 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20677])).
% 2.34/2.48 tff(20679,plain,
% 2.34/2.48 (~(op(e2, e3) = e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[26, 20678])).
% 2.34/2.48 tff(20680,plain,
% 2.34/2.48 (op(e2, e0) = e0),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[2311, 20675, 17, 20679])).
% 2.34/2.48 tff(20681,plain,
% 2.34/2.48 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.48 tff(20682,plain,
% 2.34/2.48 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20681])).
% 2.34/2.48 tff(20683,plain,
% 2.34/2.48 (~(op(e1, e0) = e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[756, 20682])).
% 2.34/2.48 tff(20684,plain,
% 2.34/2.48 ((op(e2, e0) = e2) <=> (e0 = e2)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.48 tff(20685,plain,
% 2.34/2.48 ((e0 = e2) <=> (op(e2, e0) = e2)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20684])).
% 2.34/2.48 tff(20686,plain,
% 2.34/2.48 ((~(e0 = e2)) <=> (~(op(e2, e0) = e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20685])).
% 2.34/2.48 tff(20687,plain,
% 2.34/2.48 (~(op(e2, e0) = e2)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[14, 20686])).
% 2.34/2.48 tff(20688,plain,
% 2.34/2.48 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20670])).
% 2.34/2.48 tff(20689,plain,
% 2.34/2.48 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20688])).
% 2.34/2.48 tff(20690,plain,
% 2.34/2.48 (~(op(e2, e3) = e3)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[303, 20689])).
% 2.34/2.48 tff(20691,plain,
% 2.34/2.48 ((op(e2, e0) = e3) <=> (e0 = e3)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.48 tff(20692,plain,
% 2.34/2.48 ((e0 = e3) <=> (op(e2, e0) = e3)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20691])).
% 2.34/2.48 tff(20693,plain,
% 2.34/2.48 ((~(e0 = e3)) <=> (~(op(e2, e0) = e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20692])).
% 2.34/2.48 tff(20694,plain,
% 2.34/2.48 (~(op(e2, e0) = e3)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[181, 20693])).
% 2.34/2.48 tff(20695,plain,
% 2.34/2.48 (op(e0, e1) = op(e0, op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[2685])).
% 2.34/2.48 tff(20696,plain,
% 2.34/2.48 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20695])).
% 2.34/2.48 tff(20697,plain,
% 2.34/2.48 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e1) = e0)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20696])).
% 2.34/2.48 tff(20698,plain,
% 2.34/2.48 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e0, e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[7827])).
% 2.34/2.48 tff(20699,plain,
% 2.34/2.48 ((op(e0, e3) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20698, 7797])).
% 2.34/2.48 tff(20700,plain,
% 2.34/2.48 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20699])).
% 2.34/2.48 tff(20701,plain,
% 2.34/2.48 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20700])).
% 2.34/2.48 tff(20702,plain,
% 2.34/2.48 (~(op(e0, e3) = e3)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[918, 20701])).
% 2.34/2.48 tff(20703,plain,
% 2.34/2.48 (op(e0, e3) = e0),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[687, 20702, 677, 14786])).
% 2.34/2.48 tff(20704,plain,
% 2.34/2.48 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e2, e3)) = e0)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20695, 20703])).
% 2.34/2.48 tff(20705,plain,
% 2.34/2.48 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20704, 20697])).
% 2.34/2.48 tff(20706,plain,
% 2.34/2.48 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20705])).
% 2.34/2.48 tff(20707,plain,
% 2.34/2.48 (~(op(e0, e1) = e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[818, 20706])).
% 2.34/2.48 tff(20708,plain,
% 2.34/2.48 (~(op(e2, e1) = e0)),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[7790, 14786, 677, 19058])).
% 2.34/2.48 tff(20709,plain,
% 2.34/2.48 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[2685])).
% 2.34/2.48 tff(20710,plain,
% 2.34/2.48 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20709])).
% 2.34/2.48 tff(20711,plain,
% 2.34/2.48 (~(op(e2, e3) = e3)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[303, 20710])).
% 2.34/2.48 tff(20712,plain,
% 2.34/2.48 ((op(e2, e2) = op(e0, e2)) <=> (op(e0, e2) = op(e2, e2))),
% 2.34/2.48 inference(commutativity,[status(thm)],[])).
% 2.34/2.48 tff(20713,plain,
% 2.34/2.48 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e0, e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[7827])).
% 2.34/2.48 tff(20714,plain,
% 2.34/2.48 ((op(e2, e2) = e3) <=> (op(e0, e2) = op(e2, e2))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20713, 20712])).
% 2.34/2.48 tff(20715,plain,
% 2.34/2.48 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20714])).
% 2.34/2.48 tff(20716,plain,
% 2.34/2.48 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20715])).
% 2.34/2.48 tff(20717,plain,
% 2.34/2.48 (~(op(e2, e2) = e3)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[2736, 20716])).
% 2.34/2.48 tff(20718,plain,
% 2.34/2.48 (op(e2, e1) = e3),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[1559, 20717, 20711, 3272])).
% 2.34/2.48 tff(20719,plain,
% 2.34/2.48 (op(e2, e1) = op(e0, e2)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20718, 7827])).
% 2.34/2.48 tff(20720,plain,
% 2.34/2.48 ((op(e2, e1) = e2) <=> (op(e0, e2) = e2)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20719])).
% 2.34/2.48 tff(20721,plain,
% 2.34/2.48 ((op(e0, e2) = e2) <=> (op(e2, e1) = e2)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20720])).
% 2.34/2.48 tff(20722,plain,
% 2.34/2.48 ((~(op(e0, e2) = e2)) <=> (~(op(e2, e1) = e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20721])).
% 2.34/2.48 tff(20723,plain,
% 2.34/2.48 (~(op(e2, e1) = e2)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[19326, 20722])).
% 2.34/2.48 tff(20724,plain,
% 2.34/2.48 ((op(e0, e2) = e1) <=> (e3 = op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[7826, 2685])).
% 2.34/2.48 tff(20725,plain,
% 2.34/2.48 ((op(e0, e2) = e1) <=> (op(e2, e3) = e3)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20724, 112])).
% 2.34/2.48 tff(20726,plain,
% 2.34/2.48 ((op(e2, e3) = e3) <=> (op(e0, e2) = e1)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20725])).
% 2.34/2.48 tff(20727,plain,
% 2.34/2.48 ((~(op(e2, e3) = e3)) <=> (~(op(e0, e2) = e1))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20726])).
% 2.34/2.48 tff(20728,plain,
% 2.34/2.48 (~(op(e0, e2) = e1)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[20711, 20727])).
% 2.34/2.48 tff(20729,plain,
% 2.34/2.48 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[12395])).
% 2.34/2.48 tff(20730,plain,
% 2.34/2.48 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e1))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20729])).
% 2.34/2.48 tff(20731,plain,
% 2.34/2.48 (~(op(e0, e1) = e1)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[792, 20730])).
% 2.34/2.48 tff(20732,plain,
% 2.34/2.48 (op(e0, e0) = e1),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[384, 20731, 14786, 20728])).
% 2.34/2.48 tff(20733,plain,
% 2.34/2.48 (e1 = op(e0, e0)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[20732, 74])).
% 2.34/2.48 tff(20734,plain,
% 2.34/2.48 (op(e0, e0) = op(e2, e3)),
% 2.34/2.48 inference(transitivity,[status(thm)],[20732, 2685])).
% 2.34/2.48 tff(20735,plain,
% 2.34/2.48 (op(e0, op(e0, e0)) = op(e0, op(e2, e3))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20734])).
% 2.34/2.48 tff(20736,plain,
% 2.34/2.48 (op(e0, op(e2, e3)) = op(e0, op(e0, e0))),
% 2.34/2.48 inference(symmetry,[status(thm)],[20735])).
% 2.34/2.48 tff(20737,plain,
% 2.34/2.48 ((op(e3, e1) = e2) <=> (e0 = e2)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[9983])).
% 2.34/2.48 tff(20738,plain,
% 2.34/2.48 ((e0 = e2) <=> (op(e3, e1) = e2)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20737])).
% 2.34/2.48 tff(20739,plain,
% 2.34/2.48 ((~(e0 = e2)) <=> (~(op(e3, e1) = e2))),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20738])).
% 2.34/2.48 tff(20740,plain,
% 2.34/2.48 (~(op(e3, e1) = e2)),
% 2.34/2.48 inference(modus_ponens,[status(thm)],[14, 20739])).
% 2.34/2.48 tff(20741,plain,
% 2.34/2.48 (op(e0, e1) = e2),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[1993, 20740, 68, 3540])).
% 2.34/2.48 tff(20742,plain,
% 2.34/2.48 (e2 = op(e0, e1)),
% 2.34/2.48 inference(symmetry,[status(thm)],[20741])).
% 2.34/2.48 tff(20743,plain,
% 2.34/2.48 (e2 = op(e0, op(e0, e0))),
% 2.34/2.48 inference(transitivity,[status(thm)],[20742, 4448, 20736])).
% 2.34/2.48 tff(20744,plain,
% 2.34/2.48 (op(e0, op(e0, e0)) = e2),
% 2.34/2.48 inference(transitivity,[status(thm)],[20735, 4447, 20741])).
% 2.34/2.48 tff(20745,plain,
% 2.34/2.48 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 2.34/2.48 inference(monotonicity,[status(thm)],[20744])).
% 2.34/2.48 tff(20746,plain,
% 2.34/2.48 (op(e0, e2) = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.48 inference(symmetry,[status(thm)],[20745])).
% 2.34/2.48 tff(20747,plain,
% 2.34/2.48 (e3 = op(e0, op(e0, op(e0, e0)))),
% 2.34/2.48 inference(transitivity,[status(thm)],[7827, 20746])).
% 2.34/2.48 tff(20748,plain,
% 2.34/2.48 ($false),
% 2.34/2.48 inference(unit_resolution,[status(thm)],[3582, 20747, 20743, 20733])).
% 2.34/2.48 tff(20749,plain,((op(e1, e1) = e0) | (~(op(e0, e2) = e3)) | (~(op(e2, e3) = e1)) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e1, e1) = e3) | (op(e2, e1) = e0) | (op(e0, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.49 tff(20750,plain,
% 2.34/2.49 (op(e1, e1) = e0),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[20749, 7826, 2684, 68, 20723, 1291, 20708, 20707])).
% 2.34/2.49 tff(20751,plain,
% 2.34/2.49 (e0 = op(e1, e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[20750, 123])).
% 2.34/2.49 tff(20752,plain,
% 2.34/2.49 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20750])).
% 2.34/2.49 tff(20753,plain,
% 2.34/2.49 (op(e1, e0) = op(e1, op(e1, e1))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20752])).
% 2.34/2.49 tff(20754,plain,
% 2.34/2.49 (op(e1, e0) = e3),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[247, 19400, 1291, 6613])).
% 2.34/2.49 tff(20755,plain,
% 2.34/2.49 (e3 = op(e1, e0)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20754])).
% 2.34/2.49 tff(20756,plain,
% 2.34/2.49 (e3 = op(e1, op(e1, e1))),
% 2.34/2.49 inference(transitivity,[status(thm)],[20755, 20753])).
% 2.34/2.49 tff(20757,plain,
% 2.34/2.49 (op(e1, op(e1, e1)) = op(e0, e2)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20752, 20754, 7827])).
% 2.34/2.49 tff(20758,plain,
% 2.34/2.49 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e0, e2))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20757])).
% 2.34/2.49 tff(20759,plain,
% 2.34/2.49 (op(e1, op(e0, e2)) = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20758])).
% 2.34/2.49 tff(20760,plain,
% 2.34/2.49 (op(e1, op(e0, e2)) = op(op(e2, e3), e3)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[2685, 7826])).
% 2.34/2.49 tff(20761,plain,
% 2.34/2.49 (op(op(e2, e3), e3) = op(e1, op(e0, e2))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20760])).
% 2.34/2.49 tff(20762,plain,
% 2.34/2.49 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.49 inference(transitivity,[status(thm)],[265, 7699, 20761, 20759])).
% 2.34/2.49 tff(20763,plain,
% 2.34/2.49 ($false),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[276, 20762, 20756, 20751])).
% 2.34/2.49 tff(20764,plain,((~(op(e0, e2) = e3)) | (~(op(e1, e3) = e2)) | (~(op(e2, e3) = e1)) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e2, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.49 tff(20765,plain,
% 2.34/2.49 (~(op(e0, e2) = e3)),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[20764, 1291, 20667, 68, 19002, 20694])).
% 2.34/2.49 tff(20766,plain,
% 2.34/2.49 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.49 tff(20767,plain,
% 2.34/2.49 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20766, 8115])).
% 2.34/2.49 tff(20768,plain,
% 2.34/2.49 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20767])).
% 2.34/2.49 tff(20769,plain,
% 2.34/2.49 (~(op(e3, e0) = e0)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[747, 20768])).
% 2.34/2.49 tff(20770,plain,
% 2.34/2.49 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.49 tff(20771,plain,
% 2.34/2.49 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20770])).
% 2.34/2.49 tff(20772,plain,
% 2.34/2.49 (~(op(e0, e0) = e0)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[359, 20771])).
% 2.34/2.49 tff(20773,plain,
% 2.34/2.49 (op(e2, op(e2, e0)) = op(e2, e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.49 tff(20774,plain,
% 2.34/2.49 (op(e2, op(e2, e0)) = e0),
% 2.34/2.49 inference(transitivity,[status(thm)],[20773, 20680])).
% 2.34/2.49 tff(20775,plain,
% 2.34/2.49 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[2653, 20774])).
% 2.34/2.49 tff(20776,plain,
% 2.34/2.49 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[5468, 14786, 677])).
% 2.34/2.49 tff(20777,plain,
% 2.34/2.49 ((e0 = e1) <=> (e0 = op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[2685])).
% 2.34/2.49 tff(20778,plain,
% 2.34/2.49 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20777, 86])).
% 2.34/2.49 tff(20779,plain,
% 2.34/2.49 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20778])).
% 2.34/2.49 tff(20780,plain,
% 2.34/2.49 (~(op(e2, e3) = e0)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[26, 20779])).
% 2.34/2.49 tff(20781,plain,
% 2.34/2.49 (op(e0, op(e1, e0)) = op(e0, e3)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[258])).
% 2.34/2.49 tff(20782,plain,
% 2.34/2.49 (op(e0, e3) = op(e0, op(e1, e0))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20781])).
% 2.34/2.49 tff(20783,plain,
% 2.34/2.49 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e0)) = e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20782])).
% 2.34/2.49 tff(20784,plain,
% 2.34/2.49 ((op(e0, op(e1, e0)) = e0) <=> (op(e0, e3) = e0)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20783])).
% 2.34/2.49 tff(20785,plain,
% 2.34/2.49 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[258])).
% 2.34/2.49 tff(20786,plain,
% 2.34/2.49 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20785])).
% 2.34/2.49 tff(20787,plain,
% 2.34/2.49 (~(op(e0, e0) = e3)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[2471, 20786])).
% 2.34/2.49 tff(20788,plain,
% 2.34/2.49 (op(e0, e3) = e3),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1495, 20787, 2527, 4412])).
% 2.34/2.49 tff(20789,plain,
% 2.34/2.49 (op(e0, op(e1, e0)) = op(e1, e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20781, 20788, 259])).
% 2.34/2.49 tff(20790,plain,
% 2.34/2.49 ((op(e0, op(e1, e0)) = e0) <=> (op(e1, e0) = e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20789])).
% 2.34/2.49 tff(20791,plain,
% 2.34/2.49 ((op(e1, e0) = e0) <=> (op(e0, op(e1, e0)) = e0)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20790])).
% 2.34/2.49 tff(20792,plain,
% 2.34/2.49 ((op(e1, e0) = e0) <=> (op(e0, e3) = e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20791, 20784])).
% 2.34/2.49 tff(20793,plain,
% 2.34/2.49 ((~(op(e1, e0) = e0)) <=> (~(op(e0, e3) = e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20792])).
% 2.34/2.49 tff(20794,plain,
% 2.34/2.49 (~(op(e0, e3) = e0)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[2167, 20793])).
% 2.34/2.49 tff(20795,plain,
% 2.34/2.49 (op(e3, e3) = e0),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1098, 20794, 19058, 20780])).
% 2.34/2.49 tff(20796,plain,
% 2.34/2.49 (op(op(e1, e3), e3) = e1),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[2684, 12134])).
% 2.34/2.49 tff(20797,plain,
% 2.34/2.49 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[130, 20796])).
% 2.34/2.49 tff(20798,plain,
% 2.34/2.49 (op(e1, e1) = op(e3, e3)),
% 2.34/2.49 inference(transitivity,[status(thm)],[249, 4451])).
% 2.34/2.49 tff(20799,plain,
% 2.34/2.49 (op(e1, op(e1, e1)) = op(e1, op(e3, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20798])).
% 2.34/2.49 tff(20800,plain,
% 2.34/2.49 (op(e1, op(e3, e3)) = op(e1, op(e1, e1))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20799])).
% 2.34/2.49 tff(20801,plain,
% 2.34/2.49 (e3 = op(e1, op(e1, e1))),
% 2.34/2.49 inference(transitivity,[status(thm)],[259, 7896, 20800])).
% 2.34/2.49 tff(20802,plain,
% 2.34/2.49 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20799, 4468])).
% 2.34/2.49 tff(20803,plain,
% 2.34/2.49 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20802])).
% 2.34/2.49 tff(20804,plain,
% 2.34/2.49 (op(e1, op(e1, e0)) = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20803])).
% 2.34/2.49 tff(20805,plain,
% 2.34/2.49 (op(e1, op(e1, e0)) = op(op(e2, e3), e3)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[2685, 258])).
% 2.34/2.49 tff(20806,plain,
% 2.34/2.49 (op(op(e2, e3), e3) = op(e1, op(e1, e0))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20805])).
% 2.34/2.49 tff(20807,plain,
% 2.34/2.49 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.49 inference(transitivity,[status(thm)],[265, 7699, 20806, 20804])).
% 2.34/2.49 tff(20808,plain,
% 2.34/2.49 ($false),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[276, 20807, 20801, 250])).
% 2.34/2.49 tff(20809,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e3) = e2)) | (~(op(e1, e0) = e3)) | (~(op(e2, e3) = e1)) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.49 tff(20810,plain,
% 2.34/2.49 (~(op(e1, e1) = e0)),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[20809, 258, 264, 2684, 20795])).
% 2.34/2.49 tff(20811,plain,
% 2.34/2.49 (op(e0, e1) = op(e3, e3)),
% 2.34/2.49 inference(transitivity,[status(thm)],[4477, 4451])).
% 2.34/2.49 tff(20812,plain,
% 2.34/2.49 ((op(e0, e1) = e2) <=> (op(e3, e3) = e2)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20811])).
% 2.34/2.49 tff(20813,plain,
% 2.34/2.49 ((op(e3, e3) = e2) <=> (op(e0, e1) = e2)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20812])).
% 2.34/2.49 tff(20814,plain,
% 2.34/2.49 ((~(op(e3, e3) = e2)) <=> (~(op(e0, e1) = e2))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20813])).
% 2.34/2.49 tff(20815,plain,
% 2.34/2.49 (~(op(e0, e1) = e2)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[15002, 20814])).
% 2.34/2.49 tff(20816,plain,
% 2.34/2.49 (op(e2, e1) = e2),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1993, 20815, 68, 82])).
% 2.34/2.49 tff(20817,plain,
% 2.34/2.49 (op(op(e2, e1), e1) = op(e2, op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20816, 2685])).
% 2.34/2.49 tff(20818,plain,
% 2.34/2.49 (op(op(e2, e1), e1) = e2),
% 2.34/2.49 inference(transitivity,[status(thm)],[20817, 6634, 20816])).
% 2.34/2.49 tff(20819,plain,
% 2.34/2.49 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[2371, 20818])).
% 2.34/2.49 tff(20820,plain,
% 2.34/2.49 ((op(e0, e1) = e1) <=> (op(e3, e3) = op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20811, 2685])).
% 2.34/2.49 tff(20821,plain,
% 2.34/2.49 ((op(e0, e1) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 2.34/2.49 inference(transitivity,[status(thm)],[20820, 2820])).
% 2.34/2.49 tff(20822,plain,
% 2.34/2.49 ((op(e2, e3) = op(e3, e3)) <=> (op(e0, e1) = e1)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20821])).
% 2.34/2.49 tff(20823,plain,
% 2.34/2.49 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e0, e1) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20822])).
% 2.34/2.49 tff(20824,plain,
% 2.34/2.49 (~(op(e0, e1) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[368, 20823])).
% 2.34/2.49 tff(20825,plain,
% 2.34/2.49 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[12395])).
% 2.34/2.49 tff(20826,plain,
% 2.34/2.49 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20825, 7793])).
% 2.34/2.49 tff(20827,plain,
% 2.34/2.49 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20826])).
% 2.34/2.49 tff(20828,plain,
% 2.34/2.49 (~(op(e3, e1) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[945, 20827])).
% 2.34/2.49 tff(20829,plain,
% 2.34/2.49 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 2.34/2.49 inference(symmetry,[status(thm)],[2818])).
% 2.34/2.49 tff(20830,plain,
% 2.34/2.49 (op(e3, e0) = e2),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[589, 12721, 6687, 982])).
% 2.34/2.49 tff(20831,plain,
% 2.34/2.49 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20830])).
% 2.34/2.49 tff(20832,plain,
% 2.34/2.49 (op(op(e1, e0), e0) = op(e3, e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[258])).
% 2.34/2.49 tff(20833,plain,
% 2.34/2.49 (op(e3, op(e3, e3)) = op(op(e1, e0), e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[259, 3066])).
% 2.34/2.49 tff(20834,plain,
% 2.34/2.49 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20833, 20832])).
% 2.34/2.49 tff(20835,plain,
% 2.34/2.49 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20834])).
% 2.34/2.49 tff(20836,plain,
% 2.34/2.49 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20835, 20831])).
% 2.34/2.49 tff(20837,plain,
% 2.34/2.49 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[2685, 20836])).
% 2.34/2.49 tff(20838,plain,
% 2.34/2.49 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.49 inference(transitivity,[status(thm)],[20837, 394])).
% 2.34/2.49 tff(20839,plain,
% 2.34/2.49 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20838, 20829])).
% 2.34/2.49 tff(20840,plain,
% 2.34/2.49 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20839])).
% 2.34/2.49 tff(20841,plain,
% 2.34/2.49 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20834])).
% 2.34/2.49 tff(20842,plain,
% 2.34/2.49 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20841, 5377])).
% 2.34/2.49 tff(20843,plain,
% 2.34/2.49 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 2.34/2.49 inference(symmetry,[status(thm)],[20842])).
% 2.34/2.49 tff(20844,plain,
% 2.34/2.49 (e2 = op(e3, op(e3, e3))),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[20830, 20843])).
% 2.34/2.49 tff(20845,plain,
% 2.34/2.49 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[3093, 20844, 3079])).
% 2.34/2.49 tff(20846,plain,
% 2.34/2.49 (~(op(e3, e2) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[20845, 20840])).
% 2.34/2.49 tff(20847,plain,
% 2.34/2.49 (op(e0, e0) = e1),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[3612, 12721, 6213, 11542])).
% 2.34/2.49 tff(20848,plain,
% 2.34/2.49 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20847])).
% 2.34/2.49 tff(20849,plain,
% 2.34/2.49 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20848, 6411])).
% 2.34/2.49 tff(20850,plain,
% 2.34/2.49 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20849])).
% 2.34/2.49 tff(20851,plain,
% 2.34/2.49 (~(op(e3, e0) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[6384, 20850])).
% 2.34/2.49 tff(20852,plain,
% 2.34/2.49 (op(e3, e2) = e1),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[939, 20851, 2826, 2825])).
% 2.34/2.49 tff(20853,plain,
% 2.34/2.49 ($false),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[20852, 20846])).
% 2.34/2.49 tff(20854,plain,((op(e0, e0) = e2) | (~(op(e3, e3) = e0)) | (~(op(e1, e0) = e3)) | (~(op(e2, e3) = e1)) | (op(e3, e1) = e1) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.49 tff(20855,plain,
% 2.34/2.49 (op(e0, e0) = e2),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[20854, 20828, 258, 2684, 3066, 6687, 982, 6213])).
% 2.34/2.49 tff(20856,plain,
% 2.34/2.49 ((op(e0, e0) = e1) <=> (e2 = op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20855, 2685])).
% 2.34/2.49 tff(20857,plain,
% 2.34/2.49 ((op(e0, e0) = e1) <=> (op(e2, e3) = e2)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20856, 120])).
% 2.34/2.49 tff(20858,plain,
% 2.34/2.49 ((op(e2, e3) = e2) <=> (op(e0, e0) = e1)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20857])).
% 2.34/2.49 tff(20859,plain,
% 2.34/2.49 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e0) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20858])).
% 2.34/2.49 tff(20860,plain,
% 2.34/2.49 (~(op(e0, e0) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[4382, 20859])).
% 2.34/2.49 tff(20861,plain,
% 2.34/2.49 (op(e0, e2) = e1),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[384, 20860, 14786, 20824])).
% 2.34/2.49 tff(20862,plain,
% 2.34/2.49 (op(e0, e2) = op(e2, e3)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20861, 2685])).
% 2.34/2.49 tff(20863,plain,
% 2.34/2.49 (op(op(e0, e2), e2) = op(op(e2, e3), e2)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20862])).
% 2.34/2.49 tff(20864,plain,
% 2.34/2.49 (op(op(e0, e2), e2) = e0),
% 2.34/2.49 inference(transitivity,[status(thm)],[20863, 2897, 17950])).
% 2.34/2.49 tff(20865,plain,
% 2.34/2.49 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1956, 20864])).
% 2.34/2.49 tff(20866,plain,
% 2.34/2.49 (op(e3, e1) = e3),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[446, 20828, 82, 4476])).
% 2.34/2.49 tff(20867,plain,
% 2.34/2.49 (op(op(e1, e0), e1) = op(e3, op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[258, 2685])).
% 2.34/2.49 tff(20868,plain,
% 2.34/2.49 (op(e3, e1) = op(e1, e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20866, 259])).
% 2.34/2.49 tff(20869,plain,
% 2.34/2.49 (op(op(e3, e1), e1) = op(op(e1, e0), e1)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20868])).
% 2.34/2.49 tff(20870,plain,
% 2.34/2.49 (op(op(e3, e1), e1) = e3),
% 2.34/2.49 inference(transitivity,[status(thm)],[20869, 20867, 2832, 20866])).
% 2.34/2.49 tff(20871,plain,
% 2.34/2.49 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[2416, 20870])).
% 2.34/2.49 tff(20872,plain,
% 2.34/2.49 (op(op(e1, e2), e1) = op(e0, op(e2, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[17950, 2685])).
% 2.34/2.49 tff(20873,plain,
% 2.34/2.49 (op(op(e1, e2), e1) = op(e3, e3)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20872, 4447, 4477, 4451])).
% 2.34/2.49 tff(20874,plain,
% 2.34/2.49 ((op(op(e1, e2), e1) = e2) <=> (op(e3, e3) = e2)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20873])).
% 2.34/2.49 tff(20875,plain,
% 2.34/2.49 ((op(e3, e3) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20874])).
% 2.34/2.49 tff(20876,plain,
% 2.34/2.49 ((~(op(e3, e3) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20875])).
% 2.34/2.49 tff(20877,plain,
% 2.34/2.49 (~(op(op(e1, e2), e1) = e2)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[15002, 20876])).
% 2.34/2.49 tff(20878,plain,
% 2.34/2.49 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[5959, 20877])).
% 2.34/2.49 tff(20879,plain,
% 2.34/2.49 (op(op(e1, e0), e1) = op(e3, e1)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20867, 2832])).
% 2.34/2.49 tff(20880,plain,
% 2.34/2.49 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e1) = e0)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20879])).
% 2.34/2.49 tff(20881,plain,
% 2.34/2.49 ((op(e3, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 2.34/2.49 inference(symmetry,[status(thm)],[20880])).
% 2.34/2.49 tff(20882,plain,
% 2.34/2.49 ((op(e3, e1) = op(e3, e3)) <=> (op(op(e1, e0), e1) = e0)),
% 2.34/2.49 inference(transitivity,[status(thm)],[4474, 20881])).
% 2.34/2.49 tff(20883,plain,
% 2.34/2.49 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20882])).
% 2.34/2.49 tff(20884,plain,
% 2.34/2.49 (~(op(op(e1, e0), e1) = e0)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[437, 20883])).
% 2.34/2.49 tff(20885,plain,
% 2.34/2.49 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1302, 20884])).
% 2.34/2.49 tff(20886,plain,
% 2.34/2.49 ((op(e2, e3) = e3) <=> (e1 = op(e1, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[2684, 259])).
% 2.34/2.49 tff(20887,plain,
% 2.34/2.49 ((op(e2, e3) = e3) <=> (op(e1, e0) = e1)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20886, 17546])).
% 2.34/2.49 tff(20888,plain,
% 2.34/2.49 ((~(op(e2, e3) = e3)) <=> (~(op(e1, e0) = e1))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20887])).
% 2.34/2.49 tff(20889,plain,
% 2.34/2.49 (~(op(e1, e0) = e1)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[20711, 20888])).
% 2.34/2.49 tff(20890,plain,
% 2.34/2.49 (op(e3, e0) = e1),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[1480, 20860, 2689, 20889])).
% 2.34/2.49 tff(20891,plain,
% 2.34/2.49 (op(op(e3, e0), e0) = op(e1, op(e3, e3))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20890, 4451])).
% 2.34/2.49 tff(20892,plain,
% 2.34/2.49 (op(op(e3, e0), e0) = e3),
% 2.34/2.49 inference(transitivity,[status(thm)],[20891, 4468, 258])).
% 2.34/2.49 tff(20893,plain,
% 2.34/2.49 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[4026, 20892])).
% 2.34/2.49 tff(20894,plain,
% 2.34/2.49 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20855])).
% 2.34/2.49 tff(20895,plain,
% 2.34/2.49 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.34/2.49 inference(transitivity,[status(thm)],[20894, 5377])).
% 2.34/2.49 tff(20896,plain,
% 2.34/2.49 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20895])).
% 2.34/2.49 tff(20897,plain,
% 2.34/2.49 (~(op(e3, e0) = e2)),
% 2.34/2.49 inference(modus_ponens,[status(thm)],[6384, 20896])).
% 2.34/2.49 tff(20898,plain,
% 2.34/2.49 (op(e3, e2) = e2),
% 2.34/2.49 inference(unit_resolution,[status(thm)],[15971, 20897, 82])).
% 2.34/2.49 tff(20899,plain,
% 2.34/2.49 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.34/2.49 inference(monotonicity,[status(thm)],[20898])).
% 2.34/2.49 tff(20900,plain,
% 2.34/2.49 (op(e3, op(e3, e2)) = e2),
% 2.34/2.49 inference(transitivity,[status(thm)],[20899, 20898])).
% 2.34/2.50 tff(20901,plain,
% 2.34/2.50 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1904, 20900])).
% 2.34/2.50 tff(20902,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1459, 20901, 20893, 3342, 1347, 2421, 1304, 20885, 4480, 20878, 20871, 20865, 20819])).
% 2.34/2.50 tff(20903,plain,((op(e1, e1) = e0) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e1, e0) = e3)) | (~(op(e3, e3) = e0)) | (~(op(e2, e3) = e1)) | (op(e3, e1) = e2) | (op(e2, e3) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e0, e0) = e0) | (op(e1, e1) = e2) | (op(e1, e3) = e0) | (op(e1, e0) = e0) | (op(e1, e1) = e3) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(20904,plain,
% 2.34/2.50 (op(e3, e1) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[20903, 20810, 4483, 2421, 20797, 258, 20795, 2684, 20776, 6598, 675, 982, 6213, 68, 19058, 2167, 1291, 20708])).
% 2.34/2.50 tff(20905,plain,
% 2.34/2.50 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20904])).
% 2.34/2.50 tff(20906,plain,
% 2.34/2.50 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e3, e1))),
% 2.34/2.50 inference(symmetry,[status(thm)],[20905])).
% 2.34/2.50 tff(20907,plain,
% 2.34/2.50 ((op(e1, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[258])).
% 2.34/2.50 tff(20908,plain,
% 2.34/2.50 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20907, 404])).
% 2.34/2.50 tff(20909,plain,
% 2.34/2.50 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20908])).
% 2.34/2.50 tff(20910,plain,
% 2.34/2.50 (~(op(e3, e0) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[410, 20909])).
% 2.34/2.50 tff(20911,plain,
% 2.34/2.50 (~(op(e3, e0) = e1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8647, 20904, 20795])).
% 2.34/2.50 tff(20912,plain,
% 2.34/2.50 (op(e3, e0) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5422, 20911, 1908, 20910])).
% 2.34/2.50 tff(20913,plain,
% 2.34/2.50 (op(e3, e0) = op(e3, e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[20912, 20906])).
% 2.34/2.50 tff(20914,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[580, 20913])).
% 2.34/2.50 tff(20915,plain,((~(op(e1, e0) = e3)) | (op(e3, e0) = e0) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~(op(e2, e3) = e1)) | (op(e2, e0) = e2) | (op(e0, e0) = e0) | (op(e1, e1) = e2) | (op(e1, e0) = e0) | (op(e1, e1) = e3) | (~(op(e1, e3) = e2)) | (op(e0, e1) = e3) | (op(e0, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(20916,plain,
% 2.34/2.50 (~(op(e1, e0) = e3)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[20915, 4412, 20775, 20667, 20687, 20772, 68, 20683, 1291, 19002, 2527, 20769])).
% 2.34/2.50 tff(20917,plain,
% 2.34/2.50 (op(e1, e2) = e3),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[247, 20916, 1291, 19601])).
% 2.34/2.50 tff(20918,plain,
% 2.34/2.50 (e3 = op(e1, e2)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20917])).
% 2.34/2.50 tff(20919,plain,
% 2.34/2.50 ((op(e2, e2) = e1) <=> (op(e2, e2) = op(e2, e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20670])).
% 2.34/2.50 tff(20920,plain,
% 2.34/2.50 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20919])).
% 2.34/2.50 tff(20921,plain,
% 2.34/2.50 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20920])).
% 2.34/2.50 tff(20922,plain,
% 2.34/2.50 (~(op(e2, e2) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[515, 20921])).
% 2.34/2.50 tff(20923,plain,
% 2.34/2.50 ((op(e2, e2) = e3) <=> (op(e2, e2) = op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20918])).
% 2.34/2.50 tff(20924,plain,
% 2.34/2.50 ((op(e2, e2) = e3) <=> (op(e1, e2) = op(e2, e2))),
% 2.34/2.50 inference(transitivity,[status(thm)],[20923, 8066])).
% 2.34/2.50 tff(20925,plain,
% 2.34/2.50 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20924])).
% 2.34/2.50 tff(20926,plain,
% 2.34/2.50 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20925])).
% 2.34/2.50 tff(20927,plain,
% 2.34/2.50 (~(op(e2, e2) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1273, 20926])).
% 2.34/2.50 tff(20928,plain,
% 2.34/2.50 (op(e2, e2) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[524, 20927, 17, 20922])).
% 2.34/2.50 tff(20929,plain,
% 2.34/2.50 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20928])).
% 2.34/2.50 tff(20930,plain,
% 2.34/2.50 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20929])).
% 2.34/2.50 tff(20931,plain,
% 2.34/2.50 (~(op(e0, e2) = e2)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[2736, 20930])).
% 2.34/2.50 tff(20932,plain,
% 2.34/2.50 (op(e2, e1) = e3),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1559, 20927, 20690, 20694])).
% 2.34/2.50 tff(20933,plain,
% 2.34/2.50 (op(e2, e1) = op(e1, e2)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20932, 20918])).
% 2.34/2.50 tff(20934,plain,
% 2.34/2.50 ((op(e2, e1) = e2) <=> (op(e1, e2) = e2)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20933])).
% 2.34/2.50 tff(20935,plain,
% 2.34/2.50 ((op(e1, e2) = e2) <=> (op(e2, e1) = e2)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20934])).
% 2.34/2.50 tff(20936,plain,
% 2.34/2.50 ((~(op(e1, e2) = e2)) <=> (~(op(e2, e1) = e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20935])).
% 2.34/2.50 tff(20937,plain,
% 2.34/2.50 (~(op(e2, e1) = e2)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[19486, 20936])).
% 2.34/2.50 tff(20938,plain,
% 2.34/2.50 (op(e1, e0) = e1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[728, 20916, 19180, 20683])).
% 2.34/2.50 tff(20939,plain,
% 2.34/2.50 ((op(e1, e0) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20938])).
% 2.34/2.50 tff(20940,plain,
% 2.34/2.50 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20939, 8462])).
% 2.34/2.50 tff(20941,plain,
% 2.34/2.50 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20940])).
% 2.34/2.50 tff(20942,plain,
% 2.34/2.50 (~(op(e1, e1) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[737, 20941])).
% 2.34/2.50 tff(20943,plain,
% 2.34/2.50 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20938])).
% 2.34/2.50 tff(20944,plain,
% 2.34/2.50 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20943])).
% 2.34/2.50 tff(20945,plain,
% 2.34/2.50 (~(op(e0, e0) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[2471, 20944])).
% 2.34/2.50 tff(20946,plain,
% 2.34/2.50 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20928])).
% 2.34/2.50 tff(20947,plain,
% 2.34/2.50 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20946, 2234])).
% 2.34/2.50 tff(20948,plain,
% 2.34/2.50 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20947])).
% 2.34/2.50 tff(20949,plain,
% 2.34/2.50 (~(op(e3, e2) = e2)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1546, 20948])).
% 2.34/2.50 tff(20950,plain,
% 2.34/2.50 (op(e1, op(e1, e2)) = op(op(e2, e3), e3)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20670, 20917])).
% 2.34/2.50 tff(20951,plain,
% 2.34/2.50 (op(e1, op(e1, e2)) = e2),
% 2.34/2.50 inference(transitivity,[status(thm)],[20950, 20669, 19002])).
% 2.34/2.50 tff(20952,plain,
% 2.34/2.50 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2377, 20951])).
% 2.34/2.50 tff(20953,plain,
% 2.34/2.50 (op(op(e1, e0), e0) = op(e1, e0)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20938])).
% 2.34/2.50 tff(20954,plain,
% 2.34/2.50 (op(op(e1, e0), e0) = e1),
% 2.34/2.50 inference(transitivity,[status(thm)],[20953, 20938])).
% 2.34/2.50 tff(20955,plain,
% 2.34/2.50 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3015, 20954])).
% 2.34/2.50 tff(20956,plain,
% 2.34/2.50 (op(op(e1, e3), e3) = op(e2, e3)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[19002])).
% 2.34/2.50 tff(20957,plain,
% 2.34/2.50 ((op(op(e1, e3), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20956])).
% 2.34/2.50 tff(20958,plain,
% 2.34/2.50 ((op(e2, e3) = e1) <=> (op(op(e1, e3), e3) = e1)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20957])).
% 2.34/2.50 tff(20959,plain,
% 2.34/2.50 (op(op(e1, e3), e3) = e1),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[20667, 20958])).
% 2.34/2.50 tff(20960,plain,
% 2.34/2.50 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[130, 20959])).
% 2.34/2.50 tff(20961,plain,
% 2.34/2.50 (op(op(e2, e3), e3) = e2),
% 2.34/2.50 inference(transitivity,[status(thm)],[20669, 19002])).
% 2.34/2.50 tff(20962,plain,
% 2.34/2.50 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1288, 20961])).
% 2.34/2.50 tff(20963,plain,
% 2.34/2.50 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5468, 20674, 19015])).
% 2.34/2.50 tff(20964,plain,
% 2.34/2.50 (op(e1, e1) = e0),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[630, 20942, 68, 1291])).
% 2.34/2.50 tff(20965,plain,
% 2.34/2.50 (op(e3, op(e1, e1)) = op(e3, e0)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[249])).
% 2.34/2.50 tff(20966,plain,
% 2.34/2.50 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10161])).
% 2.34/2.50 tff(20967,plain,
% 2.34/2.50 ((op(e3, e1) = e0) <=> (op(e1, e1) = op(e3, e1))),
% 2.34/2.50 inference(transitivity,[status(thm)],[20966, 15302])).
% 2.34/2.50 tff(20968,plain,
% 2.34/2.50 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20967])).
% 2.34/2.50 tff(20969,plain,
% 2.34/2.50 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20968])).
% 2.34/2.50 tff(20970,plain,
% 2.34/2.50 (~(op(e3, e1) = e0)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[945, 20969])).
% 2.34/2.50 tff(20971,plain,
% 2.34/2.50 ((op(e2, e0) = e3) <=> (e0 = e3)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[4921])).
% 2.34/2.50 tff(20972,plain,
% 2.34/2.50 ((e0 = e3) <=> (op(e2, e0) = e3)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20971])).
% 2.34/2.50 tff(20973,plain,
% 2.34/2.50 ((~(e0 = e3)) <=> (~(op(e2, e0) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20972])).
% 2.34/2.50 tff(20974,plain,
% 2.34/2.50 (~(op(e2, e0) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[181, 20973])).
% 2.34/2.50 tff(20975,plain,
% 2.34/2.50 (op(e2, e1) = e3),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1559, 9447, 20711, 20974])).
% 2.34/2.50 tff(20976,plain,
% 2.34/2.50 ((op(e2, e1) = op(e3, e1)) <=> (e3 = op(e3, op(e2, e3)))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20975, 2833])).
% 2.34/2.50 tff(20977,plain,
% 2.34/2.50 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, op(e2, e3)) = e3)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20976, 10487])).
% 2.34/2.50 tff(20978,plain,
% 2.34/2.50 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20977, 7677])).
% 2.34/2.50 tff(20979,plain,
% 2.34/2.50 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20978])).
% 2.34/2.50 tff(20980,plain,
% 2.34/2.50 (~(op(e3, e1) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[402, 20979])).
% 2.34/2.50 tff(20981,plain,
% 2.34/2.50 (op(e3, e1) = e1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[446, 82, 20980, 20970])).
% 2.34/2.50 tff(20982,plain,
% 2.34/2.50 (op(e3, e1) = op(e2, e3)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20981, 2685])).
% 2.34/2.50 tff(20983,plain,
% 2.34/2.50 ((op(e3, e1) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20982])).
% 2.34/2.50 tff(20984,plain,
% 2.34/2.50 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.50 inference(transitivity,[status(thm)],[20983, 394])).
% 2.34/2.50 tff(20985,plain,
% 2.34/2.50 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20984, 20829])).
% 2.34/2.50 tff(20986,plain,
% 2.34/2.50 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20985])).
% 2.34/2.50 tff(20987,plain,
% 2.34/2.50 (~(op(e3, e2) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[3429, 20986])).
% 2.34/2.50 tff(20988,plain,
% 2.34/2.50 (op(e3, e2) = e0),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1898, 20987, 2386, 9482])).
% 2.34/2.50 tff(20989,plain,
% 2.34/2.50 (op(e3, e2) = op(e1, e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20988, 10161])).
% 2.34/2.50 tff(20990,plain,
% 2.34/2.50 (op(e3, op(e3, e2)) = op(e3, op(e1, e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20989])).
% 2.34/2.50 tff(20991,plain,
% 2.34/2.50 (op(e3, op(e3, e2)) = e2),
% 2.34/2.50 inference(transitivity,[status(thm)],[20990, 20965, 17813])).
% 2.34/2.50 tff(20992,plain,
% 2.34/2.50 (op(e2, e1) = op(e1, e2)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20975, 2900])).
% 2.34/2.50 tff(20993,plain,
% 2.34/2.50 (op(e2, op(e2, e1)) = op(e2, op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20992])).
% 2.34/2.50 tff(20994,plain,
% 2.34/2.50 (op(e2, op(e2, e1)) = e1),
% 2.34/2.50 inference(transitivity,[status(thm)],[20993, 9377, 2684])).
% 2.34/2.50 tff(20995,plain,
% 2.34/2.50 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1355, 20994])).
% 2.34/2.50 tff(20996,plain,
% 2.34/2.50 (op(op(e3, e0), e3) = op(e2, op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[17813, 2900])).
% 2.34/2.50 tff(20997,plain,
% 2.34/2.50 (op(op(e3, e0), e3) = e1),
% 2.34/2.50 inference(transitivity,[status(thm)],[20996, 9377, 2684])).
% 2.34/2.50 tff(20998,plain,
% 2.34/2.50 ((op(op(e3, e0), e3) = e0) <=> (e1 = op(e1, e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20997, 10161])).
% 2.34/2.50 tff(20999,plain,
% 2.34/2.50 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e1) = e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[20998, 8462])).
% 2.34/2.50 tff(21000,plain,
% 2.34/2.50 ((op(e1, e1) = e1) <=> (op(op(e3, e0), e3) = e0)),
% 2.34/2.50 inference(symmetry,[status(thm)],[20999])).
% 2.34/2.50 tff(21001,plain,
% 2.34/2.50 ((~(op(e1, e1) = e1)) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21000])).
% 2.34/2.50 tff(21002,plain,
% 2.34/2.50 (~(op(op(e3, e0), e3) = e0)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1266, 21001])).
% 2.34/2.50 tff(21003,plain,
% 2.34/2.50 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1764, 21002])).
% 2.34/2.50 tff(21004,plain,
% 2.34/2.50 (op(op(e1, e2), e1) = op(e3, op(e2, e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[2899, 2685])).
% 2.34/2.50 tff(21005,plain,
% 2.34/2.50 (op(e3, op(e3, e1)) = op(op(e1, e2), e1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[2900, 20981])).
% 2.34/2.50 tff(21006,plain,
% 2.34/2.50 (op(e3, op(e3, e1)) = e1),
% 2.34/2.50 inference(transitivity,[status(thm)],[21005, 21004, 2832, 20981])).
% 2.34/2.50 tff(21007,plain,
% 2.34/2.50 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2594, 21006])).
% 2.34/2.50 tff(21008,plain,
% 2.34/2.50 (op(e2, op(e1, e1)) = op(e2, e0)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[249])).
% 2.34/2.50 tff(21009,plain,
% 2.34/2.50 (op(e0, e1) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1993, 82, 68, 3540])).
% 2.34/2.50 tff(21010,plain,
% 2.34/2.50 (op(op(e0, e1), e0) = op(e2, op(e1, e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21009, 10161])).
% 2.34/2.50 tff(21011,plain,
% 2.34/2.50 (op(op(e0, e1), e0) = op(e1, e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[21010, 21008, 4921, 10161])).
% 2.34/2.50 tff(21012,plain,
% 2.34/2.50 ((op(op(e0, e1), e0) = e1) <=> (op(e1, e1) = e1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21011])).
% 2.34/2.50 tff(21013,plain,
% 2.34/2.50 ((op(e1, e1) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 2.34/2.50 inference(symmetry,[status(thm)],[21012])).
% 2.34/2.50 tff(21014,plain,
% 2.34/2.50 ((~(op(e1, e1) = e1)) <=> (~(op(op(e0, e1), e0) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21013])).
% 2.34/2.50 tff(21015,plain,
% 2.34/2.50 (~(op(op(e0, e1), e0) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1266, 21014])).
% 2.34/2.50 tff(21016,plain,
% 2.34/2.50 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1461, 21015])).
% 2.34/2.50 tff(21017,plain,
% 2.34/2.50 (op(e2, op(e2, e0)) = op(e2, e0)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[4921])).
% 2.34/2.50 tff(21018,plain,
% 2.34/2.50 (op(e2, op(e2, e0)) = e0),
% 2.34/2.50 inference(transitivity,[status(thm)],[21017, 4921])).
% 2.34/2.50 tff(21019,plain,
% 2.34/2.50 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2653, 21018])).
% 2.34/2.50 tff(21020,plain,
% 2.34/2.50 ((op(e0, e1) = e1) <=> (e2 = op(e2, e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21009, 2685])).
% 2.34/2.50 tff(21021,plain,
% 2.34/2.50 ((op(e0, e1) = e1) <=> (op(e2, e3) = e2)),
% 2.34/2.50 inference(transitivity,[status(thm)],[21020, 120])).
% 2.34/2.50 tff(21022,plain,
% 2.34/2.50 ((op(e2, e3) = e2) <=> (op(e0, e1) = e1)),
% 2.34/2.50 inference(symmetry,[status(thm)],[21021])).
% 2.34/2.50 tff(21023,plain,
% 2.34/2.50 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e1) = e1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21022])).
% 2.34/2.50 tff(21024,plain,
% 2.34/2.50 (~(op(e0, e1) = e1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[4382, 21023])).
% 2.34/2.50 tff(21025,plain,
% 2.34/2.50 (op(e0, e2) = e1),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[384, 21024, 14786, 2379])).
% 2.34/2.50 tff(21026,plain,
% 2.34/2.50 (op(e0, op(e0, e2)) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8031, 21025, 21009])).
% 2.34/2.50 tff(21027,plain,
% 2.34/2.50 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1331, 21026])).
% 2.34/2.50 tff(21028,plain,
% 2.34/2.50 (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1459, 21027, 3342, 1347, 21019, 1304, 1357, 21016, 1358, 21007, 21003, 20995])).
% 2.34/2.50 tff(21029,plain,
% 2.34/2.50 (~(op(e3, op(e3, e2)) = e2)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1904, 21028])).
% 2.34/2.50 tff(21030,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[21029, 20991])).
% 2.34/2.50 tff(21031,plain,((op(e3, e1) = e2) | (~(op(e1, e1) = e0)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (op(e3, e2) = e2) | (op(e0, e0) = e1) | (op(e1, e1) = e1) | (~(op(e2, e3) = e1)) | (~(op(e1, e2) = e3)) | (~(op(e2, e0) = e0)) | (op(e2, e3) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(21032,plain,
% 2.34/2.50 (op(e3, e1) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[21031, 20964, 20963, 20962, 20960, 20955, 20952, 20949, 20945, 20942, 20667, 20917, 20680, 19038, 68, 20937])).
% 2.34/2.50 tff(21033,plain,
% 2.34/2.50 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e2)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21032])).
% 2.34/2.50 tff(21034,plain,
% 2.34/2.50 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21033])).
% 2.34/2.50 tff(21035,plain,
% 2.34/2.50 (~(op(e0, e1) = e2)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[3046, 21034])).
% 2.34/2.50 tff(21036,plain,
% 2.34/2.50 (op(e0, e0) = e2),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3652, 21035, 19015, 20931])).
% 2.34/2.50 tff(21037,plain,
% 2.34/2.50 ((op(e0, e0) = e3) <=> (e2 = op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21036, 20918])).
% 2.34/2.50 tff(21038,plain,
% 2.34/2.50 ((op(e0, e0) = e3) <=> (op(e1, e2) = e2)),
% 2.34/2.50 inference(transitivity,[status(thm)],[21037, 5762])).
% 2.34/2.50 tff(21039,plain,
% 2.34/2.50 ((op(e1, e2) = e2) <=> (op(e0, e0) = e3)),
% 2.34/2.50 inference(symmetry,[status(thm)],[21038])).
% 2.34/2.50 tff(21040,plain,
% 2.34/2.50 ((~(op(e1, e2) = e2)) <=> (~(op(e0, e0) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21039])).
% 2.34/2.50 tff(21041,plain,
% 2.34/2.50 (~(op(e0, e0) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[19486, 21040])).
% 2.34/2.50 tff(21042,plain,
% 2.34/2.50 (op(e0, e3) = e3),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1495, 21041, 2527, 4412])).
% 2.34/2.50 tff(21043,plain,
% 2.34/2.50 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20918])).
% 2.34/2.50 tff(21044,plain,
% 2.34/2.50 ((op(e3, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 2.34/2.50 inference(transitivity,[status(thm)],[21043, 3635])).
% 2.34/2.50 tff(21045,plain,
% 2.34/2.50 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.34/2.50 inference(symmetry,[status(thm)],[21044])).
% 2.34/2.50 tff(21046,plain,
% 2.34/2.50 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21045])).
% 2.34/2.50 tff(21047,plain,
% 2.34/2.50 (~(op(e3, e2) = e3)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[2292, 21046])).
% 2.34/2.50 tff(21048,plain,
% 2.34/2.50 ((e0 = e3) <=> (e0 = op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20918])).
% 2.34/2.50 tff(21049,plain,
% 2.34/2.50 ((e0 = e3) <=> (op(e1, e2) = e0)),
% 2.34/2.50 inference(transitivity,[status(thm)],[21048, 67])).
% 2.34/2.50 tff(21050,plain,
% 2.34/2.50 ((~(e0 = e3)) <=> (~(op(e1, e2) = e0))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[21049])).
% 2.34/2.50 tff(21051,plain,
% 2.34/2.50 (~(op(e1, e2) = e0)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[181, 21050])).
% 2.34/2.50 tff(21052,plain,
% 2.34/2.50 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[20938])).
% 2.34/2.50 tff(21053,plain,
% 2.34/2.50 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[21052, 5522])).
% 2.34/2.50 tff(21054,plain,
% 2.34/2.50 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21053])).
% 2.34/2.51 tff(21055,plain,
% 2.34/2.51 (~(op(e1, e2) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[1312, 21054])).
% 2.34/2.51 tff(21056,plain,
% 2.34/2.51 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20670])).
% 2.34/2.51 tff(21057,plain,
% 2.34/2.51 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21056])).
% 2.34/2.51 tff(21058,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21057])).
% 2.34/2.51 tff(21059,plain,
% 2.34/2.51 (~(op(e2, e1) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[197, 21058])).
% 2.34/2.51 tff(21060,plain,
% 2.34/2.51 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21032])).
% 2.34/2.51 tff(21061,plain,
% 2.34/2.51 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21060])).
% 2.34/2.51 tff(21062,plain,
% 2.34/2.51 (~(op(e3, e0) = e2)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[580, 21061])).
% 2.34/2.51 tff(21063,plain,
% 2.34/2.51 (op(e2, op(e1, e2)) = op(e2, e3)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20917])).
% 2.34/2.51 tff(21064,plain,
% 2.34/2.51 (op(e2, op(e2, e1)) = op(e2, op(e1, e2))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20933])).
% 2.34/2.51 tff(21065,plain,
% 2.34/2.51 (op(e2, op(e2, e1)) = e1),
% 2.34/2.51 inference(transitivity,[status(thm)],[21064, 21063, 20667])).
% 2.34/2.51 tff(21066,plain,
% 2.34/2.51 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1355, 21065])).
% 2.34/2.51 tff(21067,plain,
% 2.34/2.51 ((op(e1, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20938])).
% 2.34/2.51 tff(21068,plain,
% 2.34/2.51 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21067, 6411])).
% 2.34/2.51 tff(21069,plain,
% 2.34/2.51 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21068])).
% 2.34/2.51 tff(21070,plain,
% 2.34/2.51 (~(op(e3, e0) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[410, 21069])).
% 2.34/2.51 tff(21071,plain,
% 2.34/2.51 (op(e3, e0) = e3),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5422, 21062, 20769, 21070])).
% 2.34/2.51 tff(21072,plain,
% 2.34/2.51 (op(e3, op(e1, e1)) = op(e3, e0)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20964])).
% 2.34/2.51 tff(21073,plain,
% 2.34/2.51 (e0 = op(e1, e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[20964])).
% 2.34/2.51 tff(21074,plain,
% 2.34/2.51 (op(op(e3, e0), e0) = op(e3, op(e1, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21071, 21073])).
% 2.34/2.51 tff(21075,plain,
% 2.34/2.51 (op(op(e3, e0), e0) = e3),
% 2.34/2.51 inference(transitivity,[status(thm)],[21074, 21072, 21071])).
% 2.34/2.51 tff(21076,plain,
% 2.34/2.51 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4026, 21075])).
% 2.34/2.51 tff(21077,plain,
% 2.34/2.51 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21073])).
% 2.34/2.51 tff(21078,plain,
% 2.34/2.51 ((op(e3, e1) = e0) <=> (op(e1, e1) = op(e3, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21077, 15302])).
% 2.34/2.51 tff(21079,plain,
% 2.34/2.51 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21078])).
% 2.34/2.51 tff(21080,plain,
% 2.34/2.51 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21079])).
% 2.34/2.51 tff(21081,plain,
% 2.34/2.51 (~(op(e3, e1) = e0)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[945, 21080])).
% 2.34/2.51 tff(21082,plain,
% 2.34/2.51 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20667])).
% 2.34/2.51 tff(21083,plain,
% 2.34/2.51 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21082, 657])).
% 2.34/2.51 tff(21084,plain,
% 2.34/2.51 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21083])).
% 2.34/2.51 tff(21085,plain,
% 2.34/2.51 (~(op(e3, e3) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[368, 21084])).
% 2.34/2.51 tff(21086,plain,
% 2.34/2.51 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20255])).
% 2.34/2.51 tff(21087,plain,
% 2.34/2.51 ((op(e3, e1) = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21086, 6290])).
% 2.34/2.51 tff(21088,plain,
% 2.34/2.51 (op(e1, e3) = op(e3, e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[21032, 21087])).
% 2.34/2.51 tff(21089,plain,
% 2.34/2.51 (op(e3, e2) = op(e2, e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7757, 21088, 20667, 21085, 21070])).
% 2.34/2.51 tff(21090,plain,
% 2.34/2.51 (op(e3, e2) = e1),
% 2.34/2.51 inference(transitivity,[status(thm)],[21089, 20667])).
% 2.34/2.51 tff(21091,plain,
% 2.34/2.51 ((op(e3, e2) = e0) <=> (e1 = op(e1, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21090, 21073])).
% 2.34/2.51 tff(21092,plain,
% 2.34/2.51 ((op(e3, e2) = e0) <=> (op(e1, e1) = e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21091, 8462])).
% 2.34/2.51 tff(21093,plain,
% 2.34/2.51 ((op(e1, e1) = e1) <=> (op(e3, e2) = e0)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21092])).
% 2.34/2.51 tff(21094,plain,
% 2.34/2.51 ((~(op(e1, e1) = e1)) <=> (~(op(e3, e2) = e0))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21093])).
% 2.34/2.51 tff(21095,plain,
% 2.34/2.51 (~(op(e3, e2) = e0)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[20942, 21094])).
% 2.34/2.51 tff(21096,plain,
% 2.34/2.51 (op(e3, e3) = e0),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1916, 21095, 20769, 21081])).
% 2.34/2.51 tff(21097,plain,
% 2.34/2.51 (op(e0, e3) = e0),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4574, 21096, 19002, 20667, 20960, 20694, 20949, 19015, 20963, 21076, 21066, 21062, 20952, 21059, 19007, 21055, 4412, 21051, 19012, 20675, 21047])).
% 2.34/2.51 tff(21098,plain,
% 2.34/2.51 (e0 = op(e0, e3)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21097])).
% 2.34/2.51 tff(21099,plain,
% 2.34/2.51 (op(e1, e1) = op(e1, e2)),
% 2.34/2.51 inference(transitivity,[status(thm)],[20964, 21098, 21042, 20918])).
% 2.34/2.51 tff(21100,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1604, 21099])).
% 2.34/2.51 tff(21101,plain,((op(e0, e2) = e3) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e2, e2) = e0) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(21102,plain,
% 2.34/2.51 (op(e0, e1) = e3),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[21101, 20765, 68, 17, 1291])).
% 2.34/2.51 tff(21103,plain,
% 2.34/2.51 (e3 = op(e0, e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21102])).
% 2.34/2.51 tff(21104,plain,
% 2.34/2.51 ((op(e0, e3) = e3) <=> (op(e0, e3) = op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21103])).
% 2.34/2.51 tff(21105,plain,
% 2.34/2.51 ((op(e0, e3) = e3) <=> (op(e0, e1) = op(e0, e3))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21104, 15424])).
% 2.34/2.51 tff(21106,plain,
% 2.34/2.51 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21105])).
% 2.34/2.51 tff(21107,plain,
% 2.34/2.51 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21106])).
% 2.34/2.51 tff(21108,plain,
% 2.34/2.51 (~(op(e0, e3) = e3)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[818, 21107])).
% 2.34/2.51 tff(21109,plain,
% 2.34/2.51 (op(e3, e3) = e3),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[480, 21108, 19601, 20690])).
% 2.34/2.51 tff(21110,plain,
% 2.34/2.51 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21109])).
% 2.34/2.51 tff(21111,plain,
% 2.34/2.51 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21110])).
% 2.34/2.51 tff(21112,plain,
% 2.34/2.51 (~(op(e3, e0) = e3)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[157, 21111])).
% 2.34/2.51 tff(21113,plain,
% 2.34/2.51 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21102])).
% 2.34/2.51 tff(21114,plain,
% 2.34/2.51 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21113])).
% 2.34/2.51 tff(21115,plain,
% 2.34/2.51 (~(op(e0, e0) = e3)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[811, 21114])).
% 2.34/2.51 tff(21116,plain,
% 2.34/2.51 (op(e1, e0) = e3),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2713, 21112, 20694, 21115])).
% 2.34/2.51 tff(21117,plain,
% 2.34/2.51 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[20680])).
% 2.34/2.51 tff(21118,plain,
% 2.34/2.51 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21117, 10200])).
% 2.34/2.51 tff(21119,plain,
% 2.34/2.51 ((op(e0, e2) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.34/2.51 inference(symmetry,[status(thm)],[21118])).
% 2.34/2.51 tff(21120,plain,
% 2.34/2.51 (op(e0, e3) = e0),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[687, 21108, 19015, 20674])).
% 2.34/2.51 tff(21121,plain,
% 2.34/2.51 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e0)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21120])).
% 2.34/2.51 tff(21122,plain,
% 2.34/2.51 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21121, 21119])).
% 2.34/2.51 tff(21123,plain,
% 2.34/2.51 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21122])).
% 2.34/2.51 tff(21124,plain,
% 2.34/2.51 (~(op(e2, e0) = op(e0, e2))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[918, 21123])).
% 2.34/2.51 tff(21125,plain,
% 2.34/2.51 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6358, 21124])).
% 2.34/2.51 tff(21126,plain,
% 2.34/2.51 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21103])).
% 2.34/2.51 tff(21127,plain,
% 2.34/2.51 ((op(e2, e1) = e3) <=> (op(e0, e1) = op(e2, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21126, 14136])).
% 2.34/2.51 tff(21128,plain,
% 2.34/2.51 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21127])).
% 2.34/2.51 tff(21129,plain,
% 2.34/2.51 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21128])).
% 2.34/2.51 tff(21130,plain,
% 2.34/2.51 (~(op(e2, e1) = e3)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[606, 21129])).
% 2.34/2.51 tff(21131,plain,
% 2.34/2.51 (op(e2, e1) = e2),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2367, 21130, 21059, 20675])).
% 2.34/2.51 tff(21132,plain,
% 2.34/2.51 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21131])).
% 2.34/2.51 tff(21133,plain,
% 2.34/2.51 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21132, 5762])).
% 2.34/2.51 tff(21134,plain,
% 2.34/2.51 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.34/2.51 inference(symmetry,[status(thm)],[21133])).
% 2.34/2.51 tff(21135,plain,
% 2.34/2.51 ((~(op(e1, e2) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21134])).
% 2.34/2.51 tff(21136,plain,
% 2.34/2.51 (~(op(e2, e1) = op(e1, e2))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[19486, 21135])).
% 2.34/2.51 tff(21137,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[557, 21136])).
% 2.34/2.51 tff(21138,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21131])).
% 2.34/2.51 tff(21139,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21138, 637])).
% 2.34/2.51 tff(21140,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21139, 21086, 6290])).
% 2.34/2.51 tff(21141,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21140])).
% 2.34/2.51 tff(21142,plain,
% 2.34/2.51 (~(op(e1, e3) = op(e3, e1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[402, 21141])).
% 2.34/2.51 tff(21143,plain,
% 2.34/2.51 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6307, 21142])).
% 2.34/2.51 tff(21144,plain,
% 2.34/2.51 (op(e0, op(e0, e1)) = op(e0, e3)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21102])).
% 2.34/2.51 tff(21145,plain,
% 2.34/2.51 (op(e1, e0) = op(e0, e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21116, 21103])).
% 2.34/2.51 tff(21146,plain,
% 2.34/2.51 (op(e0, op(e1, e0)) = op(e0, op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21145])).
% 2.34/2.51 tff(21147,plain,
% 2.34/2.51 (op(e0, op(e1, e0)) = e0),
% 2.34/2.51 inference(transitivity,[status(thm)],[21146, 21144, 21120])).
% 2.34/2.51 tff(21148,plain,
% 2.34/2.51 (((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)) | (~(op(e0, op(e1, e0)) = e0))),
% 2.34/2.51 inference(tautology,[status(thm)],[])).
% 2.34/2.51 tff(21149,plain,
% 2.34/2.51 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[21148, 21147])).
% 2.34/2.51 tff(21150,plain,
% 2.34/2.51 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21134, 531])).
% 2.34/2.51 tff(21151,plain,
% 2.34/2.51 ((~(op(e1, e2) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21150])).
% 2.34/2.51 tff(21152,plain,
% 2.34/2.51 (~(op(e1, e2) = op(e2, e1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[19486, 21151])).
% 2.34/2.51 tff(21153,plain,
% 2.34/2.51 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[539, 21152])).
% 2.34/2.51 tff(21154,plain,
% 2.34/2.51 (op(e0, e3) = op(e0, op(e0, e1))),
% 2.34/2.51 inference(symmetry,[status(thm)],[21144])).
% 2.34/2.51 tff(21155,plain,
% 2.34/2.51 ((op(e0, e3) = e0) <=> (op(e0, op(e0, e1)) = e0)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21154])).
% 2.34/2.51 tff(21156,plain,
% 2.34/2.51 (op(e0, op(e0, e1)) = e0),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[21120, 21155])).
% 2.34/2.51 tff(21157,plain,
% 2.34/2.51 (((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)) | (~(op(e0, op(e0, e1)) = e0))),
% 2.34/2.51 inference(tautology,[status(thm)],[])).
% 2.34/2.51 tff(21158,plain,
% 2.34/2.51 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[21157, 21156])).
% 2.34/2.51 tff(21159,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21139, 21086])).
% 2.34/2.51 tff(21160,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21159])).
% 2.34/2.51 tff(21161,plain,
% 2.34/2.51 (~(op(e3, e1) = op(e1, e3))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[402, 21160])).
% 2.34/2.51 tff(21162,plain,
% 2.34/2.51 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6362, 21161])).
% 2.34/2.51 tff(21163,plain,
% 2.34/2.51 (op(e2, e2) = e3),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1559, 21130, 20690, 20694])).
% 2.34/2.51 tff(21164,plain,
% 2.34/2.51 (op(e2, e2) = op(e0, e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21163, 21103])).
% 2.34/2.51 tff(21165,plain,
% 2.34/2.51 (op(e0, op(e2, e2)) = op(e0, op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21164])).
% 2.34/2.51 tff(21166,plain,
% 2.34/2.51 (op(e0, op(e2, e2)) = e0),
% 2.34/2.51 inference(transitivity,[status(thm)],[21165, 21144, 21120])).
% 2.34/2.51 tff(21167,plain,
% 2.34/2.51 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5619, 21166])).
% 2.34/2.51 tff(21168,plain,
% 2.34/2.51 (op(e3, e3) = op(e0, e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21109, 21103])).
% 2.34/2.51 tff(21169,plain,
% 2.34/2.51 (op(e0, op(e3, e3)) = op(e0, op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21168])).
% 2.34/2.51 tff(21170,plain,
% 2.34/2.51 (op(e0, op(e3, e3)) = e0),
% 2.34/2.51 inference(transitivity,[status(thm)],[21169, 21144, 21120])).
% 2.34/2.51 tff(21171,plain,
% 2.34/2.51 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[392, 21170])).
% 2.34/2.51 tff(21172,plain,
% 2.34/2.51 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21121, 21119, 6337])).
% 2.34/2.51 tff(21173,plain,
% 2.34/2.51 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21172])).
% 2.34/2.51 tff(21174,plain,
% 2.34/2.51 (~(op(e0, e2) = op(e2, e0))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[918, 21173])).
% 2.34/2.51 tff(21175,plain,
% 2.34/2.51 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6347, 21174])).
% 2.34/2.51 tff(21176,plain,
% 2.34/2.51 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e0)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21120])).
% 2.34/2.51 tff(21177,plain,
% 2.34/2.51 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 2.34/2.51 inference(symmetry,[status(thm)],[21176])).
% 2.34/2.51 tff(21178,plain,
% 2.34/2.51 ((op(e3, e0) = e0) <=> (op(e0, e3) = op(e3, e0))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21177, 453])).
% 2.34/2.51 tff(21179,plain,
% 2.34/2.51 ((~(op(e3, e0) = e0)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21178])).
% 2.34/2.51 tff(21180,plain,
% 2.34/2.51 (~(op(e0, e3) = op(e3, e0))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[20769, 21179])).
% 2.34/2.51 tff(21181,plain,
% 2.34/2.51 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[496, 21180])).
% 2.34/2.51 tff(21182,plain,
% 2.34/2.51 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e1) = e2)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[6634])).
% 2.34/2.51 tff(21183,plain,
% 2.34/2.51 ((op(e2, e1) = e2) <=> (op(e2, op(e2, e3)) = e2)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21182])).
% 2.34/2.51 tff(21184,plain,
% 2.34/2.51 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e2, e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[2685])).
% 2.34/2.51 tff(21185,plain,
% 2.34/2.51 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21184])).
% 2.34/2.51 tff(21186,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21185])).
% 2.34/2.51 tff(21187,plain,
% 2.34/2.51 (~(op(e2, e1) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[197, 21186])).
% 2.34/2.51 tff(21188,plain,
% 2.34/2.51 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e0, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[4840])).
% 2.34/2.51 tff(21189,plain,
% 2.34/2.51 ((op(e2, e1) = e3) <=> (op(e0, e1) = op(e2, e1))),
% 2.34/2.51 inference(transitivity,[status(thm)],[21188, 14136])).
% 2.34/2.51 tff(21190,plain,
% 2.34/2.51 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21189])).
% 2.34/2.51 tff(21191,plain,
% 2.34/2.51 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21190])).
% 2.34/2.51 tff(21192,plain,
% 2.34/2.51 (~(op(e2, e1) = e3)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[606, 21191])).
% 2.34/2.51 tff(21193,plain,
% 2.34/2.51 (op(e2, e1) = e2),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2367, 21192, 21187, 2559])).
% 2.34/2.51 tff(21194,plain,
% 2.34/2.51 (op(e2, op(e2, e3)) = e2),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[21193, 21183])).
% 2.34/2.51 tff(21195,plain,
% 2.34/2.51 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[16573, 21194])).
% 2.34/2.51 tff(21196,plain,
% 2.34/2.51 (op(e1, e0) = op(e0, e1)),
% 2.34/2.51 inference(transitivity,[status(thm)],[258, 4840])).
% 2.34/2.51 tff(21197,plain,
% 2.34/2.51 ((op(e1, e0) = e1) <=> (op(e0, e1) = e1)),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21196])).
% 2.34/2.51 tff(21198,plain,
% 2.34/2.51 ((op(e0, e1) = e1) <=> (op(e1, e0) = e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21197])).
% 2.34/2.51 tff(21199,plain,
% 2.34/2.51 ((~(op(e0, e1) = e1)) <=> (~(op(e1, e0) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21198])).
% 2.34/2.51 tff(21200,plain,
% 2.34/2.51 ((op(e0, e1) = e1) <=> (e3 = op(e2, e3))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[4839, 2685])).
% 2.34/2.51 tff(21201,plain,
% 2.34/2.51 ((op(e0, e1) = e1) <=> (op(e2, e3) = e3)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21200, 112])).
% 2.34/2.51 tff(21202,plain,
% 2.34/2.51 ((op(e2, e3) = e3) <=> (op(e0, e1) = e1)),
% 2.34/2.51 inference(symmetry,[status(thm)],[21201])).
% 2.34/2.51 tff(21203,plain,
% 2.34/2.51 ((~(op(e2, e3) = e3)) <=> (~(op(e0, e1) = e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21202])).
% 2.34/2.51 tff(21204,plain,
% 2.34/2.51 (~(op(e0, e1) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[20711, 21203])).
% 2.34/2.51 tff(21205,plain,
% 2.34/2.51 (~(op(e1, e0) = e1)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[21204, 21199])).
% 2.34/2.51 tff(21206,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21193])).
% 2.34/2.51 tff(21207,plain,
% 2.34/2.51 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 2.34/2.51 inference(transitivity,[status(thm)],[21206, 637])).
% 2.34/2.51 tff(21208,plain,
% 2.34/2.51 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21207])).
% 2.34/2.51 tff(21209,plain,
% 2.34/2.51 (~(op(e3, e1) = e2)),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[402, 21208])).
% 2.34/2.51 tff(21210,plain,
% 2.34/2.51 ((e0 = op(e0, op(e2, e3))) <=> (op(e0, op(e2, e3)) = e0)),
% 2.34/2.51 inference(commutativity,[status(thm)],[])).
% 2.34/2.51 tff(21211,plain,
% 2.34/2.51 (e3 = op(e0, op(e2, e3))),
% 2.34/2.51 inference(transitivity,[status(thm)],[4840, 20695])).
% 2.34/2.51 tff(21212,plain,
% 2.34/2.51 ((e0 = e3) <=> (e0 = op(e0, op(e2, e3)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[21211])).
% 2.34/2.51 tff(21213,plain,
% 2.34/2.51 ((e0 = e3) <=> (op(e0, op(e2, e3)) = e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21212, 21210])).
% 2.34/2.52 tff(21214,plain,
% 2.34/2.52 ((e0 = e3) <=> (op(e0, e1) = e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21213, 20697])).
% 2.34/2.52 tff(21215,plain,
% 2.34/2.52 ((~(e0 = e3)) <=> (~(op(e0, e1) = e0))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21214])).
% 2.34/2.52 tff(21216,plain,
% 2.34/2.52 (~(op(e0, e1) = e0)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[181, 21215])).
% 2.34/2.52 tff(21217,plain,
% 2.34/2.52 (op(e3, e1) = e0),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[292, 84, 2559, 21216])).
% 2.34/2.52 tff(21218,plain,
% 2.34/2.52 (op(op(e2, e1), e1) = op(e2, op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21193, 2685])).
% 2.34/2.52 tff(21219,plain,
% 2.34/2.52 (op(op(e2, e1), e1) = e2),
% 2.34/2.52 inference(transitivity,[status(thm)],[21218, 6634, 21193])).
% 2.34/2.52 tff(21220,plain,
% 2.34/2.52 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2371, 21219])).
% 2.34/2.52 tff(21221,plain,
% 2.34/2.52 ((op(e0, e0) = e1) <=> (e2 = op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[12505, 2685])).
% 2.34/2.52 tff(21222,plain,
% 2.34/2.52 ((op(e0, e0) = e1) <=> (op(e2, e3) = e2)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21221, 120])).
% 2.34/2.52 tff(21223,plain,
% 2.34/2.52 ((op(e2, e3) = e2) <=> (op(e0, e0) = e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21222])).
% 2.34/2.52 tff(21224,plain,
% 2.34/2.52 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e0) = e1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21223])).
% 2.34/2.52 tff(21225,plain,
% 2.34/2.52 (~(op(e0, e0) = e1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[4382, 21224])).
% 2.34/2.52 tff(21226,plain,
% 2.34/2.52 (op(e0, e2) = e1),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[384, 21225, 14786, 21204])).
% 2.34/2.52 tff(21227,plain,
% 2.34/2.52 (op(e0, e2) = op(e2, e3)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21226, 2685])).
% 2.34/2.52 tff(21228,plain,
% 2.34/2.52 (op(op(e0, e2), e2) = op(op(e2, e3), e2)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21227])).
% 2.34/2.52 tff(21229,plain,
% 2.34/2.52 (op(op(e0, e2), e2) = e0),
% 2.34/2.52 inference(transitivity,[status(thm)],[21228, 2897, 6900])).
% 2.34/2.52 tff(21230,plain,
% 2.34/2.52 (op(op(e0, e1), e1) = op(e3, op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[4839, 2685])).
% 2.34/2.52 tff(21231,plain,
% 2.34/2.52 (op(e3, e0) = e1),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5422, 3786, 1908, 2410])).
% 2.34/2.52 tff(21232,plain,
% 2.34/2.52 (op(e3, op(e3, e0)) = op(op(e0, e1), e1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[4840, 21231])).
% 2.34/2.52 tff(21233,plain,
% 2.34/2.52 (op(e3, op(e3, e0)) = e0),
% 2.34/2.52 inference(transitivity,[status(thm)],[21232, 21230, 2832, 4731])).
% 2.34/2.52 tff(21234,plain,
% 2.34/2.52 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1345, 21233])).
% 2.34/2.52 tff(21235,plain,
% 2.34/2.52 (op(e0, op(e2, e3)) = op(e0, e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[20695])).
% 2.34/2.52 tff(21236,plain,
% 2.34/2.52 (op(op(e3, e1), e1) = op(e0, op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[4731, 2685])).
% 2.34/2.52 tff(21237,plain,
% 2.34/2.52 (op(op(e3, e1), e1) = e3),
% 2.34/2.52 inference(transitivity,[status(thm)],[21236, 21235, 4839])).
% 2.34/2.52 tff(21238,plain,
% 2.34/2.52 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2416, 21237])).
% 2.34/2.52 tff(21239,plain,
% 2.34/2.52 (op(op(e1, e2), e1) = op(e0, op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[6900, 2685])).
% 2.34/2.52 tff(21240,plain,
% 2.34/2.52 (op(op(e1, e2), e1) = op(e0, e1)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21239, 21235])).
% 2.34/2.52 tff(21241,plain,
% 2.34/2.52 ((op(op(e1, e2), e1) = e2) <=> (op(e0, e1) = e2)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21240])).
% 2.34/2.52 tff(21242,plain,
% 2.34/2.52 ((op(e0, e1) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21241])).
% 2.34/2.52 tff(21243,plain,
% 2.34/2.52 ((~(op(e0, e1) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21242])).
% 2.34/2.52 tff(21244,plain,
% 2.34/2.52 ((op(e0, e1) = e2) <=> (e3 = e2)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[4839])).
% 2.34/2.52 tff(21245,plain,
% 2.34/2.52 ((op(e0, e1) = e2) <=> (e2 = e3)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21244, 1314])).
% 2.34/2.52 tff(21246,plain,
% 2.34/2.52 ((e2 = e3) <=> (op(e0, e1) = e2)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21245])).
% 2.34/2.52 tff(21247,plain,
% 2.34/2.52 ((~(e2 = e3)) <=> (~(op(e0, e1) = e2))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21246])).
% 2.34/2.52 tff(21248,plain,
% 2.34/2.52 (~(op(e0, e1) = e2)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[1321, 21247])).
% 2.34/2.52 tff(21249,plain,
% 2.34/2.52 (~(op(op(e1, e2), e1) = e2)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[21248, 21243])).
% 2.34/2.52 tff(21250,plain,
% 2.34/2.52 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5959, 21249])).
% 2.34/2.52 tff(21251,plain,
% 2.34/2.52 (op(op(e0, e1), e1) = op(e3, e1)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21230, 2832])).
% 2.34/2.52 tff(21252,plain,
% 2.34/2.52 ((op(op(e0, e1), e1) = e0) <=> (op(e3, e1) = e0)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21251])).
% 2.34/2.52 tff(21253,plain,
% 2.34/2.52 ((op(e3, e1) = e0) <=> (op(op(e0, e1), e1) = e0)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21252])).
% 2.34/2.52 tff(21254,plain,
% 2.34/2.52 (op(op(e0, e1), e1) = e0),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[4731, 21253])).
% 2.34/2.52 tff(21255,plain,
% 2.34/2.52 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2650, 21254])).
% 2.34/2.52 tff(21256,plain,
% 2.34/2.52 (op(op(e1, e0), e0) = op(op(e0, e1), e0)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21196])).
% 2.34/2.52 tff(21257,plain,
% 2.34/2.52 (op(op(e1, e0), e0) = op(e3, e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21256, 7163])).
% 2.34/2.52 tff(21258,plain,
% 2.34/2.52 ((op(op(e1, e0), e0) = e1) <=> (op(e3, e0) = e1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21257])).
% 2.34/2.52 tff(21259,plain,
% 2.34/2.52 ((op(e3, e0) = e1) <=> (op(op(e1, e0), e0) = e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21258])).
% 2.34/2.52 tff(21260,plain,
% 2.34/2.52 (op(op(e1, e0), e0) = e1),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[21231, 21259])).
% 2.34/2.52 tff(21261,plain,
% 2.34/2.52 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3015, 21260])).
% 2.34/2.52 tff(21262,plain,
% 2.34/2.52 (op(e3, e2) = e2),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[15971, 3786, 82])).
% 2.34/2.52 tff(21263,plain,
% 2.34/2.52 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21262])).
% 2.34/2.52 tff(21264,plain,
% 2.34/2.52 (op(e3, op(e3, e2)) = e2),
% 2.34/2.52 inference(transitivity,[status(thm)],[21263, 21262])).
% 2.34/2.52 tff(21265,plain,
% 2.34/2.52 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1904, 21264])).
% 2.34/2.52 tff(21266,plain,
% 2.34/2.52 (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1459, 21265, 3342, 1347, 2421, 1304, 21261, 21255, 21250, 21238, 21234, 1936])).
% 2.34/2.52 tff(21267,plain,
% 2.34/2.52 (~(op(op(e0, e2), e2) = e0)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1956, 21266])).
% 2.34/2.52 tff(21268,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[21267, 21229])).
% 2.34/2.52 tff(21269,plain,((op(e3, e0) = e2) | (~(op(e1, e2) = e0)) | (~(op(e2, e3) = e1)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e3, e1) = e0)) | (~(op(e0, e1) = e3)) | (op(e2, e3) = e2) | (~(op(e1, e0) = e3)) | (op(e3, e1) = e2) | (op(e3, e0) = e0) | (op(e3, e0) = e3) | (op(e1, e0) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(21270,plain,
% 2.34/2.52 (op(e3, e0) = e2),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[21269, 17950, 2684, 3342, 1347, 2421, 1304, 21220, 21217, 4839, 4382, 258, 21209, 1908, 2410, 6687, 982])).
% 2.34/2.52 tff(21271,plain,
% 2.34/2.52 ((op(e3, e0) = e1) <=> (e2 = op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21270, 2685])).
% 2.34/2.52 tff(21272,plain,
% 2.34/2.52 ((op(e3, e0) = e1) <=> (op(e2, e3) = e2)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21271, 120])).
% 2.34/2.52 tff(21273,plain,
% 2.34/2.52 ((op(e2, e3) = e2) <=> (op(e3, e0) = e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21272])).
% 2.34/2.52 tff(21274,plain,
% 2.34/2.52 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e0) = e1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21273])).
% 2.34/2.52 tff(21275,plain,
% 2.34/2.52 (~(op(e3, e0) = e1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[4382, 21274])).
% 2.34/2.52 tff(21276,plain,
% 2.34/2.52 (op(e0, e0) = e1),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1480, 21275, 2689, 21205])).
% 2.34/2.52 tff(21277,plain,
% 2.34/2.52 (op(e1, op(e0, e0)) = op(e1, e1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21276])).
% 2.34/2.52 tff(21278,plain,
% 2.34/2.52 (op(e1, op(e0, e0)) = e1),
% 2.34/2.52 inference(transitivity,[status(thm)],[21277, 12395])).
% 2.34/2.52 tff(21279,plain,
% 2.34/2.52 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6717, 21278])).
% 2.34/2.52 tff(21280,plain,
% 2.34/2.52 ((op(e3, e1) = e1) <=> (e0 = op(e2, e3))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21217, 2685])).
% 2.34/2.52 tff(21281,plain,
% 2.34/2.52 ((op(e3, e1) = e1) <=> (op(e2, e3) = e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21280, 86])).
% 2.34/2.52 tff(21282,plain,
% 2.34/2.52 ((op(e2, e3) = e0) <=> (op(e3, e1) = e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21281])).
% 2.34/2.52 tff(21283,plain,
% 2.34/2.52 ((~(op(e2, e3) = e0)) <=> (~(op(e3, e1) = e1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21282])).
% 2.34/2.52 tff(21284,plain,
% 2.34/2.52 (~(op(e3, e1) = e1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[20780, 21283])).
% 2.34/2.52 tff(21285,plain,
% 2.34/2.52 (op(e3, e2) = e1),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[939, 21275, 21284, 2825])).
% 2.34/2.52 tff(21286,plain,
% 2.34/2.52 (op(e1, op(e3, e2)) = op(e1, e1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21285])).
% 2.34/2.52 tff(21287,plain,
% 2.34/2.52 (op(e1, op(e3, e2)) = e1),
% 2.34/2.52 inference(transitivity,[status(thm)],[21286, 12395])).
% 2.34/2.52 tff(21288,plain,
% 2.34/2.52 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[12544, 21287])).
% 2.34/2.52 tff(21289,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5367, 21288, 21279, 5670, 9846, 6688, 20636, 5672, 5511, 5675, 5673, 21195, 5681, 5669, 5680, 5674])).
% 2.34/2.52 tff(21290,plain,((op(e1, e1) = e0) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (op(e2, e3) = e2) | (~(op(e2, e3) = e1)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e0, e1) = e3)) | (~(op(e1, e0) = e3)) | (op(e3, e0) = e0) | (op(e3, e0) = e3) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e1, e3) = e0) | (op(e1, e0) = e0) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(21291,plain,
% 2.34/2.52 (op(e1, e1) = e0),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[21290, 21181, 21175, 21171, 21167, 21162, 21158, 21153, 21149, 21143, 21137, 21125, 19038, 20667, 20963, 20962, 20775, 20960, 21102, 21116, 20769, 21112, 19180, 20687, 19012, 20683, 68, 1291, 20675])).
% 2.34/2.52 tff(21292,plain,
% 2.34/2.52 (e0 = op(e1, e1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[21291, 123])).
% 2.34/2.52 tff(21293,plain,
% 2.34/2.52 (op(e1, op(e1, e1)) = op(e1, e0)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21291])).
% 2.34/2.52 tff(21294,plain,
% 2.34/2.52 (op(e1, e0) = op(e1, op(e1, e1))),
% 2.34/2.52 inference(symmetry,[status(thm)],[21293])).
% 2.34/2.52 tff(21295,plain,
% 2.34/2.52 (e3 = op(e1, e0)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21116])).
% 2.34/2.52 tff(21296,plain,
% 2.34/2.52 (e3 = op(e1, op(e1, e1))),
% 2.34/2.52 inference(transitivity,[status(thm)],[21295, 21294])).
% 2.34/2.52 tff(21297,plain,
% 2.34/2.52 (op(e1, op(e1, e1)) = op(e0, e1)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21293, 21116, 21103])).
% 2.34/2.52 tff(21298,plain,
% 2.34/2.52 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e0, e1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21297])).
% 2.34/2.52 tff(21299,plain,
% 2.34/2.52 (op(e1, op(e0, e1)) = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.52 inference(symmetry,[status(thm)],[21298])).
% 2.34/2.52 tff(21300,plain,
% 2.34/2.52 (op(e1, op(e0, e1)) = op(op(e2, e3), e3)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[20670, 21102])).
% 2.34/2.52 tff(21301,plain,
% 2.34/2.52 (op(op(e2, e3), e3) = op(e1, op(e0, e1))),
% 2.34/2.52 inference(symmetry,[status(thm)],[21300])).
% 2.34/2.52 tff(21302,plain,
% 2.34/2.52 (op(e1, e3) = op(op(e2, e3), e3)),
% 2.34/2.52 inference(symmetry,[status(thm)],[20669])).
% 2.34/2.52 tff(21303,plain,
% 2.34/2.52 (e2 = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.52 inference(transitivity,[status(thm)],[20255, 21302, 21301, 21299])).
% 2.34/2.52 tff(21304,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[276, 21303, 21296, 21292])).
% 2.34/2.52 tff(21305,plain,((op(e1, e1) = e3) | (op(e1, e1) = e2) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(21306,plain,
% 2.34/2.52 (op(e1, e1) = e3),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[21305, 68, 17])).
% 2.34/2.52 tff(21307,plain,
% 2.34/2.52 (op(e1, op(e1, e1)) = op(op(e2, e3), e3)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[20670, 21306])).
% 2.34/2.52 tff(21308,plain,
% 2.34/2.52 (op(e1, op(e1, e1)) = e2),
% 2.34/2.52 inference(transitivity,[status(thm)],[21307, 20669, 19002])).
% 2.34/2.52 tff(21309,plain,
% 2.34/2.52 (op(e1, op(e1, op(e1, e1))) = op(op(e2, e3), e2)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[20670, 21308])).
% 2.34/2.52 tff(21310,plain,
% 2.34/2.52 (op(e1, op(e1, op(e1, e1))) = op(e1, e2)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21309, 20668])).
% 2.34/2.52 tff(21311,plain,
% 2.34/2.52 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (e0 = op(e1, e2))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21310])).
% 2.34/2.52 tff(21312,plain,
% 2.34/2.52 ((e0 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e2) = e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21311, 67])).
% 2.34/2.52 tff(21313,plain,
% 2.34/2.52 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, op(e1, e1))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[21312])).
% 2.34/2.52 tff(21314,plain,
% 2.34/2.52 (e3 = op(e1, e1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[21306])).
% 2.34/2.52 tff(21315,plain,
% 2.34/2.52 ((e0 = e3) <=> (e0 = op(e1, e1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21314])).
% 2.34/2.52 tff(21316,plain,
% 2.34/2.52 ((e0 = e3) <=> (op(e1, e1) = e0)),
% 2.34/2.52 inference(transitivity,[status(thm)],[21315, 122])).
% 2.34/2.52 tff(21317,plain,
% 2.34/2.52 ((~(e0 = e3)) <=> (~(op(e1, e1) = e0))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[21316])).
% 2.34/2.52 tff(21318,plain,
% 2.34/2.52 (~(op(e1, e1) = e0)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[181, 21317])).
% 2.34/2.52 tff(21319,plain,
% 2.34/2.52 (op(e1, e2) = e0),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1830, 21318, 19012, 20683])).
% 2.34/2.52 tff(21320,plain,
% 2.34/2.52 (e0 = op(e1, op(e1, op(e1, e1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[21319, 21313])).
% 2.34/2.52 tff(21321,plain,
% 2.34/2.52 (e3 = op(e1, e1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[21306, 1740])).
% 2.34/2.52 tff(21322,plain,
% 2.34/2.52 (op(op(e2, e3), e3) = op(e1, op(e1, e1))),
% 2.34/2.52 inference(symmetry,[status(thm)],[21307])).
% 2.34/2.52 tff(21323,plain,
% 2.34/2.52 (e2 = op(e1, op(e1, e1))),
% 2.34/2.52 inference(transitivity,[status(thm)],[20255, 21302, 21322])).
% 2.34/2.53 tff(21324,plain,
% 2.34/2.53 (~(e0 = op(e1, op(e1, op(e1, e1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1753, 21323, 21321])).
% 2.34/2.53 tff(21325,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[21324, 21320])).
% 2.34/2.53 tff(21326,plain,((op(e1, e1) = e2) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(21327,plain,
% 2.34/2.53 (op(e1, e1) = e2),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[21326, 17])).
% 2.34/2.53 tff(21328,plain,
% 2.34/2.53 ((op(e1, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21327])).
% 2.34/2.53 tff(21329,plain,
% 2.34/2.53 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21328, 66])).
% 2.34/2.53 tff(21330,plain,
% 2.34/2.53 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21329])).
% 2.34/2.53 tff(21331,plain,
% 2.34/2.53 (~(op(e1, e3) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[619, 21330])).
% 2.34/2.53 tff(21332,plain,
% 2.34/2.53 (op(e1, e3) = e3),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[104, 80, 21331, 65])).
% 2.34/2.53 tff(21333,plain,
% 2.34/2.53 (e3 = op(e1, e3)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21332])).
% 2.34/2.53 tff(21334,plain,
% 2.34/2.53 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21333])).
% 2.34/2.53 tff(21335,plain,
% 2.34/2.53 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21334])).
% 2.34/2.53 tff(21336,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21335])).
% 2.34/2.53 tff(21337,plain,
% 2.34/2.53 (~(op(e1, e0) = e3)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[110, 21336])).
% 2.34/2.53 tff(21338,plain,
% 2.34/2.53 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21327])).
% 2.34/2.53 tff(21339,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21338])).
% 2.34/2.53 tff(21340,plain,
% 2.34/2.53 (~(op(e1, e0) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[737, 21339])).
% 2.34/2.53 tff(21341,plain,
% 2.34/2.53 ((op(e0, e3) = e2) <=> (e1 = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[19])).
% 2.34/2.53 tff(21342,plain,
% 2.34/2.53 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21341])).
% 2.34/2.53 tff(21343,plain,
% 2.34/2.53 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21342])).
% 2.34/2.53 tff(21344,plain,
% 2.34/2.53 (~(op(e0, e3) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[708, 21343])).
% 2.34/2.53 tff(21345,plain,
% 2.34/2.53 (op(e2, e3) = e2),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[15003, 21344, 21331])).
% 2.34/2.53 tff(21346,plain,
% 2.34/2.53 ((op(e2, e3) = e3) <=> (e2 = e3)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21345])).
% 2.34/2.53 tff(21347,plain,
% 2.34/2.53 ((e2 = e3) <=> (op(e2, e3) = e3)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21346])).
% 2.34/2.53 tff(21348,plain,
% 2.34/2.53 ((~(e2 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21347])).
% 2.34/2.53 tff(21349,plain,
% 2.34/2.53 (~(op(e2, e3) = e3)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1321, 21348])).
% 2.34/2.53 tff(21350,plain,
% 2.34/2.53 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21345])).
% 2.34/2.53 tff(21351,plain,
% 2.34/2.53 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21350])).
% 2.34/2.53 tff(21352,plain,
% 2.34/2.53 (~(op(e2, e2) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[515, 21351])).
% 2.34/2.53 tff(21353,plain,
% 2.34/2.53 (e2 = op(e1, e1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21327])).
% 2.34/2.53 tff(21354,plain,
% 2.34/2.53 ((e0 = e2) <=> (e0 = op(e1, e1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21353])).
% 2.34/2.53 tff(21355,plain,
% 2.34/2.53 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21354, 122])).
% 2.34/2.53 tff(21356,plain,
% 2.34/2.53 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21355])).
% 2.34/2.53 tff(21357,plain,
% 2.34/2.53 (~(op(e1, e1) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[14, 21356])).
% 2.34/2.53 tff(21358,plain,
% 2.34/2.53 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21345])).
% 2.34/2.53 tff(21359,plain,
% 2.34/2.53 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21358, 1])).
% 2.34/2.53 tff(21360,plain,
% 2.34/2.53 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21359])).
% 2.34/2.53 tff(21361,plain,
% 2.34/2.53 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21360])).
% 2.34/2.53 tff(21362,plain,
% 2.34/2.53 (~(op(e2, e3) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[14, 21361])).
% 2.34/2.53 tff(21363,plain,
% 2.34/2.53 (op(e3, e3) = e0),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1098, 80, 21362, 27])).
% 2.34/2.53 tff(21364,plain,
% 2.34/2.53 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21363])).
% 2.34/2.53 tff(21365,plain,
% 2.34/2.53 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21364])).
% 2.34/2.53 tff(21366,plain,
% 2.34/2.53 (~(op(e3, e1) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[437, 21365])).
% 2.34/2.53 tff(21367,plain,
% 2.34/2.53 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[19])).
% 2.34/2.53 tff(21368,plain,
% 2.34/2.53 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21367])).
% 2.34/2.53 tff(21369,plain,
% 2.34/2.53 (~(op(e0, e1) = e1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[818, 21368])).
% 2.34/2.53 tff(21370,plain,
% 2.34/2.53 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21327])).
% 2.34/2.53 tff(21371,plain,
% 2.34/2.53 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21370])).
% 2.34/2.53 tff(21372,plain,
% 2.34/2.53 (~(op(e0, e1) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[792, 21371])).
% 2.34/2.53 tff(21373,plain,
% 2.34/2.53 (op(e0, e1) = e0),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[829, 2527, 21372, 21369])).
% 2.34/2.53 tff(21374,plain,
% 2.34/2.53 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21373])).
% 2.34/2.53 tff(21375,plain,
% 2.34/2.53 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21374, 10200])).
% 2.34/2.53 tff(21376,plain,
% 2.34/2.53 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21375])).
% 2.34/2.53 tff(21377,plain,
% 2.34/2.53 (~(op(e0, e2) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[2102, 21376])).
% 2.34/2.53 tff(21378,plain,
% 2.34/2.53 (op(e1, e2) = e0),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[973, 21377, 17, 3099])).
% 2.34/2.53 tff(21379,plain,
% 2.34/2.53 ((op(e1, e2) = e1) <=> (e0 = e1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21378])).
% 2.34/2.53 tff(21380,plain,
% 2.34/2.53 ((e0 = e1) <=> (op(e1, e2) = e1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21379])).
% 2.34/2.53 tff(21381,plain,
% 2.34/2.53 ((~(e0 = e1)) <=> (~(op(e1, e2) = e1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21380])).
% 2.34/2.53 tff(21382,plain,
% 2.34/2.53 (~(op(e1, e2) = e1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[26, 21381])).
% 2.34/2.53 tff(21383,plain,
% 2.34/2.53 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21373])).
% 2.34/2.53 tff(21384,plain,
% 2.34/2.53 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21383, 83])).
% 2.34/2.53 tff(21385,plain,
% 2.34/2.53 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21384])).
% 2.34/2.53 tff(21386,plain,
% 2.34/2.53 (~(op(e2, e1) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[606, 21385])).
% 2.34/2.53 tff(21387,plain,
% 2.34/2.53 (op(e2, e0) = e0),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2311, 21386, 17, 21362])).
% 2.34/2.53 tff(21388,plain,
% 2.34/2.53 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21387])).
% 2.34/2.53 tff(21389,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21388])).
% 2.34/2.53 tff(21390,plain,
% 2.34/2.53 (~(op(e1, e0) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[756, 21389])).
% 2.34/2.53 tff(21391,plain,
% 2.34/2.53 (op(e1, e0) = e1),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[728, 21390, 21340, 11813])).
% 2.34/2.53 tff(21392,plain,
% 2.34/2.53 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21387])).
% 2.34/2.53 tff(21393,plain,
% 2.34/2.53 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21392, 10200])).
% 2.34/2.53 tff(21394,plain,
% 2.34/2.53 ((op(e0, e2) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.34/2.53 inference(symmetry,[status(thm)],[21393])).
% 2.34/2.53 tff(21395,plain,
% 2.34/2.53 ((~(op(e0, e2) = e0)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21394])).
% 2.34/2.53 tff(21396,plain,
% 2.34/2.53 (~(op(e2, e0) = op(e0, e2))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21377, 21395])).
% 2.34/2.53 tff(21397,plain,
% 2.34/2.53 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6358, 21396])).
% 2.34/2.53 tff(21398,plain,
% 2.34/2.53 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21378])).
% 2.34/2.53 tff(21399,plain,
% 2.34/2.53 ((op(e2, e1) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 2.34/2.53 inference(symmetry,[status(thm)],[21398])).
% 2.34/2.53 tff(21400,plain,
% 2.34/2.53 ((~(op(e2, e1) = e0)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21399])).
% 2.34/2.53 tff(21401,plain,
% 2.34/2.53 (~(op(e2, e1) = op(e1, e2))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21386, 21400])).
% 2.34/2.53 tff(21402,plain,
% 2.34/2.53 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[557, 21401])).
% 2.34/2.53 tff(21403,plain,
% 2.34/2.53 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21373])).
% 2.34/2.53 tff(21404,plain,
% 2.34/2.53 ((op(e1, e0) = e0) <=> (op(e1, e0) = op(e0, e1))),
% 2.34/2.53 inference(symmetry,[status(thm)],[21403])).
% 2.34/2.53 tff(21405,plain,
% 2.34/2.53 ((op(e1, e0) = op(e2, e0)) <=> (op(e0, e1) = op(e1, e0))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21388, 21404, 596])).
% 2.34/2.53 tff(21406,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21405])).
% 2.34/2.53 tff(21407,plain,
% 2.34/2.53 (~(op(e0, e1) = op(e1, e0))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[756, 21406])).
% 2.34/2.53 tff(21408,plain,
% 2.34/2.53 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[609, 21407])).
% 2.34/2.53 tff(21409,plain,
% 2.34/2.53 ((op(e2, e1) = e0) <=> (op(e1, e2) = op(e2, e1))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21399, 531])).
% 2.34/2.53 tff(21410,plain,
% 2.34/2.53 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21409])).
% 2.34/2.53 tff(21411,plain,
% 2.34/2.53 (~(op(e1, e2) = op(e2, e1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21386, 21410])).
% 2.34/2.53 tff(21412,plain,
% 2.34/2.53 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[539, 21411])).
% 2.34/2.53 tff(21413,plain,
% 2.34/2.53 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21388, 21404])).
% 2.34/2.53 tff(21414,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21413])).
% 2.34/2.53 tff(21415,plain,
% 2.34/2.53 (~(op(e1, e0) = op(e0, e1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[756, 21414])).
% 2.34/2.53 tff(21416,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[613, 21415])).
% 2.34/2.53 tff(21417,plain,
% 2.34/2.53 (e1 = op(e1, e0)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21391])).
% 2.34/2.53 tff(21418,plain,
% 2.34/2.53 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e1, e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21417])).
% 2.34/2.53 tff(21419,plain,
% 2.34/2.53 ((op(e3, e0) = e1) <=> (op(e1, e0) = op(e3, e0))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21418, 2294])).
% 2.34/2.53 tff(21420,plain,
% 2.34/2.53 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21419])).
% 2.34/2.53 tff(21421,plain,
% 2.34/2.53 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21420, 19345, 453])).
% 2.34/2.53 tff(21422,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21421])).
% 2.34/2.53 tff(21423,plain,
% 2.34/2.53 (~(op(e0, e3) = op(e3, e0))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[410, 21422])).
% 2.34/2.53 tff(21424,plain,
% 2.34/2.53 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[496, 21423])).
% 2.34/2.53 tff(21425,plain,
% 2.34/2.53 ((op(e0, e2) = e0) <=> (op(e0, e2) = op(e2, e0))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21394, 6337])).
% 2.34/2.53 tff(21426,plain,
% 2.34/2.53 ((~(op(e0, e2) = e0)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21425])).
% 2.34/2.53 tff(21427,plain,
% 2.34/2.53 (~(op(e0, e2) = op(e2, e0))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21377, 21426])).
% 2.34/2.53 tff(21428,plain,
% 2.34/2.53 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6347, 21427])).
% 2.34/2.53 tff(21429,plain,
% 2.34/2.53 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[2891])).
% 2.34/2.53 tff(21430,plain,
% 2.34/2.53 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21429])).
% 2.34/2.53 tff(21431,plain,
% 2.34/2.53 (~(op(e1, e0) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[737, 21430])).
% 2.34/2.53 tff(21432,plain,
% 2.34/2.53 (op(e3, e0) = e2),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[589, 12721, 21431, 9267])).
% 2.34/2.53 tff(21433,plain,
% 2.34/2.53 ((op(e3, e0) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21432])).
% 2.34/2.53 tff(21434,plain,
% 2.34/2.53 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21433, 2234])).
% 2.34/2.53 tff(21435,plain,
% 2.34/2.53 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21434])).
% 2.34/2.53 tff(21436,plain,
% 2.34/2.53 (~(op(e3, e2) = e2)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1133, 21435])).
% 2.34/2.53 tff(21437,plain,
% 2.34/2.53 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21432])).
% 2.34/2.53 tff(21438,plain,
% 2.34/2.53 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.34/2.53 inference(transitivity,[status(thm)],[7760, 21437])).
% 2.34/2.53 tff(21439,plain,
% 2.34/2.53 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e2))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21438])).
% 2.34/2.53 tff(21440,plain,
% 2.34/2.53 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21439, 7171])).
% 2.34/2.53 tff(21441,plain,
% 2.34/2.53 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21440])).
% 2.34/2.53 tff(21442,plain,
% 2.34/2.53 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3067])).
% 2.34/2.53 tff(21443,plain,
% 2.34/2.53 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21442, 5377])).
% 2.34/2.53 tff(21444,plain,
% 2.34/2.53 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[21443])).
% 2.34/2.53 tff(21445,plain,
% 2.34/2.53 (e2 = op(e3, op(e3, e3))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21432, 21444])).
% 2.34/2.53 tff(21446,plain,
% 2.34/2.53 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3093, 21445, 3079])).
% 2.34/2.53 tff(21447,plain,
% 2.34/2.53 (~(op(e3, e2) = e1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21446, 21441])).
% 2.34/2.53 tff(21448,plain,
% 2.34/2.53 (op(e3, e2) = e3),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1898, 21447, 3099, 21436])).
% 2.34/2.53 tff(21449,plain,
% 2.34/2.53 (op(e3, e2) = op(e1, e3)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21448, 11135])).
% 2.34/2.53 tff(21450,plain,
% 2.34/2.53 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21449])).
% 2.34/2.53 tff(21451,plain,
% 2.34/2.53 ((op(e3, e1) = op(e3, e2)) <=> (op(e1, e3) = op(e3, e1))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21450, 6290])).
% 2.34/2.53 tff(21452,plain,
% 2.34/2.53 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21451])).
% 2.34/2.53 tff(21453,plain,
% 2.34/2.53 (~(op(e1, e3) = op(e3, e1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[3429, 21452])).
% 2.34/2.53 tff(21454,plain,
% 2.34/2.53 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6307, 21453])).
% 2.34/2.53 tff(21455,plain,
% 2.34/2.53 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3787])).
% 2.34/2.53 tff(21456,plain,
% 2.34/2.53 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.53 inference(symmetry,[status(thm)],[21455])).
% 2.34/2.53 tff(21457,plain,
% 2.34/2.53 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21434, 21456])).
% 2.34/2.53 tff(21458,plain,
% 2.34/2.53 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21457])).
% 2.34/2.53 tff(21459,plain,
% 2.34/2.53 (~(op(e3, e2) = op(e2, e3))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1133, 21458])).
% 2.34/2.53 tff(21460,plain,
% 2.34/2.53 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[500, 21459])).
% 2.34/2.53 tff(21461,plain,
% 2.34/2.53 (op(e2, op(e1, e3)) = e2),
% 2.34/2.53 inference(transitivity,[status(thm)],[11227, 3787])).
% 2.34/2.53 tff(21462,plain,
% 2.34/2.53 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9084, 21461])).
% 2.34/2.53 tff(21463,plain,
% 2.34/2.53 ((op(e1, op(e3, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[4468])).
% 2.34/2.53 tff(21464,plain,
% 2.34/2.53 ((op(e1, e0) = e1) <=> (op(e1, op(e3, e3)) = e1)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21463])).
% 2.34/2.53 tff(21465,plain,
% 2.34/2.53 (op(e1, op(e3, e3)) = e1),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[5900, 21464])).
% 2.34/2.53 tff(21466,plain,
% 2.34/2.53 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5685, 21465])).
% 2.34/2.53 tff(21467,plain,
% 2.34/2.53 ((op(e3, e0) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.34/2.53 inference(transitivity,[status(thm)],[21434, 21456, 395])).
% 2.34/2.53 tff(21468,plain,
% 2.34/2.53 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21467])).
% 2.34/2.53 tff(21469,plain,
% 2.34/2.53 (~(op(e2, e3) = op(e3, e2))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[1133, 21468])).
% 2.34/2.53 tff(21470,plain,
% 2.34/2.53 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[430, 21469])).
% 2.34/2.53 tff(21471,assumption,(op(e0, e1) = e0), introduced(assumption)).
% 2.34/2.53 tff(21472,plain,
% 2.34/2.53 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21471])).
% 2.34/2.53 tff(21473,plain,
% 2.34/2.53 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21472])).
% 2.34/2.53 tff(21474,plain,
% 2.34/2.53 (~(op(e0, e0) = e0)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[811, 21473])).
% 2.34/2.53 tff(21475,plain,
% 2.34/2.53 (op(e0, e0) = e3),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3612, 12721, 21474, 2379])).
% 2.34/2.53 tff(21476,plain,
% 2.34/2.53 (op(e0, e0) = op(e1, e3)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21475, 11135])).
% 2.34/2.53 tff(21477,plain,
% 2.34/2.53 (op(e2, op(e0, e0)) = op(e2, op(e1, e3))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[21476])).
% 2.34/2.53 tff(21478,plain,
% 2.34/2.53 (op(e2, op(e0, e0)) = e2),
% 2.34/2.53 inference(transitivity,[status(thm)],[21477, 11227, 3787])).
% 2.34/2.53 tff(21479,plain,
% 2.34/2.53 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[593, 21478])).
% 2.34/2.53 tff(21480,plain,
% 2.34/2.53 ((op(e3, op(e1, e1)) = e3) <=> (op(e3, e2) = e3)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[4871])).
% 2.34/2.53 tff(21481,plain,
% 2.34/2.53 ((op(e3, e2) = e3) <=> (op(e3, op(e1, e1)) = e3)),
% 2.34/2.53 inference(symmetry,[status(thm)],[21480])).
% 2.34/2.53 tff(21482,plain,
% 2.34/2.53 (op(e3, op(e1, e1)) = e3),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[21448, 21481])).
% 2.34/2.53 tff(21483,plain,
% 2.34/2.53 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[14029, 21482])).
% 2.34/2.53 tff(21484,plain,
% 2.34/2.53 (op(e0, op(e1, e0)) = op(e0, e1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[5900])).
% 2.34/2.53 tff(21485,plain,
% 2.34/2.53 (op(e2, e2) = e1),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1613, 21447, 4515, 4484])).
% 2.34/2.53 tff(21486,plain,
% 2.34/2.53 (op(e2, e2) = op(e1, e0)),
% 2.34/2.53 inference(transitivity,[status(thm)],[21485, 5903])).
% 2.44/2.54 tff(21487,plain,
% 2.44/2.54 (op(e0, op(e2, e2)) = op(e0, op(e1, e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21486])).
% 2.44/2.54 tff(21488,plain,
% 2.44/2.54 (op(e0, op(e2, e2)) = e0),
% 2.44/2.54 inference(transitivity,[status(thm)],[21487, 21484, 21471])).
% 2.44/2.54 tff(21489,plain,
% 2.44/2.54 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[5619, 21488])).
% 2.44/2.54 tff(21490,plain,
% 2.44/2.54 ($false),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[5367, 21489, 21483, 21479, 9846, 5670, 21470, 21466, 21462, 5675, 5673, 21460, 5681, 21454, 5680, 5674])).
% 2.44/2.54 tff(21491,plain,((op(e0, e0) = e2) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~(op(e0, e1) = e0)) | (~(op(e1, e0) = e1)) | (~(op(e1, e3) = e3)) | (~(op(e1, e1) = e2)) | (op(e1, e2) = e1) | (op(e0, e2) = e1) | (~(op(e3, e3) = e0)) | (~(op(e2, e3) = e2)) | (op(e0, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.54 tff(21492,plain,
% 2.44/2.54 (op(e0, e0) = e2),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[21491, 21428, 21424, 21416, 21412, 21408, 21402, 21397, 21373, 21391, 164, 21327, 21382, 11315, 3066, 21345, 11527])).
% 2.44/2.54 tff(21493,plain,
% 2.44/2.54 (e2 = op(e0, e0)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[21492, 78])).
% 2.44/2.54 tff(21494,plain,
% 2.44/2.54 (op(e0, op(e0, e0)) = op(e0, e2)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21492])).
% 2.44/2.54 tff(21495,plain,
% 2.44/2.54 ((e3 = op(e0, op(e0, e0))) <=> (e3 = op(e0, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21494])).
% 2.44/2.54 tff(21496,plain,
% 2.44/2.54 ((e3 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21495, 4221])).
% 2.44/2.54 tff(21497,plain,
% 2.44/2.54 ((op(e0, e2) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 2.44/2.54 inference(symmetry,[status(thm)],[21496])).
% 2.44/2.54 tff(21498,plain,
% 2.44/2.54 ((op(e0, e0) = e3) <=> (e2 = op(e1, e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21492, 11135])).
% 2.44/2.54 tff(21499,plain,
% 2.44/2.54 ((op(e0, e0) = e3) <=> (op(e1, e3) = e2)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21498, 66])).
% 2.44/2.54 tff(21500,plain,
% 2.44/2.54 ((op(e1, e3) = e2) <=> (op(e0, e0) = e3)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21499])).
% 2.44/2.54 tff(21501,plain,
% 2.44/2.54 ((~(op(e1, e3) = e2)) <=> (~(op(e0, e0) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21500])).
% 2.44/2.54 tff(21502,plain,
% 2.44/2.54 (~(op(e0, e0) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[21331, 21501])).
% 2.44/2.54 tff(21503,plain,
% 2.44/2.54 (op(e0, e2) = e3),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1495, 21502, 11546, 2527])).
% 2.44/2.54 tff(21504,plain,
% 2.44/2.54 (e3 = op(e0, op(e0, e0))),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[21503, 21497])).
% 2.44/2.54 tff(21505,plain,
% 2.44/2.54 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21494])).
% 2.44/2.54 tff(21506,plain,
% 2.44/2.54 (op(e0, op(e0, e2)) = op(e0, op(e0, op(e0, e0)))),
% 2.44/2.54 inference(symmetry,[status(thm)],[21505])).
% 2.44/2.54 tff(21507,plain,
% 2.44/2.54 (op(e0, e2) = op(e1, e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21503, 11135])).
% 2.44/2.54 tff(21508,plain,
% 2.44/2.54 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21507])).
% 2.44/2.54 tff(21509,plain,
% 2.44/2.54 (op(e0, op(e1, e3)) = op(e0, op(e0, e2))),
% 2.44/2.54 inference(symmetry,[status(thm)],[21508])).
% 2.44/2.54 tff(21510,plain,
% 2.44/2.54 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.44/2.54 inference(transitivity,[status(thm)],[4681, 17945, 21509, 21506])).
% 2.44/2.54 tff(21511,plain,
% 2.44/2.54 ($false),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[10921, 21510, 21504, 21493])).
% 2.44/2.54 tff(21512,plain,((op(e0, e1) = e3) | (~(op(e0, e3) = e1)) | (~(op(e1, e3) = e3)) | (~(op(e3, e3) = e0)) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.54 tff(21513,plain,
% 2.44/2.54 (op(e0, e1) = e3),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[21512, 21332, 19, 21363, 17])).
% 2.44/2.54 tff(21514,plain,
% 2.44/2.54 (op(e0, e1) = op(e1, e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21513, 21333])).
% 2.44/2.54 tff(21515,plain,
% 2.44/2.54 ((op(e0, e1) = e0) <=> (op(e1, e3) = e0)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21514])).
% 2.44/2.54 tff(21516,plain,
% 2.44/2.54 ((op(e1, e3) = e0) <=> (op(e0, e1) = e0)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21515])).
% 2.44/2.54 tff(21517,plain,
% 2.44/2.54 ((~(op(e1, e3) = e0)) <=> (~(op(e0, e1) = e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21516])).
% 2.44/2.54 tff(21518,plain,
% 2.44/2.54 (~(op(e0, e1) = e0)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[80, 21517])).
% 2.44/2.54 tff(21519,plain,
% 2.44/2.54 (op(e2, e1) = e0),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[292, 21518, 21366, 21357])).
% 2.44/2.54 tff(21520,plain,
% 2.44/2.54 (op(e2, e2) = e3),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[7007, 21519, 21352, 21349])).
% 2.44/2.54 tff(21521,plain,
% 2.44/2.54 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21520])).
% 2.44/2.54 tff(21522,plain,
% 2.44/2.54 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21521])).
% 2.44/2.54 tff(21523,plain,
% 2.44/2.54 (~(op(e2, e0) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[2228, 21522])).
% 2.44/2.54 tff(21524,plain,
% 2.44/2.54 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21345])).
% 2.44/2.54 tff(21525,plain,
% 2.44/2.54 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21524])).
% 2.44/2.54 tff(21526,plain,
% 2.44/2.54 (~(op(e2, e0) = e2)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[989, 21525])).
% 2.44/2.54 tff(21527,plain,
% 2.44/2.54 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e0)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21519])).
% 2.44/2.54 tff(21528,plain,
% 2.44/2.54 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21527])).
% 2.44/2.54 tff(21529,plain,
% 2.44/2.54 (~(op(e2, e0) = e0)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[1966, 21528])).
% 2.44/2.54 tff(21530,plain,
% 2.44/2.54 (op(e2, e0) = e1),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[765, 21529, 21526, 21523])).
% 2.44/2.54 tff(21531,plain,
% 2.44/2.54 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21530])).
% 2.44/2.54 tff(21532,plain,
% 2.44/2.54 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21531])).
% 2.44/2.54 tff(21533,plain,
% 2.44/2.54 (~(op(e1, e0) = e1)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[756, 21532])).
% 2.44/2.54 tff(21534,plain,
% 2.44/2.54 (op(e1, e0) = e0),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[728, 21533, 21340, 21337])).
% 2.44/2.54 tff(21535,plain,
% 2.44/2.54 (op(e1, op(e1, e0)) = op(e1, e0)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21534])).
% 2.44/2.54 tff(21536,plain,
% 2.44/2.54 (op(e1, op(e1, e0)) = e0),
% 2.44/2.54 inference(transitivity,[status(thm)],[21535, 21534])).
% 2.44/2.54 tff(21537,plain,
% 2.44/2.54 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.54 tff(21538,plain,
% 2.44/2.54 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21537, 637])).
% 2.44/2.54 tff(21539,plain,
% 2.44/2.54 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21538])).
% 2.44/2.54 tff(21540,plain,
% 2.44/2.54 (~(op(e3, e1) = e2)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[945, 21539])).
% 2.44/2.54 tff(21541,plain,
% 2.44/2.54 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21333])).
% 2.44/2.54 tff(21542,plain,
% 2.44/2.54 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21541])).
% 2.44/2.54 tff(21543,plain,
% 2.44/2.54 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21514])).
% 2.44/2.54 tff(21544,plain,
% 2.44/2.54 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 2.44/2.54 inference(transitivity,[status(thm)],[21543, 1674])).
% 2.44/2.54 tff(21545,plain,
% 2.44/2.54 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21544, 21542])).
% 2.44/2.54 tff(21546,plain,
% 2.44/2.54 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21545])).
% 2.44/2.54 tff(21547,plain,
% 2.44/2.54 (~(op(e3, e1) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[3046, 21546])).
% 2.44/2.54 tff(21548,plain,
% 2.44/2.54 (op(e3, e1) = e1),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[446, 21547, 21366, 21540])).
% 2.44/2.54 tff(21549,plain,
% 2.44/2.54 ((op(e3, e1) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21548])).
% 2.44/2.54 tff(21550,plain,
% 2.44/2.54 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21549, 7171])).
% 2.44/2.54 tff(21551,plain,
% 2.44/2.54 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21550])).
% 2.44/2.54 tff(21552,plain,
% 2.44/2.54 (~(op(e3, e2) = e1)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[3429, 21551])).
% 2.44/2.54 tff(21553,plain,
% 2.44/2.54 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21363])).
% 2.44/2.54 tff(21554,plain,
% 2.44/2.54 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21553])).
% 2.44/2.54 tff(21555,plain,
% 2.44/2.54 (~(op(e3, e2) = e0)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[1888, 21554])).
% 2.44/2.54 tff(21556,plain,
% 2.44/2.54 ((op(e2, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21520])).
% 2.44/2.54 tff(21557,plain,
% 2.44/2.54 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21556, 3423])).
% 2.44/2.54 tff(21558,plain,
% 2.44/2.54 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21557])).
% 2.44/2.54 tff(21559,plain,
% 2.44/2.54 (~(op(e3, e2) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[1546, 21558])).
% 2.44/2.54 tff(21560,plain,
% 2.44/2.54 (op(e3, e2) = e2),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1898, 21559, 21555, 21552])).
% 2.44/2.54 tff(21561,plain,
% 2.44/2.54 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21560])).
% 2.44/2.54 tff(21562,plain,
% 2.44/2.54 (op(e3, op(e3, e2)) = e2),
% 2.44/2.54 inference(transitivity,[status(thm)],[21561, 21560])).
% 2.44/2.54 tff(21563,plain,
% 2.44/2.54 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1904, 21562])).
% 2.44/2.54 tff(21564,plain,
% 2.44/2.54 (op(e2, e2) = op(e1, e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21520, 21333])).
% 2.44/2.54 tff(21565,plain,
% 2.44/2.54 ((op(e2, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21564])).
% 2.44/2.54 tff(21566,plain,
% 2.44/2.54 ((op(e1, e3) = e1) <=> (op(e2, e2) = e1)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21565])).
% 2.44/2.54 tff(21567,plain,
% 2.44/2.54 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e2) = e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21566])).
% 2.44/2.54 tff(21568,plain,
% 2.44/2.54 (~(op(e2, e2) = e1)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[65, 21567])).
% 2.44/2.54 tff(21569,plain,
% 2.44/2.54 (op(e1, e2) = e1),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1613, 21568, 21552, 11315])).
% 2.44/2.54 tff(21570,plain,
% 2.44/2.54 (op(e1, op(e1, e2)) = op(e1, e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21569])).
% 2.44/2.54 tff(21571,plain,
% 2.44/2.54 (op(e1, op(e1, e2)) = e2),
% 2.44/2.54 inference(transitivity,[status(thm)],[21570, 21327])).
% 2.44/2.54 tff(21572,plain,
% 2.44/2.54 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2377, 21571])).
% 2.44/2.54 tff(21573,plain,
% 2.44/2.54 ((op(e3, e3) = e3) <=> (op(e3, e3) = op(e1, e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21333])).
% 2.44/2.54 tff(21574,plain,
% 2.44/2.54 ((op(e3, e3) = e3) <=> (op(e1, e3) = op(e3, e3))),
% 2.44/2.54 inference(transitivity,[status(thm)],[21573, 1659])).
% 2.44/2.54 tff(21575,plain,
% 2.44/2.54 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21574])).
% 2.44/2.54 tff(21576,plain,
% 2.44/2.54 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21575])).
% 2.44/2.54 tff(21577,plain,
% 2.44/2.54 (~(op(e3, e3) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[571, 21576])).
% 2.44/2.54 tff(21578,plain,
% 2.44/2.54 (op(e3, e0) = e3),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[422, 21559, 21577, 21547])).
% 2.44/2.54 tff(21579,plain,
% 2.44/2.54 (op(e3, op(e3, e0)) = op(e3, e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21578])).
% 2.44/2.54 tff(21580,plain,
% 2.44/2.54 (op(e3, op(e3, e0)) = e0),
% 2.44/2.54 inference(transitivity,[status(thm)],[21579, 21363])).
% 2.44/2.54 tff(21581,plain,
% 2.44/2.54 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1345, 21580])).
% 2.44/2.54 tff(21582,plain,
% 2.44/2.54 (op(e2, op(e2, e0)) = op(e2, e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21530])).
% 2.44/2.54 tff(21583,plain,
% 2.44/2.54 (op(e2, op(e2, e0)) = e0),
% 2.44/2.54 inference(transitivity,[status(thm)],[21582, 21519])).
% 2.44/2.54 tff(21584,plain,
% 2.44/2.54 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2653, 21583])).
% 2.44/2.54 tff(21585,plain,
% 2.44/2.54 (op(op(e2, e1), e2) = op(e0, e2)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21519])).
% 2.44/2.54 tff(21586,plain,
% 2.44/2.54 ((op(op(e2, e1), e2) = e1) <=> (op(e0, e2) = e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21585])).
% 2.44/2.54 tff(21587,plain,
% 2.44/2.54 ((op(e0, e2) = e1) <=> (op(op(e2, e1), e2) = e1)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21586])).
% 2.44/2.54 tff(21588,plain,
% 2.44/2.54 ((~(op(e0, e2) = e1)) <=> (~(op(op(e2, e1), e2) = e1))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21587])).
% 2.44/2.54 tff(21589,plain,
% 2.44/2.54 (~(op(op(e2, e1), e2) = e1)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[11315, 21588])).
% 2.44/2.54 tff(21590,plain,
% 2.44/2.54 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[5808, 21589])).
% 2.44/2.54 tff(21591,plain,
% 2.44/2.54 (op(op(e1, e3), e1) = op(e3, e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21332])).
% 2.44/2.54 tff(21592,plain,
% 2.44/2.54 (op(e3, op(e3, e1)) = op(op(e1, e3), e1)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21333, 21548])).
% 2.44/2.54 tff(21593,plain,
% 2.44/2.54 (op(e3, op(e3, e1)) = e1),
% 2.44/2.54 inference(transitivity,[status(thm)],[21592, 21591, 21548])).
% 2.44/2.54 tff(21594,plain,
% 2.44/2.54 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2594, 21593])).
% 2.44/2.54 tff(21595,plain,
% 2.44/2.54 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[16410, 80, 21331])).
% 2.44/2.54 tff(21596,plain,
% 2.44/2.54 ((op(e1, e0) = op(e1, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21335, 11358])).
% 2.44/2.54 tff(21597,plain,
% 2.44/2.54 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21596])).
% 2.44/2.54 tff(21598,plain,
% 2.44/2.54 (~(op(op(e0, e3), e0) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[110, 21597])).
% 2.44/2.54 tff(21599,plain,
% 2.44/2.54 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2635, 21598])).
% 2.44/2.54 tff(21600,plain,
% 2.44/2.54 (op(op(e2, e3), e3) = op(e2, e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21345])).
% 2.44/2.54 tff(21601,plain,
% 2.44/2.54 (op(op(e2, e3), e3) = e2),
% 2.44/2.54 inference(transitivity,[status(thm)],[21600, 21345])).
% 2.44/2.54 tff(21602,plain,
% 2.44/2.54 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1288, 21601])).
% 2.44/2.54 tff(21603,plain,
% 2.44/2.54 (op(e0, op(e1, e3)) = op(e0, e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21332])).
% 2.44/2.54 tff(21604,plain,
% 2.44/2.54 (op(e0, op(e0, e1)) = op(e0, op(e1, e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21514])).
% 2.44/2.54 tff(21605,plain,
% 2.44/2.54 (op(e0, op(e0, e1)) = e1),
% 2.44/2.54 inference(transitivity,[status(thm)],[21604, 21603, 19])).
% 2.44/2.54 tff(21606,plain,
% 2.44/2.54 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2449, 21605])).
% 2.44/2.54 tff(21607,plain,
% 2.44/2.54 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21569])).
% 2.44/2.54 tff(21608,plain,
% 2.44/2.54 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21607, 18])).
% 2.44/2.54 tff(21609,plain,
% 2.44/2.54 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21608])).
% 2.44/2.54 tff(21610,plain,
% 2.44/2.54 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21609])).
% 2.44/2.54 tff(21611,plain,
% 2.44/2.54 (~(op(e1, e2) = e0)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[26, 21610])).
% 2.44/2.54 tff(21612,plain,
% 2.44/2.54 (op(e0, e2) = e0),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[973, 21611, 17, 21555])).
% 2.44/2.54 tff(21613,plain,
% 2.44/2.54 (op(op(e0, e2), e2) = e0),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[4944, 21612, 21327])).
% 2.44/2.54 tff(21614,plain,
% 2.44/2.54 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1956, 21613])).
% 2.44/2.54 tff(21615,plain,
% 2.44/2.54 (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1459, 21614, 21606, 21602, 21599, 21595, 21594, 21590, 21584, 21581, 21572, 21563])).
% 2.44/2.54 tff(21616,plain,
% 2.44/2.54 (~(op(e1, op(e1, e0)) = e0)),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[1836, 21615])).
% 2.44/2.54 tff(21617,plain,
% 2.44/2.54 ($false),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[21616, 21536])).
% 2.44/2.54 tff(21618,plain,((op(e1, e3) = e0) | (op(e2, e2) = e0) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.54 tff(21619,plain,
% 2.44/2.54 (op(e1, e3) = e0),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[21618, 19, 17])).
% 2.44/2.54 tff(21620,plain,
% 2.44/2.54 (e0 = op(e1, e3)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21619])).
% 2.44/2.54 tff(21621,plain,
% 2.44/2.54 (op(e1, op(e1, e1)) = op(e1, e2)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[2891])).
% 2.44/2.54 tff(21622,plain,
% 2.44/2.54 ((e3 = op(e1, op(e1, e1))) <=> (e3 = op(e1, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21621])).
% 2.44/2.54 tff(21623,plain,
% 2.44/2.54 ((e3 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e3)),
% 2.44/2.54 inference(transitivity,[status(thm)],[21622, 532])).
% 2.44/2.54 tff(21624,plain,
% 2.44/2.54 ((op(e1, e2) = e3) <=> (e3 = op(e1, op(e1, e1)))),
% 2.44/2.54 inference(symmetry,[status(thm)],[21623])).
% 2.44/2.54 tff(21625,plain,
% 2.44/2.54 (e3 = op(e1, op(e1, e1))),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[2899, 21624])).
% 2.44/2.54 tff(21626,plain,
% 2.44/2.54 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21621])).
% 2.44/2.54 tff(21627,plain,
% 2.44/2.54 (op(e1, op(e1, e2)) = op(e1, op(e1, op(e1, e1)))),
% 2.44/2.54 inference(symmetry,[status(thm)],[21626])).
% 2.44/2.54 tff(21628,plain,
% 2.44/2.54 (e0 = op(e1, op(e1, op(e1, e1)))),
% 2.44/2.54 inference(transitivity,[status(thm)],[2909, 9274, 21627])).
% 2.44/2.54 tff(21629,plain,
% 2.44/2.54 ($false),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[2920, 21628, 21625, 2902])).
% 2.44/2.54 tff(21630,plain,((~(op(e1, e2) = e3)) | (~(op(e1, e3) = e0)) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.54 tff(21631,plain,
% 2.44/2.54 (~(op(e1, e2) = e3)),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[21630, 21619, 21327])).
% 2.44/2.54 tff(21632,plain,
% 2.44/2.54 ((e2 = e3) <=> (op(e1, e1) = e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21353])).
% 2.44/2.54 tff(21633,plain,
% 2.44/2.54 ((~(e2 = e3)) <=> (~(op(e1, e1) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21632])).
% 2.44/2.54 tff(21634,plain,
% 2.44/2.54 (~(op(e1, e1) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[1321, 21633])).
% 2.44/2.54 tff(21635,plain,
% 2.44/2.54 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21620])).
% 2.44/2.54 tff(21636,plain,
% 2.44/2.54 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21635])).
% 2.44/2.54 tff(21637,plain,
% 2.44/2.54 (~(op(e1, e3) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[181, 21636])).
% 2.44/2.54 tff(21638,plain,
% 2.44/2.54 (op(e1, e0) = e3),
% 2.44/2.54 inference(unit_resolution,[status(thm)],[247, 21637, 21634, 21631])).
% 2.44/2.54 tff(21639,plain,
% 2.44/2.54 (e3 = op(e1, e0)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21638])).
% 2.44/2.54 tff(21640,plain,
% 2.44/2.54 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21639])).
% 2.44/2.54 tff(21641,plain,
% 2.44/2.54 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.44/2.54 inference(symmetry,[status(thm)],[21640])).
% 2.44/2.54 tff(21642,plain,
% 2.44/2.54 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21641])).
% 2.44/2.54 tff(21643,plain,
% 2.44/2.54 (~(op(e0, e0) = e3)),
% 2.44/2.54 inference(modus_ponens,[status(thm)],[2471, 21642])).
% 2.44/2.54 tff(21644,plain,
% 2.44/2.54 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.44/2.54 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.54 tff(21645,plain,
% 2.44/2.54 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21644, 5762])).
% 2.44/2.55 tff(21646,plain,
% 2.44/2.55 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21645])).
% 2.44/2.55 tff(21647,plain,
% 2.44/2.55 (~(op(e1, e2) = e2)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1604, 21646])).
% 2.44/2.55 tff(21648,plain,
% 2.44/2.55 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21620])).
% 2.44/2.55 tff(21649,plain,
% 2.44/2.55 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.44/2.55 inference(symmetry,[status(thm)],[21648])).
% 2.44/2.55 tff(21650,plain,
% 2.44/2.55 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21649])).
% 2.44/2.55 tff(21651,plain,
% 2.44/2.55 (~(op(e1, e2) = e0)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1850, 21650])).
% 2.44/2.55 tff(21652,plain,
% 2.44/2.55 (op(e1, e2) = e1),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[1859, 21651, 21647, 21631])).
% 2.44/2.55 tff(21653,plain,
% 2.44/2.55 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21652])).
% 2.44/2.55 tff(21654,plain,
% 2.44/2.55 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21653, 316])).
% 2.44/2.55 tff(21655,plain,
% 2.44/2.55 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21654])).
% 2.44/2.55 tff(21656,plain,
% 2.44/2.55 (~(op(e2, e2) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1273, 21655])).
% 2.44/2.55 tff(21657,plain,
% 2.44/2.55 (op(e2, e2) = e3),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[524, 21656, 17, 21352])).
% 2.44/2.55 tff(21658,plain,
% 2.44/2.55 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e3)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21657])).
% 2.44/2.55 tff(21659,plain,
% 2.44/2.55 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21658])).
% 2.44/2.55 tff(21660,plain,
% 2.44/2.55 (~(op(e0, e2) = e3)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[2736, 21659])).
% 2.44/2.55 tff(21661,plain,
% 2.44/2.55 (op(e0, e1) = e3),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[1495, 21660, 11546, 21643])).
% 2.44/2.55 tff(21662,plain,
% 2.44/2.55 (op(e0, e1) = op(e1, e0)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21661, 21639])).
% 2.44/2.55 tff(21663,plain,
% 2.44/2.55 ((op(e0, e1) = e0) <=> (op(e1, e0) = op(e1, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21662, 21620])).
% 2.44/2.55 tff(21664,plain,
% 2.44/2.55 ((op(e1, e0) = op(e1, e3)) <=> (op(e0, e1) = e0)),
% 2.44/2.55 inference(symmetry,[status(thm)],[21663])).
% 2.44/2.55 tff(21665,plain,
% 2.44/2.55 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e0, e1) = e0))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21664])).
% 2.44/2.55 tff(21666,plain,
% 2.44/2.55 (~(op(e0, e1) = e0)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[110, 21665])).
% 2.44/2.55 tff(21667,plain,
% 2.44/2.55 (op(e1, op(e1, e1)) = op(e1, e2)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.55 tff(21668,plain,
% 2.44/2.55 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e2) = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21667])).
% 2.44/2.55 tff(21669,plain,
% 2.44/2.55 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 2.44/2.55 inference(symmetry,[status(thm)],[21668])).
% 2.44/2.55 tff(21670,plain,
% 2.44/2.55 (op(e1, op(e1, e1)) = e1),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[21652, 21669])).
% 2.44/2.55 tff(21671,plain,
% 2.44/2.55 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[5678, 21670])).
% 2.44/2.55 tff(21672,plain,
% 2.44/2.55 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21652])).
% 2.44/2.55 tff(21673,plain,
% 2.44/2.55 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21672])).
% 2.44/2.55 tff(21674,plain,
% 2.44/2.55 (~(op(e1, e0) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1312, 21673])).
% 2.44/2.55 tff(21675,plain,
% 2.44/2.55 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[19344])).
% 2.44/2.55 tff(21676,plain,
% 2.44/2.55 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[19])).
% 2.44/2.55 tff(21677,plain,
% 2.44/2.55 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21676, 657])).
% 2.44/2.55 tff(21678,plain,
% 2.44/2.55 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21677])).
% 2.44/2.55 tff(21679,plain,
% 2.44/2.55 (~(op(e3, e3) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1077, 21678])).
% 2.44/2.55 tff(21680,plain,
% 2.44/2.55 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21619])).
% 2.44/2.55 tff(21681,plain,
% 2.44/2.55 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21680, 3077])).
% 2.44/2.55 tff(21682,plain,
% 2.44/2.55 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21681])).
% 2.44/2.55 tff(21683,plain,
% 2.44/2.55 (~(op(e3, e3) = e0)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[571, 21682])).
% 2.44/2.55 tff(21684,plain,
% 2.44/2.55 (op(e3, e3) = e3),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[15018, 21683, 21679])).
% 2.44/2.55 tff(21685,plain,
% 2.44/2.55 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21684])).
% 2.44/2.55 tff(21686,plain,
% 2.44/2.55 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21685])).
% 2.44/2.55 tff(21687,plain,
% 2.44/2.55 (~(op(e3, e1) = e3)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[437, 21686])).
% 2.44/2.55 tff(21688,plain,
% 2.44/2.55 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.55 tff(21689,plain,
% 2.44/2.55 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21688, 69])).
% 2.44/2.55 tff(21690,plain,
% 2.44/2.55 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 2.44/2.55 inference(symmetry,[status(thm)],[21689])).
% 2.44/2.55 tff(21691,plain,
% 2.44/2.55 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21690])).
% 2.44/2.55 tff(21692,plain,
% 2.44/2.55 (~(op(e1, e1) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[708, 21691])).
% 2.44/2.55 tff(21693,plain,
% 2.44/2.55 (op(op(e1, e3), e3) = e1),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[1223, 21619, 19])).
% 2.44/2.55 tff(21694,plain,
% 2.44/2.55 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[130, 21693])).
% 2.44/2.55 tff(21695,plain,
% 2.44/2.55 (~(op(e3, e0) = op(e0, e3))),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[4953, 21666, 19, 21619, 21694, 21692, 21687])).
% 2.44/2.55 tff(21696,plain,
% 2.44/2.55 (~(op(e3, e0) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[21695, 21675])).
% 2.44/2.55 tff(21697,plain,
% 2.44/2.55 (op(e2, e0) = e1),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[1480, 21696, 11527, 21674])).
% 2.44/2.55 tff(21698,plain,
% 2.44/2.55 ((op(e2, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21697])).
% 2.44/2.55 tff(21699,plain,
% 2.44/2.55 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21698, 697])).
% 2.44/2.55 tff(21700,plain,
% 2.44/2.55 ((op(e0, e2) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 2.44/2.55 inference(symmetry,[status(thm)],[21699])).
% 2.44/2.55 tff(21701,plain,
% 2.44/2.55 ((~(op(e0, e2) = e1)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21700])).
% 2.44/2.55 tff(21702,plain,
% 2.44/2.55 (~(op(e2, e0) = op(e0, e2))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[11315, 21701])).
% 2.44/2.55 tff(21703,plain,
% 2.44/2.55 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[6358, 21702])).
% 2.44/2.55 tff(21704,plain,
% 2.44/2.55 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21652])).
% 2.44/2.55 tff(21705,plain,
% 2.44/2.55 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.44/2.55 inference(symmetry,[status(thm)],[21704])).
% 2.44/2.55 tff(21706,plain,
% 2.44/2.55 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21652])).
% 2.44/2.55 tff(21707,plain,
% 2.44/2.55 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21706, 7171])).
% 2.44/2.55 tff(21708,plain,
% 2.44/2.55 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21707])).
% 2.44/2.55 tff(21709,plain,
% 2.44/2.55 (~(op(e3, e2) = e1)),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[2292, 21708])).
% 2.44/2.55 tff(21710,plain,
% 2.44/2.55 (op(e3, e1) = e1),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[939, 21696, 21679, 21709])).
% 2.44/2.55 tff(21711,plain,
% 2.44/2.55 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21710])).
% 2.44/2.55 tff(21712,plain,
% 2.44/2.55 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = op(e1, e2))),
% 2.44/2.55 inference(transitivity,[status(thm)],[21711, 21705])).
% 2.44/2.55 tff(21713,plain,
% 2.44/2.55 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21712])).
% 2.44/2.55 tff(21714,plain,
% 2.44/2.55 (~(op(e2, e1) = op(e1, e2))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[402, 21713])).
% 2.44/2.55 tff(21715,plain,
% 2.44/2.55 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[557, 21714])).
% 2.44/2.55 tff(21716,plain,
% 2.44/2.55 ((op(e3, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21710])).
% 2.44/2.55 tff(21717,plain,
% 2.44/2.55 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21716, 28])).
% 2.44/2.55 tff(21718,plain,
% 2.44/2.55 ((op(e1, e3) = e1) <=> (op(e3, e1) = op(e1, e3))),
% 2.44/2.55 inference(symmetry,[status(thm)],[21717])).
% 2.44/2.55 tff(21719,plain,
% 2.44/2.55 ((op(e1, e3) = e1) <=> (op(e1, e3) = op(e3, e1))),
% 2.44/2.55 inference(transitivity,[status(thm)],[21718, 6290])).
% 2.44/2.55 tff(21720,plain,
% 2.44/2.55 ((~(op(e1, e3) = e1)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21719])).
% 2.44/2.55 tff(21721,plain,
% 2.44/2.55 (~(op(e1, e3) = op(e3, e1))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[65, 21720])).
% 2.44/2.55 tff(21722,plain,
% 2.44/2.55 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[6307, 21721])).
% 2.44/2.55 tff(21723,plain,
% 2.44/2.55 (op(e2, op(e1, e0)) = op(e2, e3)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21638])).
% 2.44/2.55 tff(21724,plain,
% 2.44/2.55 (op(e2, op(e1, e0)) = e2),
% 2.44/2.55 inference(transitivity,[status(thm)],[21723, 21345])).
% 2.44/2.55 tff(21725,plain,
% 2.44/2.55 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[10735, 21724])).
% 2.44/2.55 tff(21726,plain,
% 2.44/2.55 (op(e1, op(e2, e3)) = op(e1, e2)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21345])).
% 2.44/2.55 tff(21727,plain,
% 2.44/2.55 ((op(e1, op(e2, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21726])).
% 2.44/2.55 tff(21728,plain,
% 2.44/2.55 ((op(e1, e2) = e1) <=> (op(e1, op(e2, e3)) = e1)),
% 2.44/2.55 inference(symmetry,[status(thm)],[21727])).
% 2.44/2.55 tff(21729,plain,
% 2.44/2.55 (op(e1, op(e2, e3)) = e1),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[21652, 21728])).
% 2.44/2.55 tff(21730,plain,
% 2.44/2.55 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[10724, 21729])).
% 2.44/2.55 tff(21731,plain,
% 2.44/2.55 ((op(e2, e1) = op(e3, e1)) <=> (op(e1, e2) = op(e2, e1))),
% 2.44/2.55 inference(transitivity,[status(thm)],[21711, 21705, 531])).
% 2.44/2.55 tff(21732,plain,
% 2.44/2.55 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21731])).
% 2.44/2.55 tff(21733,plain,
% 2.44/2.55 (~(op(e1, e2) = op(e2, e1))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[402, 21732])).
% 2.44/2.55 tff(21734,plain,
% 2.44/2.55 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[539, 21733])).
% 2.44/2.55 tff(21735,plain,
% 2.44/2.55 (op(e2, op(e0, e1)) = op(e2, op(e1, e0))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21662])).
% 2.44/2.55 tff(21736,plain,
% 2.44/2.55 (op(e2, op(e0, e1)) = e2),
% 2.44/2.55 inference(transitivity,[status(thm)],[21735, 21723, 21345])).
% 2.44/2.55 tff(21737,plain,
% 2.44/2.55 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[9902, 21736])).
% 2.44/2.55 tff(21738,plain,
% 2.44/2.55 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21718])).
% 2.44/2.55 tff(21739,plain,
% 2.44/2.55 (~(op(e3, e1) = op(e1, e3))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[65, 21738])).
% 2.44/2.55 tff(21740,plain,
% 2.44/2.55 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[6362, 21739])).
% 2.44/2.55 tff(21741,plain,
% 2.44/2.55 (op(e2, op(e3, e3)) = op(e2, e3)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21684])).
% 2.44/2.55 tff(21742,plain,
% 2.44/2.55 (op(e2, op(e3, e3)) = e2),
% 2.44/2.55 inference(transitivity,[status(thm)],[21741, 21345])).
% 2.44/2.55 tff(21743,plain,
% 2.44/2.55 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[14770, 21742])).
% 2.44/2.55 tff(21744,plain,
% 2.44/2.55 (~(op(e0, e3) = op(e3, e0))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[21695, 454])).
% 2.44/2.55 tff(21745,plain,
% 2.44/2.55 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[496, 21744])).
% 2.44/2.55 tff(21746,plain,
% 2.44/2.55 (op(e2, e2) = op(e1, e0)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21657, 21639])).
% 2.44/2.55 tff(21747,plain,
% 2.44/2.55 (op(e2, op(e2, e2)) = op(e2, op(e1, e0))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21746])).
% 2.44/2.55 tff(21748,plain,
% 2.44/2.55 (op(e2, op(e2, e2)) = e2),
% 2.44/2.55 inference(transitivity,[status(thm)],[21747, 21723, 21345])).
% 2.44/2.55 tff(21749,plain,
% 2.44/2.55 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[528, 21748])).
% 2.44/2.55 tff(21750,plain,
% 2.44/2.55 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e2, e0))),
% 2.44/2.55 inference(transitivity,[status(thm)],[21700, 6337])).
% 2.44/2.55 tff(21751,plain,
% 2.44/2.55 ((~(op(e0, e2) = e1)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21750])).
% 2.44/2.55 tff(21752,plain,
% 2.44/2.55 (~(op(e0, e2) = op(e2, e0))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[11315, 21751])).
% 2.44/2.55 tff(21753,plain,
% 2.44/2.55 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[6347, 21752])).
% 2.44/2.55 tff(21754,plain,
% 2.44/2.55 (op(e0, e0) = e0),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[3612, 12721, 10447, 2379])).
% 2.44/2.55 tff(21755,plain,
% 2.44/2.55 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21754])).
% 2.44/2.55 tff(21756,plain,
% 2.44/2.55 (op(e0, op(e0, e0)) = e0),
% 2.44/2.55 inference(transitivity,[status(thm)],[21755, 21754])).
% 2.44/2.55 tff(21757,plain,
% 2.44/2.55 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[5598, 21756])).
% 2.44/2.55 tff(21758,plain,
% 2.44/2.55 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[3797])).
% 2.44/2.55 tff(21759,plain,
% 2.44/2.55 ((op(e3, e0) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[20830])).
% 2.44/2.55 tff(21760,plain,
% 2.44/2.55 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.44/2.55 inference(transitivity,[status(thm)],[21759, 2234])).
% 2.44/2.55 tff(21761,plain,
% 2.44/2.55 ((op(e3, e0) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.44/2.55 inference(transitivity,[status(thm)],[21760, 21758, 395])).
% 2.44/2.55 tff(21762,plain,
% 2.44/2.55 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.44/2.55 inference(monotonicity,[status(thm)],[21761])).
% 2.44/2.55 tff(21763,plain,
% 2.44/2.55 (~(op(e2, e3) = op(e3, e2))),
% 2.44/2.55 inference(modus_ponens,[status(thm)],[1133, 21762])).
% 2.44/2.55 tff(21764,plain,
% 2.44/2.55 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[430, 21763])).
% 2.44/2.55 tff(21765,plain,
% 2.44/2.55 ($false),
% 2.44/2.55 inference(unit_resolution,[status(thm)],[5367, 21764, 21757, 5672, 9846, 5670, 6689, 6688, 5511, 5675, 5673, 5671, 5681, 5669, 5680, 5674])).
% 2.44/2.55 tff(21766,plain,((op(e0, e0) = e2) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~(op(e2, e3) = e2)) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e0, e0) = e3) | (op(e0, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.56 tff(21767,plain,
% 2.44/2.56 (op(e0, e0) = e2),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[21766, 21753, 21749, 21745, 21643, 21743, 21740, 21737, 21734, 21730, 21725, 21722, 21715, 21703, 21345, 21340, 21526, 21671, 11527])).
% 2.44/2.56 tff(21768,plain,
% 2.44/2.56 ((op(e0, e0) = e0) <=> (e2 = op(e1, e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21767, 21620])).
% 2.44/2.56 tff(21769,plain,
% 2.44/2.56 ((op(e0, e0) = e0) <=> (op(e1, e3) = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21768, 66])).
% 2.44/2.56 tff(21770,plain,
% 2.44/2.56 ((op(e1, e3) = e2) <=> (op(e0, e0) = e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21769])).
% 2.44/2.56 tff(21771,plain,
% 2.44/2.56 ((~(op(e1, e3) = e2)) <=> (~(op(e0, e0) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21770])).
% 2.44/2.56 tff(21772,plain,
% 2.44/2.56 (~(op(e0, e0) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21331, 21771])).
% 2.44/2.56 tff(21773,plain,
% 2.44/2.56 (op(e0, e2) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[3976, 21772, 21666, 27])).
% 2.44/2.56 tff(21774,plain,
% 2.44/2.56 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21767])).
% 2.44/2.56 tff(21775,plain,
% 2.44/2.56 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21774, 5377])).
% 2.44/2.56 tff(21776,plain,
% 2.44/2.56 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21775])).
% 2.44/2.56 tff(21777,plain,
% 2.44/2.56 (~(op(e3, e0) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[6384, 21776])).
% 2.44/2.56 tff(21778,plain,
% 2.44/2.56 (op(e3, e2) = e2),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[15971, 21777, 21540])).
% 2.44/2.56 tff(21779,plain,
% 2.44/2.56 (op(e0, op(e3, e2)) = op(e0, e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21778])).
% 2.44/2.56 tff(21780,plain,
% 2.44/2.56 (op(e0, op(e3, e2)) = e0),
% 2.44/2.56 inference(transitivity,[status(thm)],[21779, 21773])).
% 2.44/2.56 tff(21781,plain,
% 2.44/2.56 (op(e1, op(e0, e0)) = op(e1, e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21767])).
% 2.44/2.56 tff(21782,plain,
% 2.44/2.56 (op(e1, op(e0, e0)) = e1),
% 2.44/2.56 inference(transitivity,[status(thm)],[21781, 21652])).
% 2.44/2.56 tff(21783,plain,
% 2.44/2.56 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[6717, 21782])).
% 2.44/2.56 tff(21784,plain,
% 2.44/2.56 (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[5367, 21783, 21671, 21749, 21745, 21753, 21743, 21740, 21737, 21734, 21730, 21725, 21722, 21715, 21703])).
% 2.44/2.56 tff(21785,plain,
% 2.44/2.56 (~(op(e0, op(e3, e2)) = e0)),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[10702, 21784])).
% 2.44/2.56 tff(21786,plain,
% 2.44/2.56 ($false),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[21785, 21780])).
% 2.44/2.56 tff(21787,plain,((~(op(e0, e3) = e1)) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.56 tff(21788,plain,
% 2.44/2.56 (~(op(e0, e3) = e1)),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[21787, 17])).
% 2.44/2.56 tff(21789,plain,
% 2.44/2.56 (e2 = op(e1, e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21327, 2254])).
% 2.44/2.56 tff(21790,plain,
% 2.44/2.56 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21667])).
% 2.44/2.56 tff(21791,plain,
% 2.44/2.56 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21790, 67])).
% 2.44/2.56 tff(21792,plain,
% 2.44/2.56 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21791])).
% 2.44/2.56 tff(21793,plain,
% 2.44/2.56 ((op(e1, e1) = e0) <=> (e2 = e0)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.56 tff(21794,plain,
% 2.44/2.56 ((op(e1, e1) = e0) <=> (e0 = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21793, 1])).
% 2.44/2.56 tff(21795,plain,
% 2.44/2.56 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21794])).
% 2.44/2.56 tff(21796,plain,
% 2.44/2.56 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21795])).
% 2.44/2.56 tff(21797,plain,
% 2.44/2.56 (~(op(e1, e1) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[14, 21796])).
% 2.44/2.56 tff(21798,plain,
% 2.44/2.56 (op(e2, e0) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[2311, 1063, 17, 2559])).
% 2.44/2.56 tff(21799,plain,
% 2.44/2.56 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21798])).
% 2.44/2.56 tff(21800,plain,
% 2.44/2.56 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21799])).
% 2.44/2.56 tff(21801,plain,
% 2.44/2.56 (~(op(e1, e0) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[756, 21800])).
% 2.44/2.56 tff(21802,plain,
% 2.44/2.56 (op(e1, e2) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[1830, 21801, 21357, 80])).
% 2.44/2.56 tff(21803,plain,
% 2.44/2.56 ((op(e1, e2) = e3) <=> (e0 = e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21802])).
% 2.44/2.56 tff(21804,plain,
% 2.44/2.56 ((e0 = e3) <=> (op(e1, e2) = e3)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21803])).
% 2.44/2.56 tff(21805,plain,
% 2.44/2.56 ((~(e0 = e3)) <=> (~(op(e1, e2) = e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21804])).
% 2.44/2.56 tff(21806,plain,
% 2.44/2.56 (~(op(e1, e2) = e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[181, 21805])).
% 2.44/2.56 tff(21807,plain,
% 2.44/2.56 (op(e1, e3) = e3),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[247, 21806, 21634, 2168])).
% 2.44/2.56 tff(21808,plain,
% 2.44/2.56 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21807])).
% 2.44/2.56 tff(21809,plain,
% 2.44/2.56 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21808, 112])).
% 2.44/2.56 tff(21810,plain,
% 2.44/2.56 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21809])).
% 2.44/2.56 tff(21811,plain,
% 2.44/2.56 (~(op(e2, e3) = e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[118, 21810])).
% 2.44/2.56 tff(21812,plain,
% 2.44/2.56 (op(e0, e3) = e2),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[12598, 21811, 76, 80, 121])).
% 2.44/2.56 tff(21813,plain,
% 2.44/2.56 (op(e1, e0) = e1),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[728, 21801, 21340, 2168])).
% 2.44/2.56 tff(21814,plain,
% 2.44/2.56 (e1 = op(e1, e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21813])).
% 2.44/2.56 tff(21815,plain,
% 2.44/2.56 ((op(e1, e3) = e1) <=> (op(e1, e3) = op(e1, e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21814])).
% 2.44/2.56 tff(21816,plain,
% 2.44/2.56 ((op(e1, e3) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 2.44/2.56 inference(transitivity,[status(thm)],[21815, 11653])).
% 2.44/2.56 tff(21817,plain,
% 2.44/2.56 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21816])).
% 2.44/2.56 tff(21818,plain,
% 2.44/2.56 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21817])).
% 2.44/2.56 tff(21819,plain,
% 2.44/2.56 (~(op(e1, e3) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[110, 21818])).
% 2.44/2.56 tff(21820,plain,
% 2.44/2.56 (op(e3, e3) = e1),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[151, 21819, 76, 121])).
% 2.44/2.56 tff(21821,plain,
% 2.44/2.56 (op(e3, e3) = op(e1, e0)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21820, 21814])).
% 2.44/2.56 tff(21822,plain,
% 2.44/2.56 ((op(e3, e3) = e0) <=> (op(e1, e0) = e0)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21821])).
% 2.44/2.56 tff(21823,plain,
% 2.44/2.56 ((op(e1, e0) = e0) <=> (op(e3, e3) = e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21822])).
% 2.44/2.56 tff(21824,plain,
% 2.44/2.56 ((~(op(e1, e0) = e0)) <=> (~(op(e3, e3) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21823])).
% 2.44/2.56 tff(21825,plain,
% 2.44/2.56 (~(op(e3, e3) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21801, 21824])).
% 2.44/2.56 tff(21826,plain,
% 2.44/2.56 (op(e0, e3) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[1098, 21825, 80, 1063])).
% 2.44/2.56 tff(21827,plain,
% 2.44/2.56 (e0 = op(e0, e3)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21826])).
% 2.44/2.56 tff(21828,plain,
% 2.44/2.56 (e0 = e2),
% 2.44/2.56 inference(transitivity,[status(thm)],[21827, 21812])).
% 2.44/2.56 tff(21829,plain,
% 2.44/2.56 ($false),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[14, 21828])).
% 2.44/2.56 tff(21830,plain,((op(e2, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e2, e2) = e0) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.56 tff(21831,plain,
% 2.44/2.56 (op(e2, e3) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[21830, 2168, 76, 121, 80, 17, 2559])).
% 2.44/2.56 tff(21832,plain,
% 2.44/2.56 ((op(e1, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[2891])).
% 2.44/2.56 tff(21833,plain,
% 2.44/2.56 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21832, 66])).
% 2.44/2.56 tff(21834,plain,
% 2.44/2.56 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21833])).
% 2.44/2.56 tff(21835,plain,
% 2.44/2.56 (~(op(e1, e3) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[619, 21834])).
% 2.44/2.56 tff(21836,plain,
% 2.44/2.56 (op(e0, e3) = e2),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[15003, 5019, 21835])).
% 2.44/2.56 tff(21837,plain,
% 2.44/2.56 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21836])).
% 2.44/2.56 tff(21838,plain,
% 2.44/2.56 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21837])).
% 2.44/2.56 tff(21839,plain,
% 2.44/2.56 (~(op(e0, e2) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[918, 21838])).
% 2.44/2.56 tff(21840,plain,
% 2.44/2.56 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21836])).
% 2.44/2.56 tff(21841,plain,
% 2.44/2.56 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21840])).
% 2.44/2.56 tff(21842,plain,
% 2.44/2.56 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21841])).
% 2.44/2.56 tff(21843,plain,
% 2.44/2.56 (~(op(e0, e3) = e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[1321, 21842])).
% 2.44/2.56 tff(21844,plain,
% 2.44/2.56 (op(e0, e0) = e3),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[1495, 4412, 2527, 21843])).
% 2.44/2.56 tff(21845,plain,
% 2.44/2.56 (op(e0, op(e0, e0)) = op(e0, e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21844])).
% 2.44/2.56 tff(21846,plain,
% 2.44/2.56 (op(e0, op(e0, e0)) = e2),
% 2.44/2.56 inference(transitivity,[status(thm)],[21845, 21836])).
% 2.44/2.56 tff(21847,plain,
% 2.44/2.56 (op(e0, op(e0, op(e0, e0))) = op(e0, e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21846])).
% 2.44/2.56 tff(21848,plain,
% 2.44/2.56 ((e1 = op(e0, op(e0, op(e0, e0)))) <=> (e1 = op(e0, e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21847])).
% 2.44/2.56 tff(21849,plain,
% 2.44/2.56 ((e1 = op(e0, op(e0, op(e0, e0)))) <=> (op(e0, e2) = e1)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21848, 697])).
% 2.44/2.56 tff(21850,plain,
% 2.44/2.56 ((~(e1 = op(e0, op(e0, op(e0, e0))))) <=> (~(op(e0, e2) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21849])).
% 2.44/2.56 tff(21851,plain,
% 2.44/2.56 (e3 = op(e0, e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21844, 71])).
% 2.44/2.56 tff(21852,plain,
% 2.44/2.56 (op(e0, e3) = op(e0, op(e0, e0))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21845])).
% 2.44/2.56 tff(21853,plain,
% 2.44/2.56 (e2 = op(e0, e3)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21836])).
% 2.44/2.56 tff(21854,plain,
% 2.44/2.56 (e2 = op(e0, op(e0, e0))),
% 2.44/2.56 inference(transitivity,[status(thm)],[21853, 21852])).
% 2.44/2.56 tff(21855,plain,
% 2.44/2.56 (~(e1 = op(e0, op(e0, op(e0, e0))))),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[2760, 21854, 21851])).
% 2.44/2.56 tff(21856,plain,
% 2.44/2.56 (~(op(e0, e2) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21855, 21850])).
% 2.44/2.56 tff(21857,plain,
% 2.44/2.56 (op(e0, e2) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[2745, 21856, 21839, 4412])).
% 2.44/2.56 tff(21858,plain,
% 2.44/2.56 (op(op(e0, e2), e2) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[4944, 21857, 2891])).
% 2.44/2.56 tff(21859,plain,
% 2.44/2.56 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21836])).
% 2.44/2.56 tff(21860,plain,
% 2.44/2.56 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21859])).
% 2.44/2.56 tff(21861,plain,
% 2.44/2.56 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21860])).
% 2.44/2.56 tff(21862,plain,
% 2.44/2.56 ((e2 = e3) <=> (op(e1, e1) = e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[4872])).
% 2.44/2.56 tff(21863,plain,
% 2.44/2.56 ((~(e2 = e3)) <=> (~(op(e1, e1) = e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21862])).
% 2.44/2.56 tff(21864,plain,
% 2.44/2.56 (~(op(e1, e1) = e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[1321, 21863])).
% 2.44/2.56 tff(21865,plain,
% 2.44/2.56 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[2891])).
% 2.44/2.56 tff(21866,plain,
% 2.44/2.56 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21865, 1960])).
% 2.44/2.56 tff(21867,plain,
% 2.44/2.56 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21866])).
% 2.44/2.56 tff(21868,plain,
% 2.44/2.56 (~(op(e2, e1) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[225, 21867])).
% 2.44/2.56 tff(21869,plain,
% 2.44/2.56 (e3 = op(e0, e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21844])).
% 2.44/2.56 tff(21870,plain,
% 2.44/2.56 ((e1 = e3) <=> (e1 = op(e0, e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21869])).
% 2.44/2.56 tff(21871,plain,
% 2.44/2.56 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21870, 73])).
% 2.44/2.56 tff(21872,plain,
% 2.44/2.56 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21871])).
% 2.44/2.56 tff(21873,plain,
% 2.44/2.56 (~(op(e0, e0) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[303, 21872])).
% 2.44/2.56 tff(21874,plain,
% 2.44/2.56 (op(e0, e1) = e1),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[384, 21856, 121, 21873])).
% 2.44/2.56 tff(21875,plain,
% 2.44/2.56 ((op(e0, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21874])).
% 2.44/2.56 tff(21876,plain,
% 2.44/2.56 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21875, 2355])).
% 2.44/2.56 tff(21877,plain,
% 2.44/2.56 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21876])).
% 2.44/2.56 tff(21878,plain,
% 2.44/2.56 (~(op(e2, e1) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[606, 21877])).
% 2.44/2.56 tff(21879,plain,
% 2.44/2.56 (op(e2, e1) = e3),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[2367, 21878, 21868, 2559])).
% 2.44/2.56 tff(21880,plain,
% 2.44/2.56 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21879])).
% 2.44/2.56 tff(21881,plain,
% 2.44/2.56 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21880, 502])).
% 2.44/2.56 tff(21882,plain,
% 2.44/2.56 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21881])).
% 2.44/2.56 tff(21883,plain,
% 2.44/2.56 (~(op(e2, e2) = e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[508, 21882])).
% 2.44/2.56 tff(21884,plain,
% 2.44/2.56 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21836])).
% 2.44/2.56 tff(21885,plain,
% 2.44/2.56 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21884])).
% 2.44/2.56 tff(21886,plain,
% 2.44/2.56 (~(op(e0, e0) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[3414, 21885])).
% 2.44/2.56 tff(21887,plain,
% 2.44/2.56 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[2891])).
% 2.44/2.56 tff(21888,plain,
% 2.44/2.56 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21887, 637])).
% 2.44/2.56 tff(21889,plain,
% 2.44/2.56 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21888])).
% 2.44/2.56 tff(21890,plain,
% 2.44/2.56 (~(op(e3, e1) = e2)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[945, 21889])).
% 2.44/2.56 tff(21891,plain,
% 2.44/2.56 ((e0 = e2) <=> (e0 = op(e1, e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[4872])).
% 2.44/2.56 tff(21892,plain,
% 2.44/2.56 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21891, 122])).
% 2.44/2.56 tff(21893,plain,
% 2.44/2.56 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21892])).
% 2.44/2.56 tff(21894,plain,
% 2.44/2.56 (~(op(e1, e1) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[14, 21893])).
% 2.44/2.56 tff(21895,plain,
% 2.44/2.56 (e0 = op(e0, e2)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21857])).
% 2.44/2.56 tff(21896,plain,
% 2.44/2.56 ((op(e0, e1) = e0) <=> (op(e0, e1) = op(e0, e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21895])).
% 2.44/2.56 tff(21897,plain,
% 2.44/2.56 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21896])).
% 2.44/2.56 tff(21898,plain,
% 2.44/2.56 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21897])).
% 2.44/2.56 tff(21899,plain,
% 2.44/2.56 (~(op(e0, e1) = e0)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[2102, 21898])).
% 2.44/2.56 tff(21900,plain,
% 2.44/2.56 (op(e3, e1) = e0),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[292, 21899, 2559, 21894])).
% 2.44/2.56 tff(21901,assumption,(op(e0, e0) = e3), introduced(assumption)).
% 2.44/2.56 tff(21902,plain,
% 2.44/2.56 (op(e1, op(e0, e0)) = op(e1, e3)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21901])).
% 2.44/2.56 tff(21903,plain,
% 2.44/2.56 (op(e1, e3) = op(e1, op(e0, e0))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21902])).
% 2.44/2.56 tff(21904,plain,
% 2.44/2.56 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21903])).
% 2.44/2.56 tff(21905,plain,
% 2.44/2.56 ((op(e1, op(e0, e0)) = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21904])).
% 2.44/2.56 tff(21906,plain,
% 2.44/2.56 (e3 = op(e0, e0)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21901])).
% 2.44/2.56 tff(21907,plain,
% 2.44/2.56 (op(e1, e3) = e3),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[247, 75, 1291, 2168])).
% 2.44/2.56 tff(21908,plain,
% 2.44/2.56 (op(e1, op(e0, e0)) = op(e0, e0)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21902, 21907, 21906])).
% 2.44/2.56 tff(21909,plain,
% 2.44/2.56 ((op(e1, op(e0, e0)) = e1) <=> (op(e0, e0) = e1)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21908])).
% 2.44/2.56 tff(21910,plain,
% 2.44/2.56 ((op(e0, e0) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.44/2.56 inference(symmetry,[status(thm)],[21909])).
% 2.44/2.56 tff(21911,plain,
% 2.44/2.56 ((op(e0, e0) = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21910, 21905])).
% 2.44/2.56 tff(21912,plain,
% 2.44/2.56 ((~(op(e0, e0) = e1)) <=> (~(op(e1, e3) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21911])).
% 2.44/2.56 tff(21913,plain,
% 2.44/2.56 ((e1 = e3) <=> (e1 = op(e0, e0))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21906])).
% 2.44/2.56 tff(21914,plain,
% 2.44/2.56 ((e1 = e3) <=> (op(e0, e0) = e1)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21913, 73])).
% 2.44/2.56 tff(21915,plain,
% 2.44/2.56 ((~(e1 = e3)) <=> (~(op(e0, e0) = e1))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21914])).
% 2.44/2.56 tff(21916,plain,
% 2.44/2.56 (~(op(e0, e0) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[303, 21915])).
% 2.44/2.56 tff(21917,plain,
% 2.44/2.56 (~(op(e1, e3) = e1)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21916, 21912])).
% 2.44/2.56 tff(21918,plain,
% 2.44/2.56 (op(e3, e3) = e1),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[151, 21917, 76, 121])).
% 2.44/2.56 tff(21919,plain,
% 2.44/2.56 (e1 = op(e3, e3)),
% 2.44/2.56 inference(modus_ponens,[status(thm)],[21918, 658])).
% 2.44/2.56 tff(21920,plain,
% 2.44/2.56 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21918])).
% 2.44/2.56 tff(21921,plain,
% 2.44/2.56 (op(e3, e1) = op(e3, op(e3, e3))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21920])).
% 2.44/2.56 tff(21922,plain,
% 2.44/2.56 (e0 = op(e3, op(e3, e3))),
% 2.44/2.56 inference(transitivity,[status(thm)],[4734, 21921])).
% 2.44/2.56 tff(21923,plain,
% 2.44/2.56 (op(e3, op(e3, e3)) = op(e0, e2)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21920, 4731, 17119])).
% 2.44/2.56 tff(21924,plain,
% 2.44/2.56 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e0, e2))),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21923])).
% 2.44/2.56 tff(21925,plain,
% 2.44/2.56 (op(e3, op(e0, e2)) = op(e3, op(e3, op(e3, e3)))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21924])).
% 2.44/2.56 tff(21926,plain,
% 2.44/2.56 (op(e3, op(e0, e2)) = op(e3, e0)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[4938])).
% 2.44/2.56 tff(21927,plain,
% 2.44/2.56 (op(e3, e0) = op(e3, op(e0, e2))),
% 2.44/2.56 inference(symmetry,[status(thm)],[21926])).
% 2.44/2.56 tff(21928,plain,
% 2.44/2.56 (op(e3, e2) = e3),
% 2.44/2.56 inference(unit_resolution,[status(thm)],[2111, 75, 4412, 2431])).
% 2.44/2.56 tff(21929,plain,
% 2.44/2.56 (op(e3, e2) = op(e0, e0)),
% 2.44/2.56 inference(transitivity,[status(thm)],[21928, 21906])).
% 2.44/2.56 tff(21930,plain,
% 2.44/2.56 ((op(e3, e2) = e2) <=> (op(e0, e0) = e2)),
% 2.44/2.56 inference(monotonicity,[status(thm)],[21929])).
% 2.44/2.57 tff(21931,plain,
% 2.44/2.57 ((op(e0, e0) = e2) <=> (op(e3, e2) = e2)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21930])).
% 2.44/2.57 tff(21932,plain,
% 2.44/2.57 ((~(op(e0, e0) = e2)) <=> (~(op(e3, e2) = e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21931])).
% 2.44/2.57 tff(21933,plain,
% 2.44/2.57 (~(op(e3, e2) = e2)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[12721, 21932])).
% 2.44/2.57 tff(21934,plain,
% 2.44/2.57 (op(e3, e0) = e2),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[15971, 21933, 82])).
% 2.44/2.57 tff(21935,plain,
% 2.44/2.57 (e2 = op(e3, e0)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21934])).
% 2.44/2.57 tff(21936,plain,
% 2.44/2.57 (e2 = op(e3, op(e3, op(e3, e3)))),
% 2.44/2.57 inference(transitivity,[status(thm)],[21935, 21927, 21925])).
% 2.44/2.57 tff(21937,plain,
% 2.44/2.57 ($false),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[5397, 21936, 21922, 21919])).
% 2.44/2.57 tff(21938,plain,((op(e1, e2) = e3) | (~(op(e0, e2) = e0)) | (~(op(e3, e1) = e0)) | (op(e3, e1) = e2) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e0, e0) = e2) | (~(op(e0, e0) = e3)) | (op(e0, e2) = e3) | (op(e2, e2) = e3) | (op(e1, e1) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.57 tff(21939,plain,
% 2.44/2.57 (op(e1, e2) = e3),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[21938, 21857, 21900, 21890, 76, 121, 21886, 21844, 4412, 21883, 21864, 2168])).
% 2.44/2.57 tff(21940,plain,
% 2.44/2.57 ((op(e1, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21939])).
% 2.44/2.57 tff(21941,plain,
% 2.44/2.57 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21940, 3423])).
% 2.44/2.57 tff(21942,plain,
% 2.44/2.57 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21941, 21861])).
% 2.44/2.57 tff(21943,plain,
% 2.44/2.57 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21942])).
% 2.44/2.57 tff(21944,plain,
% 2.44/2.57 (~(op(e3, op(e0, e3)) = e3)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[2292, 21943])).
% 2.44/2.57 tff(21945,plain,
% 2.44/2.57 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21939])).
% 2.44/2.57 tff(21946,plain,
% 2.44/2.57 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21945, 3230])).
% 2.44/2.57 tff(21947,plain,
% 2.44/2.57 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21946])).
% 2.44/2.57 tff(21948,plain,
% 2.44/2.57 (~(op(e1, e3) = e3)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[1850, 21947])).
% 2.44/2.57 tff(21949,plain,
% 2.44/2.57 ((op(e2, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[251])).
% 2.44/2.57 tff(21950,plain,
% 2.44/2.57 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21949, 3077])).
% 2.44/2.57 tff(21951,plain,
% 2.44/2.57 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21950])).
% 2.44/2.57 tff(21952,plain,
% 2.44/2.57 (~(op(e3, e3) = e0)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[368, 21951])).
% 2.44/2.57 tff(21953,plain,
% 2.44/2.57 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21853])).
% 2.44/2.57 tff(21954,plain,
% 2.44/2.57 ((op(e3, e0) = op(e0, e0)) <=> (op(e0, e0) = op(e3, e0))),
% 2.44/2.57 inference(commutativity,[status(thm)],[])).
% 2.44/2.57 tff(21955,plain,
% 2.44/2.57 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e0, e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21869])).
% 2.44/2.57 tff(21956,plain,
% 2.44/2.57 ((op(e3, e0) = e3) <=> (op(e0, e0) = op(e3, e0))),
% 2.44/2.57 inference(transitivity,[status(thm)],[21955, 21954])).
% 2.44/2.57 tff(21957,plain,
% 2.44/2.57 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21956])).
% 2.44/2.57 tff(21958,plain,
% 2.44/2.57 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21957])).
% 2.44/2.57 tff(21959,plain,
% 2.44/2.57 (~(op(e3, e0) = e3)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[6384, 21958])).
% 2.44/2.57 tff(21960,plain,
% 2.44/2.57 (op(op(e1, e2), e1) = op(e3, e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21939])).
% 2.44/2.57 tff(21961,plain,
% 2.44/2.57 (op(op(e1, e2), e1) = op(e0, e2)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21960, 21900, 21895])).
% 2.44/2.57 tff(21962,plain,
% 2.44/2.57 ((op(op(e1, e2), e1) = e2) <=> (op(e0, e2) = e2)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21961])).
% 2.44/2.57 tff(21963,plain,
% 2.44/2.57 ((op(e0, e2) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21962])).
% 2.44/2.57 tff(21964,plain,
% 2.44/2.57 ((~(op(e0, e2) = e2)) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21963])).
% 2.44/2.57 tff(21965,plain,
% 2.44/2.57 (~(op(op(e1, e2), e1) = e2)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[21839, 21964])).
% 2.44/2.57 tff(21966,plain,
% 2.44/2.57 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[5959, 21965])).
% 2.44/2.57 tff(21967,plain,
% 2.44/2.57 (op(op(e3, e1), e3) = op(e0, op(e0, e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21900, 21869])).
% 2.44/2.57 tff(21968,plain,
% 2.44/2.57 (op(op(e3, e1), e3) = e2),
% 2.44/2.57 inference(transitivity,[status(thm)],[21967, 21845, 21836])).
% 2.44/2.57 tff(21969,plain,
% 2.44/2.57 ((op(op(e3, e1), e3) = e1) <=> (e2 = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21968])).
% 2.44/2.57 tff(21970,plain,
% 2.44/2.57 ((op(op(e3, e1), e3) = e1) <=> (e1 = e2)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21969, 69])).
% 2.44/2.57 tff(21971,plain,
% 2.44/2.57 ((e1 = e2) <=> (op(op(e3, e1), e3) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21970])).
% 2.44/2.57 tff(21972,plain,
% 2.44/2.57 ((~(e1 = e2)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21971])).
% 2.44/2.57 tff(21973,plain,
% 2.44/2.57 (~(op(op(e3, e1), e3) = e1)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[708, 21972])).
% 2.44/2.57 tff(21974,plain,
% 2.44/2.57 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1050, 21973])).
% 2.44/2.57 tff(21975,plain,
% 2.44/2.57 (op(e0, op(e0, e1)) = op(e0, e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21874])).
% 2.44/2.57 tff(21976,plain,
% 2.44/2.57 (op(e0, op(e0, e1)) = e1),
% 2.44/2.57 inference(transitivity,[status(thm)],[21975, 21874])).
% 2.44/2.57 tff(21977,plain,
% 2.44/2.57 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[2449, 21976])).
% 2.44/2.57 tff(21978,plain,
% 2.44/2.57 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e0, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21895])).
% 2.44/2.57 tff(21979,plain,
% 2.44/2.57 ((op(e1, e2) = e0) <=> (op(e0, e2) = op(e1, e2))),
% 2.44/2.57 inference(transitivity,[status(thm)],[21978, 8060])).
% 2.44/2.57 tff(21980,plain,
% 2.44/2.57 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21979])).
% 2.44/2.57 tff(21981,plain,
% 2.44/2.57 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21980])).
% 2.44/2.57 tff(21982,plain,
% 2.44/2.57 (~(op(e1, e2) = e0)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[6205, 21981])).
% 2.44/2.57 tff(21983,plain,
% 2.44/2.57 (op(e1, e0) = e0),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1830, 21982, 21894, 80])).
% 2.44/2.57 tff(21984,plain,
% 2.44/2.57 (op(e1, op(e0, e2)) = op(e1, e0)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21857])).
% 2.44/2.57 tff(21985,plain,
% 2.44/2.57 (op(e1, e0) = op(e0, e2)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21983, 21895])).
% 2.44/2.57 tff(21986,plain,
% 2.44/2.57 (op(e1, op(e1, e0)) = op(e1, op(e0, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21985])).
% 2.44/2.57 tff(21987,plain,
% 2.44/2.57 (op(e1, op(e1, e0)) = e0),
% 2.44/2.57 inference(transitivity,[status(thm)],[21986, 21984, 21983])).
% 2.44/2.57 tff(21988,plain,
% 2.44/2.57 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1836, 21987])).
% 2.44/2.57 tff(21989,plain,
% 2.44/2.57 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[16410, 80, 21835])).
% 2.44/2.57 tff(21990,plain,
% 2.44/2.57 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21836])).
% 2.44/2.57 tff(21991,plain,
% 2.44/2.57 (op(op(e0, e3), e3) = e0),
% 2.44/2.57 inference(transitivity,[status(thm)],[21990, 251])).
% 2.44/2.57 tff(21992,plain,
% 2.44/2.57 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1361, 21991])).
% 2.44/2.57 tff(21993,plain,
% 2.44/2.57 ((op(op(e2, e3), e3) = e2) <=> (op(e0, e3) = e2)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[10444])).
% 2.44/2.57 tff(21994,plain,
% 2.44/2.57 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 2.44/2.57 inference(symmetry,[status(thm)],[21993])).
% 2.44/2.57 tff(21995,plain,
% 2.44/2.57 (op(op(e2, e3), e3) = e2),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[21836, 21994])).
% 2.44/2.57 tff(21996,plain,
% 2.44/2.57 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1288, 21995])).
% 2.44/2.57 tff(21997,plain,
% 2.44/2.57 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1956, 21858])).
% 2.44/2.57 tff(21998,assumption,(op(e2, e1) = e3), introduced(assumption)).
% 2.44/2.57 tff(21999,plain,
% 2.44/2.57 (op(op(e2, e1), e2) = op(e3, e2)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21998])).
% 2.44/2.57 tff(22000,plain,
% 2.44/2.57 ((op(op(e2, e1), e2) = e1) <=> (op(e3, e2) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21999])).
% 2.44/2.57 tff(22001,plain,
% 2.44/2.57 ((op(e3, e2) = e1) <=> (op(op(e2, e1), e2) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[22000])).
% 2.44/2.57 tff(22002,plain,
% 2.44/2.57 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e0)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[4731])).
% 2.44/2.57 tff(22003,plain,
% 2.44/2.57 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22002])).
% 2.44/2.57 tff(22004,plain,
% 2.44/2.57 (~(op(e3, e0) = e0)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[580, 22003])).
% 2.44/2.57 tff(22005,plain,
% 2.44/2.57 (op(e3, e0) = e1),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[5422, 3786, 2410, 22004])).
% 2.44/2.57 tff(22006,plain,
% 2.44/2.57 ((op(e3, e0) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22005])).
% 2.44/2.57 tff(22007,plain,
% 2.44/2.57 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22006, 7171])).
% 2.44/2.57 tff(22008,plain,
% 2.44/2.57 ((op(e3, e0) = op(e3, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22007, 22001])).
% 2.44/2.57 tff(22009,plain,
% 2.44/2.57 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22008])).
% 2.44/2.57 tff(22010,plain,
% 2.44/2.57 (~(op(op(e2, e1), e2) = e1)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[1133, 22009])).
% 2.44/2.57 tff(22011,plain,
% 2.44/2.57 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[5808, 22010])).
% 2.44/2.57 tff(22012,plain,
% 2.44/2.57 (op(e2, e0) = e2),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[589, 3786, 6687, 12721])).
% 2.44/2.57 tff(22013,plain,
% 2.44/2.57 (op(e2, op(e0, e2)) = op(e2, e0)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[4938])).
% 2.44/2.57 tff(22014,plain,
% 2.44/2.57 (op(op(e2, e0), e0) = op(e2, op(e0, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22012, 17119])).
% 2.44/2.57 tff(22015,plain,
% 2.44/2.57 (op(op(e2, e0), e0) = e2),
% 2.44/2.57 inference(transitivity,[status(thm)],[22014, 22013, 22012])).
% 2.44/2.57 tff(22016,plain,
% 2.44/2.57 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1945, 22015])).
% 2.44/2.57 tff(22017,plain,
% 2.44/2.57 (op(e3, op(e3, e0)) = op(e3, e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22005])).
% 2.44/2.57 tff(22018,plain,
% 2.44/2.57 (op(e3, op(e3, e0)) = e0),
% 2.44/2.57 inference(transitivity,[status(thm)],[22017, 4731])).
% 2.44/2.57 tff(22019,plain,
% 2.44/2.57 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1345, 22018])).
% 2.44/2.57 tff(22020,plain,
% 2.44/2.57 ($false),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[1459, 22019, 22016, 3342, 1347, 1363, 1304, 1357, 4549, 21265, 1275, 1358, 22011])).
% 2.44/2.57 tff(22021,plain,((op(e3, e0) = e2) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~(op(e3, e1) = e0)) | (~(op(e2, e1) = e3)) | (~(op(e0, e2) = e0)) | (op(e3, e1) = e2) | (op(e3, e0) = e3) | (op(e1, e0) = e2) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.57 tff(22022,plain,
% 2.44/2.57 (op(e3, e0) = e2),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[22021, 21997, 21996, 21992, 21989, 21988, 21977, 21974, 21966, 21900, 21879, 21857, 21890, 21959, 21431, 21886])).
% 2.44/2.57 tff(22023,plain,
% 2.44/2.57 (op(e3, e0) = op(e0, e3)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[22022, 21953])).
% 2.44/2.57 tff(22024,plain,
% 2.44/2.57 (op(e2, op(e0, e3)) = e2),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[2141, 22023, 9737, 80, 121, 21952, 21843, 21864, 21948, 21944])).
% 2.44/2.57 tff(22025,plain,
% 2.44/2.57 (op(e2, e2) = op(e2, op(e0, e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21853])).
% 2.44/2.57 tff(22026,plain,
% 2.44/2.57 (op(e2, e2) = e2),
% 2.44/2.57 inference(transitivity,[status(thm)],[22025, 22024])).
% 2.44/2.57 tff(22027,plain,
% 2.44/2.57 (op(e0, op(e2, e2)) = op(op(e0, e2), e2)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21895, 22026])).
% 2.44/2.57 tff(22028,plain,
% 2.44/2.57 (op(e0, op(e2, e2)) = e0),
% 2.44/2.57 inference(transitivity,[status(thm)],[22027, 21858])).
% 2.44/2.57 tff(22029,plain,
% 2.44/2.57 ((op(e2, e0) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21895])).
% 2.44/2.57 tff(22030,plain,
% 2.44/2.57 ((~(op(e2, e0) = e0)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22029])).
% 2.44/2.57 tff(22031,plain,
% 2.44/2.57 (~(op(e2, e0) = op(e0, e2))),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[10091, 22030])).
% 2.44/2.57 tff(22032,plain,
% 2.44/2.57 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[6358, 22031])).
% 2.44/2.57 tff(22033,plain,
% 2.44/2.57 (op(e1, e2) = op(e0, e0)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21939, 21869])).
% 2.44/2.57 tff(22034,plain,
% 2.44/2.57 (op(e1, op(e1, e2)) = op(e1, op(e0, e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22033])).
% 2.44/2.57 tff(22035,plain,
% 2.44/2.57 ((op(e1, op(e1, e2)) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22034])).
% 2.44/2.57 tff(22036,plain,
% 2.44/2.57 ((op(e1, op(e0, e0)) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[22035])).
% 2.44/2.57 tff(22037,plain,
% 2.44/2.57 (op(e1, op(e0, e0)) = op(e1, e3)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21844])).
% 2.44/2.57 tff(22038,plain,
% 2.44/2.57 (op(e1, e3) = op(e1, op(e0, e0))),
% 2.44/2.57 inference(symmetry,[status(thm)],[22037])).
% 2.44/2.57 tff(22039,plain,
% 2.44/2.57 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22038])).
% 2.44/2.57 tff(22040,plain,
% 2.44/2.57 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e2)) = e1)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22039, 22036])).
% 2.44/2.57 tff(22041,plain,
% 2.44/2.57 ((op(e1, e0) = e1) <=> (op(e0, e2) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21985])).
% 2.44/2.57 tff(22042,plain,
% 2.44/2.57 ((op(e0, e2) = e1) <=> (op(e1, e0) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[22041])).
% 2.44/2.57 tff(22043,plain,
% 2.44/2.57 ((~(op(e0, e2) = e1)) <=> (~(op(e1, e0) = e1))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22042])).
% 2.44/2.57 tff(22044,plain,
% 2.44/2.57 (~(op(e1, e0) = e1)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[21856, 22043])).
% 2.44/2.57 tff(22045,plain,
% 2.44/2.57 ((op(e1, e2) = e1) <=> (op(e0, e0) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22033])).
% 2.44/2.57 tff(22046,plain,
% 2.44/2.57 ((op(e0, e0) = e1) <=> (op(e1, e2) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[22045])).
% 2.44/2.57 tff(22047,plain,
% 2.44/2.57 ((~(op(e0, e0) = e1)) <=> (~(op(e1, e2) = e1))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22046])).
% 2.44/2.57 tff(22048,plain,
% 2.44/2.57 (~(op(e1, e2) = e1)),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[21873, 22047])).
% 2.44/2.57 tff(22049,plain,
% 2.44/2.57 (op(e1, e3) = e1),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[954, 22048, 5759, 22044])).
% 2.44/2.57 tff(22050,plain,
% 2.44/2.57 (op(e1, op(e1, e2)) = e1),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[22049, 22040])).
% 2.44/2.57 tff(22051,plain,
% 2.44/2.57 (((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)) | (~(op(e1, op(e1, e2)) = e1))),
% 2.44/2.57 inference(tautology,[status(thm)],[])).
% 2.44/2.57 tff(22052,plain,
% 2.44/2.57 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[22051, 22050])).
% 2.44/2.57 tff(22053,plain,
% 2.44/2.57 ((op(e3, e1) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21900])).
% 2.44/2.57 tff(22054,plain,
% 2.44/2.57 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22053, 6095])).
% 2.44/2.57 tff(22055,plain,
% 2.44/2.57 ((op(e1, e3) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.44/2.57 inference(symmetry,[status(thm)],[22054])).
% 2.44/2.57 tff(22056,plain,
% 2.44/2.57 ((op(e1, e3) = e0) <=> (op(e1, e3) = op(e3, e1))),
% 2.44/2.57 inference(transitivity,[status(thm)],[22055, 6290])).
% 2.44/2.57 tff(22057,plain,
% 2.44/2.57 ((~(op(e1, e3) = e0)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22056])).
% 2.44/2.57 tff(22058,plain,
% 2.44/2.57 (~(op(e1, e3) = op(e3, e1))),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[80, 22057])).
% 2.44/2.57 tff(22059,plain,
% 2.44/2.57 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[6307, 22058])).
% 2.44/2.57 tff(22060,plain,
% 2.44/2.57 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21874])).
% 2.44/2.57 tff(22061,plain,
% 2.44/2.57 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e0, e1))),
% 2.44/2.57 inference(symmetry,[status(thm)],[22060])).
% 2.44/2.57 tff(22062,plain,
% 2.44/2.57 ((op(e0, e2) = e1) <=> (op(e0, e1) = op(e1, e0))),
% 2.44/2.57 inference(transitivity,[status(thm)],[22042, 22061, 596])).
% 2.44/2.57 tff(22063,plain,
% 2.44/2.57 ((~(op(e0, e2) = e1)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22062])).
% 2.44/2.57 tff(22064,plain,
% 2.44/2.57 (~(op(e0, e1) = op(e1, e0))),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[21856, 22063])).
% 2.44/2.57 tff(22065,plain,
% 2.44/2.57 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[609, 22064])).
% 2.44/2.57 tff(22066,plain,
% 2.44/2.57 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[21857])).
% 2.44/2.57 tff(22067,plain,
% 2.44/2.57 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22066, 4959])).
% 2.44/2.57 tff(22068,plain,
% 2.44/2.57 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.44/2.57 inference(transitivity,[status(thm)],[22067, 19670])).
% 2.44/2.57 tff(22069,plain,
% 2.44/2.57 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22068])).
% 2.44/2.57 tff(22070,plain,
% 2.44/2.57 (~(op(e3, e2) = op(e2, e3))),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[1467, 22069])).
% 2.44/2.57 tff(22071,plain,
% 2.44/2.57 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[500, 22070])).
% 2.44/2.57 tff(22072,plain,
% 2.44/2.57 (op(e2, e1) = op(e0, e0)),
% 2.44/2.57 inference(transitivity,[status(thm)],[21879, 21869])).
% 2.44/2.57 tff(22073,plain,
% 2.44/2.57 (op(e1, op(e2, e1)) = op(e1, op(e0, e0))),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22072])).
% 2.44/2.57 tff(22074,plain,
% 2.44/2.57 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, op(e0, e0)) = e1)),
% 2.44/2.57 inference(monotonicity,[status(thm)],[22073])).
% 2.44/2.57 tff(22075,plain,
% 2.44/2.57 ((op(e1, op(e0, e0)) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 2.44/2.57 inference(symmetry,[status(thm)],[22074])).
% 2.44/2.57 tff(22076,plain,
% 2.44/2.57 ((op(e1, e3) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 2.44/2.57 inference(transitivity,[status(thm)],[22039, 22075])).
% 2.44/2.57 tff(22077,plain,
% 2.44/2.57 (op(e1, op(e2, e1)) = e1),
% 2.44/2.57 inference(modus_ponens,[status(thm)],[22049, 22076])).
% 2.44/2.57 tff(22078,plain,
% 2.44/2.57 (((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)) | (~(op(e1, op(e2, e1)) = e1))),
% 2.44/2.57 inference(tautology,[status(thm)],[])).
% 2.44/2.57 tff(22079,plain,
% 2.44/2.57 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.44/2.57 inference(unit_resolution,[status(thm)],[22078, 22077])).
% 2.44/2.57 tff(22080,plain,
% 2.44/2.57 ((op(e0, e2) = e1) <=> (op(e1, e0) = op(e0, e1))),
% 2.44/2.57 inference(transitivity,[status(thm)],[22042, 22061])).
% 2.44/2.57 tff(22081,plain,
% 2.44/2.57 ((~(op(e0, e2) = e1)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22080])).
% 2.44/2.58 tff(22082,plain,
% 2.44/2.58 (~(op(e1, e0) = op(e0, e1))),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[21856, 22081])).
% 2.44/2.58 tff(22083,plain,
% 2.44/2.58 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[613, 22082])).
% 2.44/2.58 tff(22084,plain,
% 2.44/2.58 ((~(op(e1, e3) = e0)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22055])).
% 2.44/2.58 tff(22085,plain,
% 2.44/2.58 (~(op(e3, e1) = op(e1, e3))),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[80, 22084])).
% 2.44/2.58 tff(22086,plain,
% 2.44/2.58 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[6362, 22085])).
% 2.44/2.58 tff(22087,plain,
% 2.44/2.58 (op(e1, op(e0, e0)) = e1),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22049, 22039])).
% 2.44/2.58 tff(22088,plain,
% 2.44/2.58 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[6717, 22087])).
% 2.44/2.58 tff(22089,plain,
% 2.44/2.58 ((op(e0, op(e1, e1)) = e0) <=> (op(e0, e2) = e0)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[4939])).
% 2.44/2.58 tff(22090,plain,
% 2.44/2.58 ((op(e0, e2) = e0) <=> (op(e0, op(e1, e1)) = e0)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22089])).
% 2.44/2.58 tff(22091,plain,
% 2.44/2.58 (op(e0, op(e1, e1)) = e0),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[21857, 22090])).
% 2.44/2.58 tff(22092,plain,
% 2.44/2.58 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[635, 22091])).
% 2.44/2.58 tff(22093,plain,
% 2.44/2.58 ((op(e0, e2) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e2))),
% 2.44/2.58 inference(commutativity,[status(thm)],[])).
% 2.44/2.58 tff(22094,plain,
% 2.44/2.58 (op(e3, e1) = op(e0, e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[21900, 21895])).
% 2.44/2.58 tff(22095,plain,
% 2.44/2.58 ((op(e3, e1) = e3) <=> (op(e0, e2) = op(e0, e0))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22094, 21869])).
% 2.44/2.58 tff(22096,plain,
% 2.44/2.58 ((op(e3, e1) = e3) <=> (op(e0, e0) = op(e0, e2))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22095, 22093])).
% 2.44/2.58 tff(22097,plain,
% 2.44/2.58 ((op(e0, e0) = op(e0, e2)) <=> (op(e3, e1) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22096])).
% 2.44/2.58 tff(22098,plain,
% 2.44/2.58 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e3, e1) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22097])).
% 2.44/2.58 tff(22099,plain,
% 2.44/2.58 (~(op(e3, e1) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[3603, 22098])).
% 2.44/2.58 tff(22100,plain,
% 2.44/2.58 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[21941])).
% 2.44/2.58 tff(22101,plain,
% 2.44/2.58 (~(op(e3, e2) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[2292, 22100])).
% 2.44/2.58 tff(22102,plain,
% 2.44/2.58 (op(e3, e3) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[422, 22101, 21959, 22099])).
% 2.44/2.58 tff(22103,plain,
% 2.44/2.58 (op(e3, e3) = op(e0, e0)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22102, 21869])).
% 2.44/2.58 tff(22104,plain,
% 2.44/2.58 (op(e1, op(e3, e3)) = op(e1, op(e0, e0))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22103])).
% 2.44/2.58 tff(22105,plain,
% 2.44/2.58 (op(e1, op(e3, e3)) = e1),
% 2.44/2.58 inference(transitivity,[status(thm)],[22104, 22037, 22049])).
% 2.44/2.58 tff(22106,plain,
% 2.44/2.58 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[5685, 22105])).
% 2.44/2.58 tff(22107,plain,
% 2.44/2.58 ((op(e2, e0) = e0) <=> (op(e0, e2) = op(e2, e0))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22029, 6337])).
% 2.44/2.58 tff(22108,plain,
% 2.44/2.58 ((~(op(e2, e0) = e0)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22107])).
% 2.44/2.58 tff(22109,plain,
% 2.44/2.58 (~(op(e0, e2) = op(e2, e0))),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[10091, 22108])).
% 2.44/2.58 tff(22110,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[6347, 22109])).
% 2.44/2.58 tff(22111,plain,
% 2.44/2.58 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22067, 19670, 395])).
% 2.44/2.58 tff(22112,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22111])).
% 2.44/2.58 tff(22113,plain,
% 2.44/2.58 (~(op(e2, e3) = op(e3, e2))),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[1467, 22112])).
% 2.44/2.58 tff(22114,plain,
% 2.44/2.58 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[430, 22113])).
% 2.44/2.58 tff(22115,plain,
% 2.44/2.58 (op(e0, op(e3, e0)) = op(op(e0, e2), e2)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[21895, 22022])).
% 2.44/2.58 tff(22116,plain,
% 2.44/2.58 (op(e0, op(e3, e0)) = e0),
% 2.44/2.58 inference(transitivity,[status(thm)],[22115, 21858])).
% 2.44/2.58 tff(22117,plain,
% 2.44/2.58 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[18826, 22116])).
% 2.44/2.58 tff(22118,plain,
% 2.44/2.58 (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[5367, 22117, 22114, 22110, 22106, 22092, 22088, 22086, 22083, 22079, 22071, 22065, 22059, 22052, 22032])).
% 2.44/2.58 tff(22119,plain,
% 2.44/2.58 (~(op(e0, op(e2, e2)) = e0)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[5619, 22118])).
% 2.44/2.58 tff(22120,plain,
% 2.44/2.58 ($false),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[22119, 22028])).
% 2.44/2.58 tff(22121,plain,((op(e0, e2) = e3) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e2, e3) = e1) | (op(e1, e0) = e3) | (op(e2, e1) = e0) | (~(op(e2, e3) = e0)) | (~(op(e1, e1) = e2)) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.58 tff(22122,plain,
% 2.44/2.58 (op(e0, e2) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[22121, 2168, 121, 76, 80, 2559, 21831, 21327, 2527])).
% 2.44/2.58 tff(22123,plain,
% 2.44/2.58 (op(e1, op(e0, e2)) = op(e1, e3)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22122])).
% 2.44/2.58 tff(22124,plain,
% 2.44/2.58 (op(e1, e3) = op(e1, op(e0, e2))),
% 2.44/2.58 inference(symmetry,[status(thm)],[22123])).
% 2.44/2.58 tff(22125,plain,
% 2.44/2.58 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e2)) = e1)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22124])).
% 2.44/2.58 tff(22126,plain,
% 2.44/2.58 ((op(e1, op(e0, e2)) = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22125])).
% 2.44/2.58 tff(22127,plain,
% 2.44/2.58 (e3 = op(e0, e2)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22122])).
% 2.44/2.58 tff(22128,plain,
% 2.44/2.58 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22127])).
% 2.44/2.58 tff(22129,plain,
% 2.44/2.58 ((op(e1, e2) = e3) <=> (op(e0, e2) = op(e1, e2))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22128, 8060])).
% 2.44/2.58 tff(22130,plain,
% 2.44/2.58 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22129])).
% 2.44/2.58 tff(22131,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22130])).
% 2.44/2.58 tff(22132,plain,
% 2.44/2.58 (~(op(e1, e2) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[6205, 22131])).
% 2.44/2.58 tff(22133,plain,
% 2.44/2.58 (op(e1, e3) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[247, 22132, 21634, 2168])).
% 2.44/2.58 tff(22134,plain,
% 2.44/2.58 (op(e1, op(e0, e2)) = op(e0, e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22123, 22133, 22127])).
% 2.44/2.58 tff(22135,plain,
% 2.44/2.58 ((op(e1, op(e0, e2)) = e1) <=> (op(e0, e2) = e1)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22134])).
% 2.44/2.58 tff(22136,plain,
% 2.44/2.58 ((op(e0, e2) = e1) <=> (op(e1, op(e0, e2)) = e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22135])).
% 2.44/2.58 tff(22137,plain,
% 2.44/2.58 ((op(e0, e2) = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22136, 22126])).
% 2.44/2.58 tff(22138,plain,
% 2.44/2.58 ((~(op(e0, e2) = e1)) <=> (~(op(e1, e3) = e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22137])).
% 2.44/2.58 tff(22139,plain,
% 2.44/2.58 ((e1 = e3) <=> (e1 = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22127])).
% 2.44/2.58 tff(22140,plain,
% 2.44/2.58 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22139, 697])).
% 2.44/2.58 tff(22141,plain,
% 2.44/2.58 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22140])).
% 2.44/2.58 tff(22142,plain,
% 2.44/2.58 (~(op(e0, e2) = e1)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[303, 22141])).
% 2.44/2.58 tff(22143,plain,
% 2.44/2.58 (~(op(e1, e3) = e1)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22142, 22138])).
% 2.44/2.58 tff(22144,plain,
% 2.44/2.58 (op(e3, e3) = e1),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[151, 22143, 76, 121])).
% 2.44/2.58 tff(22145,plain,
% 2.44/2.58 (e1 = op(e3, e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22144])).
% 2.44/2.58 tff(22146,plain,
% 2.44/2.58 ((op(e2, e3) = e2) <=> (e0 = e2)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[21831])).
% 2.44/2.58 tff(22147,plain,
% 2.44/2.58 ((e0 = e2) <=> (op(e2, e3) = e2)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22146])).
% 2.44/2.58 tff(22148,plain,
% 2.44/2.58 ((~(e0 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22147])).
% 2.44/2.58 tff(22149,plain,
% 2.44/2.58 (~(op(e2, e3) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[14, 22148])).
% 2.44/2.58 tff(22150,plain,
% 2.44/2.58 ((op(e1, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[21327])).
% 2.44/2.58 tff(22151,plain,
% 2.44/2.58 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22150, 1960])).
% 2.44/2.58 tff(22152,plain,
% 2.44/2.58 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22151])).
% 2.44/2.58 tff(22153,plain,
% 2.44/2.58 (~(op(e2, e1) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[225, 22152])).
% 2.44/2.58 tff(22154,plain,
% 2.44/2.58 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[1940])).
% 2.44/2.58 tff(22155,plain,
% 2.44/2.58 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22154, 81])).
% 2.44/2.58 tff(22156,plain,
% 2.44/2.58 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22155])).
% 2.44/2.58 tff(22157,plain,
% 2.44/2.58 (~(op(e2, e2) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[2228, 22156])).
% 2.44/2.58 tff(22158,plain,
% 2.44/2.58 (op(e2, e2) = e1),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[524, 22157, 17, 20717])).
% 2.44/2.58 tff(22159,plain,
% 2.44/2.58 (e1 = op(e2, e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22158, 317])).
% 2.44/2.58 tff(22160,plain,
% 2.44/2.58 (op(e2, e2) = op(e3, e3)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22158, 306])).
% 2.44/2.58 tff(22161,plain,
% 2.44/2.58 (op(e2, op(e2, e2)) = op(e2, op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22160])).
% 2.44/2.58 tff(22162,plain,
% 2.44/2.58 (op(e2, op(e3, e3)) = op(e2, op(e2, e2))),
% 2.44/2.58 inference(symmetry,[status(thm)],[22161])).
% 2.44/2.58 tff(22163,plain,
% 2.44/2.58 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[7827])).
% 2.44/2.58 tff(22164,plain,
% 2.44/2.58 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22163])).
% 2.44/2.58 tff(22165,plain,
% 2.44/2.58 ((op(e0, e2) = e2) <=> (op(e2, e0) = e3)),
% 2.44/2.58 inference(transitivity,[status(thm)],[14175, 22164])).
% 2.44/2.58 tff(22166,plain,
% 2.44/2.58 ((~(op(e0, e2) = e2)) <=> (~(op(e2, e0) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22165])).
% 2.44/2.58 tff(22167,plain,
% 2.44/2.58 (op(e0, e3) = e2),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[15003, 5019, 21331])).
% 2.44/2.58 tff(22168,plain,
% 2.44/2.58 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22167])).
% 2.44/2.58 tff(22169,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22168])).
% 2.44/2.58 tff(22170,plain,
% 2.44/2.58 (~(op(e0, e2) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[918, 22169])).
% 2.44/2.58 tff(22171,plain,
% 2.44/2.58 (~(op(e2, e0) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22170, 22166])).
% 2.44/2.58 tff(22172,plain,
% 2.44/2.58 (op(e2, e1) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[1559, 22171, 472, 20717])).
% 2.44/2.58 tff(22173,plain,
% 2.44/2.58 (e3 = op(e2, e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22172])).
% 2.44/2.58 tff(22174,plain,
% 2.44/2.58 (e3 = op(e2, op(e2, e2))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22173, 8858, 22162])).
% 2.44/2.58 tff(22175,plain,
% 2.44/2.58 (op(e2, op(e2, e2)) = op(e0, e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22161, 8857, 22172, 7827])).
% 2.44/2.58 tff(22176,plain,
% 2.44/2.58 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22175])).
% 2.44/2.58 tff(22177,plain,
% 2.44/2.58 (op(e2, op(e0, e2)) = op(e2, op(e2, op(e2, e2)))),
% 2.44/2.58 inference(symmetry,[status(thm)],[22176])).
% 2.44/2.58 tff(22178,plain,
% 2.44/2.58 (e0 = op(e2, op(e2, op(e2, e2)))),
% 2.44/2.58 inference(transitivity,[status(thm)],[252, 19377, 22177])).
% 2.44/2.58 tff(22179,plain,
% 2.44/2.58 ($false),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[334, 22178, 22174, 22159])).
% 2.44/2.58 tff(22180,plain,((~(op(e2, e0) = e2)) | (~(op(e2, e3) = e0)) | (~(op(e0, e2) = e3)) | (~(op(e3, e3) = e1)) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.58 tff(22181,plain,
% 2.44/2.58 (~(op(e2, e0) = e2)),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[22180, 21831, 22122, 22144, 17])).
% 2.44/2.58 tff(22182,plain,
% 2.44/2.58 (op(e2, e2) = e2),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[2088, 22181, 22153, 22149])).
% 2.44/2.58 tff(22183,plain,
% 2.44/2.58 ((op(e2, e2) = e1) <=> (e2 = op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22182, 22145])).
% 2.44/2.58 tff(22184,plain,
% 2.44/2.58 ((op(e2, e2) = e1) <=> (op(e3, e3) = e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22183, 565])).
% 2.44/2.58 tff(22185,plain,
% 2.44/2.58 ((op(e3, e3) = e2) <=> (op(e2, e2) = e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22184])).
% 2.44/2.58 tff(22186,plain,
% 2.44/2.58 ((~(op(e3, e3) = e2)) <=> (~(op(e2, e2) = e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22185])).
% 2.44/2.58 tff(22187,plain,
% 2.44/2.58 (~(op(e2, e2) = e1)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[15002, 22186])).
% 2.44/2.58 tff(22188,plain,
% 2.44/2.58 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22127])).
% 2.44/2.58 tff(22189,plain,
% 2.44/2.58 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22188])).
% 2.44/2.58 tff(22190,plain,
% 2.44/2.58 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22189])).
% 2.44/2.58 tff(22191,plain,
% 2.44/2.58 (~(op(e0, e0) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[3603, 22190])).
% 2.44/2.58 tff(22192,plain,
% 2.44/2.58 (op(e0, e3) = e2),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[15003, 22149, 21331])).
% 2.44/2.58 tff(22193,plain,
% 2.44/2.58 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22192])).
% 2.44/2.58 tff(22194,plain,
% 2.44/2.58 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22193])).
% 2.44/2.58 tff(22195,plain,
% 2.44/2.58 (~(op(e0, e0) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[3414, 22194])).
% 2.44/2.58 tff(22196,plain,
% 2.44/2.58 (op(e3, e0) = e2),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[589, 22181, 21340, 22195])).
% 2.44/2.58 tff(22197,plain,
% 2.44/2.58 ((op(e3, e0) = e3) <=> (e2 = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22196, 22127])).
% 2.44/2.58 tff(22198,plain,
% 2.44/2.58 ((op(e3, e0) = e3) <=> (op(e0, e2) = e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22197, 3491])).
% 2.44/2.58 tff(22199,plain,
% 2.44/2.58 ((op(e0, e2) = e2) <=> (op(e3, e0) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22198])).
% 2.44/2.58 tff(22200,plain,
% 2.44/2.58 ((~(op(e0, e2) = e2)) <=> (~(op(e3, e0) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22199])).
% 2.44/2.58 tff(22201,plain,
% 2.44/2.58 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22192])).
% 2.44/2.58 tff(22202,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22201])).
% 2.44/2.58 tff(22203,plain,
% 2.44/2.58 (~(op(e0, e2) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[918, 22202])).
% 2.44/2.58 tff(22204,plain,
% 2.44/2.58 (~(op(e3, e0) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22203, 22200])).
% 2.44/2.58 tff(22205,plain,
% 2.44/2.58 (op(e2, e0) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[2713, 22204, 22191, 2168])).
% 2.44/2.58 tff(22206,plain,
% 2.44/2.58 ((op(e2, e0) = e1) <=> (e3 = op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22205, 22145])).
% 2.44/2.58 tff(22207,plain,
% 2.44/2.58 ((op(e2, e0) = e1) <=> (op(e3, e3) = e3)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22206, 666])).
% 2.44/2.58 tff(22208,plain,
% 2.44/2.58 ((op(e3, e3) = e3) <=> (op(e2, e0) = e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22207])).
% 2.44/2.58 tff(22209,plain,
% 2.44/2.58 ((~(op(e3, e3) = e3)) <=> (~(op(e2, e0) = e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22208])).
% 2.44/2.58 tff(22210,plain,
% 2.44/2.58 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22133])).
% 2.44/2.58 tff(22211,plain,
% 2.44/2.58 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22210, 666])).
% 2.44/2.58 tff(22212,plain,
% 2.44/2.58 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22211])).
% 2.44/2.58 tff(22213,plain,
% 2.44/2.58 (~(op(e3, e3) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[571, 22212])).
% 2.44/2.58 tff(22214,plain,
% 2.44/2.58 (~(op(e2, e0) = e1)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[22213, 22209])).
% 2.44/2.58 tff(22215,plain,
% 2.44/2.58 (op(e2, e1) = e1),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[345, 22214, 76, 22187])).
% 2.44/2.58 tff(22216,plain,
% 2.44/2.58 (op(e2, op(e3, e3)) = op(e2, e1)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22144])).
% 2.44/2.58 tff(22217,plain,
% 2.44/2.58 (op(e2, e1) = op(e3, e3)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22215, 22145])).
% 2.44/2.58 tff(22218,plain,
% 2.44/2.58 (op(e2, op(e2, e1)) = op(e2, op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22217])).
% 2.44/2.58 tff(22219,plain,
% 2.44/2.58 (op(e2, op(e2, e1)) = e1),
% 2.44/2.58 inference(transitivity,[status(thm)],[22218, 22216, 22215])).
% 2.44/2.58 tff(22220,plain,
% 2.44/2.58 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e0, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22127])).
% 2.44/2.58 tff(22221,plain,
% 2.44/2.58 ((op(e3, e2) = e3) <=> (op(e0, e2) = op(e3, e2))),
% 2.44/2.58 inference(transitivity,[status(thm)],[22220, 19442])).
% 2.44/2.58 tff(22222,plain,
% 2.44/2.58 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22221])).
% 2.44/2.58 tff(22223,plain,
% 2.44/2.58 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22222])).
% 2.44/2.58 tff(22224,plain,
% 2.44/2.58 (~(op(e3, e2) = e3)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[1467, 22223])).
% 2.44/2.58 tff(22225,plain,
% 2.44/2.58 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22145])).
% 2.44/2.58 tff(22226,plain,
% 2.44/2.58 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.44/2.58 inference(symmetry,[status(thm)],[22225])).
% 2.44/2.58 tff(22227,plain,
% 2.44/2.58 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22226])).
% 2.44/2.58 tff(22228,plain,
% 2.44/2.58 (~(op(e3, e2) = e1)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[1888, 22227])).
% 2.44/2.58 tff(22229,plain,
% 2.44/2.58 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22182])).
% 2.44/2.58 tff(22230,plain,
% 2.44/2.58 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.44/2.58 inference(transitivity,[status(thm)],[22229, 2234])).
% 2.44/2.58 tff(22231,plain,
% 2.44/2.58 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22230])).
% 2.44/2.58 tff(22232,plain,
% 2.44/2.58 (~(op(e3, e2) = e2)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[1546, 22231])).
% 2.44/2.58 tff(22233,plain,
% 2.44/2.58 (op(e3, e2) = e0),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[1898, 22232, 22228, 22224])).
% 2.44/2.58 tff(22234,plain,
% 2.44/2.58 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e0)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22233])).
% 2.44/2.58 tff(22235,plain,
% 2.44/2.58 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e0))),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22234])).
% 2.44/2.58 tff(22236,plain,
% 2.44/2.58 (~(op(e3, e1) = e0)),
% 2.44/2.58 inference(modus_ponens,[status(thm)],[3429, 22235])).
% 2.44/2.58 tff(22237,plain,
% 2.44/2.58 (op(e0, op(e0, e2)) = op(e0, e3)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22122])).
% 2.44/2.58 tff(22238,plain,
% 2.44/2.58 (op(e0, op(e0, e2)) = e2),
% 2.44/2.58 inference(transitivity,[status(thm)],[22237, 22192])).
% 2.44/2.58 tff(22239,plain,
% 2.44/2.58 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[1331, 22238])).
% 2.44/2.58 tff(22240,plain,
% 2.44/2.58 (op(op(e0, e2), e0) = op(e3, e0)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22122])).
% 2.44/2.58 tff(22241,plain,
% 2.44/2.58 (op(e3, op(e3, e2)) = op(op(e0, e2), e0)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22127, 22233])).
% 2.44/2.58 tff(22242,plain,
% 2.44/2.58 (op(e3, op(e3, e2)) = e2),
% 2.44/2.58 inference(transitivity,[status(thm)],[22241, 22240, 22196])).
% 2.44/2.58 tff(22243,plain,
% 2.44/2.58 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[1904, 22242])).
% 2.44/2.58 tff(22244,plain,
% 2.44/2.58 (op(e3, e1) = e3),
% 2.44/2.58 inference(unit_resolution,[status(thm)],[422, 22204, 22224, 22213])).
% 2.44/2.58 tff(22245,plain,
% 2.44/2.58 (op(e3, op(e3, e1)) = op(e3, e3)),
% 2.44/2.58 inference(monotonicity,[status(thm)],[22244])).
% 2.44/2.58 tff(22246,plain,
% 2.44/2.58 (op(e3, op(e3, e1)) = e1),
% 2.44/2.58 inference(transitivity,[status(thm)],[22245, 22144])).
% 2.44/2.58 tff(22247,plain,
% 2.44/2.58 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[2594, 22246])).
% 2.44/2.59 tff(22248,plain,
% 2.44/2.59 (op(e1, e2) = e1),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1613, 22187, 22142, 22228])).
% 2.44/2.59 tff(22249,plain,
% 2.44/2.59 (op(e1, op(e1, e2)) = op(e1, e1)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22248])).
% 2.44/2.59 tff(22250,plain,
% 2.44/2.59 (op(e1, op(e1, e2)) = e2),
% 2.44/2.59 inference(transitivity,[status(thm)],[22249, 21327])).
% 2.44/2.59 tff(22251,plain,
% 2.44/2.59 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[2377, 22250])).
% 2.44/2.59 tff(22252,plain,
% 2.44/2.59 (op(op(e0, e2), e2) = op(e3, e2)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22122])).
% 2.44/2.59 tff(22253,plain,
% 2.44/2.59 (op(e3, op(e3, e0)) = op(op(e0, e2), e2)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22127, 22196])).
% 2.44/2.59 tff(22254,plain,
% 2.44/2.59 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22253, 22252])).
% 2.44/2.59 tff(22255,plain,
% 2.44/2.59 ((op(e3, op(e3, e0)) = e0) <=> (op(e3, e2) = e0)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22254])).
% 2.44/2.59 tff(22256,plain,
% 2.44/2.59 ((op(e3, e2) = e0) <=> (op(e3, op(e3, e0)) = e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22255])).
% 2.44/2.59 tff(22257,plain,
% 2.44/2.59 (op(e3, op(e3, e0)) = e0),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[22233, 22256])).
% 2.44/2.59 tff(22258,plain,
% 2.44/2.59 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1345, 22257])).
% 2.44/2.59 tff(22259,plain,
% 2.44/2.59 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22192])).
% 2.44/2.59 tff(22260,plain,
% 2.44/2.59 (op(op(e0, e3), e3) = e0),
% 2.44/2.59 inference(transitivity,[status(thm)],[22259, 21831])).
% 2.44/2.59 tff(22261,plain,
% 2.44/2.59 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1361, 22260])).
% 2.44/2.59 tff(22262,plain,
% 2.44/2.59 (op(e1, e2) = op(e3, e3)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22248, 22145])).
% 2.44/2.59 tff(22263,plain,
% 2.44/2.59 ((op(e1, e2) = e0) <=> (op(e3, e3) = e0)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22262])).
% 2.44/2.59 tff(22264,plain,
% 2.44/2.59 ((op(e3, e3) = e0) <=> (op(e1, e2) = e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22263])).
% 2.44/2.59 tff(22265,plain,
% 2.44/2.59 ((~(op(e3, e3) = e0)) <=> (~(op(e1, e2) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22264])).
% 2.44/2.59 tff(22266,plain,
% 2.44/2.59 ((op(e2, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[21831])).
% 2.44/2.59 tff(22267,plain,
% 2.44/2.59 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22266, 3077])).
% 2.44/2.59 tff(22268,plain,
% 2.44/2.59 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22267])).
% 2.44/2.59 tff(22269,plain,
% 2.44/2.59 (~(op(e3, e3) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[368, 22268])).
% 2.44/2.59 tff(22270,plain,
% 2.44/2.59 (~(op(e1, e2) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[22269, 22265])).
% 2.44/2.59 tff(22271,plain,
% 2.44/2.59 (op(op(e2, e3), e3) = op(e0, e3)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[21831])).
% 2.44/2.59 tff(22272,plain,
% 2.44/2.59 ((op(op(e2, e3), e3) = e2) <=> (op(e0, e3) = e2)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22271])).
% 2.44/2.59 tff(22273,plain,
% 2.44/2.59 ((op(e0, e3) = e2) <=> (op(op(e2, e3), e3) = e2)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22272])).
% 2.44/2.59 tff(22274,plain,
% 2.44/2.59 (op(op(e2, e3), e3) = e2),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[22192, 22273])).
% 2.44/2.59 tff(22275,plain,
% 2.44/2.59 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1288, 22274])).
% 2.44/2.59 tff(22276,plain,
% 2.44/2.59 (op(e2, op(e0, e2)) = op(e2, e3)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22122])).
% 2.44/2.59 tff(22277,plain,
% 2.44/2.59 (op(e2, e0) = op(e0, e2)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22205, 22127])).
% 2.44/2.59 tff(22278,plain,
% 2.44/2.59 (op(e2, op(e2, e0)) = op(e2, op(e0, e2))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22277])).
% 2.44/2.59 tff(22279,plain,
% 2.44/2.59 (op(e2, op(e2, e0)) = e0),
% 2.44/2.59 inference(transitivity,[status(thm)],[22278, 22276, 21831])).
% 2.44/2.59 tff(22280,plain,
% 2.44/2.59 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[2653, 22279])).
% 2.44/2.59 tff(22281,plain,
% 2.44/2.59 (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[3358, 22280, 22144, 21595, 21831, 22275, 22270, 22261, 22258, 21357, 22251, 22247, 22243, 80, 22239, 22236])).
% 2.44/2.59 tff(22282,plain,
% 2.44/2.59 (~(op(e2, op(e2, e1)) = e1)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1355, 22281])).
% 2.44/2.59 tff(22283,plain,
% 2.44/2.59 ($false),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[22282, 22219])).
% 2.44/2.59 tff(22284,plain,((op(e1, e0) = e3) | (op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e0, e3) = e1) | (op(e2, e1) = e0) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.59 tff(22285,plain,
% 2.44/2.59 (op(e1, e0) = e3),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[22284, 80, 76, 17, 121, 2559, 2527])).
% 2.44/2.59 tff(22286,plain,
% 2.44/2.59 ((op(e1, e0) = e0) <=> (e3 = e0)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22285])).
% 2.44/2.59 tff(22287,plain,
% 2.44/2.59 ((op(e1, e0) = e0) <=> (e0 = e3)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22286, 159])).
% 2.44/2.59 tff(22288,plain,
% 2.44/2.59 ((e0 = e3) <=> (op(e1, e0) = e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22287])).
% 2.44/2.59 tff(22289,plain,
% 2.44/2.59 ((~(e0 = e3)) <=> (~(op(e1, e0) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22288])).
% 2.44/2.59 tff(22290,plain,
% 2.44/2.59 (~(op(e1, e0) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[181, 22289])).
% 2.44/2.59 tff(22291,plain,
% 2.44/2.59 (op(e1, e2) = e0),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1830, 22290, 21797, 80])).
% 2.44/2.59 tff(22292,plain,
% 2.44/2.59 (e0 = op(e1, op(e1, e1))),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[22291, 21792])).
% 2.44/2.59 tff(22293,plain,
% 2.44/2.59 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[21667])).
% 2.44/2.59 tff(22294,plain,
% 2.44/2.59 (op(e1, op(e1, e2)) = op(e1, op(e1, op(e1, e1)))),
% 2.44/2.59 inference(symmetry,[status(thm)],[22293])).
% 2.44/2.59 tff(22295,plain,
% 2.44/2.59 (e0 = op(e1, e2)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22291])).
% 2.44/2.59 tff(22296,plain,
% 2.44/2.59 (op(e1, e0) = op(e1, op(e1, e2))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22295])).
% 2.44/2.59 tff(22297,plain,
% 2.44/2.59 (e3 = op(e1, e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22285])).
% 2.44/2.59 tff(22298,plain,
% 2.44/2.59 (e3 = op(e1, op(e1, op(e1, e1)))),
% 2.44/2.59 inference(transitivity,[status(thm)],[22297, 22296, 22294])).
% 2.44/2.59 tff(22299,plain,
% 2.44/2.59 ($false),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[2269, 22298, 22292, 21789])).
% 2.44/2.59 tff(22300,plain,((op(e1, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e0, e3) = e1) | (op(e2, e1) = e0) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.59 tff(22301,plain,
% 2.44/2.59 (op(e1, e3) = e0),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[22300, 2527, 17, 121, 2559, 76])).
% 2.44/2.59 tff(22302,plain,
% 2.44/2.59 ((op(e1, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.44/2.59 tff(22303,plain,
% 2.44/2.59 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22302, 86])).
% 2.44/2.59 tff(22304,plain,
% 2.44/2.59 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22303])).
% 2.44/2.59 tff(22305,plain,
% 2.44/2.59 (~(op(e2, e3) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[118, 22304])).
% 2.44/2.59 tff(22306,plain,
% 2.44/2.59 (op(e2, e0) = e0),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[2311, 22305, 17, 2559])).
% 2.44/2.59 tff(22307,plain,
% 2.44/2.59 ((op(e2, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22306])).
% 2.44/2.59 tff(22308,plain,
% 2.44/2.59 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22307, 8115])).
% 2.44/2.59 tff(22309,plain,
% 2.44/2.59 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22308])).
% 2.44/2.59 tff(22310,plain,
% 2.44/2.59 (~(op(e3, e0) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[747, 22309])).
% 2.44/2.59 tff(22311,plain,
% 2.44/2.59 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.44/2.59 tff(22312,plain,
% 2.44/2.59 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22311])).
% 2.44/2.59 tff(22313,plain,
% 2.44/2.59 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22312])).
% 2.44/2.59 tff(22314,plain,
% 2.44/2.59 (~(op(e1, e3) = e1)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[26, 22313])).
% 2.44/2.59 tff(22315,plain,
% 2.44/2.59 (op(e3, e3) = e1),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[151, 22314, 76, 121])).
% 2.44/2.59 tff(22316,plain,
% 2.44/2.59 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22315])).
% 2.44/2.59 tff(22317,plain,
% 2.44/2.59 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22316])).
% 2.44/2.59 tff(22318,plain,
% 2.44/2.59 (~(op(e3, e0) = e1)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[157, 22317])).
% 2.44/2.59 tff(22319,plain,
% 2.44/2.59 ((op(e1, e3) = e3) <=> (e0 = e3)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.44/2.59 tff(22320,plain,
% 2.44/2.59 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22319])).
% 2.44/2.59 tff(22321,plain,
% 2.44/2.59 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22320])).
% 2.44/2.59 tff(22322,plain,
% 2.44/2.59 (~(op(e1, e3) = e3)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[181, 22321])).
% 2.44/2.59 tff(22323,plain,
% 2.44/2.59 (~(op(e1, e2) = e3)),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[21630, 22301, 21327])).
% 2.44/2.59 tff(22324,plain,
% 2.44/2.59 (op(e1, e0) = e3),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[247, 22323, 21634, 22322])).
% 2.44/2.59 tff(22325,plain,
% 2.44/2.59 (e3 = op(e1, e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22324])).
% 2.44/2.59 tff(22326,plain,
% 2.44/2.59 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e1, e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22325])).
% 2.44/2.59 tff(22327,plain,
% 2.44/2.59 ((op(e3, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 2.44/2.59 inference(transitivity,[status(thm)],[22326, 2294])).
% 2.44/2.59 tff(22328,plain,
% 2.44/2.59 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22327])).
% 2.44/2.59 tff(22329,plain,
% 2.44/2.59 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22328])).
% 2.44/2.59 tff(22330,plain,
% 2.44/2.59 (~(op(e3, e0) = e3)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[410, 22329])).
% 2.44/2.59 tff(22331,plain,
% 2.44/2.59 (op(e3, e0) = e2),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[5422, 22330, 22318, 22310])).
% 2.44/2.59 tff(22332,plain,
% 2.44/2.59 (e2 = op(e3, e0)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22331])).
% 2.44/2.59 tff(22333,plain,
% 2.44/2.59 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e3, e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22332])).
% 2.44/2.59 tff(22334,plain,
% 2.44/2.59 ((op(e0, e3) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.44/2.59 inference(transitivity,[status(thm)],[22333, 452])).
% 2.44/2.59 tff(22335,plain,
% 2.44/2.59 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e2)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22331])).
% 2.44/2.59 tff(22336,plain,
% 2.44/2.59 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e2))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22335])).
% 2.44/2.59 tff(22337,plain,
% 2.44/2.59 (~(op(e0, e0) = e2)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[6384, 22336])).
% 2.44/2.59 tff(22338,plain,
% 2.44/2.59 ((op(e2, e0) = e1) <=> (e0 = e1)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22306])).
% 2.44/2.59 tff(22339,plain,
% 2.44/2.59 ((e0 = e1) <=> (op(e2, e0) = e1)),
% 2.44/2.59 inference(symmetry,[status(thm)],[22338])).
% 2.44/2.59 tff(22340,plain,
% 2.44/2.59 ((~(e0 = e1)) <=> (~(op(e2, e0) = e1))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22339])).
% 2.44/2.59 tff(22341,plain,
% 2.44/2.59 (~(op(e2, e0) = e1)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[26, 22340])).
% 2.44/2.59 tff(22342,plain,
% 2.44/2.59 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.44/2.59 tff(22343,plain,
% 2.44/2.59 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22342])).
% 2.44/2.59 tff(22344,plain,
% 2.44/2.59 (~(op(e1, e2) = e0)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[1850, 22343])).
% 2.44/2.59 tff(22345,plain,
% 2.44/2.59 (op(e1, e2) = e1),
% 2.44/2.59 inference(unit_resolution,[status(thm)],[1859, 22323, 21647, 22344])).
% 2.44/2.59 tff(22346,plain,
% 2.44/2.59 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22345])).
% 2.44/2.59 tff(22347,plain,
% 2.44/2.59 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.44/2.59 inference(transitivity,[status(thm)],[22346, 316])).
% 2.44/2.59 tff(22348,plain,
% 2.44/2.59 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.44/2.59 inference(monotonicity,[status(thm)],[22347])).
% 2.44/2.59 tff(22349,plain,
% 2.44/2.59 (~(op(e2, e2) = e1)),
% 2.44/2.59 inference(modus_ponens,[status(thm)],[1273, 22348])).
% 2.44/2.59 tff(22350,plain,
% 2.49/2.59 (op(e2, e1) = e1),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[345, 22349, 76, 22341])).
% 2.49/2.59 tff(22351,plain,
% 2.49/2.59 ((op(e2, e1) = e3) <=> (e1 = op(e1, e0))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22350, 22325])).
% 2.49/2.59 tff(22352,plain,
% 2.49/2.59 ((op(e2, e1) = e3) <=> (op(e1, e0) = e1)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22351, 17546])).
% 2.49/2.59 tff(22353,plain,
% 2.49/2.59 ((op(e1, e0) = e1) <=> (op(e2, e1) = e3)),
% 2.49/2.59 inference(symmetry,[status(thm)],[22352])).
% 2.49/2.59 tff(22354,plain,
% 2.49/2.59 ((~(op(e1, e0) = e1)) <=> (~(op(e2, e1) = e3))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22353])).
% 2.49/2.59 tff(22355,plain,
% 2.49/2.59 ((e1 = e3) <=> (e1 = op(e1, e0))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22325])).
% 2.49/2.59 tff(22356,plain,
% 2.49/2.59 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22355, 17546])).
% 2.49/2.59 tff(22357,plain,
% 2.49/2.59 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22356])).
% 2.49/2.59 tff(22358,plain,
% 2.49/2.59 (~(op(e1, e0) = e1)),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[303, 22357])).
% 2.49/2.59 tff(22359,plain,
% 2.49/2.59 (~(op(e2, e1) = e3)),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[22358, 22354])).
% 2.49/2.59 tff(22360,plain,
% 2.49/2.59 (op(e3, e1) = e3),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[1730, 22359, 21634, 2527])).
% 2.49/2.59 tff(22361,plain,
% 2.49/2.59 (e3 = op(e3, e1)),
% 2.49/2.59 inference(symmetry,[status(thm)],[22360])).
% 2.49/2.59 tff(22362,plain,
% 2.49/2.59 ((op(e2, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22306])).
% 2.49/2.59 tff(22363,plain,
% 2.49/2.59 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22362, 10200])).
% 2.49/2.59 tff(22364,plain,
% 2.49/2.59 ((op(e0, e2) = e0) <=> (op(e2, e0) = op(e0, e2))),
% 2.49/2.59 inference(symmetry,[status(thm)],[22363])).
% 2.49/2.59 tff(22365,plain,
% 2.49/2.59 (op(e0, e0) = e1),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[1480, 22358, 22318, 22341])).
% 2.49/2.59 tff(22366,plain,
% 2.49/2.59 ((op(e0, e0) = op(e0, e1)) <=> (e1 = op(e0, e1))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22365])).
% 2.49/2.59 tff(22367,plain,
% 2.49/2.59 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22366, 7013])).
% 2.49/2.59 tff(22368,plain,
% 2.49/2.59 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e1))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22367])).
% 2.49/2.59 tff(22369,plain,
% 2.49/2.59 (~(op(e0, e1) = e1)),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[811, 22368])).
% 2.49/2.59 tff(22370,plain,
% 2.49/2.59 (op(e0, e1) = e0),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[829, 22369, 21372, 2527])).
% 2.49/2.59 tff(22371,plain,
% 2.49/2.59 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22370])).
% 2.49/2.59 tff(22372,plain,
% 2.49/2.59 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22371, 10200])).
% 2.49/2.59 tff(22373,plain,
% 2.49/2.59 ((op(e0, e1) = op(e0, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 2.49/2.59 inference(transitivity,[status(thm)],[22372, 22364])).
% 2.49/2.59 tff(22374,plain,
% 2.49/2.59 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22373])).
% 2.49/2.59 tff(22375,plain,
% 2.49/2.59 (~(op(e2, e0) = op(e0, e2))),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[2102, 22374])).
% 2.49/2.59 tff(22376,plain,
% 2.49/2.59 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[6358, 22375])).
% 2.49/2.59 tff(22377,plain,
% 2.49/2.59 (op(e0, op(e1, e2)) = op(e0, e1)),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22345])).
% 2.49/2.59 tff(22378,plain,
% 2.49/2.59 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e1) = e0)),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22377])).
% 2.49/2.59 tff(22379,plain,
% 2.49/2.59 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.49/2.59 inference(symmetry,[status(thm)],[22378])).
% 2.49/2.59 tff(22380,plain,
% 2.49/2.59 (op(e0, op(e1, e2)) = e0),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[22370, 22379])).
% 2.49/2.59 tff(22381,plain,
% 2.49/2.59 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[6398, 22380])).
% 2.49/2.59 tff(22382,plain,
% 2.49/2.59 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e0)),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.49/2.59 tff(22383,plain,
% 2.49/2.59 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.49/2.59 inference(symmetry,[status(thm)],[22382])).
% 2.49/2.59 tff(22384,plain,
% 2.49/2.59 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22370])).
% 2.49/2.59 tff(22385,plain,
% 2.49/2.59 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22384, 5470])).
% 2.49/2.59 tff(22386,plain,
% 2.49/2.59 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 2.49/2.59 inference(transitivity,[status(thm)],[22385, 22383, 6290])).
% 2.49/2.59 tff(22387,plain,
% 2.49/2.59 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22386])).
% 2.49/2.59 tff(22388,plain,
% 2.49/2.59 (~(op(e1, e3) = op(e3, e1))),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[3046, 22387])).
% 2.49/2.59 tff(22389,plain,
% 2.49/2.59 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[6307, 22388])).
% 2.49/2.59 tff(22390,plain,
% 2.49/2.59 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22325])).
% 2.49/2.59 tff(22391,plain,
% 2.49/2.59 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.49/2.59 inference(transitivity,[status(thm)],[22390, 595])).
% 2.49/2.59 tff(22392,plain,
% 2.49/2.59 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.49/2.59 inference(transitivity,[status(thm)],[22391, 596])).
% 2.49/2.59 tff(22393,plain,
% 2.49/2.59 ((~(op(e0, e1) = e3)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22392])).
% 2.49/2.59 tff(22394,plain,
% 2.49/2.59 (~(op(e0, e1) = op(e1, e0))),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[2527, 22393])).
% 2.49/2.59 tff(22395,plain,
% 2.49/2.59 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[609, 22394])).
% 2.49/2.59 tff(22396,plain,
% 2.49/2.59 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22301])).
% 2.49/2.59 tff(22397,plain,
% 2.49/2.59 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22396, 3077])).
% 2.49/2.59 tff(22398,plain,
% 2.49/2.59 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22397])).
% 2.49/2.59 tff(22399,plain,
% 2.49/2.59 (~(op(e3, e3) = e0)),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[571, 22398])).
% 2.49/2.59 tff(22400,plain,
% 2.49/2.59 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22385])).
% 2.49/2.59 tff(22401,plain,
% 2.49/2.59 (~(op(e3, e1) = e0)),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[3046, 22400])).
% 2.49/2.59 tff(22402,plain,
% 2.49/2.59 (op(e3, e2) = e0),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[1916, 22401, 22399, 22310])).
% 2.49/2.59 tff(22403,plain,
% 2.49/2.59 ((op(e3, e2) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22402])).
% 2.49/2.59 tff(22404,plain,
% 2.49/2.59 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 2.49/2.59 inference(transitivity,[status(thm)],[22403, 86])).
% 2.49/2.59 tff(22405,plain,
% 2.49/2.59 ((op(e2, e3) = e0) <=> (op(e3, e2) = op(e2, e3))),
% 2.49/2.59 inference(symmetry,[status(thm)],[22404])).
% 2.49/2.59 tff(22406,plain,
% 2.49/2.59 ((~(op(e2, e3) = e0)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22405])).
% 2.49/2.59 tff(22407,plain,
% 2.49/2.59 (~(op(e3, e2) = op(e2, e3))),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[22305, 22406])).
% 2.49/2.59 tff(22408,plain,
% 2.49/2.59 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.49/2.59 inference(unit_resolution,[status(thm)],[500, 22407])).
% 2.49/2.59 tff(22409,plain,
% 2.49/2.59 (op(e0, op(e2, e1)) = op(e0, e1)),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22350])).
% 2.49/2.59 tff(22410,plain,
% 2.49/2.59 ((op(e0, op(e2, e1)) = e0) <=> (op(e0, e1) = e0)),
% 2.49/2.59 inference(monotonicity,[status(thm)],[22409])).
% 2.49/2.59 tff(22411,plain,
% 2.49/2.59 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e1)) = e0)),
% 2.49/2.59 inference(symmetry,[status(thm)],[22410])).
% 2.49/2.59 tff(22412,plain,
% 2.49/2.59 (op(e0, op(e2, e1)) = e0),
% 2.49/2.59 inference(modus_ponens,[status(thm)],[22370, 22411])).
% 2.49/2.59 tff(22413,plain,
% 2.49/2.59 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[13223, 22412])).
% 2.49/2.60 tff(22414,plain,
% 2.49/2.60 ((~(op(e0, e1) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22391])).
% 2.49/2.60 tff(22415,plain,
% 2.49/2.60 (~(op(e1, e0) = op(e0, e1))),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[2527, 22414])).
% 2.49/2.60 tff(22416,plain,
% 2.49/2.60 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[613, 22415])).
% 2.49/2.60 tff(22417,plain,
% 2.49/2.60 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22385, 22383])).
% 2.49/2.60 tff(22418,plain,
% 2.49/2.60 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22417])).
% 2.49/2.60 tff(22419,plain,
% 2.49/2.60 (~(op(e3, e1) = op(e1, e3))),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[3046, 22418])).
% 2.49/2.60 tff(22420,plain,
% 2.49/2.60 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[6362, 22419])).
% 2.49/2.60 tff(22421,plain,
% 2.49/2.60 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22365])).
% 2.49/2.60 tff(22422,plain,
% 2.49/2.60 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e1) = e0)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22421])).
% 2.49/2.60 tff(22423,plain,
% 2.49/2.60 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22422])).
% 2.49/2.60 tff(22424,plain,
% 2.49/2.60 (op(e0, op(e0, e0)) = e0),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22370, 22423])).
% 2.49/2.60 tff(22425,plain,
% 2.49/2.60 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[5598, 22424])).
% 2.49/2.60 tff(22426,plain,
% 2.49/2.60 (op(e1, op(e1, e1)) = e1),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22345, 21669])).
% 2.49/2.60 tff(22427,plain,
% 2.49/2.60 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[5678, 22426])).
% 2.49/2.60 tff(22428,plain,
% 2.49/2.60 (op(e1, op(e3, e0)) = op(e1, e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22331])).
% 2.49/2.60 tff(22429,plain,
% 2.49/2.60 (op(e1, op(e3, e0)) = e1),
% 2.49/2.60 inference(transitivity,[status(thm)],[22428, 22345])).
% 2.49/2.60 tff(22430,plain,
% 2.49/2.60 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[8474, 22429])).
% 2.49/2.60 tff(22431,plain,
% 2.49/2.60 (op(e0, op(e3, e3)) = op(e0, e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22315])).
% 2.49/2.60 tff(22432,plain,
% 2.49/2.60 ((op(e0, op(e3, e3)) = e0) <=> (op(e0, e1) = e0)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22431])).
% 2.49/2.60 tff(22433,plain,
% 2.49/2.60 ((op(e0, e1) = e0) <=> (op(e0, op(e3, e3)) = e0)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22432])).
% 2.49/2.60 tff(22434,plain,
% 2.49/2.60 (op(e0, op(e3, e3)) = e0),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22370, 22433])).
% 2.49/2.60 tff(22435,plain,
% 2.49/2.60 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[392, 22434])).
% 2.49/2.60 tff(22436,plain,
% 2.49/2.60 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = op(e2, e0))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22372, 22364, 6337])).
% 2.49/2.60 tff(22437,plain,
% 2.49/2.60 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22436])).
% 2.49/2.60 tff(22438,plain,
% 2.49/2.60 (~(op(e0, e2) = op(e2, e0))),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[2102, 22437])).
% 2.49/2.60 tff(22439,plain,
% 2.49/2.60 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[6347, 22438])).
% 2.49/2.60 tff(22440,plain,
% 2.49/2.60 ((op(e2, e3) = e0) <=> (op(e2, e3) = op(e3, e2))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22405, 395])).
% 2.49/2.60 tff(22441,plain,
% 2.49/2.60 ((~(op(e2, e3) = e0)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22440])).
% 2.49/2.60 tff(22442,plain,
% 2.49/2.60 (~(op(e2, e3) = op(e3, e2))),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22305, 22441])).
% 2.49/2.60 tff(22443,plain,
% 2.49/2.60 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[430, 22442])).
% 2.49/2.60 tff(22444,plain,
% 2.49/2.60 (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[5367, 22443, 22439, 22435, 22430, 22427, 22425, 22420, 22416, 22413, 22408, 22395, 22389, 22381, 22376])).
% 2.49/2.60 tff(22445,plain,
% 2.49/2.60 (~(op(e2, op(e2, e2)) = e2)),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[528, 22444])).
% 2.49/2.60 tff(22446,plain,
% 2.49/2.60 (e3 = op(e3, e1)),
% 2.49/2.60 inference(symmetry,[status(thm)],[5607])).
% 2.49/2.60 tff(22447,plain,
% 2.49/2.60 (op(e0, e3) = e3),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[1495, 4412, 2527, 11542])).
% 2.49/2.60 tff(22448,plain,
% 2.49/2.60 (op(e0, e3) = op(e3, e1)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22447, 22446])).
% 2.49/2.60 tff(22449,plain,
% 2.49/2.60 ((op(e0, e3) = e2) <=> (op(e3, e1) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22448])).
% 2.49/2.60 tff(22450,plain,
% 2.49/2.60 ((op(e3, e1) = e2) <=> (op(e0, e3) = e2)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22449])).
% 2.49/2.60 tff(22451,plain,
% 2.49/2.60 ((~(op(e3, e1) = e2)) <=> (~(op(e0, e3) = e2))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22450])).
% 2.49/2.60 tff(22452,plain,
% 2.49/2.60 (~(op(e0, e3) = e2)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[82, 22451])).
% 2.49/2.60 tff(22453,plain,
% 2.49/2.60 (op(e2, e3) = op(e2, op(e1, e0))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[259])).
% 2.49/2.60 tff(22454,plain,
% 2.49/2.60 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22453])).
% 2.49/2.60 tff(22455,plain,
% 2.49/2.60 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, e3) = e2)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22454])).
% 2.49/2.60 tff(22456,plain,
% 2.49/2.60 (op(e3, e1) = op(e1, e0)),
% 2.49/2.60 inference(transitivity,[status(thm)],[5607, 259])).
% 2.49/2.60 tff(22457,plain,
% 2.49/2.60 (op(e2, op(e3, e1)) = op(e2, op(e1, e0))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22456])).
% 2.49/2.60 tff(22458,plain,
% 2.49/2.60 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22446])).
% 2.49/2.60 tff(22459,plain,
% 2.49/2.60 ((op(e3, e2) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22458, 4845])).
% 2.49/2.60 tff(22460,plain,
% 2.49/2.60 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22459])).
% 2.49/2.60 tff(22461,plain,
% 2.49/2.60 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22460])).
% 2.49/2.60 tff(22462,plain,
% 2.49/2.60 (~(op(e3, e2) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[3429, 22461])).
% 2.49/2.60 tff(22463,plain,
% 2.49/2.60 (op(e2, e2) = e3),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[2111, 4412, 75, 22462])).
% 2.49/2.60 tff(22464,plain,
% 2.49/2.60 (op(e2, e2) = op(e3, e1)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22463, 22446])).
% 2.49/2.60 tff(22465,plain,
% 2.49/2.60 (op(e2, op(e2, e2)) = op(e2, op(e3, e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22464])).
% 2.49/2.60 tff(22466,plain,
% 2.49/2.60 (op(e2, op(e2, e2)) = op(e2, op(e1, e0))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22465, 22457])).
% 2.49/2.60 tff(22467,plain,
% 2.49/2.60 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22466])).
% 2.49/2.60 tff(22468,plain,
% 2.49/2.60 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, e3) = e2)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22467, 22455])).
% 2.49/2.60 tff(22469,plain,
% 2.49/2.60 ((~(op(e2, op(e2, e2)) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22468])).
% 2.49/2.60 tff(22470,assumption,(~(op(e2, op(e2, e2)) = e2)), introduced(assumption)).
% 2.49/2.60 tff(22471,plain,
% 2.49/2.60 (~(op(e2, e3) = e2)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22470, 22469])).
% 2.49/2.60 tff(22472,plain,
% 2.49/2.60 ($false),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[15003, 22471, 22452, 72])).
% 2.49/2.60 tff(22473,plain,((op(e0, e2) = e3) | (op(e1, e3) = e2) | (op(e2, op(e2, e2)) = e2) | (~(op(e1, e0) = e3)) | (~(op(e3, e1) = e3)) | (op(e3, e1) = e2) | (op(e1, e2) = e3) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.60 tff(22474,plain,
% 2.49/2.60 (op(e0, e2) = e3),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[22473, 22445, 21331, 22324, 22360, 21540, 22323, 2527])).
% 2.49/2.60 tff(22475,plain,
% 2.49/2.60 (op(e0, e2) = op(e3, e1)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22474, 22361])).
% 2.49/2.60 tff(22476,plain,
% 2.49/2.60 ((op(e0, e2) = e2) <=> (op(e3, e1) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22475])).
% 2.49/2.60 tff(22477,plain,
% 2.49/2.60 ((op(e3, e1) = e2) <=> (op(e0, e2) = e2)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22476])).
% 2.49/2.60 tff(22478,plain,
% 2.49/2.60 ((~(op(e3, e1) = e2)) <=> (~(op(e0, e2) = e2))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22477])).
% 2.49/2.60 tff(22479,plain,
% 2.49/2.60 (~(op(e0, e2) = e2)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[21540, 22478])).
% 2.49/2.60 tff(22480,plain,
% 2.49/2.60 (op(e0, e3) = e2),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[3652, 22479, 22337, 21372])).
% 2.49/2.60 tff(22481,plain,
% 2.49/2.60 (op(e3, e0) = op(e0, e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[22480, 22334])).
% 2.49/2.60 tff(22482,plain,
% 2.49/2.60 ((op(e0, e2) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22474])).
% 2.49/2.60 tff(22483,plain,
% 2.49/2.60 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22482, 1364])).
% 2.49/2.60 tff(22484,plain,
% 2.49/2.60 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22483])).
% 2.49/2.60 tff(22485,plain,
% 2.49/2.60 (~(op(e0, e3) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[918, 22484])).
% 2.49/2.60 tff(22486,plain,
% 2.49/2.60 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22361])).
% 2.49/2.60 tff(22487,plain,
% 2.49/2.60 ((op(e3, e2) = e3) <=> (op(e3, e1) = op(e3, e2))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22486, 4845])).
% 2.49/2.60 tff(22488,plain,
% 2.49/2.60 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22487])).
% 2.49/2.60 tff(22489,plain,
% 2.49/2.60 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22488])).
% 2.49/2.60 tff(22490,plain,
% 2.49/2.60 (~(op(e3, e2) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[3429, 22489])).
% 2.49/2.60 tff(22491,plain,
% 2.49/2.60 (op(e1, op(e1, e2)) = op(e1, e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22345])).
% 2.49/2.60 tff(22492,plain,
% 2.49/2.60 (op(e1, op(e1, e2)) = e2),
% 2.49/2.60 inference(transitivity,[status(thm)],[22491, 21327])).
% 2.49/2.60 tff(22493,plain,
% 2.49/2.60 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[2377, 22492])).
% 2.49/2.60 tff(22494,plain,
% 2.49/2.60 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22301])).
% 2.49/2.60 tff(22495,plain,
% 2.49/2.60 ((op(op(e1, e3), e1) = e3) <=> (op(e0, e1) = e3)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22494])).
% 2.49/2.60 tff(22496,plain,
% 2.49/2.60 ((op(e0, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22495])).
% 2.49/2.60 tff(22497,plain,
% 2.49/2.60 ((~(op(e0, e1) = e3)) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22496])).
% 2.49/2.60 tff(22498,plain,
% 2.49/2.60 (~(op(op(e1, e3), e1) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[2527, 22497])).
% 2.49/2.60 tff(22499,plain,
% 2.49/2.60 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[160, 22498])).
% 2.49/2.60 tff(22500,plain,
% 2.49/2.60 (op(e2, op(e2, e1)) = op(e2, e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22350])).
% 2.49/2.60 tff(22501,plain,
% 2.49/2.60 (op(e2, op(e2, e1)) = e1),
% 2.49/2.60 inference(transitivity,[status(thm)],[22500, 22350])).
% 2.49/2.60 tff(22502,plain,
% 2.49/2.60 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[1355, 22501])).
% 2.49/2.60 tff(22503,plain,
% 2.49/2.60 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22315])).
% 2.49/2.60 tff(22504,plain,
% 2.49/2.60 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22503])).
% 2.49/2.60 tff(22505,plain,
% 2.49/2.60 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22504])).
% 2.49/2.60 tff(22506,plain,
% 2.49/2.60 (~(op(e3, e3) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[303, 22505])).
% 2.49/2.60 tff(22507,plain,
% 2.49/2.60 (~(op(e3, e0) = op(e0, e3))),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[2656, 22480, 22301, 22506, 22502, 22499, 22493, 2559, 22323, 22490, 22399, 22485])).
% 2.49/2.60 tff(22508,plain,
% 2.49/2.60 ($false),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[22507, 22481])).
% 2.49/2.60 tff(22509,plain,((op(e0, e1) = e3) | (op(e2, e1) = e0) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.60 tff(22510,plain,
% 2.49/2.60 (op(e0, e1) = e3),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[22509, 2559, 76, 17, 121])).
% 2.49/2.60 tff(22511,plain,
% 2.49/2.60 ((op(e0, e1) = e1) <=> (e3 = e1)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.60 tff(22512,plain,
% 2.49/2.60 ((op(e0, e1) = e1) <=> (e1 = e3)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22511, 128])).
% 2.49/2.60 tff(22513,plain,
% 2.49/2.60 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22512])).
% 2.49/2.60 tff(22514,plain,
% 2.49/2.60 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22513])).
% 2.49/2.60 tff(22515,plain,
% 2.49/2.60 (~(op(e0, e1) = e1)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[303, 22514])).
% 2.49/2.60 tff(22516,plain,
% 2.49/2.60 ((op(e0, e1) = e0) <=> (e3 = e0)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.60 tff(22517,plain,
% 2.49/2.60 ((op(e0, e1) = e0) <=> (e0 = e3)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22516, 159])).
% 2.49/2.60 tff(22518,plain,
% 2.49/2.60 ((e0 = e3) <=> (op(e0, e1) = e0)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22517])).
% 2.49/2.60 tff(22519,plain,
% 2.49/2.60 ((~(e0 = e3)) <=> (~(op(e0, e1) = e0))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22518])).
% 2.49/2.60 tff(22520,plain,
% 2.49/2.60 (~(op(e0, e1) = e0)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[181, 22519])).
% 2.49/2.60 tff(22521,plain,
% 2.49/2.60 (op(e3, e1) = e0),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[292, 22520, 2559, 21357])).
% 2.49/2.60 tff(22522,plain,
% 2.49/2.60 (e0 = op(e3, e1)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22521])).
% 2.49/2.60 tff(22523,plain,
% 2.49/2.60 ((op(e3, e2) = e0) <=> (op(e3, e2) = op(e3, e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22522])).
% 2.49/2.60 tff(22524,plain,
% 2.49/2.60 ((op(e3, e2) = e0) <=> (op(e3, e1) = op(e3, e2))),
% 2.49/2.60 inference(transitivity,[status(thm)],[22523, 4845])).
% 2.49/2.60 tff(22525,plain,
% 2.49/2.60 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22524])).
% 2.49/2.60 tff(22526,plain,
% 2.49/2.60 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22525])).
% 2.49/2.60 tff(22527,plain,
% 2.49/2.60 (~(op(e3, e2) = e0)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[3429, 22526])).
% 2.49/2.60 tff(22528,plain,
% 2.49/2.60 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e3)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.60 tff(22529,plain,
% 2.49/2.60 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22528])).
% 2.49/2.60 tff(22530,plain,
% 2.49/2.60 (~(op(e0, e0) = e3)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[811, 22529])).
% 2.49/2.60 tff(22531,plain,
% 2.49/2.60 (op(e2, e3) = e0),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[21830, 80, 76, 121, 2168, 17, 2559])).
% 2.49/2.60 tff(22532,plain,
% 2.49/2.60 (op(e2, e3) = op(e3, e1)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22531, 22522])).
% 2.49/2.60 tff(22533,plain,
% 2.49/2.60 ((op(e2, e3) = e2) <=> (op(e3, e1) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22532])).
% 2.49/2.60 tff(22534,plain,
% 2.49/2.60 ((op(e3, e1) = e2) <=> (op(e2, e3) = e2)),
% 2.49/2.60 inference(symmetry,[status(thm)],[22533])).
% 2.49/2.60 tff(22535,plain,
% 2.49/2.60 ((~(op(e3, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22534])).
% 2.49/2.60 tff(22536,plain,
% 2.49/2.60 (~(op(e2, e3) = e2)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[21540, 22535])).
% 2.49/2.60 tff(22537,plain,
% 2.49/2.60 (op(e0, e3) = e2),
% 2.49/2.60 inference(unit_resolution,[status(thm)],[15003, 22536, 21331])).
% 2.49/2.60 tff(22538,plain,
% 2.49/2.60 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22537])).
% 2.49/2.60 tff(22539,plain,
% 2.49/2.60 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22538])).
% 2.49/2.60 tff(22540,plain,
% 2.49/2.60 (~(op(e0, e0) = e2)),
% 2.49/2.60 inference(modus_ponens,[status(thm)],[3414, 22539])).
% 2.49/2.60 tff(22541,plain,
% 2.49/2.60 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.60 tff(22542,plain,
% 2.49/2.60 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.49/2.60 inference(transitivity,[status(thm)],[22541, 1262])).
% 2.49/2.60 tff(22543,plain,
% 2.49/2.60 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.49/2.60 inference(monotonicity,[status(thm)],[22542])).
% 2.49/2.61 tff(22544,plain,
% 2.49/2.61 (~(op(e2, e1) = e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[606, 22543])).
% 2.49/2.61 tff(22545,plain,
% 2.49/2.61 (op(e2, e1) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[2367, 22544, 22153, 2559])).
% 2.49/2.61 tff(22546,plain,
% 2.49/2.61 ((op(e2, e1) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22545])).
% 2.49/2.61 tff(22547,plain,
% 2.49/2.61 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22546, 316])).
% 2.49/2.61 tff(22548,plain,
% 2.49/2.61 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22547])).
% 2.49/2.61 tff(22549,plain,
% 2.49/2.61 (~(op(e2, e2) = e1)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[508, 22548])).
% 2.49/2.61 tff(22550,plain,
% 2.49/2.61 (op(e2, op(e2, e1)) = op(e2, e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22545])).
% 2.49/2.61 tff(22551,plain,
% 2.49/2.61 (op(e2, op(e2, e1)) = e1),
% 2.49/2.61 inference(transitivity,[status(thm)],[22550, 22545])).
% 2.49/2.61 tff(22552,plain,
% 2.49/2.61 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1355, 22551])).
% 2.49/2.61 tff(22553,plain,
% 2.49/2.61 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22537])).
% 2.49/2.61 tff(22554,plain,
% 2.49/2.61 (op(op(e0, e3), e3) = e0),
% 2.49/2.61 inference(transitivity,[status(thm)],[22553, 22531])).
% 2.49/2.61 tff(22555,plain,
% 2.49/2.61 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1361, 22554])).
% 2.49/2.61 tff(22556,plain,
% 2.49/2.61 (op(op(e2, e3), e2) = op(e0, e2)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22531])).
% 2.49/2.61 tff(22557,plain,
% 2.49/2.61 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e2) = e3)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22556])).
% 2.49/2.61 tff(22558,plain,
% 2.49/2.61 ((op(e0, e2) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22557])).
% 2.49/2.61 tff(22559,plain,
% 2.49/2.61 ((~(op(e0, e2) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22558])).
% 2.49/2.61 tff(22560,plain,
% 2.49/2.61 ((op(e0, e1) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.61 tff(22561,plain,
% 2.49/2.61 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22560, 4221])).
% 2.49/2.61 tff(22562,plain,
% 2.49/2.61 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22561])).
% 2.49/2.61 tff(22563,plain,
% 2.49/2.61 (~(op(e0, e2) = e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[2102, 22562])).
% 2.49/2.61 tff(22564,plain,
% 2.49/2.61 (~(op(op(e2, e3), e2) = e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[22563, 22559])).
% 2.49/2.61 tff(22565,plain,
% 2.49/2.61 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1934, 22564])).
% 2.49/2.61 tff(22566,plain,
% 2.49/2.61 (op(op(e3, e1), e1) = op(e0, e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[4731])).
% 2.49/2.61 tff(22567,plain,
% 2.49/2.61 (op(e1, e3) = e3),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[247, 75, 21634, 2168])).
% 2.49/2.61 tff(22568,plain,
% 2.49/2.61 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22567])).
% 2.49/2.61 tff(22569,plain,
% 2.49/2.61 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22568, 128])).
% 2.49/2.61 tff(22570,plain,
% 2.49/2.61 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22569])).
% 2.49/2.61 tff(22571,plain,
% 2.49/2.61 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22570])).
% 2.49/2.61 tff(22572,plain,
% 2.49/2.61 (~(op(e1, e3) = e1)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[303, 22571])).
% 2.49/2.61 tff(22573,plain,
% 2.49/2.61 (op(e3, e3) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[151, 22572, 76, 121])).
% 2.49/2.61 tff(22574,plain,
% 2.49/2.61 (op(e0, op(e3, e3)) = op(op(e3, e1), e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[4734, 22573])).
% 2.49/2.61 tff(22575,plain,
% 2.49/2.61 (e1 = op(e3, e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22573])).
% 2.49/2.61 tff(22576,plain,
% 2.49/2.61 (op(op(e3, e1), e1) = e3),
% 2.49/2.61 inference(transitivity,[status(thm)],[22566, 4839])).
% 2.49/2.61 tff(22577,plain,
% 2.49/2.61 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[2416, 22576])).
% 2.49/2.61 tff(22578,plain,
% 2.49/2.61 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22573])).
% 2.49/2.61 tff(22579,plain,
% 2.49/2.61 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22578])).
% 2.49/2.61 tff(22580,plain,
% 2.49/2.61 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22579, 4810])).
% 2.49/2.61 tff(22581,plain,
% 2.49/2.61 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22580])).
% 2.49/2.61 tff(22582,plain,
% 2.49/2.61 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22581, 5377])).
% 2.49/2.61 tff(22583,plain,
% 2.49/2.61 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22582])).
% 2.49/2.61 tff(22584,plain,
% 2.49/2.61 (e1 = op(e3, e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[22573, 658])).
% 2.49/2.61 tff(22585,plain,
% 2.49/2.61 (op(e3, e1) = op(e3, op(e3, e3))),
% 2.49/2.61 inference(symmetry,[status(thm)],[22578])).
% 2.49/2.61 tff(22586,plain,
% 2.49/2.61 (e0 = op(e3, op(e3, e3))),
% 2.49/2.61 inference(transitivity,[status(thm)],[4734, 22585])).
% 2.49/2.61 tff(22587,plain,
% 2.49/2.61 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[5397, 22586, 22584])).
% 2.49/2.61 tff(22588,plain,
% 2.49/2.61 (~(op(e3, e0) = e2)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[22587, 22583])).
% 2.49/2.61 tff(22589,plain,
% 2.49/2.61 (op(e3, e2) = e2),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[15971, 22588, 21540])).
% 2.49/2.61 tff(22590,plain,
% 2.49/2.61 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22589])).
% 2.49/2.61 tff(22591,plain,
% 2.49/2.61 (op(e3, op(e3, e2)) = e2),
% 2.49/2.61 inference(transitivity,[status(thm)],[22590, 22589])).
% 2.49/2.61 tff(22592,plain,
% 2.49/2.61 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1904, 22591])).
% 2.49/2.61 tff(22593,plain,
% 2.49/2.61 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[4734])).
% 2.49/2.61 tff(22594,plain,
% 2.49/2.61 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e0)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22593])).
% 2.49/2.61 tff(22595,plain,
% 2.49/2.61 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e0))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22594])).
% 2.49/2.61 tff(22596,plain,
% 2.49/2.61 (~(op(e3, e0) = e0)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[580, 22595])).
% 2.49/2.61 tff(22597,plain,
% 2.49/2.61 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22575])).
% 2.49/2.61 tff(22598,plain,
% 2.49/2.61 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22597])).
% 2.49/2.61 tff(22599,plain,
% 2.49/2.61 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22598])).
% 2.49/2.61 tff(22600,plain,
% 2.49/2.61 (~(op(e3, e0) = e1)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[157, 22599])).
% 2.49/2.61 tff(22601,plain,
% 2.49/2.61 (op(e3, e0) = e3),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[5422, 22588, 22600, 22596])).
% 2.49/2.61 tff(22602,plain,
% 2.49/2.61 (op(op(e3, e0), e0) = op(e3, op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22601, 4734])).
% 2.49/2.61 tff(22603,plain,
% 2.49/2.61 (op(op(e3, e0), e0) = e3),
% 2.49/2.61 inference(transitivity,[status(thm)],[22602, 4810, 22601])).
% 2.49/2.61 tff(22604,plain,
% 2.49/2.61 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[4026, 22603])).
% 2.49/2.61 tff(22605,plain,
% 2.49/2.61 ((op(op(e0, e1), e1) = e0) <=> (op(e3, e1) = e0)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[7157])).
% 2.49/2.61 tff(22606,plain,
% 2.49/2.61 ((op(e3, e1) = e0) <=> (op(op(e0, e1), e1) = e0)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22605])).
% 2.49/2.61 tff(22607,plain,
% 2.49/2.61 (op(op(e0, e1), e1) = e0),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[4731, 22606])).
% 2.49/2.61 tff(22608,plain,
% 2.49/2.61 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[2650, 22607])).
% 2.49/2.61 tff(22609,plain,
% 2.49/2.61 (op(e2, e0) = e2),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[589, 22588, 21340, 12721])).
% 2.49/2.61 tff(22610,plain,
% 2.49/2.61 (op(e2, op(e3, e1)) = op(e2, e0)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[4731])).
% 2.49/2.61 tff(22611,plain,
% 2.49/2.61 (op(op(e2, e0), e0) = op(e2, op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22609, 4734])).
% 2.49/2.61 tff(22612,plain,
% 2.49/2.61 (op(op(e2, e0), e0) = e2),
% 2.49/2.61 inference(transitivity,[status(thm)],[22611, 22610, 22609])).
% 2.49/2.61 tff(22613,plain,
% 2.49/2.61 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1945, 22612])).
% 2.49/2.61 tff(22614,plain,
% 2.49/2.61 (op(e0, e2) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[973, 1947, 17, 4850])).
% 2.49/2.61 tff(22615,plain,
% 2.49/2.61 (op(op(e0, e2), e2) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[4944, 22614, 21327])).
% 2.49/2.61 tff(22616,plain,
% 2.49/2.61 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1956, 22615])).
% 2.49/2.61 tff(22617,plain,
% 2.49/2.61 (op(e1, e0) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1830, 1947, 21357, 80])).
% 2.49/2.61 tff(22618,plain,
% 2.49/2.61 (op(e1, e0) = op(e3, e1)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22617, 4734])).
% 2.49/2.61 tff(22619,plain,
% 2.49/2.61 (op(e1, op(e1, e0)) = op(e1, op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22618])).
% 2.49/2.61 tff(22620,plain,
% 2.49/2.61 (op(e1, op(e1, e0)) = e0),
% 2.49/2.61 inference(transitivity,[status(thm)],[22619, 11366, 22617])).
% 2.49/2.61 tff(22621,plain,
% 2.49/2.61 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1836, 22620])).
% 2.49/2.61 tff(22622,plain,
% 2.49/2.61 (op(e1, e2) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1859, 1947, 21647, 75])).
% 2.49/2.61 tff(22623,plain,
% 2.49/2.61 (op(e1, op(e1, e2)) = op(e1, e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22622])).
% 2.49/2.61 tff(22624,plain,
% 2.49/2.61 (op(e1, op(e1, e2)) = e2),
% 2.49/2.61 inference(transitivity,[status(thm)],[22623, 21327])).
% 2.49/2.61 tff(22625,plain,
% 2.49/2.61 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[2377, 22624])).
% 2.49/2.61 tff(22626,plain,
% 2.49/2.61 ($false),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1459, 22625, 22621, 1347, 4549, 3342, 21595, 2421, 1926, 3341, 1275, 22616, 1936])).
% 2.49/2.61 tff(22627,plain,((op(e1, e2) = e0) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e3, e1) = e0)) | (op(e1, e2) = e3) | (op(e2, e2) = e0) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.61 tff(22628,plain,
% 2.49/2.61 (op(e1, e2) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[22627, 22613, 22608, 3342, 1347, 22604, 22592, 22577, 1936, 4731, 75, 17, 80])).
% 2.49/2.61 tff(22629,plain,
% 2.49/2.61 (op(op(e1, e2), e1) = op(e0, op(e3, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22628, 22575])).
% 2.49/2.61 tff(22630,plain,
% 2.49/2.61 (op(op(e1, e2), e1) = e3),
% 2.49/2.61 inference(transitivity,[status(thm)],[22629, 22574, 22566, 4839])).
% 2.49/2.61 tff(22631,plain,
% 2.49/2.61 ((op(op(e1, e2), e1) = e2) <=> (e3 = e2)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22630])).
% 2.49/2.61 tff(22632,plain,
% 2.49/2.61 ((op(op(e1, e2), e1) = e2) <=> (e2 = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22631, 1314])).
% 2.49/2.61 tff(22633,plain,
% 2.49/2.61 ((e2 = e3) <=> (op(op(e1, e2), e1) = e2)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22632])).
% 2.49/2.61 tff(22634,plain,
% 2.49/2.61 ((~(e2 = e3)) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22633])).
% 2.49/2.61 tff(22635,plain,
% 2.49/2.61 (~(op(op(e1, e2), e1) = e2)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[1321, 22634])).
% 2.49/2.61 tff(22636,plain,
% 2.49/2.61 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[5959, 22635])).
% 2.49/2.61 tff(22637,plain,
% 2.49/2.61 (op(e1, e2) = op(e3, e1)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22628, 4734])).
% 2.49/2.61 tff(22638,plain,
% 2.49/2.61 ((op(e1, e2) = e1) <=> (op(e3, e1) = op(e3, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22637, 22575])).
% 2.49/2.61 tff(22639,plain,
% 2.49/2.61 ((op(e3, e1) = op(e3, e3)) <=> (op(e1, e2) = e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22638])).
% 2.49/2.61 tff(22640,plain,
% 2.49/2.61 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e1, e2) = e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22639])).
% 2.49/2.61 tff(22641,plain,
% 2.49/2.61 (~(op(e1, e2) = e1)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[437, 22640])).
% 2.49/2.61 tff(22642,plain,
% 2.49/2.61 (op(e1, e0) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[954, 22641, 21692, 22572])).
% 2.49/2.61 tff(22643,plain,
% 2.49/2.61 (op(op(e1, e0), e0) = op(e1, op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22642, 4734])).
% 2.49/2.61 tff(22644,plain,
% 2.49/2.61 (op(op(e1, e0), e0) = e1),
% 2.49/2.61 inference(transitivity,[status(thm)],[22643, 11366, 22642])).
% 2.49/2.61 tff(22645,plain,
% 2.49/2.61 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[3015, 22644])).
% 2.49/2.61 tff(22646,plain,
% 2.49/2.61 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22575])).
% 2.49/2.61 tff(22647,plain,
% 2.49/2.61 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22646])).
% 2.49/2.61 tff(22648,plain,
% 2.49/2.61 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22647])).
% 2.49/2.61 tff(22649,plain,
% 2.49/2.61 (~(op(e3, e2) = e1)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[1888, 22648])).
% 2.49/2.61 tff(22650,plain,
% 2.49/2.61 (op(e0, e2) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1613, 22641, 1348, 22649])).
% 2.49/2.61 tff(22651,plain,
% 2.49/2.61 (op(op(e0, e2), e2) = op(e1, e2)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22650])).
% 2.49/2.61 tff(22652,plain,
% 2.49/2.61 (op(op(e0, e2), e2) = e0),
% 2.49/2.61 inference(transitivity,[status(thm)],[22651, 22628])).
% 2.49/2.61 tff(22653,plain,
% 2.49/2.61 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1956, 22652])).
% 2.49/2.61 tff(22654,plain,
% 2.49/2.61 ($false),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1459, 22653, 22645, 1347, 22608, 3342, 21595, 22613, 22604, 22592, 22577, 22636, 1936])).
% 2.49/2.61 tff(22655,plain,((op(e1, e2) = e3) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~(op(e3, e1) = e0)) | (op(e2, e2) = e1) | (~(op(e0, e1) = e3)) | (op(e2, e2) = e0) | (op(e1, e3) = e0) | (op(e0, e0) = e2) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.61 tff(22656,plain,
% 2.49/2.61 (op(e1, e2) = e3),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[22655, 22565, 22555, 22552, 22521, 22549, 22510, 17, 80, 22540, 76, 121, 2168])).
% 2.49/2.61 tff(22657,plain,
% 2.49/2.61 ((op(e1, e2) = e0) <=> (e3 = op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22656, 22522])).
% 2.49/2.61 tff(22658,plain,
% 2.49/2.61 ((op(e1, e2) = e0) <=> (op(e3, e1) = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22657, 396])).
% 2.49/2.61 tff(22659,plain,
% 2.49/2.61 ((op(e3, e1) = e3) <=> (op(e1, e2) = e0)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22658])).
% 2.49/2.61 tff(22660,plain,
% 2.49/2.61 ((~(op(e3, e1) = e3)) <=> (~(op(e1, e2) = e0))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22659])).
% 2.49/2.61 tff(22661,plain,
% 2.49/2.61 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.61 tff(22662,plain,
% 2.49/2.61 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22661, 396])).
% 2.49/2.61 tff(22663,plain,
% 2.49/2.61 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22662])).
% 2.49/2.61 tff(22664,plain,
% 2.49/2.61 (~(op(e3, e1) = e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[3046, 22663])).
% 2.49/2.61 tff(22665,plain,
% 2.49/2.61 (~(op(e1, e2) = e0)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[22664, 22660])).
% 2.49/2.61 tff(22666,plain,
% 2.49/2.61 (op(e1, e0) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[1830, 22665, 21357, 80])).
% 2.49/2.61 tff(22667,plain,
% 2.49/2.61 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22666])).
% 2.49/2.61 tff(22668,plain,
% 2.49/2.61 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22667])).
% 2.49/2.61 tff(22669,plain,
% 2.49/2.61 (~(op(e0, e0) = e0)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[2471, 22668])).
% 2.49/2.61 tff(22670,plain,
% 2.49/2.61 (op(e0, e0) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[3612, 22669, 22540, 22530])).
% 2.49/2.61 tff(22671,plain,
% 2.49/2.61 (e1 = op(e0, e0)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[22670, 74])).
% 2.49/2.61 tff(22672,plain,
% 2.49/2.61 ((op(e1, e2) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22656])).
% 2.49/2.61 tff(22673,plain,
% 2.49/2.61 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22672, 3230])).
% 2.49/2.61 tff(22674,plain,
% 2.49/2.61 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22673])).
% 2.49/2.61 tff(22675,plain,
% 2.49/2.61 (~(op(e1, e3) = e3)),
% 2.49/2.61 inference(modus_ponens,[status(thm)],[1850, 22674])).
% 2.49/2.61 tff(22676,plain,
% 2.49/2.61 (op(e1, e3) = e1),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[104, 22675, 21331, 80])).
% 2.49/2.61 tff(22677,plain,
% 2.49/2.61 (e1 = op(e1, e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22676])).
% 2.49/2.61 tff(22678,plain,
% 2.49/2.61 (op(e0, e0) = op(e1, e3)),
% 2.49/2.61 inference(transitivity,[status(thm)],[22670, 22677])).
% 2.49/2.61 tff(22679,plain,
% 2.49/2.61 (op(e0, op(e0, e0)) = op(e0, op(e1, e3))),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22678])).
% 2.49/2.61 tff(22680,plain,
% 2.49/2.61 (op(e0, op(e1, e3)) = op(e0, op(e0, e0))),
% 2.49/2.61 inference(symmetry,[status(thm)],[22679])).
% 2.49/2.61 tff(22681,plain,
% 2.49/2.61 (op(e0, op(e1, e3)) = op(op(e3, e1), e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22522, 22676])).
% 2.49/2.61 tff(22682,plain,
% 2.49/2.61 (op(op(e3, e1), e1) = op(e0, op(e1, e3))),
% 2.49/2.61 inference(symmetry,[status(thm)],[22681])).
% 2.49/2.61 tff(22683,plain,
% 2.49/2.61 (op(op(e3, e1), e1) = op(e0, e1)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22521])).
% 2.49/2.61 tff(22684,plain,
% 2.49/2.61 (op(e0, e1) = op(op(e3, e1), e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22683])).
% 2.49/2.61 tff(22685,plain,
% 2.49/2.61 (e3 = op(e0, e1)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22510])).
% 2.49/2.61 tff(22686,plain,
% 2.49/2.61 (e3 = op(e0, op(e0, e0))),
% 2.49/2.61 inference(transitivity,[status(thm)],[22685, 22684, 22682, 22680])).
% 2.49/2.61 tff(22687,plain,
% 2.49/2.61 (op(e0, op(e0, e0)) = e3),
% 2.49/2.61 inference(transitivity,[status(thm)],[22679, 22681, 22683, 22510])).
% 2.49/2.61 tff(22688,plain,
% 2.49/2.61 (op(e0, op(e0, op(e0, e0))) = op(op(e3, e1), e3)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22522, 22687])).
% 2.49/2.61 tff(22689,plain,
% 2.49/2.61 (op(op(e3, e1), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.61 inference(symmetry,[status(thm)],[22688])).
% 2.49/2.61 tff(22690,plain,
% 2.49/2.61 (op(op(e3, e1), e3) = op(e0, e3)),
% 2.49/2.61 inference(monotonicity,[status(thm)],[22521])).
% 2.49/2.61 tff(22691,plain,
% 2.49/2.61 (op(e0, e3) = op(op(e3, e1), e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22690])).
% 2.49/2.61 tff(22692,plain,
% 2.49/2.61 (e2 = op(e0, e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22537])).
% 2.49/2.61 tff(22693,plain,
% 2.49/2.61 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.61 inference(transitivity,[status(thm)],[22692, 22691, 22689])).
% 2.49/2.61 tff(22694,plain,
% 2.49/2.61 ($false),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[16194, 22693, 22686, 22671])).
% 2.49/2.61 tff(22695,plain,((op(e1, e3) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.61 tff(22696,plain,
% 2.49/2.61 (op(e1, e3) = e0),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[22695, 2168, 76, 121, 17, 2559])).
% 2.49/2.61 tff(22697,plain,
% 2.49/2.61 (~(op(e1, e2) = e3)),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[21630, 22696, 21327])).
% 2.49/2.61 tff(22698,plain,
% 2.49/2.61 (op(e1, e3) = e3),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[247, 22697, 21634, 2168])).
% 2.49/2.61 tff(22699,plain,
% 2.49/2.61 (e0 = op(e1, e3)),
% 2.49/2.61 inference(symmetry,[status(thm)],[22696])).
% 2.49/2.61 tff(22700,plain,
% 2.49/2.61 (op(e3, e1) = e3),
% 2.49/2.61 inference(transitivity,[status(thm)],[22521, 22699, 22698])).
% 2.49/2.61 tff(22701,plain,
% 2.49/2.61 ($false),
% 2.49/2.61 inference(unit_resolution,[status(thm)],[22664, 22700])).
% 2.49/2.61 tff(22702,plain,((op(e1, e0) = e3) | (op(e2, e3) = e1) | (op(e0, e3) = e1) | (op(e2, e2) = e0) | (op(e2, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.61 tff(22703,plain,
% 2.49/2.61 (op(e1, e0) = e3),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[22702, 2559, 121, 17, 76])).
% 2.49/2.62 tff(22704,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22703])).
% 2.49/2.62 tff(22705,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22704, 532])).
% 2.49/2.62 tff(22706,plain,
% 2.49/2.62 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22705])).
% 2.49/2.62 tff(22707,plain,
% 2.49/2.62 (~(op(e1, e2) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[1312, 22706])).
% 2.49/2.62 tff(22708,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22703])).
% 2.49/2.62 tff(22709,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22708, 3230])).
% 2.49/2.62 tff(22710,plain,
% 2.49/2.62 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22709])).
% 2.49/2.62 tff(22711,plain,
% 2.49/2.62 (~(op(e1, e3) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[110, 22710])).
% 2.49/2.62 tff(22712,plain,
% 2.49/2.62 (~(op(e1, e2) = e0)),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[8194, 22711, 22153, 22520, 22515, 21372, 22707, 21540])).
% 2.49/2.62 tff(22713,plain,
% 2.49/2.62 (op(e0, e2) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[973, 22712, 17, 22527])).
% 2.49/2.62 tff(22714,plain,
% 2.49/2.62 (op(e0, e2) = op(e3, e1)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22713, 22522])).
% 2.49/2.62 tff(22715,plain,
% 2.49/2.62 ((op(e0, e2) = e1) <=> (op(e3, e1) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22714])).
% 2.49/2.62 tff(22716,plain,
% 2.49/2.62 ((op(e3, e1) = e1) <=> (op(e0, e2) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22715])).
% 2.49/2.62 tff(22717,plain,
% 2.49/2.62 ((~(op(e3, e1) = e1)) <=> (~(op(e0, e2) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22716])).
% 2.49/2.62 tff(22718,plain,
% 2.49/2.62 ((e0 = e1) <=> (op(e3, e1) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22522])).
% 2.49/2.62 tff(22719,plain,
% 2.49/2.62 ((~(e0 = e1)) <=> (~(op(e3, e1) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22718])).
% 2.49/2.62 tff(22720,plain,
% 2.49/2.62 (~(op(e3, e1) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[26, 22719])).
% 2.49/2.62 tff(22721,plain,
% 2.49/2.62 (~(op(e0, e2) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[22720, 22717])).
% 2.49/2.62 tff(22722,plain,
% 2.49/2.62 (op(e0, e0) = e1),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[384, 22721, 121, 22515])).
% 2.49/2.62 tff(22723,plain,
% 2.49/2.62 (e1 = op(e0, e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[22722, 74])).
% 2.49/2.62 tff(22724,plain,
% 2.49/2.62 (op(e0, op(e0, e0)) = op(op(e3, e1), e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22522, 22722])).
% 2.49/2.62 tff(22725,plain,
% 2.49/2.62 (op(op(e3, e1), e1) = op(e0, op(e0, e0))),
% 2.49/2.62 inference(symmetry,[status(thm)],[22724])).
% 2.49/2.62 tff(22726,plain,
% 2.49/2.62 (e3 = op(e0, op(e0, e0))),
% 2.49/2.62 inference(transitivity,[status(thm)],[22685, 22684, 22725])).
% 2.49/2.62 tff(22727,plain,
% 2.49/2.62 (op(e0, op(e0, e0)) = e3),
% 2.49/2.62 inference(transitivity,[status(thm)],[22724, 22683, 22510])).
% 2.49/2.62 tff(22728,plain,
% 2.49/2.62 (op(e0, op(e0, op(e0, e0))) = op(op(e3, e1), e3)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22522, 22727])).
% 2.49/2.62 tff(22729,plain,
% 2.49/2.62 (op(op(e3, e1), e3) = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.62 inference(symmetry,[status(thm)],[22728])).
% 2.49/2.62 tff(22730,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22510])).
% 2.49/2.62 tff(22731,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22730, 1364])).
% 2.49/2.62 tff(22732,plain,
% 2.49/2.62 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22731])).
% 2.49/2.62 tff(22733,plain,
% 2.49/2.62 (~(op(e0, e3) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[818, 22732])).
% 2.49/2.62 tff(22734,plain,
% 2.49/2.62 ((op(e1, e0) = e0) <=> (e3 = op(e3, e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22703, 22522])).
% 2.49/2.62 tff(22735,plain,
% 2.49/2.62 ((op(e1, e0) = e0) <=> (op(e3, e1) = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22734, 396])).
% 2.49/2.62 tff(22736,plain,
% 2.49/2.62 ((op(e3, e1) = e3) <=> (op(e1, e0) = e0)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22735])).
% 2.49/2.62 tff(22737,plain,
% 2.49/2.62 ((~(op(e3, e1) = e3)) <=> (~(op(e1, e0) = e0))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22736])).
% 2.49/2.62 tff(22738,plain,
% 2.49/2.62 (~(op(e1, e0) = e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[22664, 22737])).
% 2.49/2.62 tff(22739,plain,
% 2.49/2.62 (op(e1, e3) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[1830, 22712, 21357, 22738])).
% 2.49/2.62 tff(22740,plain,
% 2.49/2.62 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22739])).
% 2.49/2.62 tff(22741,plain,
% 2.49/2.62 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22740])).
% 2.49/2.62 tff(22742,plain,
% 2.49/2.62 (~(op(e0, e3) = e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[64, 22741])).
% 2.49/2.62 tff(22743,plain,
% 2.49/2.62 (op(e0, e3) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[687, 22742, 22733, 121])).
% 2.49/2.62 tff(22744,plain,
% 2.49/2.62 (e2 = op(e0, e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22743])).
% 2.49/2.62 tff(22745,plain,
% 2.49/2.62 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.62 inference(transitivity,[status(thm)],[22744, 22691, 22729])).
% 2.49/2.62 tff(22746,plain,
% 2.49/2.62 ($false),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[16194, 22745, 22726, 22723])).
% 2.49/2.62 tff(22747,plain,((op(e2, e1) = e0) | (op(e0, e3) = e1) | (op(e2, e2) = e0) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.62 tff(22748,plain,
% 2.49/2.62 (op(e2, e1) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[22747, 121, 17, 76])).
% 2.49/2.62 tff(22749,plain,
% 2.49/2.62 ((op(e2, e1) = e1) <=> (e0 = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22748])).
% 2.49/2.62 tff(22750,plain,
% 2.49/2.62 ((e0 = e1) <=> (op(e2, e1) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22749])).
% 2.49/2.62 tff(22751,plain,
% 2.49/2.62 ((~(e0 = e1)) <=> (~(op(e2, e1) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22750])).
% 2.49/2.62 tff(22752,plain,
% 2.49/2.62 (~(op(e2, e1) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[26, 22751])).
% 2.49/2.62 tff(22753,plain,
% 2.49/2.62 (op(e0, e3) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[7630, 80, 121, 3508, 76])).
% 2.49/2.62 tff(22754,plain,
% 2.49/2.62 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22755,plain,
% 2.49/2.62 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22754, 1])).
% 2.49/2.62 tff(22756,plain,
% 2.49/2.62 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22755])).
% 2.49/2.62 tff(22757,plain,
% 2.49/2.62 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22756])).
% 2.49/2.62 tff(22758,plain,
% 2.49/2.62 (~(op(e0, e3) = e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[14, 22757])).
% 2.49/2.62 tff(22759,plain,
% 2.49/2.62 (op(e3, e3) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[1098, 22758, 5446, 80])).
% 2.49/2.62 tff(22760,plain,
% 2.49/2.62 ((op(e3, e3) = e1) <=> (e0 = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22759])).
% 2.49/2.62 tff(22761,plain,
% 2.49/2.62 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22760])).
% 2.49/2.62 tff(22762,plain,
% 2.49/2.62 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22761])).
% 2.49/2.62 tff(22763,plain,
% 2.49/2.62 (~(op(e3, e3) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[26, 22762])).
% 2.49/2.62 tff(22764,plain,
% 2.49/2.62 (op(e1, e3) = e1),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[151, 22763, 76, 121])).
% 2.49/2.62 tff(22765,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22764])).
% 2.49/2.62 tff(22766,plain,
% 2.49/2.62 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22765])).
% 2.49/2.62 tff(22767,plain,
% 2.49/2.62 (~(op(e1, e0) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[110, 22766])).
% 2.49/2.62 tff(22768,plain,
% 2.49/2.62 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22764])).
% 2.49/2.62 tff(22769,plain,
% 2.49/2.62 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22768])).
% 2.49/2.62 tff(22770,plain,
% 2.49/2.62 (~(op(e1, e2) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[1850, 22769])).
% 2.49/2.62 tff(22771,plain,
% 2.49/2.62 (e1 = op(e1, e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22764])).
% 2.49/2.62 tff(22772,plain,
% 2.49/2.62 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22771])).
% 2.49/2.62 tff(22773,plain,
% 2.49/2.62 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22772])).
% 2.49/2.62 tff(22774,plain,
% 2.49/2.62 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22773])).
% 2.49/2.62 tff(22775,plain,
% 2.49/2.62 (~(op(e1, e0) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[110, 22774])).
% 2.49/2.62 tff(22776,plain,
% 2.49/2.62 (op(e1, e0) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[728, 2168, 6687, 22775])).
% 2.49/2.62 tff(22777,plain,
% 2.49/2.62 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22776])).
% 2.49/2.62 tff(22778,plain,
% 2.49/2.62 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22777])).
% 2.49/2.62 tff(22779,plain,
% 2.49/2.62 (~(op(e0, e0) = e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[2471, 22778])).
% 2.49/2.62 tff(22780,plain,
% 2.49/2.62 (op(e0, e2) = e0),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[3976, 22779, 5478, 22758])).
% 2.49/2.62 tff(22781,plain,
% 2.49/2.62 ((op(e0, e2) = e1) <=> (e0 = op(e1, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22780, 22771])).
% 2.49/2.62 tff(22782,plain,
% 2.49/2.62 ((op(e0, e2) = e1) <=> (op(e1, e3) = e0)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22781, 6095])).
% 2.49/2.62 tff(22783,plain,
% 2.49/2.62 ((op(e1, e3) = e0) <=> (op(e0, e2) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22782])).
% 2.49/2.62 tff(22784,plain,
% 2.49/2.62 ((~(op(e1, e3) = e0)) <=> (~(op(e0, e2) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22783])).
% 2.49/2.62 tff(22785,plain,
% 2.49/2.62 (~(op(e0, e2) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[80, 22784])).
% 2.49/2.62 tff(22786,plain,
% 2.49/2.62 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22787,plain,
% 2.49/2.62 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22786])).
% 2.49/2.62 tff(22788,plain,
% 2.49/2.62 (~(op(e0, e0) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[3414, 22787])).
% 2.49/2.62 tff(22789,plain,
% 2.49/2.62 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22790,plain,
% 2.49/2.62 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22789])).
% 2.49/2.62 tff(22791,plain,
% 2.49/2.62 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22792,plain,
% 2.49/2.62 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22791])).
% 2.49/2.62 tff(22793,plain,
% 2.49/2.62 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22792])).
% 2.49/2.62 tff(22794,plain,
% 2.49/2.62 (~(op(e0, e3) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[1321, 22793])).
% 2.49/2.62 tff(22795,plain,
% 2.49/2.62 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22796,plain,
% 2.49/2.62 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22795])).
% 2.49/2.62 tff(22797,plain,
% 2.49/2.62 ((op(e3, e2) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22796])).
% 2.49/2.62 tff(22798,plain,
% 2.49/2.62 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22753])).
% 2.49/2.62 tff(22799,plain,
% 2.49/2.62 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22798, 120])).
% 2.49/2.62 tff(22800,plain,
% 2.49/2.62 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22799])).
% 2.49/2.62 tff(22801,plain,
% 2.49/2.62 (~(op(e2, e3) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[964, 22800])).
% 2.49/2.62 tff(22802,plain,
% 2.49/2.62 (op(e2, e3) = e3),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[206, 22801, 76, 5446])).
% 2.49/2.62 tff(22803,plain,
% 2.49/2.62 (e3 = op(e2, e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22802])).
% 2.49/2.62 tff(22804,plain,
% 2.49/2.62 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22803])).
% 2.49/2.62 tff(22805,plain,
% 2.49/2.62 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22804])).
% 2.49/2.62 tff(22806,plain,
% 2.49/2.62 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22803])).
% 2.49/2.62 tff(22807,plain,
% 2.49/2.62 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22806])).
% 2.49/2.62 tff(22808,plain,
% 2.49/2.62 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22807])).
% 2.49/2.62 tff(22809,plain,
% 2.49/2.62 (~(op(e1, e3) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[118, 22808])).
% 2.49/2.62 tff(22810,plain,
% 2.49/2.62 (op(e1, e2) = e3),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[247, 2168, 1291, 22809])).
% 2.49/2.62 tff(22811,plain,
% 2.49/2.62 (op(e1, e2) = op(e2, e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22810, 22803])).
% 2.49/2.62 tff(22812,plain,
% 2.49/2.62 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22811])).
% 2.49/2.62 tff(22813,plain,
% 2.49/2.62 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.49/2.62 inference(transitivity,[status(thm)],[22812, 394])).
% 2.49/2.62 tff(22814,plain,
% 2.49/2.62 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22813, 22805, 22797])).
% 2.49/2.62 tff(22815,plain,
% 2.49/2.62 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22814])).
% 2.49/2.62 tff(22816,plain,
% 2.49/2.62 (~(op(e3, op(e0, e3)) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[2292, 22815])).
% 2.49/2.62 tff(22817,plain,
% 2.49/2.62 (~(op(e3, e0) = op(e0, e3))),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[3228, 22816, 121, 22794, 22759])).
% 2.49/2.62 tff(22818,plain,
% 2.49/2.62 (~(op(e3, e0) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[22817, 22790])).
% 2.49/2.62 tff(22819,plain,
% 2.49/2.62 (op(e2, e0) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[589, 22818, 6687, 22788])).
% 2.49/2.62 tff(22820,plain,
% 2.49/2.62 ((op(e2, e0) = e1) <=> (e2 = op(e1, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22819, 22771])).
% 2.49/2.62 tff(22821,plain,
% 2.49/2.62 ((op(e2, e0) = e1) <=> (op(e1, e3) = e2)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22820, 66])).
% 2.49/2.62 tff(22822,plain,
% 2.49/2.62 ((op(e1, e3) = e2) <=> (op(e2, e0) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22821])).
% 2.49/2.62 tff(22823,plain,
% 2.49/2.62 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22822])).
% 2.49/2.62 tff(22824,plain,
% 2.49/2.62 (~(op(e2, e0) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[72, 22823])).
% 2.49/2.62 tff(22825,plain,
% 2.49/2.62 (op(e2, e2) = e1),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[345, 22824, 76, 5582])).
% 2.49/2.62 tff(22826,plain,
% 2.49/2.62 (e1 = op(e2, e2)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22825])).
% 2.49/2.62 tff(22827,plain,
% 2.49/2.62 (op(e3, e1) = e3),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[1730, 2527, 1291, 5487])).
% 2.49/2.62 tff(22828,plain,
% 2.49/2.62 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e3)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.62 tff(22829,plain,
% 2.49/2.62 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22828])).
% 2.49/2.62 tff(22830,plain,
% 2.49/2.62 (~(op(e1, e1) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[945, 22829])).
% 2.49/2.62 tff(22831,plain,
% 2.49/2.62 (op(e0, e3) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[7466, 1087, 84, 22830, 80, 121, 3508, 72])).
% 2.49/2.62 tff(22832,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.62 tff(22833,plain,
% 2.49/2.62 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22832])).
% 2.49/2.62 tff(22834,plain,
% 2.49/2.62 (~(op(e0, e1) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[818, 22833])).
% 2.49/2.62 tff(22835,plain,
% 2.49/2.62 (op(e0, e1) = e1),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[829, 22834, 3849, 2527])).
% 2.49/2.62 tff(22836,plain,
% 2.49/2.62 (op(op(e0, e1), e0) = op(e1, op(e3, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22835, 6444])).
% 2.49/2.62 tff(22837,plain,
% 2.49/2.62 (op(e1, op(e0, e3)) = op(e1, e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.62 tff(22838,plain,
% 2.49/2.62 (op(e1, e2) = op(e1, op(e0, e3))),
% 2.49/2.62 inference(symmetry,[status(thm)],[22837])).
% 2.49/2.62 tff(22839,plain,
% 2.49/2.62 ((op(e1, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22838])).
% 2.49/2.62 tff(22840,plain,
% 2.49/2.62 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22839])).
% 2.49/2.62 tff(22841,plain,
% 2.49/2.62 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22835])).
% 2.49/2.62 tff(22842,plain,
% 2.49/2.62 (e1 = op(e0, e1)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22835])).
% 2.49/2.62 tff(22843,plain,
% 2.49/2.62 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[6444])).
% 2.49/2.62 tff(22844,plain,
% 2.49/2.62 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22843])).
% 2.49/2.62 tff(22845,plain,
% 2.49/2.62 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22844])).
% 2.49/2.62 tff(22846,plain,
% 2.49/2.62 (~(op(e3, e0) = e0)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[157, 22845])).
% 2.49/2.62 tff(22847,plain,
% 2.49/2.62 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e3)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.62 tff(22848,plain,
% 2.49/2.62 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22847])).
% 2.49/2.62 tff(22849,plain,
% 2.49/2.62 (~(op(e3, e0) = e3)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[580, 22848])).
% 2.49/2.62 tff(22850,plain,
% 2.49/2.62 (e2 = op(e0, e3)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22831])).
% 2.49/2.62 tff(22851,plain,
% 2.49/2.62 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22850])).
% 2.49/2.62 tff(22852,plain,
% 2.49/2.62 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22851])).
% 2.49/2.62 tff(22853,plain,
% 2.49/2.62 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22852])).
% 2.49/2.62 tff(22854,plain,
% 2.49/2.62 (~(op(e3, e0) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[5528, 22853])).
% 2.49/2.62 tff(22855,plain,
% 2.49/2.62 (op(e3, e0) = e1),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[5422, 22854, 22849, 22846])).
% 2.49/2.62 tff(22856,plain,
% 2.49/2.62 (op(e3, e0) = op(e0, e1)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22855, 22842])).
% 2.49/2.62 tff(22857,plain,
% 2.49/2.62 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = op(e0, e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22856])).
% 2.49/2.62 tff(22858,plain,
% 2.49/2.62 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e1)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22857, 22841])).
% 2.49/2.62 tff(22859,plain,
% 2.49/2.62 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22858])).
% 2.49/2.62 tff(22860,plain,
% 2.49/2.62 (~(op(e1, e0) = e1)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[410, 22859])).
% 2.49/2.62 tff(22861,plain,
% 2.49/2.62 ((op(e3, e1) = e2) <=> (e3 = e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.62 tff(22862,plain,
% 2.49/2.62 ((op(e3, e1) = e2) <=> (e2 = e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22861, 1314])).
% 2.49/2.62 tff(22863,plain,
% 2.49/2.62 ((e2 = e3) <=> (op(e3, e1) = e2)),
% 2.49/2.62 inference(symmetry,[status(thm)],[22862])).
% 2.49/2.62 tff(22864,plain,
% 2.49/2.62 ((~(e2 = e3)) <=> (~(op(e3, e1) = e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22863])).
% 2.49/2.62 tff(22865,plain,
% 2.49/2.62 (~(op(e3, e1) = e2)),
% 2.49/2.62 inference(modus_ponens,[status(thm)],[1321, 22864])).
% 2.49/2.62 tff(22866,plain,
% 2.49/2.62 (op(e1, e1) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[1993, 22834, 22865, 5515])).
% 2.49/2.62 tff(22867,plain,
% 2.49/2.62 (op(e3, e2) = e2),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[2015, 22854, 22865, 7427])).
% 2.49/2.62 tff(22868,plain,
% 2.49/2.62 (op(e3, op(e0, e3)) = op(e3, e2)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.62 tff(22869,plain,
% 2.49/2.62 (op(e3, e2) = op(e0, e3)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22867, 22850])).
% 2.49/2.62 tff(22870,plain,
% 2.49/2.62 (op(e3, op(e3, e2)) = op(e3, op(e0, e3))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22869])).
% 2.49/2.62 tff(22871,plain,
% 2.49/2.62 (op(e3, op(e3, e2)) = e2),
% 2.49/2.62 inference(transitivity,[status(thm)],[22870, 22868, 22867])).
% 2.49/2.62 tff(22872,plain,
% 2.49/2.62 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[1904, 22871])).
% 2.49/2.62 tff(22873,plain,
% 2.49/2.62 (op(op(e3, e1), e1) = op(e3, e1)),
% 2.49/2.62 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.62 tff(22874,plain,
% 2.49/2.62 (op(op(e3, e1), e1) = e3),
% 2.49/2.62 inference(transitivity,[status(thm)],[22873, 5607])).
% 2.49/2.62 tff(22875,plain,
% 2.49/2.62 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.49/2.62 inference(unit_resolution,[status(thm)],[2416, 22874])).
% 2.49/2.62 tff(22876,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22835])).
% 2.49/2.62 tff(22877,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22876, 697])).
% 2.49/2.62 tff(22878,plain,
% 2.49/2.62 ((op(e0, e1) = op(e0, e2)) <=> (op(op(e2, e1), e2) = e1)),
% 2.49/2.62 inference(transitivity,[status(thm)],[22877, 5799])).
% 2.49/2.62 tff(22879,plain,
% 2.49/2.62 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(op(e2, e1), e2) = e1))),
% 2.49/2.62 inference(monotonicity,[status(thm)],[22878])).
% 2.49/2.63 tff(22880,plain,
% 2.49/2.63 (~(op(op(e2, e1), e2) = e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[2102, 22879])).
% 2.49/2.63 tff(22881,plain,
% 2.49/2.63 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[5808, 22880])).
% 2.49/2.63 tff(22882,plain,
% 2.49/2.63 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.63 tff(22883,plain,
% 2.49/2.63 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22882])).
% 2.49/2.63 tff(22884,plain,
% 2.49/2.63 (~(op(e0, e0) = e2)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[3414, 22883])).
% 2.49/2.63 tff(22885,plain,
% 2.49/2.63 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e2)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22866])).
% 2.49/2.63 tff(22886,plain,
% 2.49/2.63 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e2))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22885])).
% 2.49/2.63 tff(22887,plain,
% 2.49/2.63 (~(op(e1, e0) = e2)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[737, 22886])).
% 2.49/2.63 tff(22888,plain,
% 2.49/2.63 (op(e2, e0) = e2),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[589, 22887, 22884, 22854])).
% 2.49/2.63 tff(22889,plain,
% 2.49/2.63 (op(op(e0, e3), e0) = op(e2, op(e3, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22831, 6444])).
% 2.49/2.63 tff(22890,plain,
% 2.49/2.63 (op(e2, e0) = op(e0, e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22888, 22850])).
% 2.49/2.63 tff(22891,plain,
% 2.49/2.63 (op(op(e2, e0), e0) = op(op(e0, e3), e0)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22890])).
% 2.49/2.63 tff(22892,plain,
% 2.49/2.63 (op(op(e2, e0), e0) = e2),
% 2.49/2.63 inference(transitivity,[status(thm)],[22891, 22889, 6448, 22888])).
% 2.49/2.63 tff(22893,plain,
% 2.49/2.63 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1945, 22892])).
% 2.49/2.63 tff(22894,plain,
% 2.49/2.63 (op(op(e0, e3), e0) = op(e2, e0)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22889, 6448])).
% 2.49/2.63 tff(22895,plain,
% 2.49/2.63 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22894])).
% 2.49/2.63 tff(22896,plain,
% 2.49/2.63 ((op(e2, e0) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22895])).
% 2.49/2.63 tff(22897,plain,
% 2.49/2.63 ((op(e2, e0) = e3) <=> (op(e0, e3) = e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22890])).
% 2.49/2.63 tff(22898,plain,
% 2.49/2.63 ((op(e0, e3) = e3) <=> (op(e2, e0) = e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22897])).
% 2.49/2.63 tff(22899,plain,
% 2.49/2.63 ((op(e0, e3) = e3) <=> (op(op(e0, e3), e0) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22898, 22896])).
% 2.49/2.63 tff(22900,plain,
% 2.49/2.63 ((~(op(e0, e3) = e3)) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22899])).
% 2.49/2.63 tff(22901,plain,
% 2.49/2.63 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.63 tff(22902,plain,
% 2.49/2.63 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22901])).
% 2.49/2.63 tff(22903,plain,
% 2.49/2.63 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22902])).
% 2.49/2.63 tff(22904,plain,
% 2.49/2.63 (~(op(e0, e3) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[1321, 22903])).
% 2.49/2.63 tff(22905,plain,
% 2.49/2.63 (~(op(op(e0, e3), e0) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[22904, 22900])).
% 2.49/2.63 tff(22906,plain,
% 2.49/2.63 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[2635, 22905])).
% 2.49/2.63 tff(22907,plain,
% 2.49/2.63 (op(op(e3, e0), e3) = op(e1, e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22855])).
% 2.49/2.63 tff(22908,plain,
% 2.49/2.63 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e3) = op(e3, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22907, 6444])).
% 2.49/2.63 tff(22909,plain,
% 2.49/2.63 ((op(e1, e3) = op(e3, e3)) <=> (op(op(e3, e0), e3) = e0)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22908])).
% 2.49/2.63 tff(22910,plain,
% 2.49/2.63 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22909])).
% 2.49/2.63 tff(22911,plain,
% 2.49/2.63 (~(op(op(e3, e0), e3) = e0)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[571, 22910])).
% 2.49/2.63 tff(22912,plain,
% 2.49/2.63 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1764, 22911])).
% 2.49/2.63 tff(22913,plain,
% 2.49/2.63 (op(e1, e0) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[728, 5505, 21431, 929])).
% 2.49/2.63 tff(22914,plain,
% 2.49/2.63 (op(e0, e1) = e1),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[829, 18332, 3849, 2527])).
% 2.49/2.63 tff(22915,plain,
% 2.49/2.63 (op(op(e0, e1), e0) = op(e1, op(e3, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22914, 4451])).
% 2.49/2.63 tff(22916,plain,
% 2.49/2.63 (e1 = op(e0, e1)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22914])).
% 2.49/2.63 tff(22917,plain,
% 2.49/2.63 (op(e1, op(e1, e0)) = op(op(e0, e1), e0)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22916, 22913])).
% 2.49/2.63 tff(22918,plain,
% 2.49/2.63 (op(e1, op(e1, e0)) = e0),
% 2.49/2.63 inference(transitivity,[status(thm)],[22917, 22915, 4468, 22913])).
% 2.49/2.63 tff(22919,plain,
% 2.49/2.63 (op(e1, e1) = op(e0, e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[2891, 2560])).
% 2.49/2.63 tff(22920,plain,
% 2.49/2.63 ((op(e1, e1) = e1) <=> (op(e0, e3) = e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22919])).
% 2.49/2.63 tff(22921,plain,
% 2.49/2.63 ((op(e0, e3) = e1) <=> (op(e1, e1) = e1)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22920])).
% 2.49/2.63 tff(22922,plain,
% 2.49/2.63 ((~(op(e0, e3) = e1)) <=> (~(op(e1, e1) = e1))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22921])).
% 2.49/2.63 tff(22923,plain,
% 2.49/2.63 (~(op(e1, e1) = e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[121, 22922])).
% 2.49/2.63 tff(22924,plain,
% 2.49/2.63 (op(e1, e2) = e1),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[954, 87, 22923, 929])).
% 2.49/2.63 tff(22925,plain,
% 2.49/2.63 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[4451])).
% 2.49/2.63 tff(22926,plain,
% 2.49/2.63 ((~(e0 = e1)) <=> (~(op(e3, e3) = e1))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22925])).
% 2.49/2.63 tff(22927,plain,
% 2.49/2.63 (~(op(e3, e3) = e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[26, 22926])).
% 2.49/2.63 tff(22928,plain,
% 2.49/2.63 (op(e2, e3) = e1),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[151, 87, 121, 22927])).
% 2.49/2.63 tff(22929,plain,
% 2.49/2.63 (op(op(e2, e3), e2) = op(e1, op(e0, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22928, 2560])).
% 2.49/2.63 tff(22930,plain,
% 2.49/2.63 (op(op(e2, e3), e2) = op(e0, e1)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22929, 10421, 22924, 22916])).
% 2.49/2.63 tff(22931,plain,
% 2.49/2.63 ((op(op(e2, e3), e2) = e3) <=> (op(e0, e1) = e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22930])).
% 2.49/2.63 tff(22932,plain,
% 2.49/2.63 ((op(e0, e1) = e3) <=> (op(op(e2, e3), e2) = e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22931])).
% 2.49/2.63 tff(22933,plain,
% 2.49/2.63 ((~(op(e0, e1) = e3)) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22932])).
% 2.49/2.63 tff(22934,plain,
% 2.49/2.63 (~(op(op(e2, e3), e2) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[2527, 22933])).
% 2.49/2.63 tff(22935,plain,
% 2.49/2.63 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1934, 22934])).
% 2.49/2.63 tff(22936,plain,
% 2.49/2.63 (op(e1, op(e1, e2)) = op(e1, e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22924])).
% 2.49/2.63 tff(22937,plain,
% 2.49/2.63 (op(e1, op(e1, e2)) = e2),
% 2.49/2.63 inference(transitivity,[status(thm)],[22936, 2891])).
% 2.49/2.63 tff(22938,plain,
% 2.49/2.63 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[2377, 22937])).
% 2.49/2.63 tff(22939,plain,
% 2.49/2.63 (op(e0, op(e0, e1)) = op(e0, e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22914])).
% 2.49/2.63 tff(22940,plain,
% 2.49/2.63 (op(e0, op(e0, e1)) = e1),
% 2.49/2.63 inference(transitivity,[status(thm)],[22939, 22914])).
% 2.49/2.63 tff(22941,plain,
% 2.49/2.63 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[2449, 22940])).
% 2.49/2.63 tff(22942,plain,
% 2.49/2.63 (op(e1, e2) = op(e0, e1)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22924, 22916])).
% 2.49/2.63 tff(22943,plain,
% 2.49/2.63 ((op(e1, e2) = e0) <=> (op(e0, e1) = e0)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22942])).
% 2.49/2.63 tff(22944,plain,
% 2.49/2.63 ((op(e0, e1) = e0) <=> (op(e1, e2) = e0)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22943])).
% 2.49/2.63 tff(22945,plain,
% 2.49/2.63 ((~(op(e0, e1) = e0)) <=> (~(op(e1, e2) = e0))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22944])).
% 2.49/2.63 tff(22946,plain,
% 2.49/2.63 (~(op(e1, e2) = e0)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[3849, 22945])).
% 2.49/2.63 tff(22947,plain,
% 2.49/2.63 (op(e0, e2) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[973, 22946, 17, 4455])).
% 2.49/2.63 tff(22948,plain,
% 2.49/2.63 (op(op(e0, e2), e2) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[4944, 22947, 2891])).
% 2.49/2.63 tff(22949,plain,
% 2.49/2.63 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1956, 22948])).
% 2.49/2.63 tff(22950,plain,
% 2.49/2.63 (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1459, 22949, 1926, 22941, 3342, 1304, 2421, 1936, 22938, 1275, 3341, 22935])).
% 2.49/2.63 tff(22951,plain,
% 2.49/2.63 (~(op(e1, op(e1, e0)) = e0)),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1836, 22950])).
% 2.49/2.63 tff(22952,plain,
% 2.49/2.63 ($false),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[22951, 22918])).
% 2.49/2.63 tff(22953,plain,((op(e1, e3) = e1) | (~(op(e3, e3) = e0)) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e0) | (op(e1, e0) = e1) | (op(e0, e1) = e3) | (~(op(e0, e3) = e2)) | (op(e0, e1) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.63 tff(22954,plain,
% 2.49/2.63 (op(e1, e3) = e1),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[22953, 6443, 22912, 22906, 1304, 22893, 22881, 22875, 22872, 22866, 5552, 22860, 2527, 22831, 3849, 121, 80, 72])).
% 2.49/2.63 tff(22955,plain,
% 2.49/2.63 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, op(e0, e3)) = e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22838, 22954])).
% 2.49/2.63 tff(22956,plain,
% 2.49/2.63 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22955, 22840])).
% 2.49/2.63 tff(22957,plain,
% 2.49/2.63 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22956])).
% 2.49/2.63 tff(22958,plain,
% 2.49/2.63 (~(op(e1, e2) = e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[1850, 22957])).
% 2.49/2.63 tff(22959,plain,
% 2.49/2.63 ((op(e3, e1) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.63 tff(22960,plain,
% 2.49/2.63 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22959, 666])).
% 2.49/2.63 tff(22961,plain,
% 2.49/2.63 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22960])).
% 2.49/2.63 tff(22962,plain,
% 2.49/2.63 (~(op(e3, e3) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[437, 22961])).
% 2.49/2.63 tff(22963,plain,
% 2.49/2.63 ((op(e3, e1) = op(e1, e3)) <=> (e3 = op(e1, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.63 tff(22964,plain,
% 2.49/2.63 ((op(e3, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22963, 3230])).
% 2.49/2.63 tff(22965,plain,
% 2.49/2.63 ((op(e1, e3) = op(e3, e1)) <=> (op(e1, e3) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[1674, 22964])).
% 2.49/2.63 tff(22966,plain,
% 2.49/2.63 ((~(op(e1, e3) = op(e3, e1))) <=> (~(op(e1, e3) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22965])).
% 2.49/2.63 tff(22967,plain,
% 2.49/2.63 (op(op(e3, e1), e3) = op(e3, e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5607])).
% 2.49/2.63 tff(22968,plain,
% 2.49/2.63 ((op(op(e3, e1), e3) = e1) <=> (op(e3, e3) = e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22967])).
% 2.49/2.63 tff(22969,plain,
% 2.49/2.63 ((op(e3, e3) = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.49/2.63 inference(symmetry,[status(thm)],[22968])).
% 2.49/2.63 tff(22970,plain,
% 2.49/2.63 ((e0 = e1) <=> (op(e3, e3) = e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[6444])).
% 2.49/2.63 tff(22971,plain,
% 2.49/2.63 ((e0 = e1) <=> (op(op(e3, e1), e3) = e1)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22970, 22969])).
% 2.49/2.63 tff(22972,plain,
% 2.49/2.63 ((~(e0 = e1)) <=> (~(op(op(e3, e1), e3) = e1))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22971])).
% 2.49/2.63 tff(22973,plain,
% 2.49/2.63 (~(op(op(e3, e1), e3) = e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[26, 22972])).
% 2.49/2.63 tff(22974,plain,
% 2.49/2.63 (op(e3, e1) = op(e1, e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[7748])).
% 2.49/2.63 tff(22975,plain,
% 2.49/2.63 (op(e3, e1) = e1),
% 2.49/2.63 inference(transitivity,[status(thm)],[22974, 132])).
% 2.49/2.63 tff(22976,plain,
% 2.49/2.63 (op(op(e3, e1), e3) = op(e1, e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22975])).
% 2.49/2.63 tff(22977,plain,
% 2.49/2.63 (op(op(e3, e1), e3) = e1),
% 2.49/2.63 inference(transitivity,[status(thm)],[22976, 132])).
% 2.49/2.63 tff(22978,assumption,(~(op(op(e3, e1), e3) = e1)), introduced(assumption)).
% 2.49/2.63 tff(22979,plain,
% 2.49/2.63 ($false),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[22978, 22977])).
% 2.49/2.63 tff(22980,plain,((~(op(e1, e3) = e1)) | (op(op(e3, e1), e3) = e1) | (~(op(e1, e3) = op(e3, e1)))), inference(lemma,lemma(discharge,[]))).
% 2.49/2.63 tff(22981,plain,
% 2.49/2.63 (~(op(e1, e3) = op(e3, e1))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[22980, 22954, 22973])).
% 2.49/2.63 tff(22982,plain,
% 2.49/2.63 (~(op(e1, e3) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[22981, 22966])).
% 2.49/2.63 tff(22983,plain,
% 2.49/2.63 (op(e2, e3) = e3),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[480, 22982, 22904, 22962])).
% 2.49/2.63 tff(22984,plain,
% 2.49/2.63 (op(op(e0, e3), e3) = op(e2, e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22831])).
% 2.49/2.63 tff(22985,plain,
% 2.49/2.63 (op(e2, op(e2, e3)) = op(op(e0, e3), e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22850, 22983])).
% 2.49/2.63 tff(22986,plain,
% 2.49/2.63 (op(e2, op(e2, e3)) = e3),
% 2.49/2.63 inference(transitivity,[status(thm)],[22985, 22984, 22983])).
% 2.49/2.63 tff(22987,plain,
% 2.49/2.63 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[2344, 22986])).
% 2.49/2.63 tff(22988,plain,
% 2.49/2.63 (op(e0, e2) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[973, 1947, 17, 4455])).
% 2.49/2.63 tff(22989,plain,
% 2.49/2.63 (op(op(e0, e2), e2) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[4944, 22988, 2891])).
% 2.49/2.63 tff(22990,plain,
% 2.49/2.63 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1956, 22989])).
% 2.49/2.63 tff(22991,plain,
% 2.49/2.63 (op(op(e0, e1), e0) = op(e1, op(e3, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5800, 4451])).
% 2.49/2.63 tff(22992,plain,
% 2.49/2.63 (op(e1, op(e1, e0)) = op(op(e0, e1), e0)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5801, 7594])).
% 2.49/2.63 tff(22993,plain,
% 2.49/2.63 (op(e1, op(e1, e0)) = e0),
% 2.49/2.63 inference(transitivity,[status(thm)],[22992, 22991, 4468, 7594])).
% 2.49/2.63 tff(22994,plain,
% 2.49/2.63 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1836, 22993])).
% 2.49/2.63 tff(22995,plain,
% 2.49/2.63 (op(e3, op(e0, e1)) = op(e3, e1)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[5800])).
% 2.49/2.63 tff(22996,plain,
% 2.49/2.63 (op(e1, e2) = e3),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1859, 1947, 5766, 4515])).
% 2.49/2.63 tff(22997,plain,
% 2.49/2.63 (op(op(e1, e2), e1) = op(e3, op(e0, e1))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22996, 5801])).
% 2.49/2.63 tff(22998,plain,
% 2.49/2.63 (op(op(e1, e2), e1) = e3),
% 2.49/2.63 inference(transitivity,[status(thm)],[22997, 22995, 5607])).
% 2.49/2.63 tff(22999,plain,
% 2.49/2.63 ((op(op(e1, e2), e1) = e2) <=> (e3 = op(e0, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22998, 2560])).
% 2.49/2.63 tff(23000,plain,
% 2.49/2.63 ((op(op(e1, e2), e1) = e2) <=> (op(e0, e3) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22999, 1364])).
% 2.49/2.63 tff(23001,plain,
% 2.49/2.63 ((op(e0, e3) = e3) <=> (op(op(e1, e2), e1) = e2)),
% 2.49/2.63 inference(symmetry,[status(thm)],[23000])).
% 2.49/2.63 tff(23002,plain,
% 2.49/2.63 ((~(op(e0, e3) = e3)) <=> (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23001])).
% 2.49/2.63 tff(23003,plain,
% 2.49/2.63 (~(op(op(e1, e2), e1) = e2)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[16740, 23002])).
% 2.49/2.63 tff(23004,plain,
% 2.49/2.63 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[5959, 23003])).
% 2.49/2.63 tff(23005,plain,
% 2.49/2.63 ($false),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[1459, 23004, 22994, 1926, 5818, 3342, 1304, 2421, 1936, 22990, 22875, 3341, 1347])).
% 2.49/2.63 tff(23006,plain,((op(e1, e2) = e0) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~(op(e0, e3) = e2)) | (~(op(e3, e1) = e3)) | (~(op(e0, e1) = e1)) | (~(op(e3, e3) = e0)) | (~(op(e1, e1) = e2)) | (op(e2, e2) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.63 tff(23007,plain,
% 2.49/2.63 (op(e1, e2) = e0),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[23006, 22912, 22906, 1304, 22893, 22881, 22872, 22987, 22831, 5607, 22835, 6443, 22866, 5552, 80, 84, 22958])).
% 2.49/2.63 tff(23008,plain,
% 2.49/2.63 (op(e1, op(e1, e2)) = op(op(e0, e1), e0)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[22842, 23007])).
% 2.49/2.63 tff(23009,plain,
% 2.49/2.63 (op(e1, e1) = op(e0, e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[22866, 22850])).
% 2.49/2.63 tff(23010,plain,
% 2.49/2.63 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23009])).
% 2.49/2.63 tff(23011,plain,
% 2.49/2.63 (op(e1, op(e1, e1)) = op(e1, e2)),
% 2.49/2.63 inference(transitivity,[status(thm)],[23010, 22837])).
% 2.49/2.63 tff(23012,plain,
% 2.49/2.63 (op(e1, op(e1, op(e1, e1))) = op(e1, op(e1, e2))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23011])).
% 2.49/2.63 tff(23013,plain,
% 2.49/2.63 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.49/2.63 inference(transitivity,[status(thm)],[23012, 23008, 22836, 7460])).
% 2.49/2.63 tff(23014,plain,
% 2.49/2.63 ((e3 = op(e1, op(e1, op(e1, e1)))) <=> (e3 = op(e1, e0))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23013])).
% 2.49/2.63 tff(23015,plain,
% 2.49/2.63 ((e3 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[23014, 3497])).
% 2.49/2.63 tff(23016,plain,
% 2.49/2.63 ((~(e3 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23015])).
% 2.49/2.63 tff(23017,plain,
% 2.49/2.63 (e2 = op(e1, e1)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[22866, 2254])).
% 2.49/2.63 tff(23018,plain,
% 2.49/2.63 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23011])).
% 2.49/2.63 tff(23019,plain,
% 2.49/2.63 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 2.49/2.63 inference(transitivity,[status(thm)],[23018, 67])).
% 2.49/2.63 tff(23020,plain,
% 2.49/2.63 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 2.49/2.63 inference(symmetry,[status(thm)],[23019])).
% 2.49/2.63 tff(23021,plain,
% 2.49/2.63 (e0 = op(e1, op(e1, e1))),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[23007, 23020])).
% 2.49/2.63 tff(23022,plain,
% 2.49/2.63 (~(e3 = op(e1, op(e1, op(e1, e1))))),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[2269, 23021, 23017])).
% 2.49/2.63 tff(23023,plain,
% 2.49/2.63 (~(op(e1, e0) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[23022, 23016])).
% 2.49/2.63 tff(23024,plain,
% 2.49/2.63 (op(e1, e2) = op(e3, e3)),
% 2.49/2.63 inference(transitivity,[status(thm)],[23007, 6444])).
% 2.49/2.63 tff(23025,plain,
% 2.49/2.63 ((op(e1, e2) = e3) <=> (op(e3, e3) = e3)),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23024])).
% 2.49/2.63 tff(23026,plain,
% 2.49/2.63 ((op(e3, e3) = e3) <=> (op(e1, e2) = e3)),
% 2.49/2.63 inference(symmetry,[status(thm)],[23025])).
% 2.49/2.63 tff(23027,plain,
% 2.49/2.63 ((~(op(e3, e3) = e3)) <=> (~(op(e1, e2) = e3))),
% 2.49/2.63 inference(monotonicity,[status(thm)],[23026])).
% 2.49/2.63 tff(23028,plain,
% 2.49/2.63 (~(op(e1, e2) = e3)),
% 2.49/2.63 inference(modus_ponens,[status(thm)],[22962, 23027])).
% 2.49/2.63 tff(23029,plain,
% 2.49/2.63 (op(e1, e0) = e3),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[247, 23028, 22830, 22982])).
% 2.49/2.63 tff(23030,plain,
% 2.49/2.63 ($false),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[23029, 23023])).
% 2.49/2.63 tff(23031,plain,((op(e0, e3) = e0) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~(op(e3, e1) = e3)) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e0, e1) = e3) | (op(e0, e1) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e2) | (~(op(e2, e1) = e0)) | (op(e3, e0) = op(e0, e3))), inference(lemma,lemma(discharge,[]))).
% 2.49/2.63 tff(23032,plain,
% 2.49/2.63 ($false),
% 2.49/2.63 inference(unit_resolution,[status(thm)],[23031, 22827, 2527, 72, 3508, 80, 121, 16411, 5478, 1087, 84, 5528])).
% 2.49/2.64 tff(23033,plain,((op(e0, e1) = e3) | (op(e1, e3) = e2) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e3) = e0) | (op(e1, e1) = e0) | (op(e3, e0) = op(e0, e3)) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.64 tff(23034,plain,
% 2.49/2.64 (op(e0, e1) = e3),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[23033, 22817, 3508, 80, 121, 22758, 84, 72, 1291])).
% 2.49/2.64 tff(23035,plain,
% 2.49/2.64 (op(e0, e1) = op(e2, e3)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23034, 22803])).
% 2.49/2.64 tff(23036,plain,
% 2.49/2.64 ((op(e0, e1) = e1) <=> (op(e2, e3) = op(e2, e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23035, 22826])).
% 2.49/2.64 tff(23037,plain,
% 2.49/2.64 ((op(e0, e1) = e1) <=> (op(e2, e2) = op(e2, e3))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23036, 10611])).
% 2.49/2.64 tff(23038,plain,
% 2.49/2.64 ((op(e2, e2) = op(e2, e3)) <=> (op(e0, e1) = e1)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23037])).
% 2.49/2.64 tff(23039,plain,
% 2.49/2.64 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e0, e1) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23038])).
% 2.49/2.64 tff(23040,plain,
% 2.49/2.64 (~(op(e0, e1) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[515, 23039])).
% 2.49/2.64 tff(23041,plain,
% 2.49/2.64 (op(e0, e0) = e1),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[384, 23040, 121, 22785])).
% 2.49/2.64 tff(23042,plain,
% 2.49/2.64 (e1 = op(e0, e0)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23041, 74])).
% 2.49/2.64 tff(23043,plain,
% 2.49/2.64 (op(e0, e0) = op(e2, e2)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23041, 22826])).
% 2.49/2.64 tff(23044,plain,
% 2.49/2.64 (op(e0, op(e0, e0)) = op(e0, op(e2, e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23043])).
% 2.49/2.64 tff(23045,plain,
% 2.49/2.64 (op(e0, op(e2, e2)) = op(e0, op(e0, e0))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23044])).
% 2.49/2.64 tff(23046,plain,
% 2.49/2.64 (op(e2, e2) = op(e1, e3)),
% 2.49/2.64 inference(transitivity,[status(thm)],[22825, 22771])).
% 2.49/2.64 tff(23047,plain,
% 2.49/2.64 (op(e0, op(e2, e2)) = op(e0, op(e1, e3))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23046])).
% 2.49/2.64 tff(23048,plain,
% 2.49/2.64 (op(e0, op(e1, e3)) = op(e0, op(e2, e2))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23047])).
% 2.49/2.64 tff(23049,plain,
% 2.49/2.64 (op(e0, op(e1, e3)) = op(e0, e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[22764])).
% 2.49/2.64 tff(23050,plain,
% 2.49/2.64 (op(e0, e1) = op(e0, op(e1, e3))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23049])).
% 2.49/2.64 tff(23051,plain,
% 2.49/2.64 (e3 = op(e0, e1)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23034])).
% 2.49/2.64 tff(23052,plain,
% 2.49/2.64 (e3 = op(e0, op(e0, e0))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23051, 23050, 23048, 23045])).
% 2.49/2.64 tff(23053,plain,
% 2.49/2.64 (op(e0, op(e0, e0)) = op(e2, e3)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23044, 23047, 23049, 23034, 22803])).
% 2.49/2.64 tff(23054,plain,
% 2.49/2.64 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e2, e3))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23053])).
% 2.49/2.64 tff(23055,plain,
% 2.49/2.64 (op(e0, op(e2, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23054])).
% 2.49/2.64 tff(23056,plain,
% 2.49/2.64 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[22802])).
% 2.49/2.64 tff(23057,plain,
% 2.49/2.64 (op(e0, e3) = op(e0, op(e2, e3))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23056])).
% 2.49/2.64 tff(23058,plain,
% 2.49/2.64 (e2 = op(e0, e3)),
% 2.49/2.64 inference(symmetry,[status(thm)],[22753])).
% 2.49/2.64 tff(23059,plain,
% 2.49/2.64 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23058, 23057, 23055])).
% 2.49/2.64 tff(23060,plain,
% 2.49/2.64 ($false),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[16194, 23059, 23052, 23042])).
% 2.49/2.64 tff(23061,plain,((op(e1, e0) = e3) | (op(e0, e3) = e1) | (~(op(e2, e1) = e0)) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e1, e3) = e2) | (op(e1, e1) = e3) | (op(e2, e3) = e1) | (op(e1, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.64 tff(23062,plain,
% 2.49/2.64 (op(e1, e0) = e3),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[23061, 80, 3508, 121, 84, 72, 1291, 76, 6687])).
% 2.49/2.64 tff(23063,plain,
% 2.49/2.64 (op(e1, e2) = e3),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[7899, 23062, 3785, 72, 6687, 22759, 22770])).
% 2.49/2.64 tff(23064,plain,
% 2.49/2.64 (op(e1, e0) = e0),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[9437, 23063, 80, 22759, 22767])).
% 2.49/2.64 tff(23065,plain,
% 2.49/2.64 (e3 = op(e1, e0)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23062])).
% 2.49/2.64 tff(23066,plain,
% 2.49/2.64 (op(e2, e3) = e0),
% 2.49/2.64 inference(transitivity,[status(thm)],[22802, 23065, 23064])).
% 2.49/2.64 tff(23067,plain,
% 2.49/2.64 ($false),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[5446, 23066])).
% 2.49/2.64 tff(23068,plain,((op(e1, e3) = e0) | (op(e1, e2) = e2) | (op(e1, e3) = e2) | (op(e1, e0) = e2) | (~(op(e2, e1) = e0)) | (op(e0, e3) = e1) | (op(e1, e1) = e0) | (op(e1, e1) = e3) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.64 tff(23069,plain,
% 2.49/2.64 (op(e1, e3) = e0),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[23068, 22748, 21331, 21340, 21647, 121, 21357, 21634, 76])).
% 2.49/2.64 tff(23070,plain,
% 2.49/2.64 (~(op(e1, e2) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[21630, 23069, 21327])).
% 2.49/2.64 tff(23071,plain,
% 2.49/2.64 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23069])).
% 2.49/2.64 tff(23072,plain,
% 2.49/2.64 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23071])).
% 2.49/2.64 tff(23073,plain,
% 2.49/2.64 (~(op(e1, e2) = e0)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[1850, 23072])).
% 2.49/2.64 tff(23074,plain,
% 2.49/2.64 (op(e1, e2) = e1),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[1859, 23073, 21647, 23070])).
% 2.49/2.64 tff(23075,plain,
% 2.49/2.64 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23074])).
% 2.49/2.64 tff(23076,plain,
% 2.49/2.64 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23075, 316])).
% 2.49/2.64 tff(23077,plain,
% 2.49/2.64 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23076])).
% 2.49/2.64 tff(23078,plain,
% 2.49/2.64 (~(op(e2, e2) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[1273, 23077])).
% 2.49/2.64 tff(23079,plain,
% 2.49/2.64 (op(e2, e0) = e1),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[345, 23078, 76, 22752])).
% 2.49/2.64 tff(23080,plain,
% 2.49/2.64 ((op(e2, e0) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23079])).
% 2.49/2.64 tff(23081,plain,
% 2.49/2.64 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23080, 697])).
% 2.49/2.64 tff(23082,plain,
% 2.49/2.64 ((op(e0, e2) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23081])).
% 2.49/2.64 tff(23083,plain,
% 2.49/2.64 ((~(op(e0, e2) = e1)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23082])).
% 2.49/2.64 tff(23084,plain,
% 2.49/2.64 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23074])).
% 2.49/2.64 tff(23085,plain,
% 2.49/2.64 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23084])).
% 2.49/2.64 tff(23086,plain,
% 2.49/2.64 (~(op(e0, e2) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[6205, 23085])).
% 2.49/2.64 tff(23087,plain,
% 2.49/2.64 (~(op(e2, e0) = op(e0, e2))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23086, 23083])).
% 2.49/2.64 tff(23088,plain,
% 2.49/2.64 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[6358, 23087])).
% 2.49/2.64 tff(23089,plain,
% 2.49/2.64 ((op(e2, e1) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[22748])).
% 2.49/2.64 tff(23090,plain,
% 2.49/2.64 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23089, 67])).
% 2.49/2.64 tff(23091,plain,
% 2.49/2.64 ((op(e1, e2) = e0) <=> (op(e2, e1) = op(e1, e2))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23090])).
% 2.49/2.64 tff(23092,plain,
% 2.49/2.64 ((op(e1, e2) = op(e1, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23071, 23091])).
% 2.49/2.64 tff(23093,plain,
% 2.49/2.64 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23092])).
% 2.49/2.64 tff(23094,plain,
% 2.49/2.64 (~(op(e2, e1) = op(e1, e2))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[1850, 23093])).
% 2.49/2.64 tff(23095,plain,
% 2.49/2.64 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[557, 23094])).
% 2.49/2.64 tff(23096,plain,
% 2.49/2.64 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e0)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23069])).
% 2.49/2.64 tff(23097,plain,
% 2.49/2.64 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23096])).
% 2.49/2.64 tff(23098,plain,
% 2.49/2.64 ((op(e3, e1) = e0) <=> (op(e1, e3) = op(e3, e1))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23097, 6290])).
% 2.49/2.64 tff(23099,plain,
% 2.49/2.64 ((~(op(e3, e1) = e0)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23098])).
% 2.49/2.64 tff(23100,plain,
% 2.49/2.64 ((op(e2, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[22748])).
% 2.49/2.64 tff(23101,plain,
% 2.49/2.64 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23100, 5470])).
% 2.49/2.64 tff(23102,plain,
% 2.49/2.64 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23101])).
% 2.49/2.64 tff(23103,plain,
% 2.49/2.64 (~(op(e3, e1) = e0)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[402, 23102])).
% 2.49/2.64 tff(23104,plain,
% 2.49/2.64 (~(op(e1, e3) = op(e3, e1))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23103, 23099])).
% 2.49/2.64 tff(23105,plain,
% 2.49/2.64 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[6307, 23104])).
% 2.49/2.64 tff(23106,plain,
% 2.49/2.64 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23069])).
% 2.49/2.64 tff(23107,plain,
% 2.49/2.64 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23106])).
% 2.49/2.64 tff(23108,plain,
% 2.49/2.64 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23107])).
% 2.49/2.64 tff(23109,plain,
% 2.49/2.64 (~(op(e1, e3) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[26, 23108])).
% 2.49/2.64 tff(23110,plain,
% 2.49/2.64 (op(e3, e3) = e1),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[151, 23109, 76, 121])).
% 2.49/2.64 tff(23111,plain,
% 2.49/2.64 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23110])).
% 2.49/2.64 tff(23112,plain,
% 2.49/2.64 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23111])).
% 2.49/2.64 tff(23113,plain,
% 2.49/2.64 (~(op(e3, e1) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[437, 23112])).
% 2.49/2.64 tff(23114,plain,
% 2.49/2.64 (op(e0, e1) = e1),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[1252, 23113, 22752, 21692])).
% 2.49/2.64 tff(23115,plain,
% 2.49/2.64 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23114])).
% 2.49/2.64 tff(23116,plain,
% 2.49/2.64 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e0, e1))),
% 2.49/2.64 inference(symmetry,[status(thm)],[23115])).
% 2.49/2.64 tff(23117,plain,
% 2.49/2.64 ((op(e1, e0) = e1) <=> (op(e0, e1) = op(e1, e0))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23116, 596])).
% 2.49/2.64 tff(23118,plain,
% 2.49/2.64 ((~(op(e1, e0) = e1)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23117])).
% 2.49/2.64 tff(23119,plain,
% 2.49/2.64 ((op(e1, e3) = e3) <=> (e0 = e3)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23069])).
% 2.49/2.64 tff(23120,plain,
% 2.49/2.64 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23119])).
% 2.49/2.64 tff(23121,plain,
% 2.49/2.64 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23120])).
% 2.49/2.64 tff(23122,plain,
% 2.49/2.64 (~(op(e1, e3) = e3)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[181, 23121])).
% 2.49/2.64 tff(23123,plain,
% 2.49/2.64 (op(e1, e0) = e3),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[247, 23122, 21634, 23070])).
% 2.49/2.64 tff(23124,plain,
% 2.49/2.64 (e3 = op(e1, e0)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23123])).
% 2.49/2.64 tff(23125,plain,
% 2.49/2.64 ((e1 = e3) <=> (e1 = op(e1, e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23124])).
% 2.49/2.64 tff(23126,plain,
% 2.49/2.64 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23125, 17546])).
% 2.49/2.64 tff(23127,plain,
% 2.49/2.64 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23126])).
% 2.49/2.64 tff(23128,plain,
% 2.49/2.64 (~(op(e1, e0) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[303, 23127])).
% 2.49/2.64 tff(23129,plain,
% 2.49/2.64 (~(op(e0, e1) = op(e1, e0))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23128, 23118])).
% 2.49/2.64 tff(23130,plain,
% 2.49/2.64 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[609, 23129])).
% 2.49/2.64 tff(23131,plain,
% 2.49/2.64 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23110])).
% 2.49/2.64 tff(23132,plain,
% 2.49/2.64 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23131])).
% 2.49/2.64 tff(23133,plain,
% 2.49/2.64 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23132])).
% 2.49/2.64 tff(23134,plain,
% 2.49/2.64 (~(op(e3, e3) = e3)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[303, 23133])).
% 2.49/2.64 tff(23135,plain,
% 2.49/2.64 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23124])).
% 2.49/2.64 tff(23136,plain,
% 2.49/2.64 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23135, 595])).
% 2.49/2.64 tff(23137,plain,
% 2.49/2.64 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23136])).
% 2.49/2.64 tff(23138,plain,
% 2.49/2.64 ((op(e1, e0) = e1) <=> (op(e0, e1) = e3)),
% 2.49/2.64 inference(transitivity,[status(thm)],[23116, 23137])).
% 2.49/2.64 tff(23139,plain,
% 2.49/2.64 ((~(op(e1, e0) = e1)) <=> (~(op(e0, e1) = e3))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23138])).
% 2.49/2.64 tff(23140,plain,
% 2.49/2.64 (~(op(e0, e1) = e3)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23128, 23139])).
% 2.49/2.64 tff(23141,plain,
% 2.49/2.64 (op(e3, e1) = e3),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[446, 23113, 23103, 21540])).
% 2.49/2.64 tff(23142,plain,
% 2.49/2.64 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e1)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23114])).
% 2.49/2.64 tff(23143,plain,
% 2.49/2.64 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e1))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23142])).
% 2.49/2.64 tff(23144,plain,
% 2.49/2.64 (~(op(e0, e0) = e1)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[811, 23143])).
% 2.49/2.64 tff(23145,plain,
% 2.49/2.64 ((op(e2, e0) = e2) <=> (e1 = e2)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23079])).
% 2.49/2.64 tff(23146,plain,
% 2.49/2.64 ((e1 = e2) <=> (op(e2, e0) = e2)),
% 2.49/2.64 inference(symmetry,[status(thm)],[23145])).
% 2.49/2.64 tff(23147,plain,
% 2.49/2.64 ((~(e1 = e2)) <=> (~(op(e2, e0) = e2))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23146])).
% 2.49/2.64 tff(23148,plain,
% 2.49/2.64 (~(op(e2, e0) = e2)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[708, 23147])).
% 2.49/2.64 tff(23149,plain,
% 2.49/2.64 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e0)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23069])).
% 2.49/2.64 tff(23150,plain,
% 2.49/2.64 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23149])).
% 2.49/2.64 tff(23151,plain,
% 2.49/2.64 (~(op(e0, e3) = e0)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[64, 23150])).
% 2.49/2.64 tff(23152,plain,
% 2.49/2.64 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e0)),
% 2.49/2.64 inference(monotonicity,[status(thm)],[22748])).
% 2.49/2.64 tff(23153,plain,
% 2.49/2.64 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e0))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23152])).
% 2.49/2.64 tff(23154,plain,
% 2.49/2.64 (~(op(e0, e1) = e0)),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[606, 23153])).
% 2.49/2.64 tff(23155,plain,
% 2.49/2.64 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.49/2.64 inference(transitivity,[status(thm)],[23071, 23091, 531])).
% 2.49/2.64 tff(23156,plain,
% 2.49/2.64 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23155])).
% 2.49/2.64 tff(23157,plain,
% 2.49/2.64 (~(op(e1, e2) = op(e2, e1))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[1850, 23156])).
% 2.49/2.64 tff(23158,plain,
% 2.49/2.64 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[539, 23157])).
% 2.49/2.64 tff(23159,plain,
% 2.49/2.64 ((~(op(e1, e0) = e1)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23116])).
% 2.49/2.64 tff(23160,plain,
% 2.49/2.64 (~(op(e1, e0) = op(e0, e1))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23128, 23159])).
% 2.49/2.64 tff(23161,plain,
% 2.49/2.64 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.49/2.64 inference(unit_resolution,[status(thm)],[613, 23160])).
% 2.49/2.64 tff(23162,plain,
% 2.49/2.64 ((~(op(e3, e1) = e0)) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.49/2.64 inference(monotonicity,[status(thm)],[23097])).
% 2.49/2.64 tff(23163,plain,
% 2.49/2.64 (~(op(e3, e1) = op(e1, e3))),
% 2.49/2.64 inference(modus_ponens,[status(thm)],[23103, 23162])).
% 2.49/2.64 tff(23164,plain,
% 2.49/2.64 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[6362, 23163])).
% 2.49/2.65 tff(23165,plain,
% 2.49/2.65 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23110])).
% 2.49/2.65 tff(23166,plain,
% 2.49/2.65 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23165])).
% 2.49/2.65 tff(23167,plain,
% 2.49/2.65 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.49/2.65 inference(symmetry,[status(thm)],[23166])).
% 2.49/2.65 tff(23168,plain,
% 2.49/2.65 (op(e3, op(e3, e3)) = e3),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[23141, 23167])).
% 2.49/2.65 tff(23169,plain,
% 2.49/2.65 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[6277, 23168])).
% 2.49/2.65 tff(23170,plain,
% 2.49/2.65 (op(e1, op(e1, e1)) = e1),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[23074, 21669])).
% 2.49/2.65 tff(23171,plain,
% 2.49/2.65 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[5678, 23170])).
% 2.49/2.65 tff(23172,plain,
% 2.49/2.65 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e2, e0))),
% 2.49/2.65 inference(transitivity,[status(thm)],[23082, 6337])).
% 2.49/2.65 tff(23173,plain,
% 2.49/2.65 ((~(op(e0, e2) = e1)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23172])).
% 2.49/2.65 tff(23174,plain,
% 2.49/2.65 (~(op(e0, e2) = op(e2, e0))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[23086, 23173])).
% 2.49/2.65 tff(23175,plain,
% 2.49/2.65 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[6347, 23174])).
% 2.49/2.65 tff(23176,plain,
% 2.49/2.65 (op(e1, op(e2, e3)) = op(e1, e2)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[16115])).
% 2.49/2.65 tff(23177,plain,
% 2.49/2.65 (op(e1, op(e2, e3)) = e1),
% 2.49/2.65 inference(transitivity,[status(thm)],[23176, 6683])).
% 2.49/2.65 tff(23178,plain,
% 2.49/2.65 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[10724, 23177])).
% 2.49/2.65 tff(23179,plain,
% 2.49/2.65 (op(e0, e3) = e3),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[687, 79, 1087, 121])).
% 2.49/2.65 tff(23180,plain,
% 2.49/2.65 (op(e0, e3) = op(e1, e0)),
% 2.49/2.65 inference(transitivity,[status(thm)],[23179, 259])).
% 2.49/2.65 tff(23181,plain,
% 2.49/2.65 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = op(e1, e0))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23180])).
% 2.49/2.65 tff(23182,plain,
% 2.49/2.65 ((op(e3, e0) = op(e0, e3)) <=> (op(e1, e0) = op(e3, e0))),
% 2.49/2.65 inference(transitivity,[status(thm)],[23181, 2294])).
% 2.49/2.65 tff(23183,plain,
% 2.49/2.65 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.49/2.65 inference(symmetry,[status(thm)],[23182])).
% 2.49/2.65 tff(23184,plain,
% 2.49/2.65 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.49/2.65 inference(transitivity,[status(thm)],[23183, 453])).
% 2.49/2.65 tff(23185,plain,
% 2.49/2.65 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23184])).
% 2.49/2.65 tff(23186,plain,
% 2.49/2.65 (~(op(e0, e3) = op(e3, e0))),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[410, 23185])).
% 2.49/2.65 tff(23187,plain,
% 2.49/2.65 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[496, 23186])).
% 2.49/2.65 tff(23188,plain,
% 2.49/2.65 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23179])).
% 2.49/2.65 tff(23189,plain,
% 2.49/2.65 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23188])).
% 2.49/2.65 tff(23190,plain,
% 2.49/2.65 (~(op(e0, e2) = e3)),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[918, 23189])).
% 2.49/2.65 tff(23191,plain,
% 2.49/2.65 (op(e2, op(e2, e2)) = e2),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[22473, 23190, 72, 258, 5607, 82, 75, 2527])).
% 2.49/2.65 tff(23192,plain,
% 2.49/2.65 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[528, 23191])).
% 2.49/2.65 tff(23193,plain,
% 2.49/2.65 (op(e0, e0) = e2),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[21766, 23192, 9846, 23187, 6689, 6688, 5511, 5675, 5673, 23178, 5681, 5669, 5680, 5674, 16115, 6687, 982, 11542, 2379])).
% 2.49/2.65 tff(23194,plain,
% 2.49/2.65 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23193])).
% 2.49/2.65 tff(23195,plain,
% 2.49/2.65 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 2.49/2.65 inference(transitivity,[status(thm)],[23194, 1])).
% 2.49/2.65 tff(23196,plain,
% 2.49/2.65 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 2.49/2.65 inference(symmetry,[status(thm)],[23195])).
% 2.49/2.65 tff(23197,plain,
% 2.49/2.65 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23196])).
% 2.49/2.65 tff(23198,plain,
% 2.49/2.65 (~(op(e0, e0) = e0)),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[14, 23197])).
% 2.49/2.65 tff(23199,plain,
% 2.49/2.65 (op(e0, e2) = e0),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[3976, 23198, 3849, 1087])).
% 2.49/2.65 tff(23200,plain,
% 2.49/2.65 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23193])).
% 2.49/2.65 tff(23201,plain,
% 2.49/2.65 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.49/2.65 inference(transitivity,[status(thm)],[23200, 5377])).
% 2.49/2.65 tff(23202,plain,
% 2.49/2.65 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23201])).
% 2.49/2.65 tff(23203,plain,
% 2.49/2.65 (~(op(e3, e0) = e2)),
% 2.49/2.65 inference(modus_ponens,[status(thm)],[6384, 23202])).
% 2.49/2.65 tff(23204,plain,
% 2.49/2.65 (op(e3, e2) = e2),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[15971, 23203, 82])).
% 2.49/2.65 tff(23205,plain,
% 2.49/2.65 (op(e0, op(e3, e2)) = op(e0, e2)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23204])).
% 2.49/2.65 tff(23206,plain,
% 2.49/2.65 (op(e0, op(e3, e2)) = e0),
% 2.49/2.65 inference(transitivity,[status(thm)],[23205, 23199])).
% 2.49/2.65 tff(23207,plain,
% 2.49/2.65 (op(e1, op(e0, e0)) = op(e1, e2)),
% 2.49/2.65 inference(monotonicity,[status(thm)],[23193])).
% 2.49/2.65 tff(23208,plain,
% 2.49/2.65 (op(e1, op(e0, e0)) = e1),
% 2.49/2.65 inference(transitivity,[status(thm)],[23207, 6683])).
% 2.49/2.65 tff(23209,plain,
% 2.49/2.65 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[6717, 23208])).
% 2.49/2.65 tff(23210,plain,
% 2.49/2.65 (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[5367, 23209, 23192, 9846, 23187, 6689, 6688, 5511, 5675, 5673, 23178, 5681, 5669, 5680, 5674])).
% 2.49/2.65 tff(23211,plain,
% 2.49/2.65 (~(op(e0, op(e3, e2)) = e0)),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[10702, 23210])).
% 2.49/2.65 tff(23212,plain,
% 2.49/2.65 ($false),
% 2.49/2.65 inference(unit_resolution,[status(thm)],[23211, 23206])).
% 2.49/2.65 tff(23213,plain,((op(e0, e3) = e2) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (op(e3, e1) = e2) | (op(e0, e1) = e0) | (op(e0, e3) = e0) | (~(op(e1, e2) = e1)) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e0, e0) = e1) | (op(e1, e3) = e2) | (~(op(e1, e0) = e3)) | (~(op(e3, e1) = e3)) | (op(e1, e2) = e3) | (op(e0, e1) = e3) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.65 tff(23214,plain,
% 2.55/2.65 (op(e0, e3) = e2),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[23213, 23175, 23171, 23169, 23164, 23161, 23158, 23130, 23105, 23095, 23088, 21540, 23154, 23151, 23074, 21340, 23148, 23144, 21331, 23123, 23141, 23070, 23140, 121])).
% 2.55/2.65 tff(23215,plain,
% 2.55/2.65 ((op(e0, e3) = e3) <=> (e2 = op(e1, e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23214, 23124])).
% 2.55/2.65 tff(23216,plain,
% 2.55/2.65 ((op(e0, e3) = e3) <=> (op(e1, e0) = e2)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23215, 2154])).
% 2.55/2.65 tff(23217,plain,
% 2.55/2.65 ((op(e1, e0) = e2) <=> (op(e0, e3) = e3)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23216])).
% 2.55/2.65 tff(23218,plain,
% 2.55/2.65 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e3) = e3))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23217])).
% 2.55/2.65 tff(23219,plain,
% 2.55/2.65 (~(op(e0, e3) = e3)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[21340, 23218])).
% 2.55/2.65 tff(23220,plain,
% 2.55/2.65 (op(e2, e3) = e3),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[480, 23219, 23134, 23122])).
% 2.55/2.65 tff(23221,plain,
% 2.55/2.65 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23220])).
% 2.55/2.65 tff(23222,plain,
% 2.55/2.65 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.55/2.65 inference(symmetry,[status(thm)],[23221])).
% 2.55/2.65 tff(23223,plain,
% 2.55/2.65 ((~(op(e3, e2) = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23222])).
% 2.55/2.65 tff(23224,plain,
% 2.55/2.65 ((op(e3, e1) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23141])).
% 2.55/2.65 tff(23225,plain,
% 2.55/2.65 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23224, 3423])).
% 2.55/2.65 tff(23226,plain,
% 2.55/2.65 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23225])).
% 2.55/2.65 tff(23227,plain,
% 2.55/2.65 (~(op(e3, e2) = e3)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[3429, 23226])).
% 2.55/2.65 tff(23228,plain,
% 2.55/2.65 (~(op(e3, e2) = op(e2, e3))),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[23227, 23223])).
% 2.55/2.65 tff(23229,plain,
% 2.55/2.65 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[500, 23228])).
% 2.55/2.65 tff(23230,plain,
% 2.55/2.65 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23214])).
% 2.55/2.65 tff(23231,plain,
% 2.55/2.65 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23230])).
% 2.55/2.65 tff(23232,plain,
% 2.55/2.65 (~(op(e0, e0) = e2)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[3414, 23231])).
% 2.55/2.65 tff(23233,plain,
% 2.55/2.65 (op(e3, e0) = e2),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[589, 23232, 21340, 23148])).
% 2.55/2.65 tff(23234,plain,
% 2.55/2.65 (op(e1, op(e3, e0)) = op(e1, e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23233])).
% 2.55/2.65 tff(23235,plain,
% 2.55/2.65 (op(e1, op(e3, e0)) = e1),
% 2.55/2.65 inference(transitivity,[status(thm)],[23234, 23074])).
% 2.55/2.65 tff(23236,plain,
% 2.55/2.65 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[8474, 23235])).
% 2.55/2.65 tff(23237,plain,
% 2.55/2.65 (op(e2, op(e1, e0)) = op(e2, e3)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23123])).
% 2.55/2.65 tff(23238,plain,
% 2.55/2.65 (op(e2, e3) = op(e2, op(e1, e0))),
% 2.55/2.65 inference(symmetry,[status(thm)],[23237])).
% 2.55/2.65 tff(23239,plain,
% 2.55/2.65 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23238])).
% 2.55/2.65 tff(23240,plain,
% 2.55/2.65 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, e3) = e2)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23239])).
% 2.55/2.65 tff(23241,plain,
% 2.55/2.65 ((e2 = op(e2, op(e1, e0))) <=> (op(e2, op(e1, e0)) = e2)),
% 2.55/2.65 inference(commutativity,[status(thm)],[])).
% 2.55/2.65 tff(23242,plain,
% 2.55/2.65 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, op(e1, e0)))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23214, 23238])).
% 2.55/2.65 tff(23243,plain,
% 2.55/2.65 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, op(e1, e0)) = e2)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23242, 23241])).
% 2.55/2.65 tff(23244,plain,
% 2.55/2.65 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23243, 23240])).
% 2.55/2.65 tff(23245,plain,
% 2.55/2.65 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23244])).
% 2.55/2.65 tff(23246,plain,
% 2.55/2.65 (~(op(e2, e3) = e2)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[964, 23245])).
% 2.55/2.65 tff(23247,plain,
% 2.55/2.65 (op(e2, e2) = e2),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[2088, 23246, 22153, 23148])).
% 2.55/2.65 tff(23248,plain,
% 2.55/2.65 (op(e1, op(e2, e2)) = op(e1, e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23247])).
% 2.55/2.65 tff(23249,plain,
% 2.55/2.65 (op(e1, op(e2, e2)) = e1),
% 2.55/2.65 inference(transitivity,[status(thm)],[23248, 23074])).
% 2.55/2.65 tff(23250,plain,
% 2.55/2.65 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[6714, 23249])).
% 2.55/2.65 tff(23251,plain,
% 2.55/2.65 ((op(e3, e2) = e3) <=> (op(e2, e3) = op(e3, e2))),
% 2.55/2.65 inference(transitivity,[status(thm)],[23222, 395])).
% 2.55/2.65 tff(23252,plain,
% 2.55/2.65 ((~(op(e3, e2) = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23251])).
% 2.55/2.65 tff(23253,plain,
% 2.55/2.65 (~(op(e2, e3) = op(e3, e2))),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[23227, 23252])).
% 2.55/2.65 tff(23254,plain,
% 2.55/2.65 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[430, 23253])).
% 2.55/2.65 tff(23255,plain,
% 2.55/2.65 ((op(e0, e0) = e3) <=> (op(e0, e0) = op(e1, e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23124])).
% 2.55/2.65 tff(23256,plain,
% 2.55/2.65 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23255])).
% 2.55/2.65 tff(23257,plain,
% 2.55/2.65 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23256])).
% 2.55/2.65 tff(23258,plain,
% 2.55/2.65 (~(op(e0, e0) = e3)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[2471, 23257])).
% 2.55/2.65 tff(23259,plain,
% 2.55/2.65 (op(e0, e0) = e0),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[3612, 23232, 23258, 23144])).
% 2.55/2.65 tff(23260,plain,
% 2.55/2.65 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23259])).
% 2.55/2.65 tff(23261,plain,
% 2.55/2.65 (op(e0, op(e0, e0)) = e0),
% 2.55/2.65 inference(transitivity,[status(thm)],[23260, 23259])).
% 2.55/2.65 tff(23262,plain,
% 2.55/2.65 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[5598, 23261])).
% 2.55/2.65 tff(23263,plain,
% 2.55/2.65 ($false),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[5367, 23262, 23254, 23250, 23175, 23236, 23171, 23169, 23164, 23161, 23158, 23229, 23130, 23105, 23095, 23088])).
% 2.55/2.65 tff(23264,plain,((op(e0, e3) = e1) | (op(e2, e3) = e1) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.55/2.65 tff(23265,plain,
% 2.55/2.65 (op(e2, e3) = e1),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[23264, 21788, 17])).
% 2.55/2.65 tff(23266,plain,
% 2.55/2.65 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e1)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23265])).
% 2.55/2.65 tff(23267,plain,
% 2.55/2.65 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e1))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23266])).
% 2.55/2.65 tff(23268,plain,
% 2.55/2.65 (~(op(e2, e1) = e1)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[197, 23267])).
% 2.55/2.65 tff(23269,plain,
% 2.55/2.65 ((op(e2, e3) = e2) <=> (e1 = e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23265])).
% 2.55/2.65 tff(23270,plain,
% 2.55/2.65 ((e1 = e2) <=> (op(e2, e3) = e2)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23269])).
% 2.55/2.65 tff(23271,plain,
% 2.55/2.65 ((~(e1 = e2)) <=> (~(op(e2, e3) = e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23270])).
% 2.55/2.65 tff(23272,plain,
% 2.55/2.65 (~(op(e2, e3) = e2)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[708, 23271])).
% 2.55/2.65 tff(23273,plain,
% 2.55/2.65 (op(e0, e3) = e2),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[15003, 23272, 21331])).
% 2.55/2.65 tff(23274,plain,
% 2.55/2.65 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23273])).
% 2.55/2.65 tff(23275,plain,
% 2.55/2.65 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23274])).
% 2.55/2.65 tff(23276,plain,
% 2.55/2.65 (~(op(e0, e0) = e2)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[3414, 23275])).
% 2.55/2.65 tff(23277,plain,
% 2.55/2.65 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23265])).
% 2.55/2.65 tff(23278,plain,
% 2.55/2.65 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23277])).
% 2.55/2.65 tff(23279,plain,
% 2.55/2.65 (~(op(e1, e3) = e1)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[118, 23278])).
% 2.55/2.65 tff(23280,plain,
% 2.55/2.65 (op(e1, e3) = e3),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[104, 80, 21331, 23279])).
% 2.55/2.65 tff(23281,plain,
% 2.55/2.65 (e3 = op(e1, e3)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23280])).
% 2.55/2.65 tff(23282,plain,
% 2.55/2.65 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23273])).
% 2.55/2.65 tff(23283,plain,
% 2.55/2.65 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23282, 1])).
% 2.55/2.65 tff(23284,plain,
% 2.55/2.65 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23283])).
% 2.55/2.65 tff(23285,plain,
% 2.55/2.65 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23284])).
% 2.55/2.65 tff(23286,plain,
% 2.55/2.65 (~(op(e0, e3) = e0)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[14, 23285])).
% 2.55/2.65 tff(23287,plain,
% 2.55/2.65 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23265])).
% 2.55/2.65 tff(23288,plain,
% 2.55/2.65 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23287, 18])).
% 2.55/2.65 tff(23289,plain,
% 2.55/2.65 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23288])).
% 2.55/2.65 tff(23290,plain,
% 2.55/2.65 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23289])).
% 2.55/2.65 tff(23291,plain,
% 2.55/2.65 (~(op(e2, e3) = e0)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[26, 23290])).
% 2.55/2.65 tff(23292,plain,
% 2.55/2.65 (op(e3, e3) = e0),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[1098, 80, 23291, 23286])).
% 2.55/2.65 tff(23293,plain,
% 2.55/2.65 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23292])).
% 2.55/2.65 tff(23294,plain,
% 2.55/2.65 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23293])).
% 2.55/2.65 tff(23295,plain,
% 2.55/2.65 (~(op(e3, e1) = e0)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[437, 23294])).
% 2.55/2.65 tff(23296,plain,
% 2.55/2.65 (op(e0, e1) = e0),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[292, 2559, 23295, 21357])).
% 2.55/2.65 tff(23297,plain,
% 2.55/2.65 ((op(e0, e1) = e1) <=> (e0 = e1)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23296])).
% 2.55/2.65 tff(23298,plain,
% 2.55/2.65 ((e0 = e1) <=> (op(e0, e1) = e1)),
% 2.55/2.65 inference(symmetry,[status(thm)],[23297])).
% 2.55/2.65 tff(23299,plain,
% 2.55/2.65 ((~(e0 = e1)) <=> (~(op(e0, e1) = e1))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23298])).
% 2.55/2.65 tff(23300,plain,
% 2.55/2.65 (~(op(e0, e1) = e1)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[26, 23299])).
% 2.55/2.65 tff(23301,plain,
% 2.55/2.65 (op(e3, e1) = e1),
% 2.55/2.65 inference(unit_resolution,[status(thm)],[1252, 23300, 23268, 21692])).
% 2.55/2.65 tff(23302,plain,
% 2.55/2.65 ((op(e3, e1) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23301])).
% 2.55/2.65 tff(23303,plain,
% 2.55/2.65 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.55/2.65 inference(transitivity,[status(thm)],[23302, 7171])).
% 2.55/2.65 tff(23304,plain,
% 2.55/2.65 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23303])).
% 2.55/2.65 tff(23305,plain,
% 2.55/2.65 (~(op(e3, e2) = e1)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[3429, 23304])).
% 2.55/2.65 tff(23306,plain,
% 2.55/2.65 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e1)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23265])).
% 2.55/2.65 tff(23307,plain,
% 2.55/2.65 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e1))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23306])).
% 2.55/2.65 tff(23308,plain,
% 2.55/2.65 (~(op(e2, e2) = e1)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[515, 23307])).
% 2.55/2.65 tff(23309,plain,
% 2.55/2.65 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e0)),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23292])).
% 2.55/2.65 tff(23310,plain,
% 2.55/2.65 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e0))),
% 2.55/2.65 inference(monotonicity,[status(thm)],[23309])).
% 2.55/2.65 tff(23311,plain,
% 2.55/2.65 (~(op(e3, e2) = e0)),
% 2.55/2.65 inference(modus_ponens,[status(thm)],[1888, 23310])).
% 2.55/2.65 tff(23312,plain,
% 2.55/2.65 ((op(e0, e1) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23296])).
% 2.56/2.66 tff(23313,plain,
% 2.56/2.66 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23312, 10200])).
% 2.56/2.66 tff(23314,plain,
% 2.56/2.66 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23313])).
% 2.56/2.66 tff(23315,plain,
% 2.56/2.66 (~(op(e0, e2) = e0)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[2102, 23314])).
% 2.56/2.66 tff(23316,plain,
% 2.56/2.66 (op(e1, e2) = e0),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[973, 23315, 17, 23311])).
% 2.56/2.66 tff(23317,plain,
% 2.56/2.66 ((op(e1, e2) = e1) <=> (e0 = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23316])).
% 2.56/2.66 tff(23318,plain,
% 2.56/2.66 ((e0 = e1) <=> (op(e1, e2) = e1)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23317])).
% 2.56/2.66 tff(23319,plain,
% 2.56/2.66 ((~(e0 = e1)) <=> (~(op(e1, e2) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23318])).
% 2.56/2.66 tff(23320,plain,
% 2.56/2.66 (~(op(e1, e2) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[26, 23319])).
% 2.56/2.66 tff(23321,plain,
% 2.56/2.66 (op(e0, e2) = e1),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[1613, 23320, 23308, 23305])).
% 2.56/2.66 tff(23322,plain,
% 2.56/2.66 (op(e2, e0) = e0),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[2311, 2559, 17, 23291])).
% 2.56/2.66 tff(23323,plain,
% 2.56/2.66 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23322])).
% 2.56/2.66 tff(23324,plain,
% 2.56/2.66 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e0))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23323])).
% 2.56/2.66 tff(23325,plain,
% 2.56/2.66 (~(op(e1, e0) = e0)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[756, 23324])).
% 2.56/2.66 tff(23326,plain,
% 2.56/2.66 (op(e0, e2) = e3),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[17959, 23305, 23308, 23273, 23280, 21357, 80, 23295, 2559, 23325])).
% 2.56/2.66 tff(23327,plain,
% 2.56/2.66 (e3 = op(e0, e2)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23326])).
% 2.56/2.66 tff(23328,plain,
% 2.56/2.66 (op(e1, e3) = e1),
% 2.56/2.66 inference(transitivity,[status(thm)],[23280, 23327, 23321])).
% 2.56/2.66 tff(23329,plain,
% 2.56/2.66 ($false),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[23279, 23328])).
% 2.56/2.66 tff(23330,plain,((op(e2, e1) = e0) | (op(e1, e3) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.66 tff(23331,plain,
% 2.56/2.66 (op(e2, e1) = e0),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[23330, 80, 17])).
% 2.56/2.66 tff(23332,plain,
% 2.56/2.66 (op(e2, e0) = e3),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[18093, 23331, 23265, 80, 23280])).
% 2.56/2.66 tff(23333,plain,
% 2.56/2.66 (op(e2, e0) = op(e1, e3)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23332, 23281])).
% 2.56/2.66 tff(23334,plain,
% 2.56/2.66 ((op(e2, e0) = e2) <=> (op(e1, e3) = e2)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23333])).
% 2.56/2.66 tff(23335,plain,
% 2.56/2.66 ((op(e1, e3) = e2) <=> (op(e2, e0) = e2)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23334])).
% 2.56/2.66 tff(23336,plain,
% 2.56/2.66 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23335])).
% 2.56/2.66 tff(23337,plain,
% 2.56/2.66 (~(op(e2, e0) = e2)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[21331, 23336])).
% 2.56/2.66 tff(23338,plain,
% 2.56/2.66 (op(e3, e0) = e2),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[589, 23337, 21340, 23276])).
% 2.56/2.66 tff(23339,plain,
% 2.56/2.66 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23338])).
% 2.56/2.66 tff(23340,plain,
% 2.56/2.66 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23339, 69])).
% 2.56/2.66 tff(23341,plain,
% 2.56/2.66 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23340])).
% 2.56/2.66 tff(23342,plain,
% 2.56/2.66 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23341])).
% 2.56/2.66 tff(23343,plain,
% 2.56/2.66 (~(op(e3, e0) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[708, 23342])).
% 2.56/2.66 tff(23344,plain,
% 2.56/2.66 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23265])).
% 2.56/2.66 tff(23345,plain,
% 2.56/2.66 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23344])).
% 2.56/2.66 tff(23346,plain,
% 2.56/2.66 (~(op(e2, e0) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[989, 23345])).
% 2.56/2.66 tff(23347,plain,
% 2.56/2.66 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23332])).
% 2.56/2.66 tff(23348,plain,
% 2.56/2.66 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23347])).
% 2.56/2.66 tff(23349,plain,
% 2.56/2.66 (~(op(e0, e0) = e3)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[359, 23348])).
% 2.56/2.66 tff(23350,plain,
% 2.56/2.66 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23273])).
% 2.56/2.66 tff(23351,plain,
% 2.56/2.66 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23350])).
% 2.56/2.66 tff(23352,plain,
% 2.56/2.66 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23351])).
% 2.56/2.66 tff(23353,plain,
% 2.56/2.66 (~(op(e0, e3) = e3)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[1321, 23352])).
% 2.56/2.66 tff(23354,plain,
% 2.56/2.66 (e2 = op(e0, e3)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23273])).
% 2.56/2.66 tff(23355,plain,
% 2.56/2.66 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23354])).
% 2.56/2.66 tff(23356,plain,
% 2.56/2.66 (op(e3, e0) = op(e0, e3)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23338, 23355])).
% 2.56/2.66 tff(23357,plain,
% 2.56/2.66 (op(e3, op(e0, e3)) = e3),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[3102, 23356, 23273, 23292])).
% 2.56/2.66 tff(23358,plain,
% 2.56/2.66 (op(e3, e2) = op(e3, op(e0, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23354])).
% 2.56/2.66 tff(23359,plain,
% 2.56/2.66 (op(e3, e2) = e3),
% 2.56/2.66 inference(transitivity,[status(thm)],[23358, 23357])).
% 2.56/2.66 tff(23360,plain,
% 2.56/2.66 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e3)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23359])).
% 2.56/2.66 tff(23361,plain,
% 2.56/2.66 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23360])).
% 2.56/2.66 tff(23362,plain,
% 2.56/2.66 (~(op(e0, e2) = e3)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[1467, 23361])).
% 2.56/2.66 tff(23363,plain,
% 2.56/2.66 (op(e0, e1) = e3),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[1495, 23362, 23353, 23349])).
% 2.56/2.66 tff(23364,plain,
% 2.56/2.66 (e1 = op(e0, e0)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[10406, 74])).
% 2.56/2.66 tff(23365,plain,
% 2.56/2.66 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[10406])).
% 2.56/2.66 tff(23366,plain,
% 2.56/2.66 (op(e0, e1) = op(e0, op(e0, e0))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23365])).
% 2.56/2.66 tff(23367,plain,
% 2.56/2.66 (e3 = op(e0, op(e0, e0))),
% 2.56/2.66 inference(transitivity,[status(thm)],[4840, 23366])).
% 2.56/2.66 tff(23368,plain,
% 2.56/2.66 (op(e0, op(e0, e0)) = op(e1, e3)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23365, 4839, 11135])).
% 2.56/2.66 tff(23369,plain,
% 2.56/2.66 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23368])).
% 2.56/2.66 tff(23370,plain,
% 2.56/2.66 (op(e0, op(e1, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23369])).
% 2.56/2.66 tff(23371,plain,
% 2.56/2.66 (e2 = op(e0, op(e0, op(e0, e0)))),
% 2.56/2.66 inference(transitivity,[status(thm)],[2560, 17945, 23370])).
% 2.56/2.66 tff(23372,plain,
% 2.56/2.66 ($false),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[16194, 23371, 23367, 23364])).
% 2.56/2.66 tff(23373,plain,((~(op(e0, e0) = e1)) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e3)) | (~(op(e0, e1) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.66 tff(23374,plain,
% 2.56/2.66 (~(op(e0, e0) = e1)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[23373, 23280, 23273, 23363])).
% 2.56/2.66 tff(23375,plain,
% 2.56/2.66 (op(e1, e0) = e1),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[1480, 23374, 23346, 23343])).
% 2.56/2.66 tff(23376,plain,
% 2.56/2.66 ((op(e2, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23265])).
% 2.56/2.66 tff(23377,plain,
% 2.56/2.66 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23376, 657])).
% 2.56/2.66 tff(23378,plain,
% 2.56/2.66 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23377])).
% 2.56/2.66 tff(23379,plain,
% 2.56/2.66 (~(op(e3, e3) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[368, 23378])).
% 2.56/2.66 tff(23380,plain,
% 2.56/2.66 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23338])).
% 2.56/2.66 tff(23381,plain,
% 2.56/2.66 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23292])).
% 2.56/2.66 tff(23382,plain,
% 2.56/2.66 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23381])).
% 2.56/2.66 tff(23383,plain,
% 2.56/2.66 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23382, 23380])).
% 2.56/2.66 tff(23384,plain,
% 2.56/2.66 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e2))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23383])).
% 2.56/2.66 tff(23385,plain,
% 2.56/2.66 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23384, 7171])).
% 2.56/2.66 tff(23386,plain,
% 2.56/2.66 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23385])).
% 2.56/2.66 tff(23387,plain,
% 2.56/2.66 (e0 = op(e3, e3)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23292, 3078])).
% 2.56/2.66 tff(23388,plain,
% 2.56/2.66 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23381])).
% 2.56/2.66 tff(23389,plain,
% 2.56/2.66 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23388, 5377])).
% 2.56/2.66 tff(23390,plain,
% 2.56/2.66 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23389])).
% 2.56/2.66 tff(23391,plain,
% 2.56/2.66 (e2 = op(e3, op(e3, e3))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23338, 23390])).
% 2.56/2.66 tff(23392,plain,
% 2.56/2.66 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[3093, 23391, 23387])).
% 2.56/2.66 tff(23393,plain,
% 2.56/2.66 (~(op(e3, e2) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23392, 23386])).
% 2.56/2.66 tff(23394,plain,
% 2.56/2.66 (op(e3, e1) = e1),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[939, 23393, 23379, 23343])).
% 2.56/2.66 tff(23395,plain,
% 2.56/2.66 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23394])).
% 2.56/2.66 tff(23396,plain,
% 2.56/2.66 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e1))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23395])).
% 2.56/2.66 tff(23397,plain,
% 2.56/2.66 (~(op(e0, e1) = e1)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[3046, 23396])).
% 2.56/2.66 tff(23398,plain,
% 2.56/2.66 (op(e0, e2) = e1),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[384, 23374, 21788, 23397])).
% 2.56/2.66 tff(23399,plain,
% 2.56/2.66 ((op(e0, e2) = e0) <=> (e1 = e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23398])).
% 2.56/2.66 tff(23400,plain,
% 2.56/2.66 ((op(e0, e2) = e0) <=> (e0 = e1)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23399, 18])).
% 2.56/2.66 tff(23401,plain,
% 2.56/2.66 ((e0 = e1) <=> (op(e0, e2) = e0)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23400])).
% 2.56/2.66 tff(23402,plain,
% 2.56/2.66 ((~(e0 = e1)) <=> (~(op(e0, e2) = e0))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23401])).
% 2.56/2.66 tff(23403,plain,
% 2.56/2.66 (~(op(e0, e2) = e0)),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[26, 23402])).
% 2.56/2.66 tff(23404,plain,
% 2.56/2.66 (op(e1, e2) = e0),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[973, 23403, 17, 23311])).
% 2.56/2.66 tff(23405,plain,
% 2.56/2.66 (op(e1, op(e1, e2)) = op(e1, e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23404])).
% 2.56/2.66 tff(23406,plain,
% 2.56/2.66 (op(e1, op(e1, e2)) = e1),
% 2.56/2.66 inference(transitivity,[status(thm)],[23405, 23375])).
% 2.56/2.66 tff(23407,plain,
% 2.56/2.66 ((op(e2, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23332])).
% 2.56/2.66 tff(23408,plain,
% 2.56/2.66 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23407, 4221])).
% 2.56/2.66 tff(23409,plain,
% 2.56/2.66 ((op(e0, e2) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23408])).
% 2.56/2.66 tff(23410,plain,
% 2.56/2.66 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e0) = op(e0, e2))),
% 2.56/2.66 inference(transitivity,[status(thm)],[23360, 23409])).
% 2.56/2.66 tff(23411,plain,
% 2.56/2.66 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23410])).
% 2.56/2.66 tff(23412,plain,
% 2.56/2.66 (~(op(e2, e0) = op(e0, e2))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[1467, 23411])).
% 2.56/2.66 tff(23413,plain,
% 2.56/2.66 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[6358, 23412])).
% 2.56/2.66 tff(23414,plain,
% 2.56/2.66 (op(e1, op(e3, e3)) = op(e1, e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23292])).
% 2.56/2.66 tff(23415,plain,
% 2.56/2.66 ((op(e1, op(e3, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23414])).
% 2.56/2.66 tff(23416,plain,
% 2.56/2.66 ((op(e1, e0) = e1) <=> (op(e1, op(e3, e3)) = e1)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23415])).
% 2.56/2.66 tff(23417,plain,
% 2.56/2.66 (op(e1, op(e3, e3)) = e1),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23375, 23416])).
% 2.56/2.66 tff(23418,plain,
% 2.56/2.66 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[5685, 23417])).
% 2.56/2.66 tff(23419,plain,
% 2.56/2.66 (op(e3, e2) = op(e1, e3)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23358, 23357, 23281])).
% 2.56/2.66 tff(23420,plain,
% 2.56/2.66 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23419])).
% 2.56/2.66 tff(23421,plain,
% 2.56/2.66 ((op(e3, e1) = op(e3, e2)) <=> (op(e1, e3) = op(e3, e1))),
% 2.56/2.66 inference(transitivity,[status(thm)],[23420, 6290])).
% 2.56/2.66 tff(23422,plain,
% 2.56/2.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23421])).
% 2.56/2.66 tff(23423,plain,
% 2.56/2.66 (~(op(e1, e3) = op(e3, e1))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[3429, 23422])).
% 2.56/2.66 tff(23424,plain,
% 2.56/2.66 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[6307, 23423])).
% 2.56/2.66 tff(23425,plain,
% 2.56/2.66 (op(e0, e1) = op(e1, e3)),
% 2.56/2.66 inference(transitivity,[status(thm)],[23363, 23281])).
% 2.56/2.66 tff(23426,plain,
% 2.56/2.66 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = op(e1, e3))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23425])).
% 2.56/2.66 tff(23427,plain,
% 2.56/2.66 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23426])).
% 2.56/2.66 tff(23428,plain,
% 2.56/2.66 ((op(e1, e0) = op(e1, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 2.56/2.66 inference(transitivity,[status(thm)],[23427, 596])).
% 2.56/2.66 tff(23429,plain,
% 2.56/2.66 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23428])).
% 2.56/2.66 tff(23430,plain,
% 2.56/2.66 (~(op(e0, e1) = op(e1, e0))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[110, 23429])).
% 2.56/2.66 tff(23431,plain,
% 2.56/2.66 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[609, 23430])).
% 2.56/2.66 tff(23432,plain,
% 2.56/2.66 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23265])).
% 2.56/2.66 tff(23433,plain,
% 2.56/2.66 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.66 inference(symmetry,[status(thm)],[23432])).
% 2.56/2.66 tff(23434,plain,
% 2.56/2.66 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.66 inference(transitivity,[status(thm)],[23385, 23433])).
% 2.56/2.66 tff(23435,plain,
% 2.56/2.66 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23434])).
% 2.56/2.66 tff(23436,plain,
% 2.56/2.66 (~(op(e3, e2) = op(e2, e3))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23392, 23435])).
% 2.56/2.66 tff(23437,plain,
% 2.56/2.66 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[500, 23436])).
% 2.56/2.66 tff(23438,plain,
% 2.56/2.66 (op(e1, op(e2, e1)) = op(e1, e0)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23331])).
% 2.56/2.66 tff(23439,plain,
% 2.56/2.66 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e0) = e1)),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23438])).
% 2.56/2.66 tff(23440,plain,
% 2.56/2.66 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 2.56/2.66 inference(symmetry,[status(thm)],[23439])).
% 2.56/2.66 tff(23441,plain,
% 2.56/2.66 (op(e1, op(e2, e1)) = e1),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[23375, 23440])).
% 2.56/2.66 tff(23442,plain,
% 2.56/2.66 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[22078, 23441])).
% 2.56/2.66 tff(23443,plain,
% 2.56/2.66 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.56/2.66 inference(monotonicity,[status(thm)],[23427])).
% 2.56/2.66 tff(23444,plain,
% 2.56/2.66 (~(op(e1, e0) = op(e0, e1))),
% 2.56/2.66 inference(modus_ponens,[status(thm)],[110, 23443])).
% 2.56/2.66 tff(23445,plain,
% 2.56/2.66 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.56/2.66 inference(unit_resolution,[status(thm)],[613, 23444])).
% 2.56/2.66 tff(23446,plain,
% 2.56/2.66 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23420])).
% 2.56/2.67 tff(23447,plain,
% 2.56/2.67 (~(op(e3, e1) = op(e1, e3))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[3429, 23446])).
% 2.56/2.67 tff(23448,plain,
% 2.56/2.67 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6362, 23447])).
% 2.56/2.67 tff(23449,plain,
% 2.56/2.67 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e2, e3) = op(e3, e2))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23385, 23433, 395])).
% 2.56/2.67 tff(23450,plain,
% 2.56/2.67 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23449])).
% 2.56/2.67 tff(23451,plain,
% 2.56/2.67 (~(op(e2, e3) = op(e3, e2))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23392, 23450])).
% 2.56/2.67 tff(23452,plain,
% 2.56/2.67 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[430, 23451])).
% 2.56/2.67 tff(23453,plain,
% 2.56/2.67 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = op(e2, e0))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23360, 23409, 6337])).
% 2.56/2.67 tff(23454,plain,
% 2.56/2.67 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23453])).
% 2.56/2.67 tff(23455,plain,
% 2.56/2.67 (~(op(e0, e2) = op(e2, e0))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[1467, 23454])).
% 2.56/2.67 tff(23456,plain,
% 2.56/2.67 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6347, 23455])).
% 2.56/2.67 tff(23457,plain,
% 2.56/2.67 (~(op(e2, e2) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6638, 23331, 23265])).
% 2.56/2.67 tff(23458,plain,
% 2.56/2.67 (op(e2, e2) = e2),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[524, 23457, 17, 23308])).
% 2.56/2.67 tff(23459,plain,
% 2.56/2.67 (op(e2, op(e3, e0)) = op(e2, e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23338])).
% 2.56/2.67 tff(23460,plain,
% 2.56/2.67 (op(e2, op(e3, e0)) = e2),
% 2.56/2.67 inference(transitivity,[status(thm)],[23459, 23458])).
% 2.56/2.67 tff(23461,plain,
% 2.56/2.67 (((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)) | (~(op(e2, op(e3, e0)) = e2))),
% 2.56/2.67 inference(tautology,[status(thm)],[])).
% 2.56/2.67 tff(23462,plain,
% 2.56/2.67 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[23461, 23460])).
% 2.56/2.67 tff(23463,plain,
% 2.56/2.67 (op(e2, op(e2, e2)) = op(e2, e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23458])).
% 2.56/2.67 tff(23464,plain,
% 2.56/2.67 (op(e2, op(e2, e2)) = e2),
% 2.56/2.67 inference(transitivity,[status(thm)],[23463, 23458])).
% 2.56/2.67 tff(23465,plain,
% 2.56/2.67 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[528, 23464])).
% 2.56/2.67 tff(23466,plain,
% 2.56/2.67 (op(e2, op(e1, e1)) = op(e2, e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[21327])).
% 2.56/2.67 tff(23467,plain,
% 2.56/2.67 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, e2) = e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23466])).
% 2.56/2.67 tff(23468,plain,
% 2.56/2.67 ((op(e2, e2) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23467])).
% 2.56/2.67 tff(23469,plain,
% 2.56/2.67 (op(e2, op(e1, e1)) = e2),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23458, 23468])).
% 2.56/2.67 tff(23470,plain,
% 2.56/2.67 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[16830, 23469])).
% 2.56/2.67 tff(23471,plain,
% 2.56/2.67 (op(e0, e0) = e0),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[3612, 23374, 23276, 23349])).
% 2.56/2.67 tff(23472,plain,
% 2.56/2.67 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23471])).
% 2.56/2.67 tff(23473,plain,
% 2.56/2.67 (op(e0, op(e0, e0)) = e0),
% 2.56/2.67 inference(transitivity,[status(thm)],[23472, 23471])).
% 2.56/2.67 tff(23474,plain,
% 2.56/2.67 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[5598, 23473])).
% 2.56/2.67 tff(23475,plain,
% 2.56/2.67 (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[5367, 23474, 23470, 23465, 23462, 23456, 23452, 23448, 23445, 23442, 23437, 23431, 23424, 23418, 23413])).
% 2.56/2.67 tff(23476,plain,
% 2.56/2.67 (~(op(e1, op(e1, e2)) = e1)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[22051, 23475])).
% 2.56/2.67 tff(23477,plain,
% 2.56/2.67 ($false),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[23476, 23406])).
% 2.56/2.67 tff(23478,plain,((op(e1, e3) = e0) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.67 tff(23479,plain,
% 2.56/2.67 (op(e1, e3) = e0),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[23478, 17])).
% 2.56/2.67 tff(23480,plain,
% 2.56/2.67 (~(op(e1, e2) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[21630, 23479, 21327])).
% 2.56/2.67 tff(23481,plain,
% 2.56/2.67 (e0 = op(e1, e3)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23479])).
% 2.56/2.67 tff(23482,plain,
% 2.56/2.67 ((e0 = e3) <=> (op(e1, e3) = e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23481])).
% 2.56/2.67 tff(23483,plain,
% 2.56/2.67 ((~(e0 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23482])).
% 2.56/2.67 tff(23484,plain,
% 2.56/2.67 (~(op(e1, e3) = e3)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[181, 23483])).
% 2.56/2.67 tff(23485,plain,
% 2.56/2.67 (op(e1, e0) = e3),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[247, 23484, 21634, 23480])).
% 2.56/2.67 tff(23486,plain,
% 2.56/2.67 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23485])).
% 2.56/2.67 tff(23487,plain,
% 2.56/2.67 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23486])).
% 2.56/2.67 tff(23488,plain,
% 2.56/2.67 (~(op(e0, e0) = e3)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[2471, 23487])).
% 2.56/2.67 tff(23489,plain,
% 2.56/2.67 (op(e0, e2) = e3),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[1495, 2527, 23353, 23488])).
% 2.56/2.67 tff(23490,plain,
% 2.56/2.67 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23489])).
% 2.56/2.67 tff(23491,plain,
% 2.56/2.67 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.56/2.67 inference(symmetry,[status(thm)],[23490])).
% 2.56/2.67 tff(23492,plain,
% 2.56/2.67 ((~(op(e2, e0) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23491])).
% 2.56/2.67 tff(23493,plain,
% 2.56/2.67 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23485])).
% 2.56/2.67 tff(23494,plain,
% 2.56/2.67 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23493, 660])).
% 2.56/2.67 tff(23495,plain,
% 2.56/2.67 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23494])).
% 2.56/2.67 tff(23496,plain,
% 2.56/2.67 (~(op(e2, e0) = e3)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[756, 23495])).
% 2.56/2.67 tff(23497,plain,
% 2.56/2.67 (~(op(e2, e0) = op(e0, e2))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23496, 23492])).
% 2.56/2.67 tff(23498,plain,
% 2.56/2.67 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6358, 23497])).
% 2.56/2.67 tff(23499,plain,
% 2.56/2.67 ((op(e1, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23479])).
% 2.56/2.67 tff(23500,plain,
% 2.56/2.67 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23499, 3077])).
% 2.56/2.67 tff(23501,plain,
% 2.56/2.67 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23500])).
% 2.56/2.67 tff(23502,plain,
% 2.56/2.67 (~(op(e3, e3) = e0)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[571, 23501])).
% 2.56/2.67 tff(23503,plain,
% 2.56/2.67 (op(e3, e3) = e3),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[15018, 23502, 23379])).
% 2.56/2.67 tff(23504,plain,
% 2.56/2.67 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23503])).
% 2.56/2.67 tff(23505,plain,
% 2.56/2.67 (op(e3, op(e3, e3)) = e3),
% 2.56/2.67 inference(transitivity,[status(thm)],[23504, 23503])).
% 2.56/2.67 tff(23506,plain,
% 2.56/2.67 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6277, 23505])).
% 2.56/2.67 tff(23507,plain,
% 2.56/2.67 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e1, e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23481])).
% 2.56/2.67 tff(23508,plain,
% 2.56/2.67 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e0)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23507])).
% 2.56/2.67 tff(23509,plain,
% 2.56/2.67 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23508])).
% 2.56/2.67 tff(23510,plain,
% 2.56/2.67 (~(op(e1, e2) = e0)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[1850, 23509])).
% 2.56/2.67 tff(23511,plain,
% 2.56/2.67 ((op(e0, e2) = e0) <=> (e3 = op(e1, e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23489, 23481])).
% 2.56/2.67 tff(23512,plain,
% 2.56/2.67 ((op(e0, e2) = e0) <=> (op(e1, e3) = e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23511, 3230])).
% 2.56/2.67 tff(23513,plain,
% 2.56/2.67 ((op(e1, e3) = e3) <=> (op(e0, e2) = e0)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23512])).
% 2.56/2.67 tff(23514,plain,
% 2.56/2.67 ((~(op(e1, e3) = e3)) <=> (~(op(e0, e2) = e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23513])).
% 2.56/2.67 tff(23515,plain,
% 2.56/2.67 (~(op(e0, e2) = e0)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23484, 23514])).
% 2.56/2.67 tff(23516,plain,
% 2.56/2.67 (op(e3, e2) = e0),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[973, 23515, 17, 23510])).
% 2.56/2.67 tff(23517,plain,
% 2.56/2.67 (op(e3, e2) = op(e1, e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23516, 23481])).
% 2.56/2.67 tff(23518,plain,
% 2.56/2.67 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23517])).
% 2.56/2.67 tff(23519,plain,
% 2.56/2.67 ((op(e3, e1) = op(e3, e2)) <=> (op(e1, e3) = op(e3, e1))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23518, 6290])).
% 2.56/2.67 tff(23520,plain,
% 2.56/2.67 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23519])).
% 2.56/2.67 tff(23521,plain,
% 2.56/2.67 (~(op(e1, e3) = op(e3, e1))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[3429, 23520])).
% 2.56/2.67 tff(23522,plain,
% 2.56/2.67 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6307, 23521])).
% 2.56/2.67 tff(23523,plain,
% 2.56/2.67 (op(e3, op(e1, e0)) = op(e3, e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23485])).
% 2.56/2.67 tff(23524,plain,
% 2.56/2.67 (op(e3, op(e1, e0)) = e3),
% 2.56/2.67 inference(transitivity,[status(thm)],[23523, 23503])).
% 2.56/2.67 tff(23525,plain,
% 2.56/2.67 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[9792, 23524])).
% 2.56/2.67 tff(23526,plain,
% 2.56/2.67 (op(e1, e2) = e1),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[1859, 23510, 21647, 23480])).
% 2.56/2.67 tff(23527,plain,
% 2.56/2.67 (e1 = op(e1, e2)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23526])).
% 2.56/2.67 tff(23528,plain,
% 2.56/2.67 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e1, e2))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23527])).
% 2.56/2.67 tff(23529,plain,
% 2.56/2.67 ((op(e3, e2) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23528, 3635])).
% 2.56/2.67 tff(23530,plain,
% 2.56/2.67 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23529])).
% 2.56/2.67 tff(23531,plain,
% 2.56/2.67 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23530, 23433])).
% 2.56/2.67 tff(23532,plain,
% 2.56/2.67 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23531])).
% 2.56/2.67 tff(23533,plain,
% 2.56/2.67 (~(op(e3, e2) = op(e2, e3))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[2292, 23532])).
% 2.56/2.67 tff(23534,plain,
% 2.56/2.67 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[500, 23533])).
% 2.56/2.67 tff(23535,plain,
% 2.56/2.67 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23527])).
% 2.56/2.67 tff(23536,plain,
% 2.56/2.67 ((op(e2, e1) = e1) <=> (op(e1, e2) = op(e2, e1))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23535, 531])).
% 2.56/2.67 tff(23537,plain,
% 2.56/2.67 ((~(op(e2, e1) = e1)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23536])).
% 2.56/2.67 tff(23538,plain,
% 2.56/2.67 (~(op(e1, e2) = op(e2, e1))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23268, 23537])).
% 2.56/2.67 tff(23539,plain,
% 2.56/2.67 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[539, 23538])).
% 2.56/2.67 tff(23540,plain,
% 2.56/2.67 ((op(e1, e0) = op(e0, e1)) <=> (e3 = op(e0, e1))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23485])).
% 2.56/2.67 tff(23541,plain,
% 2.56/2.67 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23540, 127])).
% 2.56/2.67 tff(23542,plain,
% 2.56/2.67 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.56/2.67 inference(symmetry,[status(thm)],[23541])).
% 2.56/2.67 tff(23543,plain,
% 2.56/2.67 ((~(op(e0, e1) = e3)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23542])).
% 2.56/2.67 tff(23544,plain,
% 2.56/2.67 (~(op(e1, e0) = op(e0, e1))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[2527, 23543])).
% 2.56/2.67 tff(23545,plain,
% 2.56/2.67 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[613, 23544])).
% 2.56/2.67 tff(23546,plain,
% 2.56/2.67 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23518])).
% 2.56/2.67 tff(23547,plain,
% 2.56/2.67 (~(op(e3, e1) = op(e1, e3))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[3429, 23546])).
% 2.56/2.67 tff(23548,plain,
% 2.56/2.67 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6362, 23547])).
% 2.56/2.67 tff(23549,plain,
% 2.56/2.67 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23530, 23433, 395])).
% 2.56/2.67 tff(23550,plain,
% 2.56/2.67 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23549])).
% 2.56/2.67 tff(23551,plain,
% 2.56/2.67 (~(op(e2, e3) = op(e3, e2))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[2292, 23550])).
% 2.56/2.67 tff(23552,plain,
% 2.56/2.67 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[430, 23551])).
% 2.56/2.67 tff(23553,plain,
% 2.56/2.67 ((op(e2, e0) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.56/2.67 inference(transitivity,[status(thm)],[23491, 6337])).
% 2.56/2.67 tff(23554,plain,
% 2.56/2.67 ((~(op(e2, e0) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23553])).
% 2.56/2.67 tff(23555,plain,
% 2.56/2.67 (~(op(e0, e2) = op(e2, e0))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23496, 23554])).
% 2.56/2.67 tff(23556,plain,
% 2.56/2.67 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6347, 23555])).
% 2.56/2.67 tff(23557,plain,
% 2.56/2.67 (op(op(e1, e2), e2) = op(e1, e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23526])).
% 2.56/2.67 tff(23558,plain,
% 2.56/2.67 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23503])).
% 2.56/2.67 tff(23559,plain,
% 2.56/2.67 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23558])).
% 2.56/2.67 tff(23560,plain,
% 2.56/2.67 (~(op(e3, e1) = e3)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[437, 23559])).
% 2.56/2.67 tff(23561,plain,
% 2.56/2.67 (op(e2, e1) = e3),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[1730, 2527, 21634, 23560])).
% 2.56/2.67 tff(23562,plain,
% 2.56/2.67 ((op(e2, e1) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23561])).
% 2.56/2.67 tff(23563,plain,
% 2.56/2.67 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23562, 502])).
% 2.56/2.67 tff(23564,plain,
% 2.56/2.67 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23563])).
% 2.56/2.67 tff(23565,plain,
% 2.56/2.67 (~(op(e2, e2) = e3)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[508, 23564])).
% 2.56/2.67 tff(23566,plain,
% 2.56/2.67 (op(e2, e2) = e2),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[524, 23565, 17, 23308])).
% 2.56/2.67 tff(23567,plain,
% 2.56/2.67 (op(e1, op(e2, e2)) = op(op(e1, e2), e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23527, 23566])).
% 2.56/2.67 tff(23568,plain,
% 2.56/2.67 (op(e1, op(e2, e2)) = e1),
% 2.56/2.67 inference(transitivity,[status(thm)],[23567, 23557, 23526])).
% 2.56/2.67 tff(23569,plain,
% 2.56/2.67 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[6714, 23568])).
% 2.56/2.67 tff(23570,plain,
% 2.56/2.67 ((~(op(e2, e1) = e1)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23535])).
% 2.56/2.67 tff(23571,plain,
% 2.56/2.67 (~(op(e2, e1) = op(e1, e2))),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23268, 23570])).
% 2.56/2.67 tff(23572,plain,
% 2.56/2.67 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[557, 23571])).
% 2.56/2.67 tff(23573,plain,
% 2.56/2.67 (op(e1, op(e1, e1)) = e1),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23526, 21669])).
% 2.56/2.67 tff(23574,plain,
% 2.56/2.67 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[5678, 23573])).
% 2.56/2.67 tff(23575,plain,
% 2.56/2.67 ((op(e2, e1) = e0) <=> (e3 = op(e1, e3))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23561, 23481])).
% 2.56/2.67 tff(23576,plain,
% 2.56/2.67 ((op(e2, e1) = e0) <=> (op(e1, e3) = e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23575, 3230])).
% 2.56/2.67 tff(23577,plain,
% 2.56/2.67 ((op(e1, e3) = e3) <=> (op(e2, e1) = e0)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23576])).
% 2.56/2.67 tff(23578,plain,
% 2.56/2.67 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e1) = e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23577])).
% 2.56/2.67 tff(23579,plain,
% 2.56/2.67 (~(op(e2, e1) = e0)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[23484, 23578])).
% 2.56/2.67 tff(23580,plain,
% 2.56/2.67 (op(e2, e0) = e0),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[2311, 23579, 17, 23291])).
% 2.56/2.67 tff(23581,plain,
% 2.56/2.67 (op(e2, e0) = op(e1, e3)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23580, 23481])).
% 2.56/2.67 tff(23582,plain,
% 2.56/2.67 ((op(e2, e0) = e2) <=> (op(e1, e3) = e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23581])).
% 2.56/2.67 tff(23583,plain,
% 2.56/2.67 ((op(e1, e3) = e2) <=> (op(e2, e0) = e2)),
% 2.56/2.67 inference(symmetry,[status(thm)],[23582])).
% 2.56/2.67 tff(23584,plain,
% 2.56/2.67 ((~(op(e1, e3) = e2)) <=> (~(op(e2, e0) = e2))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23583])).
% 2.56/2.67 tff(23585,plain,
% 2.56/2.67 (~(op(e2, e0) = e2)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[21331, 23584])).
% 2.56/2.67 tff(23586,plain,
% 2.56/2.67 (op(e3, e0) = e2),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[589, 23585, 21340, 23276])).
% 2.56/2.67 tff(23587,plain,
% 2.56/2.67 (op(e1, op(e3, e0)) = op(op(e1, e2), e2)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23527, 23586])).
% 2.56/2.67 tff(23588,plain,
% 2.56/2.67 (op(e1, op(e3, e0)) = e1),
% 2.56/2.67 inference(transitivity,[status(thm)],[23587, 23557, 23526])).
% 2.56/2.67 tff(23589,plain,
% 2.56/2.67 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[8474, 23588])).
% 2.56/2.67 tff(23590,plain,
% 2.56/2.67 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e0)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23580])).
% 2.56/2.67 tff(23591,plain,
% 2.56/2.67 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e0))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23590])).
% 2.56/2.67 tff(23592,plain,
% 2.56/2.67 (~(op(e0, e0) = e0)),
% 2.56/2.67 inference(modus_ponens,[status(thm)],[359, 23591])).
% 2.56/2.67 tff(23593,plain,
% 2.56/2.67 (op(e0, e1) = e0),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[3976, 23592, 23515, 23286])).
% 2.56/2.67 tff(23594,plain,
% 2.56/2.67 (op(op(e1, e3), e1) = op(e0, e1)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23479])).
% 2.56/2.67 tff(23595,plain,
% 2.56/2.67 (op(e0, op(e1, e2)) = op(op(e1, e3), e1)),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23481, 23526])).
% 2.56/2.67 tff(23596,plain,
% 2.56/2.67 (op(e0, e0) = e1),
% 2.56/2.67 inference(unit_resolution,[status(thm)],[3612, 23592, 23276, 23488])).
% 2.56/2.67 tff(23597,plain,
% 2.56/2.67 (op(e0, e0) = op(e1, e2)),
% 2.56/2.67 inference(transitivity,[status(thm)],[23596, 23527])).
% 2.56/2.67 tff(23598,plain,
% 2.56/2.67 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.56/2.67 inference(monotonicity,[status(thm)],[23597])).
% 2.56/2.67 tff(23599,plain,
% 2.56/2.67 (op(e0, op(e0, e0)) = e0),
% 2.56/2.67 inference(transitivity,[status(thm)],[23598, 23595, 23594, 23593])).
% 2.56/2.67 tff(23600,plain,
% 2.56/2.67 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[5598, 23599])).
% 2.56/2.68 tff(23601,plain,
% 2.56/2.68 ($false),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[5367, 23600, 23589, 23574, 23572, 23569, 23556, 23552, 23548, 23545, 23539, 23534, 23525, 23522, 23506, 23498])).
% 2.56/2.68 tff(23602,plain,((op(e0, e1) = e3) | (op(e2, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.68 tff(23603,plain,
% 2.56/2.68 (op(e0, e1) = e3),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23602, 17])).
% 2.56/2.68 tff(23604,plain,
% 2.56/2.68 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23603])).
% 2.56/2.68 tff(23605,plain,
% 2.56/2.68 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23604, 1262])).
% 2.56/2.68 tff(23606,plain,
% 2.56/2.68 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23605])).
% 2.56/2.68 tff(23607,plain,
% 2.56/2.68 (~(op(e2, e1) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[606, 23606])).
% 2.56/2.68 tff(23608,plain,
% 2.56/2.68 (op(e2, e1) = e0),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[2367, 23607, 22153, 23268])).
% 2.56/2.68 tff(23609,plain,
% 2.56/2.68 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23265])).
% 2.56/2.68 tff(23610,plain,
% 2.56/2.68 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23609])).
% 2.56/2.68 tff(23611,plain,
% 2.56/2.68 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23610])).
% 2.56/2.68 tff(23612,plain,
% 2.56/2.68 (~(op(e2, e3) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[303, 23611])).
% 2.56/2.68 tff(23613,plain,
% 2.56/2.68 (op(e2, e2) = e3),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[1559, 23607, 23612, 23496])).
% 2.56/2.68 tff(23614,plain,
% 2.56/2.68 ($false),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[6638, 23613, 23608, 23265])).
% 2.56/2.68 tff(23615,plain,(op(e2, e2) = e0), inference(lemma,lemma(discharge,[]))).
% 2.56/2.68 tff(23616,plain,
% 2.56/2.68 (op(e2, op(e2, e2)) = op(e2, e0)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.68 tff(23617,plain,
% 2.56/2.68 ((e1 = op(e2, op(e2, e2))) <=> (e1 = op(e2, e0))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23616])).
% 2.56/2.68 tff(23618,plain,
% 2.56/2.68 ((e1 = op(e2, op(e2, e2))) <=> (op(e2, e0) = e1)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23617, 16])).
% 2.56/2.68 tff(23619,plain,
% 2.56/2.68 ((op(e2, e0) = e1) <=> (e1 = op(e2, op(e2, e2)))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23618])).
% 2.56/2.68 tff(23620,plain,
% 2.56/2.68 ((op(e1, e3) = e2) <=> (e0 = e2)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[1219])).
% 2.56/2.68 tff(23621,plain,
% 2.56/2.68 ((e0 = e2) <=> (op(e1, e3) = e2)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23620])).
% 2.56/2.68 tff(23622,plain,
% 2.56/2.68 ((~(e0 = e2)) <=> (~(op(e1, e3) = e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23621])).
% 2.56/2.68 tff(23623,plain,
% 2.56/2.68 (~(op(e1, e3) = e2)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[14, 23622])).
% 2.56/2.68 tff(23624,plain,
% 2.56/2.68 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e0, e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4681])).
% 2.56/2.68 tff(23625,plain,
% 2.56/2.68 ((op(e2, e3) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23624, 925])).
% 2.56/2.68 tff(23626,plain,
% 2.56/2.68 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23625])).
% 2.56/2.68 tff(23627,plain,
% 2.56/2.68 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23626])).
% 2.56/2.68 tff(23628,plain,
% 2.56/2.68 (~(op(e2, e3) = e1)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[964, 23627])).
% 2.56/2.68 tff(23629,plain,
% 2.56/2.68 (op(e3, e3) = e3),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[15018, 21679, 17084])).
% 2.56/2.68 tff(23630,plain,
% 2.56/2.68 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23629])).
% 2.56/2.68 tff(23631,plain,
% 2.56/2.68 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23630])).
% 2.56/2.68 tff(23632,plain,
% 2.56/2.68 (~(op(e2, e3) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[368, 23631])).
% 2.56/2.68 tff(23633,plain,
% 2.56/2.68 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4960])).
% 2.56/2.68 tff(23634,plain,
% 2.56/2.68 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23633, 1262])).
% 2.56/2.68 tff(23635,plain,
% 2.56/2.68 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23634])).
% 2.56/2.68 tff(23636,plain,
% 2.56/2.68 (~(op(e2, e1) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[225, 23635])).
% 2.56/2.68 tff(23637,plain,
% 2.56/2.68 (e0 = op(e2, e2)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23615])).
% 2.56/2.68 tff(23638,plain,
% 2.56/2.68 ((e0 = e3) <=> (op(e2, e2) = e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23637])).
% 2.56/2.68 tff(23639,plain,
% 2.56/2.68 ((~(e0 = e3)) <=> (~(op(e2, e2) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23638])).
% 2.56/2.68 tff(23640,plain,
% 2.56/2.68 (~(op(e2, e2) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[181, 23639])).
% 2.56/2.68 tff(23641,plain,
% 2.56/2.68 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e3) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[1559, 23640])).
% 2.56/2.68 tff(23642,plain,
% 2.56/2.68 (op(e2, e0) = e3),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23641, 23636, 23632])).
% 2.56/2.68 tff(23643,plain,
% 2.56/2.68 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23642])).
% 2.56/2.68 tff(23644,plain,
% 2.56/2.68 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23643])).
% 2.56/2.68 tff(23645,plain,
% 2.56/2.68 (~(op(e0, e0) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[359, 23644])).
% 2.56/2.68 tff(23646,plain,
% 2.56/2.68 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23629])).
% 2.56/2.68 tff(23647,plain,
% 2.56/2.68 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23646])).
% 2.56/2.68 tff(23648,plain,
% 2.56/2.68 (~(op(e3, e2) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[1888, 23647])).
% 2.56/2.68 tff(23649,plain,
% 2.56/2.68 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4960])).
% 2.56/2.68 tff(23650,plain,
% 2.56/2.68 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23649, 532])).
% 2.56/2.68 tff(23651,plain,
% 2.56/2.68 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23650])).
% 2.56/2.68 tff(23652,plain,
% 2.56/2.68 (~(op(e1, e2) = e3)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[1604, 23651])).
% 2.56/2.68 tff(23653,plain,
% 2.56/2.68 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e3, e2) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[2111, 23640])).
% 2.56/2.68 tff(23654,plain,
% 2.56/2.68 (op(e0, e2) = e3),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23653, 23652, 23648])).
% 2.56/2.68 tff(23655,plain,
% 2.56/2.68 (e3 = op(e0, op(e0, e0))),
% 2.56/2.68 inference(transitivity,[status(thm)],[7827, 2382])).
% 2.56/2.68 tff(23656,plain,
% 2.56/2.68 (op(e0, op(e0, e0)) = e3),
% 2.56/2.68 inference(transitivity,[status(thm)],[2381, 7826])).
% 2.56/2.68 tff(23657,plain,
% 2.56/2.68 (op(e0, op(e0, op(e0, e0))) = op(e0, e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23656])).
% 2.56/2.68 tff(23658,plain,
% 2.56/2.68 (op(e0, e3) = op(e0, op(e0, op(e0, e0)))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23657])).
% 2.56/2.68 tff(23659,plain,
% 2.56/2.68 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.56/2.68 inference(transitivity,[status(thm)],[4681, 23658])).
% 2.56/2.68 tff(23660,plain,
% 2.56/2.68 ($false),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[10921, 23659, 23655, 8486])).
% 2.56/2.68 tff(23661,plain,((~(op(e0, e0) = e2)) | (~(op(e0, e3) = e1)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.68 tff(23662,plain,
% 2.56/2.68 (~(op(e0, e0) = e2)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23661, 23654, 19])).
% 2.56/2.68 tff(23663,plain,
% 2.56/2.68 (op(e0, e0) = e0),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[3612, 23662, 5048, 23645])).
% 2.56/2.68 tff(23664,plain,
% 2.56/2.68 (op(e2, e3) = e2),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[15003, 4717, 23623])).
% 2.56/2.68 tff(23665,plain,
% 2.56/2.68 (op(e2, op(e1, e1)) = e2),
% 2.56/2.68 inference(transitivity,[status(thm)],[15725, 23664])).
% 2.56/2.68 tff(23666,plain,
% 2.56/2.68 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[16830, 23665])).
% 2.56/2.68 tff(23667,plain,
% 2.56/2.68 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23664])).
% 2.56/2.68 tff(23668,plain,
% 2.56/2.68 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23667])).
% 2.56/2.68 tff(23669,plain,
% 2.56/2.68 (~(op(e2, e0) = e2)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[989, 23668])).
% 2.56/2.68 tff(23670,plain,
% 2.56/2.68 (op(e1, op(e1, e1)) = op(op(e0, e3), e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4681, 4960])).
% 2.56/2.68 tff(23671,plain,
% 2.56/2.68 (op(e1, op(e1, e1)) = e0),
% 2.56/2.68 inference(transitivity,[status(thm)],[23670, 4735, 1219])).
% 2.56/2.68 tff(23672,plain,
% 2.56/2.68 (op(e1, op(e1, op(e1, e1))) = op(op(e0, e3), e0)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4681, 23671])).
% 2.56/2.68 tff(23673,plain,
% 2.56/2.68 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23672, 5069])).
% 2.56/2.68 tff(23674,plain,
% 2.56/2.68 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23673])).
% 2.56/2.68 tff(23675,plain,
% 2.56/2.68 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23674, 2154])).
% 2.56/2.68 tff(23676,plain,
% 2.56/2.68 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23675])).
% 2.56/2.68 tff(23677,plain,
% 2.56/2.68 (op(op(e0, e3), e3) = op(e1, op(e1, e1))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23670])).
% 2.56/2.68 tff(23678,plain,
% 2.56/2.68 (e0 = op(e1, op(e1, e1))),
% 2.56/2.68 inference(transitivity,[status(thm)],[2909, 4759, 23677])).
% 2.56/2.68 tff(23679,plain,
% 2.56/2.68 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[3009, 23678, 6906])).
% 2.56/2.68 tff(23680,plain,
% 2.56/2.68 (~(op(e1, e0) = e2)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[23679, 23676])).
% 2.56/2.68 tff(23681,plain,
% 2.56/2.68 (op(e2, op(e3, e3)) = op(e2, e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23629])).
% 2.56/2.68 tff(23682,plain,
% 2.56/2.68 (op(e2, op(e3, e3)) = e2),
% 2.56/2.68 inference(transitivity,[status(thm)],[23681, 23664])).
% 2.56/2.68 tff(23683,plain,
% 2.56/2.68 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[14770, 23682])).
% 2.56/2.68 tff(23684,plain,
% 2.56/2.68 (op(e2, op(e0, e2)) = op(e2, e3)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23654])).
% 2.56/2.68 tff(23685,plain,
% 2.56/2.68 (op(e2, op(e0, e2)) = e2),
% 2.56/2.68 inference(transitivity,[status(thm)],[23684, 23664])).
% 2.56/2.68 tff(23686,plain,
% 2.56/2.68 (((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)) | (~(op(e2, op(e0, e2)) = e2))),
% 2.56/2.68 inference(tautology,[status(thm)],[])).
% 2.56/2.68 tff(23687,plain,
% 2.56/2.68 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23686, 23685])).
% 2.56/2.68 tff(23688,plain,
% 2.56/2.68 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, op(e0, e3)) = e2)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[13402, 23664])).
% 2.56/2.68 tff(23689,plain,
% 2.56/2.68 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23688, 13404])).
% 2.56/2.68 tff(23690,plain,
% 2.56/2.68 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23689])).
% 2.56/2.68 tff(23691,plain,
% 2.56/2.68 (~(op(e2, e1) = e2)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[197, 23690])).
% 2.56/2.68 tff(23692,plain,
% 2.56/2.68 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e1) = e0)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.68 tff(23693,plain,
% 2.56/2.68 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = e0))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23692])).
% 2.56/2.68 tff(23694,plain,
% 2.56/2.68 (~(op(e2, e1) = e0)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[508, 23693])).
% 2.56/2.68 tff(23695,plain,
% 2.56/2.68 ((op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[2367, 23694])).
% 2.56/2.68 tff(23696,plain,
% 2.56/2.68 (op(e2, e1) = e1),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[23695, 23636, 23691])).
% 2.56/2.68 tff(23697,plain,
% 2.56/2.68 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23696])).
% 2.56/2.68 tff(23698,plain,
% 2.56/2.68 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23697, 5522])).
% 2.56/2.68 tff(23699,plain,
% 2.56/2.68 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23698])).
% 2.56/2.68 tff(23700,plain,
% 2.56/2.68 ((op(e1, e1) = e2) <=> (e3 = e2)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[4960])).
% 2.56/2.68 tff(23701,plain,
% 2.56/2.68 ((op(e1, e1) = e2) <=> (e2 = e3)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23700, 1314])).
% 2.56/2.68 tff(23702,plain,
% 2.56/2.68 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23701])).
% 2.56/2.68 tff(23703,plain,
% 2.56/2.68 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23702])).
% 2.56/2.68 tff(23704,plain,
% 2.56/2.68 (~(op(e1, e1) = e2)),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[1321, 23703])).
% 2.56/2.68 tff(23705,plain,
% 2.56/2.68 (op(e1, e2) = e2),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[2285, 23680, 23623, 23704])).
% 2.56/2.68 tff(23706,plain,
% 2.56/2.68 ((op(e1, e2) = e1) <=> (e2 = op(e0, e3))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23705, 4681])).
% 2.56/2.68 tff(23707,plain,
% 2.56/2.68 ((op(e1, e2) = e1) <=> (op(e0, e3) = e2)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23706, 1681])).
% 2.56/2.68 tff(23708,plain,
% 2.56/2.68 ((op(e0, e3) = e2) <=> (op(e1, e2) = e1)),
% 2.56/2.68 inference(symmetry,[status(thm)],[23707])).
% 2.56/2.68 tff(23709,plain,
% 2.56/2.68 ((op(e0, e3) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23708, 23699, 531])).
% 2.56/2.68 tff(23710,plain,
% 2.56/2.68 ((~(op(e0, e3) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23709])).
% 2.56/2.68 tff(23711,plain,
% 2.56/2.68 (~(op(e1, e2) = op(e2, e1))),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[4717, 23710])).
% 2.56/2.68 tff(23712,plain,
% 2.56/2.68 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[539, 23711])).
% 2.56/2.68 tff(23713,plain,
% 2.56/2.68 ((op(e0, e3) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23708, 23699])).
% 2.56/2.68 tff(23714,plain,
% 2.56/2.68 ((~(op(e0, e3) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23713])).
% 2.56/2.68 tff(23715,plain,
% 2.56/2.68 (~(op(e2, e1) = op(e1, e2))),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[4717, 23714])).
% 2.56/2.68 tff(23716,plain,
% 2.56/2.68 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[557, 23715])).
% 2.56/2.68 tff(23717,plain,
% 2.56/2.68 (op(e1, e0) = e1),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[728, 23680, 17127, 12623])).
% 2.56/2.68 tff(23718,plain,
% 2.56/2.68 (op(e1, e0) = op(e0, e3)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23717, 4681])).
% 2.56/2.68 tff(23719,plain,
% 2.56/2.68 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e3) = op(e0, e1))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23718])).
% 2.56/2.68 tff(23720,plain,
% 2.56/2.68 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e3))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23719, 15424])).
% 2.56/2.68 tff(23721,plain,
% 2.56/2.68 ((op(e0, e1) = op(e0, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23720])).
% 2.56/2.68 tff(23722,plain,
% 2.56/2.68 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23721, 596])).
% 2.56/2.68 tff(23723,plain,
% 2.56/2.68 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23722])).
% 2.56/2.68 tff(23724,plain,
% 2.56/2.68 (~(op(e0, e1) = op(e1, e0))),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[818, 23723])).
% 2.56/2.68 tff(23725,plain,
% 2.56/2.68 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.56/2.68 inference(unit_resolution,[status(thm)],[609, 23724])).
% 2.56/2.68 tff(23726,plain,
% 2.56/2.68 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23664])).
% 2.56/2.68 tff(23727,plain,
% 2.56/2.68 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.68 inference(symmetry,[status(thm)],[23726])).
% 2.56/2.68 tff(23728,plain,
% 2.56/2.68 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23705])).
% 2.56/2.68 tff(23729,plain,
% 2.56/2.68 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.56/2.68 inference(transitivity,[status(thm)],[23728, 2234])).
% 2.56/2.68 tff(23730,plain,
% 2.56/2.68 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.68 inference(transitivity,[status(thm)],[23729, 23727])).
% 2.56/2.68 tff(23731,plain,
% 2.56/2.68 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.56/2.68 inference(monotonicity,[status(thm)],[23730])).
% 2.56/2.68 tff(23732,plain,
% 2.56/2.68 (~(op(e3, e2) = op(e2, e3))),
% 2.56/2.68 inference(modus_ponens,[status(thm)],[2292, 23731])).
% 2.56/2.69 tff(23733,plain,
% 2.56/2.69 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[500, 23732])).
% 2.56/2.69 tff(23734,plain,
% 2.56/2.69 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23721])).
% 2.56/2.69 tff(23735,plain,
% 2.56/2.69 (~(op(e1, e0) = op(e0, e1))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[818, 23734])).
% 2.56/2.69 tff(23736,plain,
% 2.56/2.69 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[613, 23735])).
% 2.56/2.69 tff(23737,plain,
% 2.56/2.69 (op(e2, op(e2, e0)) = op(e2, e3)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23642])).
% 2.56/2.69 tff(23738,plain,
% 2.56/2.69 (op(e2, op(e2, e0)) = e2),
% 2.56/2.69 inference(transitivity,[status(thm)],[23737, 23664])).
% 2.56/2.69 tff(23739,plain,
% 2.56/2.69 (((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)) | (~(op(e2, op(e2, e0)) = e2))),
% 2.56/2.69 inference(tautology,[status(thm)],[])).
% 2.56/2.69 tff(23740,plain,
% 2.56/2.69 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23739, 23738])).
% 2.56/2.69 tff(23741,plain,
% 2.56/2.69 ((op(e1, op(e1, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[11579])).
% 2.56/2.69 tff(23742,plain,
% 2.56/2.69 ((op(e1, e0) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23741])).
% 2.56/2.69 tff(23743,plain,
% 2.56/2.69 (op(e1, op(e1, e3)) = e1),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23717, 23742])).
% 2.56/2.69 tff(23744,plain,
% 2.56/2.69 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[6674, 23743])).
% 2.56/2.69 tff(23745,plain,
% 2.56/2.69 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23718])).
% 2.56/2.69 tff(23746,plain,
% 2.56/2.69 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23745, 452])).
% 2.56/2.69 tff(23747,plain,
% 2.56/2.69 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23746, 453])).
% 2.56/2.69 tff(23748,plain,
% 2.56/2.69 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23747])).
% 2.56/2.69 tff(23749,plain,
% 2.56/2.69 (~(op(e0, e3) = op(e3, e0))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[410, 23748])).
% 2.56/2.69 tff(23750,plain,
% 2.56/2.69 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[496, 23749])).
% 2.56/2.69 tff(23751,plain,
% 2.56/2.69 (op(e1, op(e2, e2)) = op(e1, e0)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23752,plain,
% 2.56/2.69 ((op(e1, op(e2, e2)) = e1) <=> (op(e1, e0) = e1)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23751])).
% 2.56/2.69 tff(23753,plain,
% 2.56/2.69 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e2)) = e1)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23752])).
% 2.56/2.69 tff(23754,plain,
% 2.56/2.69 (op(e1, op(e2, e2)) = e1),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23717, 23753])).
% 2.56/2.69 tff(23755,plain,
% 2.56/2.69 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[6714, 23754])).
% 2.56/2.69 tff(23756,plain,
% 2.56/2.69 (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[21766, 23662, 23664, 23645, 23755, 23750, 23744, 23740, 23736, 23733, 23725, 23716, 23712, 23687, 23683, 23680, 23669, 23666, 5048])).
% 2.56/2.69 tff(23757,plain,
% 2.56/2.69 (op(e1, e3) = op(e3, e1)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[6307, 23756])).
% 2.56/2.69 tff(23758,plain,
% 2.56/2.69 (op(e3, e1) = op(e1, e3)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23757])).
% 2.56/2.69 tff(23759,plain,
% 2.56/2.69 (op(e3, e1) = e0),
% 2.56/2.69 inference(transitivity,[status(thm)],[23758, 1219])).
% 2.56/2.69 tff(23760,plain,
% 2.56/2.69 (op(e0, op(e3, e1)) = op(e0, e0)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23759])).
% 2.56/2.69 tff(23761,plain,
% 2.56/2.69 (op(e0, op(e3, e1)) = e0),
% 2.56/2.69 inference(transitivity,[status(thm)],[23760, 23663])).
% 2.56/2.69 tff(23762,plain,
% 2.56/2.69 (~(op(e0, op(e3, e1)) = e0)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[5610, 23756])).
% 2.56/2.69 tff(23763,plain,
% 2.56/2.69 ($false),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23762, 23761])).
% 2.56/2.69 tff(23764,plain,((~(op(e1, e1) = e3)) | (~(op(e1, e3) = e0)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.69 tff(23765,plain,
% 2.56/2.69 (~(op(e1, e1) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23764, 19, 1219])).
% 2.56/2.69 tff(23766,plain,
% 2.56/2.69 (~(op(e1, e2) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[21630, 2891, 1219])).
% 2.56/2.69 tff(23767,plain,
% 2.56/2.69 (op(e0, e2) = e3),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23653, 23766, 23648])).
% 2.56/2.69 tff(23768,plain,
% 2.56/2.69 (~(op(e0, e0) = e2)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23661, 23767, 19])).
% 2.56/2.69 tff(23769,plain,
% 2.56/2.69 ((op(e0, e2) = e2) <=> (e3 = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23767])).
% 2.56/2.69 tff(23770,plain,
% 2.56/2.69 ((op(e0, e2) = e2) <=> (e2 = e3)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23769, 1314])).
% 2.56/2.69 tff(23771,plain,
% 2.56/2.69 ((e2 = e3) <=> (op(e0, e2) = e2)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23770])).
% 2.56/2.69 tff(23772,plain,
% 2.56/2.69 ((~(e2 = e3)) <=> (~(op(e0, e2) = e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23771])).
% 2.56/2.69 tff(23773,plain,
% 2.56/2.69 (~(op(e0, e2) = e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[1321, 23772])).
% 2.56/2.69 tff(23774,plain,
% 2.56/2.69 ($false),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[3652, 23773, 5774, 23768, 4717])).
% 2.56/2.69 tff(23775,plain,((~(op(e1, e1) = e2)) | (~(op(e0, e3) = e1)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.69 tff(23776,plain,
% 2.56/2.69 (~(op(e1, e1) = e2)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23775, 19, 1219])).
% 2.56/2.69 tff(23777,plain,
% 2.56/2.69 (op(e1, e1) = e1),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[630, 23776, 23765, 2639])).
% 2.56/2.69 tff(23778,plain,
% 2.56/2.69 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23777])).
% 2.56/2.69 tff(23779,plain,
% 2.56/2.69 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23778, 2355])).
% 2.56/2.69 tff(23780,plain,
% 2.56/2.69 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23779])).
% 2.56/2.69 tff(23781,plain,
% 2.56/2.69 (~(op(e2, e1) = e1)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[225, 23780])).
% 2.56/2.69 tff(23782,plain,
% 2.56/2.69 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23637])).
% 2.56/2.69 tff(23783,plain,
% 2.56/2.69 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23782])).
% 2.56/2.69 tff(23784,plain,
% 2.56/2.69 (~(op(e2, e2) = e1)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[26, 23783])).
% 2.56/2.69 tff(23785,plain,
% 2.56/2.69 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e3) = e1)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[345, 23784])).
% 2.56/2.69 tff(23786,plain,
% 2.56/2.69 (op(e2, e0) = e1),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23785, 23781, 23628])).
% 2.56/2.69 tff(23787,plain,
% 2.56/2.69 (e1 = op(e2, op(e2, e2))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23786, 23619])).
% 2.56/2.69 tff(23788,plain,
% 2.56/2.69 (op(e2, op(e2, op(e2, e2))) = op(e2, op(e2, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23616])).
% 2.56/2.69 tff(23789,plain,
% 2.56/2.69 (op(e2, op(e2, e0)) = op(e2, op(e2, op(e2, e2)))),
% 2.56/2.69 inference(symmetry,[status(thm)],[23788])).
% 2.56/2.69 tff(23790,plain,
% 2.56/2.69 (op(e2, e0) = op(e0, e3)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23786, 4681])).
% 2.56/2.69 tff(23791,plain,
% 2.56/2.69 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23790])).
% 2.56/2.69 tff(23792,plain,
% 2.56/2.69 (op(e2, op(e0, e3)) = op(e2, op(e2, e0))),
% 2.56/2.69 inference(symmetry,[status(thm)],[23791])).
% 2.56/2.69 tff(23793,plain,
% 2.56/2.69 (op(e2, e1) = e3),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23695, 23781, 23691])).
% 2.56/2.69 tff(23794,plain,
% 2.56/2.69 (e3 = op(e2, e1)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23793])).
% 2.56/2.69 tff(23795,plain,
% 2.56/2.69 (e3 = op(e2, op(e2, op(e2, e2)))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23794, 13402, 23792, 23789])).
% 2.56/2.69 tff(23796,plain,
% 2.56/2.69 (e0 = op(e2, e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23615, 995])).
% 2.56/2.69 tff(23797,plain,
% 2.56/2.69 ((~(e3 = op(e2, op(e2, op(e2, e2))))) | (~(e1 = op(e2, op(e2, e2))))),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[1539, 23796])).
% 2.56/2.69 tff(23798,plain,
% 2.56/2.69 ($false),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23797, 23795, 23787])).
% 2.56/2.69 tff(23799,plain,((~(op(e0, e3) = e1)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.69 tff(23800,plain,
% 2.56/2.69 (~(op(e0, e3) = e1)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23799, 1219])).
% 2.56/2.69 tff(23801,plain,
% 2.56/2.69 ((op(e2, e2) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23802,plain,
% 2.56/2.69 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23801, 86])).
% 2.56/2.69 tff(23803,plain,
% 2.56/2.69 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23802])).
% 2.56/2.69 tff(23804,plain,
% 2.56/2.69 (~(op(e2, e3) = e0)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[515, 23803])).
% 2.56/2.69 tff(23805,plain,
% 2.56/2.69 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e0)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23806,plain,
% 2.56/2.69 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23805])).
% 2.56/2.69 tff(23807,plain,
% 2.56/2.69 (~(op(e2, e0) = e0)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[2228, 23806])).
% 2.56/2.69 tff(23808,plain,
% 2.56/2.69 ((~(op(e2, e3) = e1)) | (~(op(e0, e3) = e2)) | (op(e2, e0) = e2)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[2698, 23807, 23694, 23804])).
% 2.56/2.69 tff(23809,plain,
% 2.56/2.69 (op(e2, e0) = e2),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23808, 2684, 2])).
% 2.56/2.69 tff(23810,plain,
% 2.56/2.69 (e2 = op(e2, e0)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23809])).
% 2.56/2.69 tff(23811,plain,
% 2.56/2.69 (op(e1, e0) = e3),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[247, 21864, 2605, 23766])).
% 2.56/2.69 tff(23812,plain,
% 2.56/2.69 (e3 = op(e1, e0)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23811])).
% 2.56/2.69 tff(23813,plain,
% 2.56/2.69 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23812])).
% 2.56/2.69 tff(23814,plain,
% 2.56/2.69 ((op(e2, e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23813, 749])).
% 2.56/2.69 tff(23815,plain,
% 2.56/2.69 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23814])).
% 2.56/2.69 tff(23816,plain,
% 2.56/2.69 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23815])).
% 2.56/2.69 tff(23817,plain,
% 2.56/2.69 (~(op(e2, e0) = e3)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[756, 23816])).
% 2.56/2.69 tff(23818,plain,
% 2.56/2.69 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e0)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23819,plain,
% 2.56/2.69 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23818])).
% 2.56/2.69 tff(23820,plain,
% 2.56/2.69 (~(op(e1, e2) = e0)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[1273, 23819])).
% 2.56/2.69 tff(23821,plain,
% 2.56/2.69 ((op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[1859, 23820])).
% 2.56/2.69 tff(23822,plain,
% 2.56/2.69 (op(e1, e2) = e1),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23821, 5766, 23766])).
% 2.56/2.69 tff(23823,plain,
% 2.56/2.69 ((op(e1, op(e1, e1)) = e1) <=> (op(e1, e2) = e1)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[21621])).
% 2.56/2.69 tff(23824,plain,
% 2.56/2.69 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23823])).
% 2.56/2.69 tff(23825,plain,
% 2.56/2.69 (op(e1, op(e1, e1)) = e1),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23822, 23824])).
% 2.56/2.69 tff(23826,plain,
% 2.56/2.69 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[5678, 23825])).
% 2.56/2.69 tff(23827,plain,
% 2.56/2.69 (op(e2, e3) = op(e2, op(e1, e0))),
% 2.56/2.69 inference(symmetry,[status(thm)],[17439])).
% 2.56/2.69 tff(23828,plain,
% 2.56/2.69 ((op(e2, e3) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23827])).
% 2.56/2.69 tff(23829,plain,
% 2.56/2.69 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, e3) = e2)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23828])).
% 2.56/2.69 tff(23830,plain,
% 2.56/2.69 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, op(e1, e0)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[2, 23827])).
% 2.56/2.69 tff(23831,plain,
% 2.56/2.69 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, op(e1, e0)) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23830, 23241])).
% 2.56/2.69 tff(23832,plain,
% 2.56/2.69 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23831, 23829])).
% 2.56/2.69 tff(23833,plain,
% 2.56/2.69 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23832])).
% 2.56/2.69 tff(23834,plain,
% 2.56/2.69 (~(op(e2, e3) = e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[964, 23833])).
% 2.56/2.69 tff(23835,plain,
% 2.56/2.69 ((op(e2, e2) = e2) <=> (e0 = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23836,plain,
% 2.56/2.69 ((e0 = e2) <=> (op(e2, e2) = e2)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23835])).
% 2.56/2.69 tff(23837,plain,
% 2.56/2.69 ((~(e0 = e2)) <=> (~(op(e2, e2) = e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23836])).
% 2.56/2.69 tff(23838,plain,
% 2.56/2.69 (~(op(e2, e2) = e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[14, 23837])).
% 2.56/2.69 tff(23839,plain,
% 2.56/2.69 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e3) = e2)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[2088, 23838])).
% 2.56/2.69 tff(23840,plain,
% 2.56/2.69 (op(e2, e0) = e2),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23839, 23834, 3540])).
% 2.56/2.69 tff(23841,plain,
% 2.56/2.69 ((op(e2, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23840])).
% 2.56/2.69 tff(23842,plain,
% 2.56/2.69 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23841, 3491])).
% 2.56/2.69 tff(23843,plain,
% 2.56/2.69 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.56/2.69 inference(symmetry,[status(thm)],[23842])).
% 2.56/2.69 tff(23844,plain,
% 2.56/2.69 ((~(op(e0, e2) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23843])).
% 2.56/2.69 tff(23845,plain,
% 2.56/2.69 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[2])).
% 2.56/2.69 tff(23846,plain,
% 2.56/2.69 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23845])).
% 2.56/2.69 tff(23847,plain,
% 2.56/2.69 (~(op(e0, e2) = e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[918, 23846])).
% 2.56/2.69 tff(23848,plain,
% 2.56/2.69 (~(op(e2, e0) = op(e0, e2))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23847, 23844])).
% 2.56/2.69 tff(23849,plain,
% 2.56/2.69 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[6358, 23848])).
% 2.56/2.69 tff(23850,plain,
% 2.56/2.69 (op(e3, op(e1, e2)) = op(op(e1, e0), e1)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[259, 6683])).
% 2.56/2.69 tff(23851,plain,
% 2.56/2.69 ((op(e0, e3) = e3) <=> (e2 = op(e1, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[2, 259])).
% 2.56/2.69 tff(23852,plain,
% 2.56/2.69 ((op(e0, e3) = e3) <=> (op(e1, e0) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23851, 2154])).
% 2.56/2.69 tff(23853,plain,
% 2.56/2.69 ((op(e1, e0) = e2) <=> (op(e0, e3) = e3)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23852])).
% 2.56/2.69 tff(23854,plain,
% 2.56/2.69 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e3) = e3))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23853])).
% 2.56/2.69 tff(23855,plain,
% 2.56/2.69 (~(op(e0, e3) = e3)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[6687, 23854])).
% 2.56/2.69 tff(23856,plain,
% 2.56/2.69 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e3, e2) = e2)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[1151, 23838])).
% 2.56/2.69 tff(23857,plain,
% 2.56/2.69 (op(e3, e2) = e2),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23856, 23847, 3785])).
% 2.56/2.69 tff(23858,plain,
% 2.56/2.69 ((op(e3, e2) = op(e2, e3)) <=> (e2 = op(e2, op(e1, e0)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23857, 23827])).
% 2.56/2.69 tff(23859,plain,
% 2.56/2.69 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, op(e1, e0)) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23858, 23241])).
% 2.56/2.69 tff(23860,plain,
% 2.56/2.69 ((op(e2, op(e1, e0)) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.56/2.69 inference(symmetry,[status(thm)],[23859])).
% 2.56/2.69 tff(23861,plain,
% 2.56/2.69 ((~(op(e2, op(e1, e0)) = e2)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23860])).
% 2.56/2.69 tff(23862,plain,
% 2.56/2.69 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, op(e1, e0)) = e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23831])).
% 2.56/2.69 tff(23863,plain,
% 2.56/2.69 (~(op(e2, op(e1, e0)) = e2)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[964, 23862])).
% 2.56/2.69 tff(23864,plain,
% 2.56/2.69 (~(op(e3, e2) = op(e2, e3))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[23863, 23861])).
% 2.56/2.69 tff(23865,plain,
% 2.56/2.69 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[2])).
% 2.56/2.69 tff(23866,plain,
% 2.56/2.69 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e0, e3))),
% 2.56/2.69 inference(symmetry,[status(thm)],[23865])).
% 2.56/2.69 tff(23867,plain,
% 2.56/2.69 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23840])).
% 2.56/2.69 tff(23868,plain,
% 2.56/2.69 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23867, 5377])).
% 2.56/2.69 tff(23869,plain,
% 2.56/2.69 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23868, 23866, 453])).
% 2.56/2.69 tff(23870,plain,
% 2.56/2.69 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23869])).
% 2.56/2.69 tff(23871,plain,
% 2.56/2.69 (~(op(e0, e3) = op(e3, e0))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[747, 23870])).
% 2.56/2.69 tff(23872,plain,
% 2.56/2.69 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[496, 23871])).
% 2.56/2.69 tff(23873,plain,
% 2.56/2.69 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[18022])).
% 2.56/2.69 tff(23874,plain,
% 2.56/2.69 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23873])).
% 2.56/2.69 tff(23875,plain,
% 2.56/2.69 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23874])).
% 2.56/2.69 tff(23876,plain,
% 2.56/2.69 (~(op(e0, e2) = e1)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[6205, 23875])).
% 2.56/2.69 tff(23877,plain,
% 2.56/2.69 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e0)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.69 tff(23878,plain,
% 2.56/2.69 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23877])).
% 2.56/2.69 tff(23879,plain,
% 2.56/2.69 (~(op(e0, e2) = e0)),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[2736, 23878])).
% 2.56/2.69 tff(23880,plain,
% 2.56/2.69 ((op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[2745, 23879])).
% 2.56/2.69 tff(23881,plain,
% 2.56/2.69 (op(e0, e2) = e3),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[23880, 23847, 23876])).
% 2.56/2.69 tff(23882,plain,
% 2.56/2.69 (op(e0, e2) = op(e1, e0)),
% 2.56/2.69 inference(transitivity,[status(thm)],[23881, 259])).
% 2.56/2.69 tff(23883,plain,
% 2.56/2.69 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = op(e1, e0))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23882])).
% 2.56/2.69 tff(23884,plain,
% 2.56/2.69 ((op(e0, e1) = op(e0, e2)) <=> (op(e1, e0) = op(e0, e1))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23883, 595])).
% 2.56/2.69 tff(23885,plain,
% 2.56/2.69 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = op(e1, e0))),
% 2.56/2.69 inference(transitivity,[status(thm)],[23884, 596])).
% 2.56/2.69 tff(23886,plain,
% 2.56/2.69 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23885])).
% 2.56/2.69 tff(23887,plain,
% 2.56/2.69 (~(op(e0, e1) = op(e1, e0))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[2102, 23886])).
% 2.56/2.69 tff(23888,plain,
% 2.56/2.69 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[609, 23887])).
% 2.56/2.69 tff(23889,plain,
% 2.56/2.69 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.56/2.69 inference(monotonicity,[status(thm)],[23884])).
% 2.56/2.69 tff(23890,plain,
% 2.56/2.69 (~(op(e1, e0) = op(e0, e1))),
% 2.56/2.69 inference(modus_ponens,[status(thm)],[2102, 23889])).
% 2.56/2.69 tff(23891,plain,
% 2.56/2.69 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.56/2.69 inference(unit_resolution,[status(thm)],[613, 23890])).
% 2.56/2.69 tff(23892,plain,
% 2.56/2.69 ((op(e2, op(e1, e3)) = e2) <=> (op(e2, e0) = e2)),
% 2.56/2.69 inference(monotonicity,[status(thm)],[4893])).
% 2.56/2.69 tff(23893,plain,
% 2.56/2.69 ((op(e2, e0) = e2) <=> (op(e2, op(e1, e3)) = e2)),
% 2.56/2.69 inference(symmetry,[status(thm)],[23892])).
% 2.56/2.70 tff(23894,plain,
% 2.56/2.70 (op(e2, op(e1, e3)) = e2),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23840, 23893])).
% 2.56/2.70 tff(23895,plain,
% 2.56/2.70 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[9084, 23894])).
% 2.56/2.70 tff(23896,plain,
% 2.56/2.70 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23860, 395])).
% 2.56/2.70 tff(23897,plain,
% 2.56/2.70 ((~(op(e2, op(e1, e0)) = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23896])).
% 2.56/2.70 tff(23898,plain,
% 2.56/2.70 (~(op(e2, e3) = op(e3, e2))),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23863, 23897])).
% 2.56/2.70 tff(23899,plain,
% 2.56/2.70 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[430, 23898])).
% 2.56/2.70 tff(23900,plain,
% 2.56/2.70 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23843, 6337])).
% 2.56/2.70 tff(23901,plain,
% 2.56/2.70 ((~(op(e0, e2) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23900])).
% 2.56/2.70 tff(23902,plain,
% 2.56/2.70 (~(op(e0, e2) = op(e2, e0))),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23847, 23901])).
% 2.56/2.70 tff(23903,plain,
% 2.56/2.70 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[6347, 23902])).
% 2.56/2.70 tff(23904,plain,
% 2.56/2.70 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, e0) = e2)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23616])).
% 2.56/2.70 tff(23905,plain,
% 2.56/2.70 ((op(e2, e0) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23904])).
% 2.56/2.70 tff(23906,plain,
% 2.56/2.70 (op(e2, op(e2, e2)) = e2),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23840, 23905])).
% 2.56/2.70 tff(23907,plain,
% 2.56/2.70 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[528, 23906])).
% 2.56/2.70 tff(23908,plain,
% 2.56/2.70 ((op(e2, e0) = e1) <=> (e2 = op(e1, e2))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23840, 18022])).
% 2.56/2.70 tff(23909,plain,
% 2.56/2.70 ((op(e2, e0) = e1) <=> (op(e1, e2) = e2)),
% 2.56/2.70 inference(transitivity,[status(thm)],[23908, 5762])).
% 2.56/2.70 tff(23910,plain,
% 2.56/2.70 ((op(e1, e2) = e2) <=> (op(e2, e0) = e1)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23909])).
% 2.56/2.70 tff(23911,plain,
% 2.56/2.70 ((~(op(e1, e2) = e2)) <=> (~(op(e2, e0) = e1))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23910])).
% 2.56/2.70 tff(23912,plain,
% 2.56/2.70 (~(op(e2, e0) = e1)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[3785, 23911])).
% 2.56/2.70 tff(23913,plain,
% 2.56/2.70 ((~(op(e2, e0) = e2)) | (op(e2, op(e2, e0)) = e0)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[14232, 23615])).
% 2.56/2.70 tff(23914,plain,
% 2.56/2.70 (op(e2, op(e2, e0)) = e0),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23913, 23840])).
% 2.56/2.70 tff(23915,plain,
% 2.56/2.70 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[2653, 23914])).
% 2.56/2.70 tff(23916,plain,
% 2.56/2.70 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23857])).
% 2.56/2.70 tff(23917,plain,
% 2.56/2.70 (op(e3, op(e3, e2)) = e2),
% 2.56/2.70 inference(transitivity,[status(thm)],[23916, 23857])).
% 2.56/2.70 tff(23918,plain,
% 2.56/2.70 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[1904, 23917])).
% 2.56/2.70 tff(23919,plain,
% 2.56/2.70 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e0) = e3)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[11579])).
% 2.56/2.70 tff(23920,plain,
% 2.56/2.70 ((op(e1, e0) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23919])).
% 2.56/2.70 tff(23921,plain,
% 2.56/2.70 (op(e1, op(e1, e3)) = e3),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[258, 23920])).
% 2.56/2.70 tff(23922,plain,
% 2.56/2.70 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[162, 23921])).
% 2.56/2.70 tff(23923,plain,
% 2.56/2.70 (op(e0, op(e0, e2)) = op(e0, op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23882])).
% 2.56/2.70 tff(23924,plain,
% 2.56/2.70 (op(e0, op(e0, e2)) = e2),
% 2.56/2.70 inference(transitivity,[status(thm)],[23923, 20781, 2])).
% 2.56/2.70 tff(23925,plain,
% 2.56/2.70 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[1331, 23924])).
% 2.56/2.70 tff(23926,plain,
% 2.56/2.70 ((op(op(e0, e3), e0) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[2583, 259])).
% 2.56/2.70 tff(23927,plain,
% 2.56/2.70 ((op(op(e0, e3), e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23926, 749])).
% 2.56/2.70 tff(23928,plain,
% 2.56/2.70 ((op(e1, e0) = op(e2, e0)) <=> (op(op(e0, e3), e0) = e3)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23927])).
% 2.56/2.70 tff(23929,plain,
% 2.56/2.70 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23928])).
% 2.56/2.70 tff(23930,plain,
% 2.56/2.70 (~(op(op(e0, e3), e0) = e3)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[756, 23929])).
% 2.56/2.70 tff(23931,plain,
% 2.56/2.70 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[2635, 23930])).
% 2.56/2.70 tff(23932,plain,
% 2.56/2.70 ((e1 = e3) <=> (e1 = op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[259])).
% 2.56/2.70 tff(23933,plain,
% 2.56/2.70 ((e1 = e3) <=> (op(e1, e0) = e1)),
% 2.56/2.70 inference(transitivity,[status(thm)],[23932, 17546])).
% 2.56/2.70 tff(23934,plain,
% 2.56/2.70 ((~(e1 = e3)) <=> (~(op(e1, e0) = e1))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23933])).
% 2.56/2.70 tff(23935,plain,
% 2.56/2.70 (~(op(e1, e0) = e1)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[303, 23934])).
% 2.56/2.70 tff(23936,plain,
% 2.56/2.70 (op(e2, e3) = op(e1, e2)),
% 2.56/2.70 inference(transitivity,[status(thm)],[2684, 18022])).
% 2.56/2.70 tff(23937,plain,
% 2.56/2.70 ((op(e2, e3) = e3) <=> (op(e1, e2) = op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23936, 259])).
% 2.56/2.70 tff(23938,plain,
% 2.56/2.70 ((op(e2, e3) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23937, 1305])).
% 2.56/2.70 tff(23939,plain,
% 2.56/2.70 ((op(e1, e0) = op(e1, e2)) <=> (op(e2, e3) = e3)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23938])).
% 2.56/2.70 tff(23940,plain,
% 2.56/2.70 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e2, e3) = e3))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23939])).
% 2.56/2.70 tff(23941,plain,
% 2.56/2.70 (~(op(e2, e3) = e3)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[1312, 23940])).
% 2.56/2.70 tff(23942,plain,
% 2.56/2.70 (op(e3, e3) = e3),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[480, 23941, 1080, 661])).
% 2.56/2.70 tff(23943,plain,
% 2.56/2.70 (op(e3, op(e3, e3)) = op(e3, e3)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23942])).
% 2.56/2.70 tff(23944,plain,
% 2.56/2.70 (op(e3, op(e3, e3)) = e3),
% 2.56/2.70 inference(transitivity,[status(thm)],[23943, 23942])).
% 2.56/2.70 tff(23945,plain,
% 2.56/2.70 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[6277, 23944])).
% 2.56/2.70 tff(23946,plain,
% 2.56/2.70 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23936])).
% 2.56/2.70 tff(23947,plain,
% 2.56/2.70 ((op(e2, e1) = op(e2, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23946, 531])).
% 2.56/2.70 tff(23948,plain,
% 2.56/2.70 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23947])).
% 2.56/2.70 tff(23949,plain,
% 2.56/2.70 (~(op(e1, e2) = op(e2, e1))),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[197, 23948])).
% 2.56/2.70 tff(23950,plain,
% 2.56/2.70 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[539, 23949])).
% 2.56/2.70 tff(23951,plain,
% 2.56/2.70 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23946])).
% 2.56/2.70 tff(23952,plain,
% 2.56/2.70 (~(op(e2, e1) = op(e1, e2))),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[197, 23951])).
% 2.56/2.70 tff(23953,plain,
% 2.56/2.70 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[557, 23952])).
% 2.56/2.70 tff(23954,plain,
% 2.56/2.70 (op(e0, e0) = op(e1, e2)),
% 2.56/2.70 inference(transitivity,[status(thm)],[10406, 18022])).
% 2.56/2.70 tff(23955,plain,
% 2.56/2.70 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23954])).
% 2.56/2.70 tff(23956,plain,
% 2.56/2.70 (op(e0, op(e0, e0)) = op(e0, e1)),
% 2.56/2.70 inference(transitivity,[status(thm)],[23955, 18021])).
% 2.56/2.70 tff(23957,plain,
% 2.56/2.70 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e1) = e0)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23956])).
% 2.56/2.70 tff(23958,plain,
% 2.56/2.70 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23957])).
% 2.56/2.70 tff(23959,plain,
% 2.56/2.70 ((op(e0, e0) = e0) <=> (op(e1, e2) = e0)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23954])).
% 2.56/2.70 tff(23960,plain,
% 2.56/2.70 ((op(e1, e2) = e0) <=> (op(e0, e0) = e0)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23959])).
% 2.56/2.70 tff(23961,plain,
% 2.56/2.70 ((~(op(e1, e2) = e0)) <=> (~(op(e0, e0) = e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23960])).
% 2.56/2.70 tff(23962,plain,
% 2.56/2.70 (~(op(e0, e0) = e0)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23820, 23961])).
% 2.56/2.70 tff(23963,plain,
% 2.56/2.70 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e3) = e0)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[3976, 23879])).
% 2.56/2.70 tff(23964,plain,
% 2.56/2.70 (op(e0, e1) = e0),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23963, 23962, 1087])).
% 2.56/2.70 tff(23965,plain,
% 2.56/2.70 (op(e0, op(e0, e0)) = e0),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23964, 23958])).
% 2.56/2.70 tff(23966,plain,
% 2.56/2.70 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[500, 7754])).
% 2.56/2.70 tff(23967,plain,
% 2.56/2.70 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[10406])).
% 2.56/2.70 tff(23968,plain,
% 2.56/2.70 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 2.56/2.70 inference(transitivity,[status(thm)],[23967, 6411])).
% 2.56/2.70 tff(23969,plain,
% 2.56/2.70 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23968])).
% 2.56/2.70 tff(23970,plain,
% 2.56/2.70 (~(op(e3, e0) = e1)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[6384, 23969])).
% 2.56/2.70 tff(23971,plain,
% 2.56/2.70 (~(op(e2, e3) = e1)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[7757, 926, 931, 7754, 7748])).
% 2.56/2.70 tff(23972,plain,
% 2.56/2.70 ($false),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[151, 23971, 926, 87, 121])).
% 2.56/2.70 tff(23973,plain,((op(e3, e3) = e1) | (op(e1, e3) = e1) | (op(e0, e3) = e1) | (op(e3, e0) = e1) | (op(e3, e2) = op(e2, e3)) | (~(op(e1, e3) = op(e3, e1)))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.70 tff(23974,plain,
% 2.56/2.70 (~(op(e1, e3) = op(e3, e1))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23973, 23970, 121, 7754, 87, 926])).
% 2.56/2.70 tff(23975,plain,
% 2.56/2.70 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[6307, 23974])).
% 2.56/2.70 tff(23976,plain,
% 2.56/2.70 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[5367, 23975, 6689, 5672, 5680, 9846, 5668, 5511, 5675, 5673, 23966, 5681, 5670, 6688, 5674])).
% 2.56/2.70 tff(23977,plain,
% 2.56/2.70 (~(op(e0, op(e0, e0)) = e0)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[5598, 23976])).
% 2.56/2.70 tff(23978,plain,
% 2.56/2.70 ($false),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23977, 23965])).
% 2.56/2.70 tff(23979,plain,((~(op(e0, e0) = e1)) | (~(op(e1, e2) = e1)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (op(e0, e3) = e1) | (op(e3, e2) = op(e2, e3)) | (op(e1, e3) = e1) | (op(e3, e3) = e1) | (op(e0, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.70 tff(23980,plain,
% 2.56/2.70 (~(op(e0, e0) = e1)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23979, 23953, 6689, 5672, 6683, 9846, 5668, 5511, 5675, 23950, 5681, 5670, 23945, 5674, 121, 7754, 87, 18041, 1087])).
% 2.56/2.70 tff(23981,plain,
% 2.56/2.70 (op(e3, e0) = e1),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[1480, 23980, 1349, 23935])).
% 2.56/2.70 tff(23982,plain,
% 2.56/2.70 (op(e0, e1) = e1),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[384, 23980, 121, 23876])).
% 2.56/2.70 tff(23983,plain,
% 2.56/2.70 (op(e0, e1) = op(e1, e2)),
% 2.56/2.70 inference(transitivity,[status(thm)],[23982, 18022])).
% 2.56/2.70 tff(23984,plain,
% 2.56/2.70 ((op(e0, e1) = e0) <=> (op(e1, e2) = e0)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23983])).
% 2.56/2.70 tff(23985,plain,
% 2.56/2.70 ((op(e1, e2) = e0) <=> (op(e0, e1) = e0)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23984])).
% 2.56/2.70 tff(23986,plain,
% 2.56/2.70 ((~(op(e1, e2) = e0)) <=> (~(op(e0, e1) = e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23985])).
% 2.56/2.70 tff(23987,plain,
% 2.56/2.70 (~(op(e0, e1) = e0)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[23820, 23986])).
% 2.56/2.70 tff(23988,plain,
% 2.56/2.70 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e3, e1) = e0)),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[292, 23694])).
% 2.56/2.70 tff(23989,plain,
% 2.56/2.70 (op(e3, e1) = e0),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23988, 23987, 84])).
% 2.56/2.70 tff(23990,plain,
% 2.56/2.70 (op(e3, op(e3, e1)) = op(op(e1, e0), e0)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[259, 23989])).
% 2.56/2.70 tff(23991,plain,
% 2.56/2.70 (op(e3, op(e3, e1)) = e1),
% 2.56/2.70 inference(transitivity,[status(thm)],[23990, 20832, 23981])).
% 2.56/2.70 tff(23992,plain,
% 2.56/2.70 (op(op(e3, e0), e0) = op(e1, e0)),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23981])).
% 2.56/2.70 tff(23993,plain,
% 2.56/2.70 (op(op(e3, e0), e0) = e3),
% 2.56/2.70 inference(transitivity,[status(thm)],[23992, 258])).
% 2.56/2.70 tff(23994,plain,
% 2.56/2.70 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[4026, 23993])).
% 2.56/2.70 tff(23995,plain,
% 2.56/2.70 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[259])).
% 2.56/2.70 tff(23996,plain,
% 2.56/2.70 ((op(e2, e0) = e3) <=> (op(e1, e0) = op(e2, e0))),
% 2.56/2.70 inference(transitivity,[status(thm)],[23995, 749])).
% 2.56/2.70 tff(23997,plain,
% 2.56/2.70 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.56/2.70 inference(symmetry,[status(thm)],[23996])).
% 2.56/2.70 tff(23998,plain,
% 2.56/2.70 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[23997])).
% 2.56/2.70 tff(23999,plain,
% 2.56/2.70 (~(op(e2, e0) = e3)),
% 2.56/2.70 inference(modus_ponens,[status(thm)],[756, 23998])).
% 2.56/2.70 tff(24000,plain,
% 2.56/2.70 (op(e2, e1) = e3),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[23641, 23941, 23999])).
% 2.56/2.70 tff(24001,plain,
% 2.56/2.70 (op(e2, e1) = op(e1, e0)),
% 2.56/2.70 inference(transitivity,[status(thm)],[24000, 259])).
% 2.56/2.70 tff(24002,plain,
% 2.56/2.70 (op(e2, op(e2, e1)) = op(e2, op(e1, e0))),
% 2.56/2.70 inference(monotonicity,[status(thm)],[24001])).
% 2.56/2.70 tff(24003,plain,
% 2.56/2.70 (op(e2, op(e2, e1)) = e1),
% 2.56/2.70 inference(transitivity,[status(thm)],[24002, 17439, 2684])).
% 2.56/2.70 tff(24004,plain,
% 2.56/2.70 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.56/2.70 inference(unit_resolution,[status(thm)],[1355, 24003])).
% 2.56/2.71 tff(24005,plain,
% 2.56/2.71 (op(op(e2, e3), e2) = op(op(e1, e2), e2)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23936])).
% 2.56/2.71 tff(24006,plain,
% 2.56/2.71 (op(op(e2, e3), e2) = op(e1, e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24005, 18017])).
% 2.56/2.71 tff(24007,plain,
% 2.56/2.71 ((op(op(e2, e3), e2) = e3) <=> (op(e1, e2) = op(e1, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24006, 259])).
% 2.56/2.71 tff(24008,plain,
% 2.56/2.71 ((op(op(e2, e3), e2) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24007, 1305])).
% 2.56/2.71 tff(24009,plain,
% 2.56/2.71 ((op(e1, e0) = op(e1, e2)) <=> (op(op(e2, e3), e2) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24008])).
% 2.56/2.71 tff(24010,plain,
% 2.56/2.71 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(op(e2, e3), e2) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24009])).
% 2.56/2.71 tff(24011,plain,
% 2.56/2.71 (~(op(op(e2, e3), e2) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[1312, 24010])).
% 2.56/2.71 tff(24012,plain,
% 2.56/2.71 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1934, 24011])).
% 2.56/2.71 tff(24013,plain,
% 2.56/2.71 (op(e0, op(e0, e1)) = op(e0, op(e1, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23983])).
% 2.56/2.71 tff(24014,plain,
% 2.56/2.71 (op(e0, op(e0, e1)) = e1),
% 2.56/2.71 inference(transitivity,[status(thm)],[24013, 18021, 23982])).
% 2.56/2.71 tff(24015,plain,
% 2.56/2.71 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[2449, 24014])).
% 2.56/2.71 tff(24016,plain,
% 2.56/2.71 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1459, 24015, 3342, 1357, 1363, 1304, 24012, 3341, 2421, 24004, 18019, 23994])).
% 2.56/2.71 tff(24017,plain,
% 2.56/2.71 (~(op(e3, op(e3, e1)) = e1)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[2594, 24016])).
% 2.56/2.71 tff(24018,plain,
% 2.56/2.71 ($false),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24017, 23991])).
% 2.56/2.71 tff(24019,plain,((~(op(e2, e3) = e1)) | (~(op(e1, e0) = e3)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (op(e1, e1) = e0) | (~(op(e1, e2) = e1)) | (op(e2, e0) = e1) | (op(e0, e3) = e1) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (op(e3, e2) = op(e2, e3)) | (op(e1, e3) = e1) | (op(e0, e3) = e0) | (op(e1, e3) = e3) | (op(e0, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.71 tff(24020,plain,
% 2.56/2.71 (~(op(e2, e3) = e1)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24019, 23931, 258, 11584, 23925, 23922, 23918, 23915, 2639, 6683, 23912, 23800, 6689, 23907, 23903, 23899, 23895, 23891, 23888, 23872, 23849, 23864, 2672, 2500, 2605, 23855])).
% 2.56/2.71 tff(24021,plain,
% 2.56/2.71 (op(e3, e3) = e1),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[151, 24020, 23800, 2672])).
% 2.56/2.71 tff(24022,plain,
% 2.56/2.71 (op(e3, e3) = op(e1, e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24021, 18022])).
% 2.56/2.71 tff(24023,plain,
% 2.56/2.71 (op(e3, op(e3, e3)) = op(e3, op(e1, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24022])).
% 2.56/2.71 tff(24024,plain,
% 2.56/2.71 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24023, 23850, 2412])).
% 2.56/2.71 tff(24025,plain,
% 2.56/2.71 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24024])).
% 2.56/2.71 tff(24026,plain,
% 2.56/2.71 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24025])).
% 2.56/2.71 tff(24027,plain,
% 2.56/2.71 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e1, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[259])).
% 2.56/2.71 tff(24028,plain,
% 2.56/2.71 ((op(e3, e0) = e3) <=> (op(e1, e0) = op(e3, e0))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24027, 2294])).
% 2.56/2.71 tff(24029,plain,
% 2.56/2.71 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24028])).
% 2.56/2.71 tff(24030,plain,
% 2.56/2.71 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24029])).
% 2.56/2.71 tff(24031,plain,
% 2.56/2.71 (~(op(e3, e0) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[410, 24030])).
% 2.56/2.71 tff(24032,plain,
% 2.56/2.71 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23881])).
% 2.56/2.71 tff(24033,plain,
% 2.56/2.71 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24032, 3423])).
% 2.56/2.71 tff(24034,plain,
% 2.56/2.71 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24033])).
% 2.56/2.71 tff(24035,plain,
% 2.56/2.71 (~(op(e3, e2) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[1467, 24034])).
% 2.56/2.71 tff(24036,plain,
% 2.56/2.71 ((op(e3, e3) = e3) <=> (op(e1, e2) = op(e1, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24022, 259])).
% 2.56/2.71 tff(24037,plain,
% 2.56/2.71 ((op(e3, e3) = e3) <=> (op(e1, e0) = op(e1, e2))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24036, 1305])).
% 2.56/2.71 tff(24038,plain,
% 2.56/2.71 ((op(e1, e0) = op(e1, e2)) <=> (op(e3, e3) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24037])).
% 2.56/2.71 tff(24039,plain,
% 2.56/2.71 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e3, e3) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24038])).
% 2.56/2.71 tff(24040,plain,
% 2.56/2.71 (~(op(e3, e3) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[1312, 24039])).
% 2.56/2.71 tff(24041,plain,
% 2.56/2.71 (op(e3, e1) = e3),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[422, 24040, 24035, 24031])).
% 2.56/2.71 tff(24042,plain,
% 2.56/2.71 (op(e3, op(e3, e3)) = e3),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[24041, 24026])).
% 2.56/2.71 tff(24043,plain,
% 2.56/2.71 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[6277, 24042])).
% 2.56/2.71 tff(24044,plain,
% 2.56/2.71 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[500, 23864])).
% 2.56/2.71 tff(24045,plain,
% 2.56/2.71 ((op(e2, e2) = e1) <=> (e0 = e1)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.71 tff(24046,plain,
% 2.56/2.71 ((e0 = e1) <=> (op(e2, e2) = e1)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24045])).
% 2.56/2.71 tff(24047,plain,
% 2.56/2.71 ((~(e0 = e1)) <=> (~(op(e2, e2) = e1))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24046])).
% 2.56/2.71 tff(24048,plain,
% 2.56/2.71 (~(op(e2, e2) = e1)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[26, 24047])).
% 2.56/2.71 tff(24049,plain,
% 2.56/2.71 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e3) = e1)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[345, 24048])).
% 2.56/2.71 tff(24050,plain,
% 2.56/2.71 (op(e2, e1) = e1),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24049, 24020, 23912])).
% 2.56/2.71 tff(24051,plain,
% 2.56/2.71 (op(e2, e1) = op(e1, e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24050, 18022])).
% 2.56/2.71 tff(24052,plain,
% 2.56/2.71 (op(e3, op(e2, e1)) = op(e3, op(e1, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24051])).
% 2.56/2.71 tff(24053,plain,
% 2.56/2.71 (op(e3, op(e2, e1)) = op(e3, e1)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24052, 23850, 2412])).
% 2.56/2.71 tff(24054,plain,
% 2.56/2.71 ((op(e3, op(e2, e1)) = e3) <=> (op(e3, e1) = e3)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24053])).
% 2.56/2.71 tff(24055,plain,
% 2.56/2.71 ((op(e3, e1) = e3) <=> (op(e3, op(e2, e1)) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24054])).
% 2.56/2.71 tff(24056,plain,
% 2.56/2.71 (op(e3, op(e2, e1)) = e3),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[24041, 24055])).
% 2.56/2.71 tff(24057,plain,
% 2.56/2.71 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[6334, 24056])).
% 2.56/2.71 tff(24058,plain,
% 2.56/2.71 (op(e3, op(e1, e2)) = op(e3, e1)),
% 2.56/2.71 inference(transitivity,[status(thm)],[23850, 2412])).
% 2.56/2.71 tff(24059,plain,
% 2.56/2.71 ((op(e3, op(e1, e2)) = e3) <=> (op(e3, e1) = e3)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24058])).
% 2.56/2.71 tff(24060,plain,
% 2.56/2.71 ((op(e3, e1) = e3) <=> (op(e3, op(e1, e2)) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24059])).
% 2.56/2.71 tff(24061,plain,
% 2.56/2.71 (op(e3, op(e1, e2)) = e3),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[24041, 24060])).
% 2.56/2.71 tff(24062,plain,
% 2.56/2.71 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[11442, 24061])).
% 2.56/2.71 tff(24063,plain,
% 2.56/2.71 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e0)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[1219])).
% 2.56/2.71 tff(24064,plain,
% 2.56/2.71 ((op(e3, e1) = e0) <=> (op(e3, e1) = op(e1, e3))),
% 2.56/2.71 inference(symmetry,[status(thm)],[24063])).
% 2.56/2.71 tff(24065,plain,
% 2.56/2.71 (op(e3, e1) = op(op(e1, e0), e1)),
% 2.56/2.71 inference(symmetry,[status(thm)],[2412])).
% 2.56/2.71 tff(24066,plain,
% 2.56/2.71 ((op(e3, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24065])).
% 2.56/2.71 tff(24067,plain,
% 2.56/2.71 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e1) = e0)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24066])).
% 2.56/2.71 tff(24068,plain,
% 2.56/2.71 (op(op(e1, e0), e1) = op(e1, e0)),
% 2.56/2.71 inference(transitivity,[status(thm)],[2412, 24041, 259])).
% 2.56/2.71 tff(24069,plain,
% 2.56/2.71 ((op(op(e1, e0), e1) = e0) <=> (op(e1, e0) = e0)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24068])).
% 2.56/2.71 tff(24070,plain,
% 2.56/2.71 ((op(e1, e0) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24069])).
% 2.56/2.71 tff(24071,plain,
% 2.56/2.71 ((op(e1, e0) = e0) <=> (op(e1, e3) = op(e3, e1))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24070, 24067, 24064, 6290])).
% 2.56/2.71 tff(24072,plain,
% 2.56/2.71 ((~(op(e1, e0) = e0)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24071])).
% 2.56/2.71 tff(24073,plain,
% 2.56/2.71 (~(op(e1, e3) = op(e3, e1))),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[17127, 24072])).
% 2.56/2.71 tff(24074,plain,
% 2.56/2.71 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[6307, 24073])).
% 2.56/2.71 tff(24075,plain,
% 2.56/2.71 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e1, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[259])).
% 2.56/2.71 tff(24076,plain,
% 2.56/2.71 ((op(e0, e1) = e3) <=> (op(e1, e0) = op(e0, e1))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24075, 595])).
% 2.56/2.71 tff(24077,plain,
% 2.56/2.71 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24076])).
% 2.56/2.71 tff(24078,plain,
% 2.56/2.71 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 2.56/2.71 inference(transitivity,[status(thm)],[23884, 24077])).
% 2.56/2.71 tff(24079,plain,
% 2.56/2.71 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24078])).
% 2.56/2.71 tff(24080,plain,
% 2.56/2.71 (~(op(e0, e1) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[2102, 24079])).
% 2.56/2.71 tff(24081,plain,
% 2.56/2.71 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e1)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24050])).
% 2.56/2.71 tff(24082,plain,
% 2.56/2.71 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e1))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24081])).
% 2.56/2.71 tff(24083,plain,
% 2.56/2.71 (~(op(e0, e1) = e1)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[606, 24082])).
% 2.56/2.71 tff(24084,plain,
% 2.56/2.71 (op(e0, e1) = e0),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[829, 24083, 5828, 24080])).
% 2.56/2.71 tff(24085,plain,
% 2.56/2.71 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24021])).
% 2.56/2.71 tff(24086,plain,
% 2.56/2.71 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24085])).
% 2.56/2.71 tff(24087,plain,
% 2.56/2.71 (~(op(e3, e0) = e1)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[157, 24086])).
% 2.56/2.71 tff(24088,plain,
% 2.56/2.71 (op(e0, e0) = e1),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1480, 24087, 23912, 23935])).
% 2.56/2.71 tff(24089,plain,
% 2.56/2.71 (op(e0, e0) = op(e1, e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24088, 18022])).
% 2.56/2.71 tff(24090,plain,
% 2.56/2.71 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24089])).
% 2.56/2.71 tff(24091,plain,
% 2.56/2.71 (op(e0, op(e0, e0)) = e0),
% 2.56/2.71 inference(transitivity,[status(thm)],[24090, 18021, 24084])).
% 2.56/2.71 tff(24092,plain,
% 2.56/2.71 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[5598, 24091])).
% 2.56/2.71 tff(24093,plain,
% 2.56/2.71 ($false),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[5367, 24092, 24074, 6689, 23907, 24062, 23903, 23899, 23895, 23891, 24057, 24044, 23888, 23872, 24043, 23849])).
% 2.56/2.71 tff(24094,plain,((~(op(e0, e3) = e2)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~(op(e1, e2) = e1)) | (~(op(e1, e0) = e3)) | (~(op(e1, e3) = e0)) | (op(e0, e1) = e2) | (op(e1, e2) = e2) | (op(e2, e1) = e2) | (op(e1, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.56/2.71 tff(24095,plain,
% 2.56/2.71 (~(op(e0, e3) = e2)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24094, 23826, 23822, 23811, 1219, 5774, 5766, 21868, 21431])).
% 2.56/2.71 tff(24096,plain,
% 2.56/2.71 (op(e2, e3) = e2),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[15003, 24095, 23623])).
% 2.56/2.71 tff(24097,plain,
% 2.56/2.71 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24096])).
% 2.56/2.71 tff(24098,plain,
% 2.56/2.71 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24097])).
% 2.56/2.71 tff(24099,plain,
% 2.56/2.71 (~(op(e2, e0) = e2)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[989, 24098])).
% 2.56/2.71 tff(24100,plain,
% 2.56/2.71 ((op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[765, 23807])).
% 2.56/2.71 tff(24101,plain,
% 2.56/2.71 (op(e2, e0) = e1),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24100, 24099, 23817])).
% 2.56/2.71 tff(24102,plain,
% 2.56/2.71 (e1 = op(e2, op(e2, e2))),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[24101, 23619])).
% 2.56/2.71 tff(24103,plain,
% 2.56/2.71 (e1 = op(e1, e2)),
% 2.56/2.71 inference(symmetry,[status(thm)],[23822])).
% 2.56/2.71 tff(24104,plain,
% 2.56/2.71 (op(e2, e0) = op(e1, e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24101, 24103])).
% 2.56/2.71 tff(24105,plain,
% 2.56/2.71 (op(e2, op(e2, e0)) = op(e2, op(e1, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24104])).
% 2.56/2.71 tff(24106,plain,
% 2.56/2.71 (op(e2, op(e1, e2)) = op(e2, op(e2, e0))),
% 2.56/2.71 inference(symmetry,[status(thm)],[24105])).
% 2.56/2.71 tff(24107,plain,
% 2.56/2.71 (op(e2, op(e1, e2)) = op(e2, e1)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23822])).
% 2.56/2.71 tff(24108,plain,
% 2.56/2.71 (op(e2, e1) = op(e2, op(e1, e2))),
% 2.56/2.71 inference(symmetry,[status(thm)],[24107])).
% 2.56/2.71 tff(24109,plain,
% 2.56/2.71 ((op(e2, e3) = e3) <=> (e2 = op(e1, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24096, 23812])).
% 2.56/2.71 tff(24110,plain,
% 2.56/2.71 ((op(e2, e3) = e3) <=> (op(e1, e0) = e2)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24109, 2154])).
% 2.56/2.71 tff(24111,plain,
% 2.56/2.71 ((op(e1, e0) = e2) <=> (op(e2, e3) = e3)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24110])).
% 2.56/2.71 tff(24112,plain,
% 2.56/2.71 ((~(op(e1, e0) = e2)) <=> (~(op(e2, e3) = e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24111])).
% 2.56/2.71 tff(24113,plain,
% 2.56/2.71 (~(op(e2, e3) = e3)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[21431, 24112])).
% 2.56/2.71 tff(24114,plain,
% 2.56/2.71 (op(e2, e1) = e3),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[23641, 24113, 23817])).
% 2.56/2.71 tff(24115,plain,
% 2.56/2.71 (e3 = op(e2, e1)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24114])).
% 2.56/2.71 tff(24116,plain,
% 2.56/2.71 (e3 = op(e2, op(e2, op(e2, e2)))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24115, 24108, 24106, 23789])).
% 2.56/2.71 tff(24117,plain,
% 2.56/2.71 ($false),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[23797, 24116, 24102])).
% 2.56/2.71 tff(24118,plain,((~(op(e1, e1) = e2)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.56/2.71 tff(24119,plain,
% 2.56/2.71 (~(op(e1, e1) = e2)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24118, 1219])).
% 2.56/2.71 tff(24120,plain,
% 2.56/2.71 ((op(e2, e1) = e2) <=> (op(e2, e1) = op(e2, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23810])).
% 2.56/2.71 tff(24121,plain,
% 2.56/2.71 ((op(e2, e1) = e2) <=> (op(e2, e0) = op(e2, e1))),
% 2.56/2.71 inference(transitivity,[status(thm)],[24120, 10625])).
% 2.56/2.71 tff(24122,plain,
% 2.56/2.71 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24121])).
% 2.56/2.71 tff(24123,plain,
% 2.56/2.71 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24122])).
% 2.56/2.71 tff(24124,plain,
% 2.56/2.71 (~(op(e2, e1) = e2)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[1966, 24123])).
% 2.56/2.71 tff(24125,plain,
% 2.56/2.71 (op(e3, e1) = e2),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1993, 24124, 24119, 10380])).
% 2.56/2.71 tff(24126,plain,
% 2.56/2.71 (op(e3, e1) = op(e2, e0)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24125, 23810])).
% 2.56/2.71 tff(24127,plain,
% 2.56/2.71 ((op(e3, e1) = e0) <=> (op(e2, e0) = e0)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24126])).
% 2.56/2.71 tff(24128,plain,
% 2.56/2.71 ((op(e2, e0) = e0) <=> (op(e3, e1) = e0)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24127])).
% 2.56/2.71 tff(24129,plain,
% 2.56/2.71 ((~(op(e2, e0) = e0)) <=> (~(op(e3, e1) = e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24128])).
% 2.56/2.71 tff(24130,plain,
% 2.56/2.71 (~(op(e3, e1) = e0)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[23807, 24129])).
% 2.56/2.71 tff(24131,plain,
% 2.56/2.71 ((op(e2, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23615])).
% 2.56/2.71 tff(24132,plain,
% 2.56/2.71 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24131, 4959])).
% 2.56/2.71 tff(24133,plain,
% 2.56/2.71 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24132])).
% 2.56/2.71 tff(24134,plain,
% 2.56/2.71 (~(op(e3, e2) = e0)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[1546, 24133])).
% 2.56/2.71 tff(24135,plain,
% 2.56/2.71 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e3) = e0)),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1916, 24134])).
% 2.56/2.71 tff(24136,plain,
% 2.56/2.71 (op(e3, e0) = e0),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[24135, 24130, 17084])).
% 2.56/2.71 tff(24137,plain,
% 2.56/2.71 (op(e3, op(e3, e0)) = op(e3, e0)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24136])).
% 2.56/2.71 tff(24138,plain,
% 2.56/2.71 (op(e3, op(e3, e0)) = e0),
% 2.56/2.71 inference(transitivity,[status(thm)],[24137, 24136])).
% 2.56/2.71 tff(24139,plain,
% 2.56/2.71 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[1345, 24138])).
% 2.56/2.71 tff(24140,plain,
% 2.56/2.71 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e2, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[23810])).
% 2.56/2.71 tff(24141,plain,
% 2.56/2.71 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 2.56/2.71 inference(symmetry,[status(thm)],[24140])).
% 2.56/2.71 tff(24142,plain,
% 2.56/2.71 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24141])).
% 2.56/2.71 tff(24143,plain,
% 2.56/2.71 (~(op(e1, e0) = e2)),
% 2.56/2.71 inference(modus_ponens,[status(thm)],[756, 24142])).
% 2.56/2.71 tff(24144,plain,
% 2.56/2.71 (op(e1, e2) = e2),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[2285, 24143, 23623, 24119])).
% 2.56/2.71 tff(24145,plain,
% 2.56/2.71 (op(op(e2, e3), e2) = op(e1, op(e0, e3))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[2684, 2560])).
% 2.56/2.71 tff(24146,plain,
% 2.56/2.71 (op(e1, op(e2, e0)) = op(op(e2, e3), e2)),
% 2.56/2.71 inference(monotonicity,[status(thm)],[2685, 23809])).
% 2.56/2.71 tff(24147,plain,
% 2.56/2.71 (op(e1, e2) = op(e2, e0)),
% 2.56/2.71 inference(transitivity,[status(thm)],[24144, 23810])).
% 2.56/2.71 tff(24148,plain,
% 2.56/2.71 (op(e1, op(e1, e2)) = op(e1, op(e2, e0))),
% 2.56/2.71 inference(monotonicity,[status(thm)],[24147])).
% 2.56/2.71 tff(24149,plain,
% 2.56/2.71 (op(e1, op(e1, e2)) = e2),
% 2.56/2.71 inference(transitivity,[status(thm)],[24148, 24146, 24145, 10421, 24144])).
% 2.56/2.71 tff(24150,plain,
% 2.56/2.71 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.56/2.71 inference(unit_resolution,[status(thm)],[2377, 24149])).
% 2.56/2.72 tff(24151,plain,
% 2.56/2.72 (op(e2, e1) = e3),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[23695, 21187, 24124])).
% 2.56/2.72 tff(24152,plain,
% 2.56/2.72 (op(e2, op(e2, e1)) = op(op(e0, e3), e3)),
% 2.56/2.72 inference(monotonicity,[status(thm)],[2560, 24151])).
% 2.56/2.72 tff(24153,plain,
% 2.56/2.72 (op(e2, op(e2, e1)) = e1),
% 2.56/2.72 inference(transitivity,[status(thm)],[24152, 2607, 2684])).
% 2.56/2.72 tff(24154,plain,
% 2.56/2.72 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[1355, 24153])).
% 2.56/2.72 tff(24155,plain,
% 2.56/2.72 (op(e2, op(e2, e0)) = e0),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[23913, 23809])).
% 2.56/2.72 tff(24156,plain,
% 2.56/2.72 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[2653, 24155])).
% 2.56/2.72 tff(24157,plain,
% 2.56/2.72 (op(op(e2, e1), e1) = op(e3, op(e2, e3))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24151, 2685])).
% 2.56/2.72 tff(24158,plain,
% 2.56/2.72 (op(e3, e3) = e3),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[15018, 2825, 17084])).
% 2.56/2.72 tff(24159,plain,
% 2.56/2.72 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.56/2.72 inference(monotonicity,[status(thm)],[10458, 24158])).
% 2.56/2.72 tff(24160,plain,
% 2.56/2.72 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 2.56/2.72 inference(transitivity,[status(thm)],[24159, 10460])).
% 2.56/2.72 tff(24161,plain,
% 2.56/2.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24160])).
% 2.56/2.72 tff(24162,plain,
% 2.56/2.72 (~(op(e3, e2) = e3)),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[1888, 24161])).
% 2.56/2.72 tff(24163,plain,
% 2.56/2.72 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24144])).
% 2.56/2.72 tff(24164,plain,
% 2.56/2.72 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.56/2.72 inference(transitivity,[status(thm)],[24163, 2234])).
% 2.56/2.72 tff(24165,plain,
% 2.56/2.72 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24164])).
% 2.56/2.72 tff(24166,plain,
% 2.56/2.72 (~(op(e3, e2) = e2)),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[2292, 24165])).
% 2.56/2.72 tff(24167,plain,
% 2.56/2.72 ((op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[1898, 24134])).
% 2.56/2.72 tff(24168,plain,
% 2.56/2.72 (op(e3, e2) = e1),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[24167, 24166, 24162])).
% 2.56/2.72 tff(24169,plain,
% 2.56/2.72 (e3 = op(e2, e1)),
% 2.56/2.72 inference(symmetry,[status(thm)],[24151])).
% 2.56/2.72 tff(24170,plain,
% 2.56/2.72 (op(e3, op(e3, e2)) = op(op(e2, e1), e1)),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24169, 24168])).
% 2.56/2.72 tff(24171,plain,
% 2.56/2.72 (op(e3, op(e3, e2)) = e2),
% 2.56/2.72 inference(transitivity,[status(thm)],[24170, 24157, 2832, 24125])).
% 2.56/2.72 tff(24172,plain,
% 2.56/2.72 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[1904, 24171])).
% 2.56/2.72 tff(24173,plain,
% 2.56/2.72 (op(e2, e1) = op(e2, op(e2, e3))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[2685])).
% 2.56/2.72 tff(24174,plain,
% 2.56/2.72 ((op(e2, e1) = e3) <=> (op(e2, op(e2, e3)) = e3)),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24173])).
% 2.56/2.72 tff(24175,plain,
% 2.56/2.72 (op(e2, op(e2, e3)) = e3),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[24151, 24174])).
% 2.56/2.72 tff(24176,plain,
% 2.56/2.72 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[2344, 24175])).
% 2.56/2.72 tff(24177,plain,
% 2.56/2.72 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e2, e1))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24169])).
% 2.56/2.72 tff(24178,plain,
% 2.56/2.72 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 2.56/2.72 inference(symmetry,[status(thm)],[24177])).
% 2.56/2.72 tff(24179,plain,
% 2.56/2.72 ((op(e0, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.56/2.72 inference(transitivity,[status(thm)],[24178, 18356])).
% 2.56/2.72 tff(24180,plain,
% 2.56/2.72 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.56/2.72 inference(monotonicity,[status(thm)],[24179])).
% 2.56/2.72 tff(24181,plain,
% 2.56/2.72 (~(op(op(e1, e3), e1) = e3)),
% 2.56/2.72 inference(modus_ponens,[status(thm)],[606, 24180])).
% 2.56/2.72 tff(24182,plain,
% 2.56/2.72 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.56/2.72 inference(unit_resolution,[status(thm)],[160, 24181])).
% 2.56/2.72 tff(24183,plain,
% 2.62/2.72 (op(e0, op(e2, e1)) = op(e0, e3)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24151])).
% 2.62/2.72 tff(24184,plain,
% 2.62/2.72 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e2, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24169])).
% 2.62/2.72 tff(24185,plain,
% 2.62/2.72 ((op(e1, e2) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.72 inference(transitivity,[status(thm)],[24184, 530])).
% 2.62/2.72 tff(24186,plain,
% 2.62/2.72 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24185])).
% 2.62/2.72 tff(24187,plain,
% 2.62/2.72 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, op(e2, e3)) = e2)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24173, 24144])).
% 2.62/2.72 tff(24188,plain,
% 2.62/2.72 ((op(e2, op(e2, e3)) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24187])).
% 2.62/2.72 tff(24189,plain,
% 2.62/2.72 ((op(e2, op(e2, e3)) = e2) <=> (op(e1, e2) = e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24188, 24186])).
% 2.62/2.72 tff(24190,plain,
% 2.62/2.72 ((~(op(e2, op(e2, e3)) = e2)) <=> (~(op(e1, e2) = e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24189])).
% 2.62/2.72 tff(24191,plain,
% 2.62/2.72 ((e2 = op(e2, op(e2, e3))) <=> (op(e2, op(e2, e3)) = e2)),
% 2.62/2.72 inference(commutativity,[status(thm)],[])).
% 2.62/2.72 tff(24192,plain,
% 2.62/2.72 ((op(e2, e0) = op(e2, e1)) <=> (e2 = op(e2, op(e2, e3)))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[23809, 24173])).
% 2.62/2.72 tff(24193,plain,
% 2.62/2.72 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, op(e2, e3)) = e2)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24192, 24191])).
% 2.62/2.72 tff(24194,plain,
% 2.62/2.72 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, op(e2, e3)) = e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24193])).
% 2.62/2.72 tff(24195,plain,
% 2.62/2.72 (~(op(e2, op(e2, e3)) = e2)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[1966, 24194])).
% 2.62/2.72 tff(24196,plain,
% 2.62/2.72 (~(op(e1, e2) = e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24195, 24190])).
% 2.62/2.72 tff(24197,plain,
% 2.62/2.72 (op(e0, e2) = e3),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23653, 24162, 24196])).
% 2.62/2.72 tff(24198,plain,
% 2.62/2.72 (op(e0, e2) = op(e2, e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24197, 24169])).
% 2.62/2.72 tff(24199,plain,
% 2.62/2.72 (op(e0, op(e0, e2)) = op(e0, op(e2, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24198])).
% 2.62/2.72 tff(24200,plain,
% 2.62/2.72 (op(e0, op(e0, e2)) = e2),
% 2.62/2.72 inference(transitivity,[status(thm)],[24199, 24183, 2])).
% 2.62/2.72 tff(24201,plain,
% 2.62/2.72 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[1331, 24200])).
% 2.62/2.72 tff(24202,plain,
% 2.62/2.72 (op(e2, op(e2, e3)) = op(e2, e1)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24173])).
% 2.62/2.72 tff(24203,plain,
% 2.62/2.72 (op(op(e3, e1), e1) = op(e2, op(e2, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24125, 2685])).
% 2.62/2.72 tff(24204,plain,
% 2.62/2.72 (op(op(e3, e1), e1) = e3),
% 2.62/2.72 inference(transitivity,[status(thm)],[24203, 24202, 24151])).
% 2.62/2.72 tff(24205,plain,
% 2.62/2.72 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[2416, 24204])).
% 2.62/2.72 tff(24206,plain,
% 2.62/2.72 ((~(op(e2, e0) = e3)) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[17696])).
% 2.62/2.72 tff(24207,plain,
% 2.62/2.72 ((~(op(e2, e0) = e3)) | (~(op(e2, e3) = e1))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[14078, 23615])).
% 2.62/2.72 tff(24208,plain,
% 2.62/2.72 (~(op(e2, e0) = e3)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24207, 2684])).
% 2.62/2.72 tff(24209,plain,
% 2.62/2.72 (~(op(op(e0, e3), e0) = e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24208, 24206])).
% 2.62/2.72 tff(24210,plain,
% 2.62/2.72 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[2635, 24209])).
% 2.62/2.72 tff(24211,plain,
% 2.62/2.72 (op(e1, op(e2, e1)) = op(op(e2, e3), e3)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[2685, 24151])).
% 2.62/2.72 tff(24212,plain,
% 2.62/2.72 ((op(e1, e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24169])).
% 2.62/2.72 tff(24213,plain,
% 2.62/2.72 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e3)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24212])).
% 2.62/2.72 tff(24214,plain,
% 2.62/2.72 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24213])).
% 2.62/2.72 tff(24215,plain,
% 2.62/2.72 (~(op(e1, e1) = e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[225, 24214])).
% 2.62/2.72 tff(24216,plain,
% 2.62/2.72 (op(e1, e0) = e3),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[247, 24215, 2605, 24196])).
% 2.62/2.72 tff(24217,plain,
% 2.62/2.72 (op(e1, e0) = op(e2, e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24216, 24169])).
% 2.62/2.72 tff(24218,plain,
% 2.62/2.72 (op(e1, op(e1, e0)) = op(e1, op(e2, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24217])).
% 2.62/2.72 tff(24219,plain,
% 2.62/2.72 (op(e1, op(e1, e0)) = e0),
% 2.62/2.72 inference(transitivity,[status(thm)],[24218, 24211, 4481, 1219])).
% 2.62/2.72 tff(24220,plain,
% 2.62/2.72 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[1836, 24219])).
% 2.62/2.72 tff(24221,plain,
% 2.62/2.72 (op(e0, e1) = e0),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23988, 24130, 2639])).
% 2.62/2.72 tff(24222,plain,
% 2.62/2.72 (op(op(e0, e1), e1) = op(e0, op(e2, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24221, 2685])).
% 2.62/2.72 tff(24223,plain,
% 2.62/2.72 (op(op(e0, e1), e1) = e0),
% 2.62/2.72 inference(transitivity,[status(thm)],[24222, 4447, 24221])).
% 2.62/2.72 tff(24224,plain,
% 2.62/2.72 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[2650, 24223])).
% 2.62/2.72 tff(24225,plain,
% 2.62/2.72 ($false),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[1459, 24224, 24220, 24210, 24205, 24201, 24182, 24176, 24172, 24156, 24154, 24150, 24139])).
% 2.62/2.72 tff(24226,plain,((~(op(e2, e3) = e1)) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.72 tff(24227,plain,
% 2.62/2.72 (~(op(e2, e3) = e1)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24226, 2, 1219])).
% 2.62/2.72 tff(24228,plain,
% 2.62/2.72 (op(e3, e3) = e1),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[151, 24227, 23800, 2672])).
% 2.62/2.72 tff(24229,plain,
% 2.62/2.72 (e1 = op(e3, e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24228, 658])).
% 2.62/2.72 tff(24230,plain,
% 2.62/2.72 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24228])).
% 2.62/2.72 tff(24231,plain,
% 2.62/2.72 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24230])).
% 2.62/2.72 tff(24232,plain,
% 2.62/2.72 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24231, 5470])).
% 2.62/2.72 tff(24233,plain,
% 2.62/2.72 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24232])).
% 2.62/2.72 tff(24234,plain,
% 2.62/2.72 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24228])).
% 2.62/2.72 tff(24235,plain,
% 2.62/2.72 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24234])).
% 2.62/2.72 tff(24236,plain,
% 2.62/2.72 (~(op(e3, e2) = e1)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[1888, 24235])).
% 2.62/2.72 tff(24237,plain,
% 2.62/2.72 ((op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[206, 23804])).
% 2.62/2.72 tff(24238,plain,
% 2.62/2.72 (op(e2, e3) = e3),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24237, 24227, 17647])).
% 2.62/2.72 tff(24239,plain,
% 2.62/2.72 (e3 = op(e2, e3)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24238])).
% 2.62/2.72 tff(24240,plain,
% 2.62/2.72 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[2560])).
% 2.62/2.72 tff(24241,plain,
% 2.62/2.72 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24240])).
% 2.62/2.72 tff(24242,plain,
% 2.62/2.72 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24241])).
% 2.62/2.72 tff(24243,plain,
% 2.62/2.72 (~(op(e0, e2) = e2)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[918, 24242])).
% 2.62/2.72 tff(24244,plain,
% 2.62/2.72 (e3 = op(e0, e0)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[21901, 71])).
% 2.62/2.72 tff(24245,plain,
% 2.62/2.72 (op(e0, e3) = op(e0, op(e1, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[4971])).
% 2.62/2.72 tff(24246,plain,
% 2.62/2.72 (op(e0, op(e1, e1)) = op(e0, e3)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24245])).
% 2.62/2.72 tff(24247,plain,
% 2.62/2.72 (op(e0, e0) = op(e1, e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[21901, 4971])).
% 2.62/2.72 tff(24248,plain,
% 2.62/2.72 (op(e0, op(e0, e0)) = op(e0, op(e1, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24247])).
% 2.62/2.72 tff(24249,plain,
% 2.62/2.72 (op(e0, op(e0, e0)) = op(e0, e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24248, 24246])).
% 2.62/2.72 tff(24250,plain,
% 2.62/2.72 ((e2 = op(e0, op(e0, e0))) <=> (e2 = op(e0, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24249])).
% 2.62/2.72 tff(24251,plain,
% 2.62/2.72 ((e2 = op(e0, op(e0, e0))) <=> (op(e0, e3) = e2)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24250, 1681])).
% 2.62/2.72 tff(24252,plain,
% 2.62/2.72 ((op(e0, e3) = e2) <=> (e2 = op(e0, op(e0, e0)))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24251])).
% 2.62/2.72 tff(24253,plain,
% 2.62/2.72 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[21901])).
% 2.62/2.72 tff(24254,plain,
% 2.62/2.72 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24253, 660])).
% 2.62/2.72 tff(24255,plain,
% 2.62/2.72 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24254])).
% 2.62/2.72 tff(24256,plain,
% 2.62/2.72 (~(op(e2, e0) = e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[359, 24255])).
% 2.62/2.72 tff(24257,plain,
% 2.62/2.72 (op(e2, e3) = e3),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23641, 24256, 15670])).
% 2.62/2.72 tff(24258,plain,
% 2.62/2.72 (op(e2, op(e1, e1)) = op(e1, e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[15725, 24257, 4971])).
% 2.62/2.72 tff(24259,plain,
% 2.62/2.72 ((op(e2, op(e1, e1)) = e2) <=> (op(e1, e1) = e2)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24258])).
% 2.62/2.72 tff(24260,plain,
% 2.62/2.72 ((op(e1, e1) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24259])).
% 2.62/2.72 tff(24261,plain,
% 2.62/2.72 ((op(e1, e1) = e2) <=> (op(e2, e3) = e2)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24260, 15728])).
% 2.62/2.72 tff(24262,plain,
% 2.62/2.72 ((~(op(e1, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24261])).
% 2.62/2.72 tff(24263,plain,
% 2.62/2.72 (~(op(e2, e3) = e2)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[68, 24262])).
% 2.62/2.72 tff(24264,plain,
% 2.62/2.72 (op(e0, e3) = e2),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[15003, 24263, 72])).
% 2.62/2.72 tff(24265,plain,
% 2.62/2.72 (e2 = op(e0, op(e0, e0))),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24264, 24252])).
% 2.62/2.72 tff(24266,plain,
% 2.62/2.72 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24249])).
% 2.62/2.72 tff(24267,plain,
% 2.62/2.72 (op(e0, op(e0, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24266])).
% 2.62/2.72 tff(24268,plain,
% 2.62/2.72 (op(e0, op(e0, e3)) = op(e0, e2)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24264])).
% 2.62/2.72 tff(24269,plain,
% 2.62/2.72 (op(e0, e2) = op(e0, op(e0, e3))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24268])).
% 2.62/2.72 tff(24270,plain,
% 2.62/2.72 ((op(e0, e0) = op(e0, e2)) <=> (e3 = op(e0, e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[21901])).
% 2.62/2.72 tff(24271,plain,
% 2.62/2.72 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24270, 4221])).
% 2.62/2.72 tff(24272,plain,
% 2.62/2.72 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24271])).
% 2.62/2.72 tff(24273,plain,
% 2.62/2.72 (~(op(e0, e2) = e3)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[3603, 24272])).
% 2.62/2.72 tff(24274,plain,
% 2.62/2.72 (op(e0, e2) = e1),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23880, 24273, 6229])).
% 2.62/2.72 tff(24275,plain,
% 2.62/2.72 (e1 = op(e0, e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24274])).
% 2.62/2.72 tff(24276,plain,
% 2.62/2.72 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.62/2.72 inference(transitivity,[status(thm)],[24275, 24269, 24267])).
% 2.62/2.72 tff(24277,plain,
% 2.62/2.72 ($false),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[2760, 24276, 24265, 24244])).
% 2.62/2.72 tff(24278,plain,((~(op(e0, e0) = e3)) | (~(op(e1, e1) = e3)) | (op(e1, e3) = e2) | (op(e1, e1) = e2) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.72 tff(24279,plain,
% 2.62/2.72 (~(op(e0, e0) = e3)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24278, 4960, 23623, 24243, 24119])).
% 2.62/2.72 tff(24280,plain,
% 2.62/2.72 (op(e0, e2) = e3),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[1495, 12019, 17791, 24279])).
% 2.62/2.72 tff(24281,plain,
% 2.62/2.72 (op(e0, e2) = op(e2, e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24280, 24239])).
% 2.62/2.72 tff(24282,plain,
% 2.62/2.72 ((op(e0, e2) = e1) <=> (op(e2, e3) = e1)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24281])).
% 2.62/2.72 tff(24283,plain,
% 2.62/2.72 ((op(e2, e3) = e1) <=> (op(e0, e2) = e1)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24282])).
% 2.62/2.72 tff(24284,plain,
% 2.62/2.72 ((~(op(e2, e3) = e1)) <=> (~(op(e0, e2) = e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24283])).
% 2.62/2.72 tff(24285,plain,
% 2.62/2.72 (~(op(e0, e2) = e1)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24227, 24284])).
% 2.62/2.72 tff(24286,plain,
% 2.62/2.72 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e3, e2) = e1)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[1613, 23784])).
% 2.62/2.72 tff(24287,plain,
% 2.62/2.72 (op(e1, e2) = e1),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24286, 24285, 24236])).
% 2.62/2.72 tff(24288,plain,
% 2.62/2.72 (op(e1, op(e2, e3)) = op(e1, e3)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24238])).
% 2.62/2.72 tff(24289,plain,
% 2.62/2.72 (op(e1, e1) = op(e2, e3)),
% 2.62/2.72 inference(transitivity,[status(thm)],[4960, 24239])).
% 2.62/2.72 tff(24290,plain,
% 2.62/2.72 (op(e1, op(e1, e1)) = op(e1, op(e2, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24289])).
% 2.62/2.72 tff(24291,plain,
% 2.62/2.72 (op(e1, op(e1, e1)) = e0),
% 2.62/2.72 inference(transitivity,[status(thm)],[24290, 24288, 1219])).
% 2.62/2.72 tff(24292,plain,
% 2.62/2.72 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24291])).
% 2.62/2.72 tff(24293,plain,
% 2.62/2.72 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24292])).
% 2.62/2.72 tff(24294,plain,
% 2.62/2.72 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24293, 2154])).
% 2.62/2.72 tff(24295,plain,
% 2.62/2.72 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24294])).
% 2.62/2.72 tff(24296,plain,
% 2.62/2.72 (op(e1, op(e2, e3)) = op(e1, op(e1, e1))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24290])).
% 2.62/2.72 tff(24297,plain,
% 2.62/2.72 (op(e1, e3) = op(e1, op(e2, e3))),
% 2.62/2.72 inference(symmetry,[status(thm)],[24288])).
% 2.62/2.72 tff(24298,plain,
% 2.62/2.72 (e0 = op(e1, op(e1, e1))),
% 2.62/2.72 inference(transitivity,[status(thm)],[2909, 24297, 24296])).
% 2.62/2.72 tff(24299,plain,
% 2.62/2.72 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[3009, 24298, 6906])).
% 2.62/2.72 tff(24300,plain,
% 2.62/2.72 (~(op(e1, e0) = e2)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[24299, 24295])).
% 2.62/2.72 tff(24301,plain,
% 2.62/2.72 (op(e1, e2) = e2),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[2285, 24300, 23623, 24119])).
% 2.62/2.72 tff(24302,plain,
% 2.62/2.72 (e2 = op(e1, e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24301])).
% 2.62/2.72 tff(24303,plain,
% 2.62/2.72 (op(e0, e3) = e1),
% 2.62/2.72 inference(transitivity,[status(thm)],[2, 24302, 24287])).
% 2.62/2.72 tff(24304,plain,
% 2.62/2.72 ($false),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23800, 24303])).
% 2.62/2.72 tff(24305,plain,((~(op(e1, e1) = e3)) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.72 tff(24306,plain,
% 2.62/2.72 (~(op(e1, e1) = e3)),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[24305, 2, 1219])).
% 2.62/2.72 tff(24307,plain,
% 2.62/2.72 (op(e1, e1) = e1),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[630, 24306, 24119, 2639])).
% 2.62/2.72 tff(24308,plain,
% 2.62/2.72 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24307])).
% 2.62/2.72 tff(24309,plain,
% 2.62/2.72 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24308, 2355])).
% 2.62/2.72 tff(24310,plain,
% 2.62/2.72 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24309])).
% 2.62/2.72 tff(24311,plain,
% 2.62/2.72 (~(op(e2, e1) = e1)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[225, 24310])).
% 2.62/2.72 tff(24312,plain,
% 2.62/2.72 (op(e2, e0) = e1),
% 2.62/2.72 inference(unit_resolution,[status(thm)],[23785, 24311, 24227])).
% 2.62/2.72 tff(24313,plain,
% 2.62/2.72 ((op(e2, e0) = e2) <=> (e1 = op(e0, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24312, 2560])).
% 2.62/2.72 tff(24314,plain,
% 2.62/2.72 ((op(e2, e0) = e2) <=> (op(e0, e3) = e1)),
% 2.62/2.72 inference(transitivity,[status(thm)],[24313, 10225])).
% 2.62/2.72 tff(24315,plain,
% 2.62/2.72 ((op(e0, e3) = e1) <=> (op(e2, e0) = e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24314])).
% 2.62/2.72 tff(24316,plain,
% 2.62/2.72 ((~(op(e0, e3) = e1)) <=> (~(op(e2, e0) = e2))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[24315])).
% 2.62/2.72 tff(24317,plain,
% 2.62/2.72 (~(op(e2, e0) = e2)),
% 2.62/2.72 inference(modus_ponens,[status(thm)],[23800, 24316])).
% 2.62/2.72 tff(24318,plain,
% 2.62/2.72 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e0, e3))),
% 2.62/2.72 inference(monotonicity,[status(thm)],[2560])).
% 2.62/2.72 tff(24319,plain,
% 2.62/2.72 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 2.62/2.72 inference(symmetry,[status(thm)],[24318])).
% 2.62/2.72 tff(24320,plain,
% 2.62/2.72 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24319])).
% 2.62/2.73 tff(24321,plain,
% 2.62/2.73 (~(op(e0, e0) = e2)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[3414, 24320])).
% 2.62/2.73 tff(24322,plain,
% 2.62/2.73 (op(e0, e2) = op(e0, op(e0, e3))),
% 2.62/2.73 inference(symmetry,[status(thm)],[17663])).
% 2.62/2.73 tff(24323,plain,
% 2.62/2.73 ((op(e0, e2) = e3) <=> (op(e0, op(e0, e3)) = e3)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24322])).
% 2.62/2.73 tff(24324,plain,
% 2.62/2.73 ((op(e0, op(e0, e3)) = e3) <=> (op(e0, e2) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24323])).
% 2.62/2.73 tff(24325,plain,
% 2.62/2.73 (op(e1, e2) = op(e1, op(e0, e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[2560])).
% 2.62/2.73 tff(24326,plain,
% 2.62/2.73 ((op(e1, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24325])).
% 2.62/2.73 tff(24327,plain,
% 2.62/2.73 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24326])).
% 2.62/2.73 tff(24328,plain,
% 2.62/2.73 ((e1 = op(e1, op(e0, e3))) <=> (op(e1, op(e0, e3)) = e1)),
% 2.62/2.73 inference(commutativity,[status(thm)],[])).
% 2.62/2.73 tff(24329,plain,
% 2.62/2.73 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, op(e0, e3)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24307, 24325])).
% 2.62/2.73 tff(24330,plain,
% 2.62/2.73 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, op(e0, e3)) = e1)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24329, 24328])).
% 2.62/2.73 tff(24331,plain,
% 2.62/2.73 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24330, 24327])).
% 2.62/2.73 tff(24332,plain,
% 2.62/2.73 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24331])).
% 2.62/2.73 tff(24333,plain,
% 2.62/2.73 (~(op(e1, e2) = e1)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[1604, 24332])).
% 2.62/2.73 tff(24334,plain,
% 2.62/2.73 (op(e0, e2) = e1),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[24286, 24333, 24236])).
% 2.62/2.73 tff(24335,plain,
% 2.62/2.73 (op(e0, op(e0, e3)) = e1),
% 2.62/2.73 inference(transitivity,[status(thm)],[17663, 24334])).
% 2.62/2.73 tff(24336,plain,
% 2.62/2.73 ((op(e0, op(e0, e3)) = e3) <=> (e1 = op(e2, e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24335, 24239])).
% 2.62/2.73 tff(24337,plain,
% 2.62/2.73 ((op(e0, op(e0, e3)) = e3) <=> (op(e2, e3) = e1)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24336, 5574])).
% 2.62/2.73 tff(24338,plain,
% 2.62/2.73 ((op(e2, e3) = e1) <=> (op(e0, op(e0, e3)) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24337])).
% 2.62/2.73 tff(24339,plain,
% 2.62/2.73 ((op(e2, e3) = e1) <=> (op(e0, e2) = e3)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24338, 24324])).
% 2.62/2.73 tff(24340,plain,
% 2.62/2.73 ((~(op(e2, e3) = e1)) <=> (~(op(e0, e2) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24339])).
% 2.62/2.73 tff(24341,plain,
% 2.62/2.73 (~(op(e0, e2) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[24227, 24340])).
% 2.62/2.73 tff(24342,plain,
% 2.62/2.73 (op(e1, e0) = op(e0, e3)),
% 2.62/2.73 inference(transitivity,[status(thm)],[920, 2560])).
% 2.62/2.73 tff(24343,plain,
% 2.62/2.73 ((op(e1, e0) = e3) <=> (op(e0, e3) = op(e2, e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24342, 24239])).
% 2.62/2.73 tff(24344,plain,
% 2.62/2.73 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e0) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24343])).
% 2.62/2.73 tff(24345,plain,
% 2.62/2.73 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e0) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24344])).
% 2.62/2.73 tff(24346,plain,
% 2.62/2.73 (~(op(e1, e0) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[964, 24345])).
% 2.62/2.73 tff(24347,plain,
% 2.62/2.73 (op(e1, e2) = e3),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[247, 24346, 2605, 24306])).
% 2.62/2.73 tff(24348,plain,
% 2.62/2.73 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[857, 24239])).
% 2.62/2.73 tff(24349,plain,
% 2.62/2.73 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24348])).
% 2.62/2.73 tff(24350,plain,
% 2.62/2.73 (e3 = op(e1, e2)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24347])).
% 2.62/2.73 tff(24351,plain,
% 2.62/2.73 (op(e2, e3) = op(e1, e2)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24238, 24350])).
% 2.62/2.73 tff(24352,plain,
% 2.62/2.73 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = op(e1, e2))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24351])).
% 2.62/2.73 tff(24353,plain,
% 2.62/2.73 ((op(e3, e2) = op(e2, e3)) <=> (op(e1, e2) = op(e3, e2))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24352, 3635])).
% 2.62/2.73 tff(24354,plain,
% 2.62/2.73 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.62/2.73 inference(symmetry,[status(thm)],[24353])).
% 2.62/2.73 tff(24355,plain,
% 2.62/2.73 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24354, 24349, 10460])).
% 2.62/2.73 tff(24356,plain,
% 2.62/2.73 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24355])).
% 2.62/2.73 tff(24357,plain,
% 2.62/2.73 (~(op(e3, e2) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[2292, 24356])).
% 2.62/2.73 tff(24358,plain,
% 2.62/2.73 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24239])).
% 2.62/2.73 tff(24359,plain,
% 2.62/2.73 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24358])).
% 2.62/2.73 tff(24360,plain,
% 2.62/2.73 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24359])).
% 2.62/2.73 tff(24361,plain,
% 2.62/2.73 (~(op(e2, e1) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[197, 24360])).
% 2.62/2.73 tff(24362,plain,
% 2.62/2.73 (op(e2, e1) = e2),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[23695, 24311, 24361])).
% 2.62/2.73 tff(24363,plain,
% 2.62/2.73 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24362])).
% 2.62/2.73 tff(24364,plain,
% 2.62/2.73 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24363, 5762])).
% 2.62/2.73 tff(24365,plain,
% 2.62/2.73 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.73 inference(symmetry,[status(thm)],[24364])).
% 2.62/2.73 tff(24366,plain,
% 2.62/2.73 ((op(e1, e0) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[920])).
% 2.62/2.73 tff(24367,plain,
% 2.62/2.73 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24366, 5762])).
% 2.62/2.73 tff(24368,plain,
% 2.62/2.73 ((op(e1, e0) = op(e1, e2)) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24367, 24365])).
% 2.62/2.73 tff(24369,plain,
% 2.62/2.73 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24368])).
% 2.62/2.73 tff(24370,plain,
% 2.62/2.73 (~(op(e2, e1) = op(e1, e2))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[1312, 24369])).
% 2.62/2.73 tff(24371,plain,
% 2.62/2.73 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[557, 24370])).
% 2.62/2.73 tff(24372,plain,
% 2.62/2.73 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = op(e2, e1))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24367, 24365, 531])).
% 2.62/2.73 tff(24373,plain,
% 2.62/2.73 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24372])).
% 2.62/2.73 tff(24374,plain,
% 2.62/2.73 (~(op(e1, e2) = op(e2, e1))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[1312, 24373])).
% 2.62/2.73 tff(24375,plain,
% 2.62/2.73 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[539, 24374])).
% 2.62/2.73 tff(24376,plain,
% 2.62/2.73 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24354, 395])).
% 2.62/2.73 tff(24377,plain,
% 2.62/2.73 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24376])).
% 2.62/2.73 tff(24378,plain,
% 2.62/2.73 (~(op(e2, e3) = op(e3, e2))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[2292, 24377])).
% 2.62/2.73 tff(24379,plain,
% 2.62/2.73 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[430, 24378])).
% 2.62/2.73 tff(24380,plain,
% 2.62/2.73 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24354])).
% 2.62/2.73 tff(24381,plain,
% 2.62/2.73 (~(op(e3, e2) = op(e2, e3))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[2292, 24380])).
% 2.62/2.73 tff(24382,plain,
% 2.62/2.73 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[500, 24381])).
% 2.62/2.73 tff(24383,plain,
% 2.62/2.73 (op(e1, op(e0, e2)) = op(e1, e1)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24334])).
% 2.62/2.73 tff(24384,plain,
% 2.62/2.73 (op(e1, op(e0, e2)) = e1),
% 2.62/2.73 inference(transitivity,[status(thm)],[24383, 24307])).
% 2.62/2.73 tff(24385,plain,
% 2.62/2.73 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[14259, 24384])).
% 2.62/2.73 tff(24386,plain,
% 2.62/2.73 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e3) = op(e0, e1))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24342])).
% 2.62/2.73 tff(24387,plain,
% 2.62/2.73 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e3))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24386, 15424])).
% 2.62/2.73 tff(24388,plain,
% 2.62/2.73 ((op(e0, e1) = op(e0, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 2.62/2.73 inference(symmetry,[status(thm)],[24387])).
% 2.62/2.73 tff(24389,plain,
% 2.62/2.73 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24388, 596])).
% 2.62/2.73 tff(24390,plain,
% 2.62/2.73 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24389])).
% 2.62/2.73 tff(24391,plain,
% 2.62/2.73 (~(op(e0, e1) = op(e1, e0))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[818, 24390])).
% 2.62/2.73 tff(24392,plain,
% 2.62/2.73 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[609, 24391])).
% 2.62/2.73 tff(24393,plain,
% 2.62/2.73 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24388])).
% 2.62/2.73 tff(24394,plain,
% 2.62/2.73 (~(op(e1, e0) = op(e0, e1))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[818, 24393])).
% 2.62/2.73 tff(24395,plain,
% 2.62/2.73 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[613, 24394])).
% 2.62/2.73 tff(24396,plain,
% 2.62/2.73 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24342])).
% 2.62/2.73 tff(24397,plain,
% 2.62/2.73 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24396, 452])).
% 2.62/2.73 tff(24398,plain,
% 2.62/2.73 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.62/2.73 inference(transitivity,[status(thm)],[24397, 453])).
% 2.62/2.73 tff(24399,plain,
% 2.62/2.73 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24398])).
% 2.62/2.73 tff(24400,plain,
% 2.62/2.73 (~(op(e0, e3) = op(e3, e0))),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[410, 24399])).
% 2.62/2.73 tff(24401,plain,
% 2.62/2.73 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[496, 24400])).
% 2.62/2.73 tff(24402,plain,
% 2.62/2.73 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[5523])).
% 2.62/2.73 tff(24403,plain,
% 2.62/2.73 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24402, 2355])).
% 2.62/2.73 tff(24404,plain,
% 2.62/2.73 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24403])).
% 2.62/2.73 tff(24405,plain,
% 2.62/2.73 (~(op(e2, e1) = e1)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[225, 24404])).
% 2.62/2.73 tff(24406,plain,
% 2.62/2.73 (op(e0, op(e2, e2)) = op(e0, e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[23615])).
% 2.62/2.73 tff(24407,plain,
% 2.62/2.73 ((op(e0, op(e2, e2)) = e0) <=> (op(e0, e0) = e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24406])).
% 2.62/2.73 tff(24408,plain,
% 2.62/2.73 ((op(e0, e0) = e0) <=> (op(e0, op(e2, e2)) = e0)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24407])).
% 2.62/2.73 tff(24409,plain,
% 2.62/2.73 (op(e0, e1) = op(e1, e2)),
% 2.62/2.73 inference(transitivity,[status(thm)],[4839, 2900])).
% 2.62/2.73 tff(24410,plain,
% 2.62/2.73 ((op(e0, e1) = e0) <=> (op(e1, e2) = e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24409])).
% 2.62/2.73 tff(24411,plain,
% 2.62/2.73 ((op(e1, e2) = e0) <=> (op(e0, e1) = e0)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24410])).
% 2.62/2.73 tff(24412,plain,
% 2.62/2.73 ((~(op(e1, e2) = e0)) <=> (~(op(e0, e1) = e0))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24411])).
% 2.62/2.73 tff(24413,plain,
% 2.62/2.73 (~(op(e0, e1) = e0)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[23820, 24412])).
% 2.62/2.73 tff(24414,plain,
% 2.62/2.73 (op(e0, e0) = e0),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[23963, 24413, 2500])).
% 2.62/2.73 tff(24415,plain,
% 2.62/2.73 (op(e0, op(e2, e2)) = e0),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[24414, 24408])).
% 2.62/2.73 tff(24416,plain,
% 2.62/2.73 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[5619, 24415])).
% 2.62/2.73 tff(24417,plain,
% 2.62/2.73 (op(e3, e3) = e1),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[151, 76, 23800, 2672])).
% 2.62/2.73 tff(24418,plain,
% 2.62/2.73 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24417])).
% 2.62/2.73 tff(24419,plain,
% 2.62/2.73 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24418])).
% 2.62/2.73 tff(24420,plain,
% 2.62/2.73 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24419])).
% 2.62/2.73 tff(24421,plain,
% 2.62/2.73 (~(op(e3, e3) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[303, 24420])).
% 2.62/2.73 tff(24422,plain,
% 2.62/2.73 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[4839])).
% 2.62/2.73 tff(24423,plain,
% 2.62/2.73 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.62/2.73 inference(transitivity,[status(thm)],[24422, 396])).
% 2.62/2.73 tff(24424,plain,
% 2.62/2.73 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e3))),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24423])).
% 2.62/2.73 tff(24425,plain,
% 2.62/2.73 (~(op(e3, e1) = e3)),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[3046, 24424])).
% 2.62/2.73 tff(24426,plain,
% 2.62/2.73 (op(e3, e0) = e3),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[422, 24425, 24421, 1890])).
% 2.62/2.73 tff(24427,plain,
% 2.62/2.73 (op(e3, e1) = e0),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[23988, 24413, 2639])).
% 2.62/2.73 tff(24428,plain,
% 2.62/2.73 (op(e3, op(e3, e1)) = op(e3, e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24427])).
% 2.62/2.73 tff(24429,plain,
% 2.62/2.73 (op(e3, op(e3, e1)) = e3),
% 2.62/2.73 inference(transitivity,[status(thm)],[24428, 24426])).
% 2.62/2.73 tff(24430,plain,
% 2.62/2.73 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[450, 24429])).
% 2.62/2.73 tff(24431,plain,
% 2.62/2.73 (op(e0, op(e1, e3)) = op(e0, e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[1219])).
% 2.62/2.73 tff(24432,plain,
% 2.62/2.73 ((op(e0, op(e1, e3)) = e0) <=> (op(e0, e0) = e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24431])).
% 2.62/2.73 tff(24433,plain,
% 2.62/2.73 ((op(e0, e0) = e0) <=> (op(e0, op(e1, e3)) = e0)),
% 2.62/2.73 inference(symmetry,[status(thm)],[24432])).
% 2.62/2.73 tff(24434,plain,
% 2.62/2.73 (op(e0, op(e1, e3)) = e0),
% 2.62/2.73 inference(modus_ponens,[status(thm)],[24414, 24433])).
% 2.62/2.73 tff(24435,plain,
% 2.62/2.73 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[5501, 24434])).
% 2.62/2.73 tff(24436,plain,
% 2.62/2.73 (op(e0, op(e0, e0)) = op(e0, e0)),
% 2.62/2.73 inference(monotonicity,[status(thm)],[24414])).
% 2.62/2.73 tff(24437,plain,
% 2.62/2.73 (op(e0, op(e0, e0)) = e0),
% 2.62/2.73 inference(transitivity,[status(thm)],[24436, 24414])).
% 2.62/2.73 tff(24438,plain,
% 2.62/2.73 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.62/2.73 inference(unit_resolution,[status(thm)],[5598, 24437])).
% 2.62/2.73 tff(24439,plain,
% 2.62/2.73 ((op(e2, e3) = e1) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~(op(e1, e1) = e1)) | (op(e2, e1) = e1) | (op(e0, e3) = e1) | (op(e1, e3) = e1)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[5693, 23784])).
% 2.62/2.74 tff(24440,plain,
% 2.62/2.74 ($false),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[24439, 24438, 24435, 23800, 76, 5523, 5670, 5675, 5681, 5674, 5671, 24430, 5668, 5673, 24416, 24405, 5680, 2672])).
% 2.62/2.74 tff(24441,plain,((~(op(e0, e1) = e3)) | (op(e2, e3) = e1) | (~(op(e1, e1) = e1)) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~(op(e1, e3) = e0)) | (op(e3, e2) = e3) | (~(op(e1, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.74 tff(24442,plain,
% 2.62/2.74 (~(op(e0, e1) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[24441, 24401, 24307, 24227, 24395, 24392, 24385, 24382, 24379, 24375, 24371, 1219, 24357, 24347])).
% 2.62/2.74 tff(24443,plain,
% 2.62/2.74 (op(e0, e0) = e3),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[1495, 24442, 17791, 24341])).
% 2.62/2.74 tff(24444,plain,
% 2.62/2.74 (e3 = op(e0, e0)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24443, 71])).
% 2.62/2.74 tff(24445,plain,
% 2.62/2.74 (op(e0, e0) = op(e1, e2)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24443, 24350])).
% 2.62/2.74 tff(24446,plain,
% 2.62/2.74 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24445])).
% 2.62/2.74 tff(24447,plain,
% 2.62/2.74 (op(e0, op(e1, e2)) = op(e0, op(e0, e0))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24446])).
% 2.62/2.74 tff(24448,plain,
% 2.62/2.74 (op(e1, e2) = op(e2, e3)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24347, 24239])).
% 2.62/2.74 tff(24449,plain,
% 2.62/2.74 (op(e0, op(e1, e2)) = op(e0, op(e2, e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24448])).
% 2.62/2.74 tff(24450,plain,
% 2.62/2.74 (op(e0, op(e2, e3)) = op(e0, op(e1, e2))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24449])).
% 2.62/2.74 tff(24451,plain,
% 2.62/2.74 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24238])).
% 2.62/2.74 tff(24452,plain,
% 2.62/2.74 (op(e0, e3) = op(e0, op(e2, e3))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24451])).
% 2.62/2.74 tff(24453,plain,
% 2.62/2.74 (e2 = op(e0, op(e0, e0))),
% 2.62/2.74 inference(transitivity,[status(thm)],[2560, 24452, 24450, 24447])).
% 2.62/2.74 tff(24454,plain,
% 2.62/2.74 (op(e0, op(e0, e0)) = op(e0, e3)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24446, 24449, 24451])).
% 2.62/2.74 tff(24455,plain,
% 2.62/2.74 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e0, e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24454])).
% 2.62/2.74 tff(24456,plain,
% 2.62/2.74 (op(e0, op(e0, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24455])).
% 2.62/2.74 tff(24457,plain,
% 2.62/2.74 (e1 = op(e0, e2)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24334])).
% 2.62/2.74 tff(24458,plain,
% 2.62/2.74 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24457, 24322, 24456])).
% 2.62/2.74 tff(24459,plain,
% 2.62/2.74 ($false),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[2760, 24458, 24453, 24444])).
% 2.62/2.74 tff(24460,plain,((~(op(e1, e0) = e2)) | (~(op(e0, e3) = e2)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.74 tff(24461,plain,
% 2.62/2.74 (~(op(e1, e0) = e2)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[24460, 2, 1219])).
% 2.62/2.74 tff(24462,plain,
% 2.62/2.74 (op(e3, e0) = e2),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[589, 24461, 24321, 24317])).
% 2.62/2.74 tff(24463,plain,
% 2.62/2.74 (op(e3, e0) = op(e0, e3)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24462, 2560])).
% 2.62/2.74 tff(24464,plain,
% 2.62/2.74 ((op(e3, e0) = e0) <=> (op(e0, e3) = e0)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24463])).
% 2.62/2.74 tff(24465,plain,
% 2.62/2.74 ((op(e0, e3) = e0) <=> (op(e3, e0) = e0)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24464])).
% 2.62/2.74 tff(24466,plain,
% 2.62/2.74 ((~(op(e0, e3) = e0)) <=> (~(op(e3, e0) = e0))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24465])).
% 2.62/2.74 tff(24467,plain,
% 2.62/2.74 (~(op(e3, e0) = e0)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[2500, 24466])).
% 2.62/2.74 tff(24468,plain,
% 2.62/2.74 (op(e3, e1) = e0),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[24135, 24467, 17084])).
% 2.62/2.74 tff(24469,plain,
% 2.62/2.74 (e0 = op(e3, op(e3, e3))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24468, 24233])).
% 2.62/2.74 tff(24470,plain,
% 2.62/2.74 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24230])).
% 2.62/2.74 tff(24471,plain,
% 2.62/2.74 (op(e3, op(e3, e1)) = op(e3, op(e3, op(e3, e3)))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24470])).
% 2.62/2.74 tff(24472,plain,
% 2.62/2.74 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24307])).
% 2.62/2.74 tff(24473,plain,
% 2.62/2.74 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24472])).
% 2.62/2.74 tff(24474,plain,
% 2.62/2.74 (~(op(e1, e0) = e1)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[737, 24473])).
% 2.62/2.74 tff(24475,plain,
% 2.62/2.74 (op(e1, e0) = e3),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[728, 24461, 17127, 24474])).
% 2.62/2.74 tff(24476,plain,
% 2.62/2.74 (e3 = op(e1, e0)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24475])).
% 2.62/2.74 tff(24477,plain,
% 2.62/2.74 (op(e3, op(e3, e1)) = op(op(e1, e0), e0)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24476, 24468])).
% 2.62/2.74 tff(24478,plain,
% 2.62/2.74 (op(op(e1, e0), e0) = op(e3, op(e3, e1))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24477])).
% 2.62/2.74 tff(24479,plain,
% 2.62/2.74 (op(op(e1, e0), e0) = op(e3, e0)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24475])).
% 2.62/2.74 tff(24480,plain,
% 2.62/2.74 (op(e3, e0) = op(op(e1, e0), e0)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24479])).
% 2.62/2.74 tff(24481,plain,
% 2.62/2.74 (e2 = op(e3, e0)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24462])).
% 2.62/2.74 tff(24482,plain,
% 2.62/2.74 (e2 = op(e3, op(e3, op(e3, e3)))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24481, 24480, 24478, 24471])).
% 2.62/2.74 tff(24483,plain,
% 2.62/2.74 ($false),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[5397, 24482, 24469, 24229])).
% 2.62/2.74 tff(24484,plain,((~(op(e0, e3) = e2)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.74 tff(24485,plain,
% 2.62/2.74 (~(op(e0, e3) = e2)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[24484, 1219])).
% 2.62/2.74 tff(24486,plain,
% 2.62/2.74 (op(e2, e3) = e2),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[15003, 24485, 23623])).
% 2.62/2.74 tff(24487,plain,
% 2.62/2.74 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.74 tff(24488,plain,
% 2.62/2.74 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24487, 69])).
% 2.62/2.74 tff(24489,plain,
% 2.62/2.74 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24488])).
% 2.62/2.74 tff(24490,plain,
% 2.62/2.74 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24489])).
% 2.62/2.74 tff(24491,plain,
% 2.62/2.74 (~(op(e2, e3) = e1)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[708, 24490])).
% 2.62/2.74 tff(24492,plain,
% 2.62/2.74 (op(e0, e3) = e3),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[687, 24485, 2500, 23800])).
% 2.62/2.74 tff(24493,plain,
% 2.62/2.74 (op(op(e0, e3), e0) = op(e3, e0)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24492])).
% 2.62/2.74 tff(24494,plain,
% 2.62/2.74 (op(e1, op(e0, e3)) = op(e1, e3)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24492])).
% 2.62/2.74 tff(24495,plain,
% 2.62/2.74 (e3 = op(e0, e3)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24492])).
% 2.62/2.74 tff(24496,plain,
% 2.62/2.74 (op(e1, e1) = op(e0, e3)),
% 2.62/2.74 inference(transitivity,[status(thm)],[4960, 24495])).
% 2.62/2.74 tff(24497,plain,
% 2.62/2.74 (op(e1, op(e1, e1)) = op(e1, op(e0, e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24496])).
% 2.62/2.74 tff(24498,plain,
% 2.62/2.74 (op(e1, op(e1, e1)) = e0),
% 2.62/2.74 inference(transitivity,[status(thm)],[24497, 24494, 1219])).
% 2.62/2.74 tff(24499,plain,
% 2.62/2.74 (op(e1, op(e1, op(e1, e1))) = op(e1, e0)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24498])).
% 2.62/2.74 tff(24500,plain,
% 2.62/2.74 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (e2 = op(e1, e0))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24499])).
% 2.62/2.74 tff(24501,plain,
% 2.62/2.74 ((e2 = op(e1, op(e1, op(e1, e1)))) <=> (op(e1, e0) = e2)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24500, 2154])).
% 2.62/2.74 tff(24502,plain,
% 2.62/2.74 ((~(e2 = op(e1, op(e1, op(e1, e1))))) <=> (~(op(e1, e0) = e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24501])).
% 2.62/2.74 tff(24503,plain,
% 2.62/2.74 (op(e1, op(e0, e3)) = op(e1, op(e1, e1))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24497])).
% 2.62/2.74 tff(24504,plain,
% 2.62/2.74 (op(e1, e3) = op(e1, op(e0, e3))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24494])).
% 2.62/2.74 tff(24505,plain,
% 2.62/2.74 (e0 = op(e1, op(e1, e1))),
% 2.62/2.74 inference(transitivity,[status(thm)],[2909, 24504, 24503])).
% 2.62/2.74 tff(24506,plain,
% 2.62/2.74 (~(e2 = op(e1, op(e1, op(e1, e1))))),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[3009, 24505, 6906])).
% 2.62/2.74 tff(24507,plain,
% 2.62/2.74 (~(op(e1, e0) = e2)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24506, 24502])).
% 2.62/2.74 tff(24508,plain,
% 2.62/2.74 (op(e1, e2) = e2),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[2285, 24507, 23623, 24119])).
% 2.62/2.74 tff(24509,plain,
% 2.62/2.74 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24508])).
% 2.62/2.74 tff(24510,plain,
% 2.62/2.74 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24509])).
% 2.62/2.74 tff(24511,plain,
% 2.62/2.74 (~(op(e0, e2) = e2)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[6205, 24510])).
% 2.62/2.74 tff(24512,plain,
% 2.62/2.74 ((op(e2, e3) = e3) <=> (e2 = e3)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.74 tff(24513,plain,
% 2.62/2.74 ((e2 = e3) <=> (op(e2, e3) = e3)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24512])).
% 2.62/2.74 tff(24514,plain,
% 2.62/2.74 ((~(e2 = e3)) <=> (~(op(e2, e3) = e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24513])).
% 2.62/2.74 tff(24515,plain,
% 2.62/2.74 (~(op(e2, e3) = e3)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[1321, 24514])).
% 2.62/2.74 tff(24516,plain,
% 2.62/2.74 (op(e2, e0) = e3),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[23641, 23636, 24515])).
% 2.62/2.74 tff(24517,plain,
% 2.62/2.74 (op(e2, e0) = op(e0, e3)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24516, 24495])).
% 2.62/2.74 tff(24518,plain,
% 2.62/2.74 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e3) = op(e0, e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24517])).
% 2.62/2.74 tff(24519,plain,
% 2.62/2.74 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24518, 7797])).
% 2.62/2.74 tff(24520,plain,
% 2.62/2.74 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24519])).
% 2.62/2.74 tff(24521,plain,
% 2.62/2.74 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24520])).
% 2.62/2.74 tff(24522,plain,
% 2.62/2.74 (~(op(e2, e0) = op(e0, e2))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[918, 24521])).
% 2.62/2.74 tff(24523,plain,
% 2.62/2.74 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[6358, 24522])).
% 2.62/2.74 tff(24524,plain,
% 2.62/2.74 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24517])).
% 2.62/2.74 tff(24525,plain,
% 2.62/2.74 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24524, 452])).
% 2.62/2.74 tff(24526,plain,
% 2.62/2.74 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24525, 453])).
% 2.62/2.74 tff(24527,plain,
% 2.62/2.74 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24526])).
% 2.62/2.74 tff(24528,plain,
% 2.62/2.74 (~(op(e0, e3) = op(e3, e0))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[747, 24527])).
% 2.62/2.74 tff(24529,plain,
% 2.62/2.74 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[496, 24528])).
% 2.62/2.74 tff(24530,plain,
% 2.62/2.74 (op(e1, e0) = e1),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[728, 24507, 17127, 12623])).
% 2.62/2.74 tff(24531,plain,
% 2.62/2.74 ((op(e1, e0) = op(e0, e1)) <=> (e1 = op(e0, e1))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24530])).
% 2.62/2.74 tff(24532,plain,
% 2.62/2.74 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24531, 7013])).
% 2.62/2.74 tff(24533,plain,
% 2.62/2.74 ((op(e0, e1) = e1) <=> (op(e1, e0) = op(e0, e1))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24532])).
% 2.62/2.74 tff(24534,plain,
% 2.62/2.74 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e1, e0))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24533, 596])).
% 2.62/2.74 tff(24535,plain,
% 2.62/2.74 ((~(op(e0, e1) = e1)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24534])).
% 2.62/2.74 tff(24536,plain,
% 2.62/2.74 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.74 tff(24537,plain,
% 2.62/2.74 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24536])).
% 2.62/2.74 tff(24538,plain,
% 2.62/2.74 (~(op(e2, e1) = e2)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[197, 24537])).
% 2.62/2.74 tff(24539,plain,
% 2.62/2.74 (op(e2, e1) = e1),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[23695, 23636, 24538])).
% 2.62/2.74 tff(24540,plain,
% 2.62/2.74 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e1)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24539])).
% 2.62/2.74 tff(24541,plain,
% 2.62/2.74 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e1))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24540])).
% 2.62/2.74 tff(24542,plain,
% 2.62/2.74 (~(op(e0, e1) = e1)),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[606, 24541])).
% 2.62/2.74 tff(24543,plain,
% 2.62/2.74 (~(op(e0, e1) = op(e1, e0))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24542, 24535])).
% 2.62/2.74 tff(24544,plain,
% 2.62/2.74 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[609, 24543])).
% 2.62/2.74 tff(24545,plain,
% 2.62/2.74 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24539])).
% 2.62/2.74 tff(24546,plain,
% 2.62/2.74 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24545, 5522])).
% 2.62/2.74 tff(24547,plain,
% 2.62/2.74 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.74 inference(symmetry,[status(thm)],[24546])).
% 2.62/2.74 tff(24548,plain,
% 2.62/2.74 (op(e3, e3) = e1),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[151, 24491, 23800, 2672])).
% 2.62/2.74 tff(24549,plain,
% 2.62/2.74 (e1 = op(e3, e3)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24548])).
% 2.62/2.74 tff(24550,plain,
% 2.62/2.74 ((op(e1, e2) = e1) <=> (e2 = op(e3, e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24508, 24549])).
% 2.62/2.74 tff(24551,plain,
% 2.62/2.74 ((op(e1, e2) = e1) <=> (op(e3, e3) = e2)),
% 2.62/2.74 inference(transitivity,[status(thm)],[24550, 565])).
% 2.62/2.74 tff(24552,plain,
% 2.62/2.74 ((op(e3, e3) = e2) <=> (op(e1, e2) = e1)),
% 2.62/2.74 inference(symmetry,[status(thm)],[24551])).
% 2.62/2.74 tff(24553,plain,
% 2.62/2.74 ((op(e3, e3) = e2) <=> (op(e1, e2) = op(e2, e1))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24552, 24547, 531])).
% 2.62/2.74 tff(24554,plain,
% 2.62/2.74 ((~(op(e3, e3) = e2)) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24553])).
% 2.62/2.74 tff(24555,plain,
% 2.62/2.74 (~(op(e1, e2) = op(e2, e1))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[15002, 24554])).
% 2.62/2.74 tff(24556,plain,
% 2.62/2.74 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[539, 24555])).
% 2.62/2.74 tff(24557,plain,
% 2.62/2.74 ((~(op(e0, e1) = e1)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24533])).
% 2.62/2.74 tff(24558,plain,
% 2.62/2.74 (~(op(e1, e0) = op(e0, e1))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24542, 24557])).
% 2.62/2.74 tff(24559,plain,
% 2.62/2.74 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[613, 24558])).
% 2.62/2.74 tff(24560,plain,
% 2.62/2.74 (op(e1, op(e1, e3)) = e1),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24530, 23742])).
% 2.62/2.74 tff(24561,plain,
% 2.62/2.74 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[6674, 24560])).
% 2.62/2.74 tff(24562,plain,
% 2.62/2.74 (op(e2, op(e0, e3)) = op(e2, e3)),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24492])).
% 2.62/2.74 tff(24563,plain,
% 2.62/2.74 (op(e2, op(e2, e0)) = op(e2, op(e0, e3))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24517])).
% 2.62/2.74 tff(24564,plain,
% 2.62/2.74 (op(e2, op(e2, e0)) = e2),
% 2.62/2.74 inference(transitivity,[status(thm)],[24563, 24562, 24486])).
% 2.62/2.74 tff(24565,plain,
% 2.62/2.74 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[23739, 24564])).
% 2.62/2.74 tff(24566,plain,
% 2.62/2.74 ((op(e3, e3) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.62/2.74 inference(transitivity,[status(thm)],[24552, 24547])).
% 2.62/2.74 tff(24567,plain,
% 2.62/2.74 ((~(op(e3, e3) = e2)) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.62/2.74 inference(monotonicity,[status(thm)],[24566])).
% 2.62/2.74 tff(24568,plain,
% 2.62/2.74 (~(op(e2, e1) = op(e1, e2))),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[15002, 24567])).
% 2.62/2.74 tff(24569,plain,
% 2.62/2.74 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[557, 24568])).
% 2.62/2.74 tff(24570,plain,
% 2.62/2.74 (op(e1, op(e2, e2)) = e1),
% 2.62/2.74 inference(modus_ponens,[status(thm)],[24530, 23753])).
% 2.62/2.74 tff(24571,plain,
% 2.62/2.74 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.62/2.74 inference(unit_resolution,[status(thm)],[6714, 24570])).
% 2.62/2.75 tff(24572,plain,
% 2.62/2.75 (op(e2, op(e1, e1)) = op(e2, op(e0, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24496])).
% 2.62/2.75 tff(24573,plain,
% 2.62/2.75 (op(e2, op(e1, e1)) = e2),
% 2.62/2.75 inference(transitivity,[status(thm)],[24572, 24562, 24486])).
% 2.62/2.75 tff(24574,plain,
% 2.62/2.75 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[16830, 24573])).
% 2.62/2.75 tff(24575,plain,
% 2.62/2.75 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e0, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24495])).
% 2.62/2.75 tff(24576,plain,
% 2.62/2.75 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24575])).
% 2.62/2.75 tff(24577,plain,
% 2.62/2.75 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24576])).
% 2.62/2.75 tff(24578,plain,
% 2.62/2.75 (~(op(e0, e2) = e3)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[918, 24577])).
% 2.62/2.75 tff(24579,plain,
% 2.62/2.75 (op(e3, e2) = e3),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23653, 23652, 24578])).
% 2.62/2.75 tff(24580,plain,
% 2.62/2.75 ((op(e0, e1) = e2) <=> (e0 = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[21471])).
% 2.62/2.75 tff(24581,plain,
% 2.62/2.75 ((e0 = e2) <=> (op(e0, e1) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24580])).
% 2.62/2.75 tff(24582,plain,
% 2.62/2.75 ((~(e0 = e2)) <=> (~(op(e0, e1) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24581])).
% 2.62/2.75 tff(24583,plain,
% 2.62/2.75 (~(op(e0, e1) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[14, 24582])).
% 2.62/2.75 tff(24584,plain,
% 2.62/2.75 (op(e0, e0) = e2),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[3652, 24583, 24485, 6229])).
% 2.62/2.75 tff(24585,plain,
% 2.62/2.75 (op(e3, op(e0, e0)) = op(e3, e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24584])).
% 2.62/2.75 tff(24586,plain,
% 2.62/2.75 (op(e3, op(e0, e0)) = e3),
% 2.62/2.75 inference(transitivity,[status(thm)],[24585, 856])).
% 2.62/2.75 tff(24587,plain,
% 2.62/2.75 (op(e0, op(e3, e3)) = op(e0, e1)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24548])).
% 2.62/2.75 tff(24588,plain,
% 2.62/2.75 ((op(e0, op(e3, e3)) = e0) <=> (op(e0, e1) = e0)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24587])).
% 2.62/2.75 tff(24589,plain,
% 2.62/2.75 ((op(e0, e1) = e0) <=> (op(e0, op(e3, e3)) = e0)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24588])).
% 2.62/2.75 tff(24590,plain,
% 2.62/2.75 (op(e0, op(e3, e3)) = e0),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[21471, 24589])).
% 2.62/2.75 tff(24591,plain,
% 2.62/2.75 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[392, 24590])).
% 2.62/2.75 tff(24592,plain,
% 2.62/2.75 (op(e3, op(e2, e3)) = op(e3, e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.75 tff(24593,plain,
% 2.62/2.75 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e2) = e3)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24592])).
% 2.62/2.75 tff(24594,plain,
% 2.62/2.75 ((op(e3, e2) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24593])).
% 2.62/2.75 tff(24595,plain,
% 2.62/2.75 (op(e3, op(e2, e3)) = e3),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[856, 24594])).
% 2.62/2.75 tff(24596,plain,
% 2.62/2.75 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[11931, 24595])).
% 2.62/2.75 tff(24597,plain,
% 2.62/2.75 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.75 tff(24598,plain,
% 2.62/2.75 ((op(e3, e2) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.62/2.75 inference(symmetry,[status(thm)],[24597])).
% 2.62/2.75 tff(24599,plain,
% 2.62/2.75 (op(e3, e2) = op(e0, e3)),
% 2.62/2.75 inference(transitivity,[status(thm)],[856, 24495])).
% 2.62/2.75 tff(24600,plain,
% 2.62/2.75 ((op(e3, e2) = e2) <=> (op(e0, e3) = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24599])).
% 2.62/2.75 tff(24601,plain,
% 2.62/2.75 ((op(e0, e3) = e2) <=> (op(e3, e2) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24600])).
% 2.62/2.75 tff(24602,plain,
% 2.62/2.75 ((op(e0, e3) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.62/2.75 inference(transitivity,[status(thm)],[24601, 24598, 395])).
% 2.62/2.75 tff(24603,plain,
% 2.62/2.75 ((~(op(e0, e3) = e2)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24602])).
% 2.62/2.75 tff(24604,plain,
% 2.62/2.75 (~(op(e2, e3) = op(e3, e2))),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[24485, 24603])).
% 2.62/2.75 tff(24605,plain,
% 2.62/2.75 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[430, 24604])).
% 2.62/2.75 tff(24606,plain,
% 2.62/2.75 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24548])).
% 2.62/2.75 tff(24607,plain,
% 2.62/2.75 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24606])).
% 2.62/2.75 tff(24608,plain,
% 2.62/2.75 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24607, 5470])).
% 2.62/2.75 tff(24609,plain,
% 2.62/2.75 (op(e3, e1) = op(e3, op(e3, e3))),
% 2.62/2.75 inference(symmetry,[status(thm)],[24606])).
% 2.62/2.75 tff(24610,plain,
% 2.62/2.75 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, op(e3, e3)))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[21471, 24609])).
% 2.62/2.75 tff(24611,plain,
% 2.62/2.75 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 2.62/2.75 inference(transitivity,[status(thm)],[24610, 24608, 18728, 6290])).
% 2.62/2.75 tff(24612,plain,
% 2.62/2.75 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24611])).
% 2.62/2.75 tff(24613,plain,
% 2.62/2.75 (~(op(e1, e3) = op(e3, e1))),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[3046, 24612])).
% 2.62/2.75 tff(24614,plain,
% 2.62/2.75 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[6307, 24613])).
% 2.62/2.75 tff(24615,plain,
% 2.62/2.75 (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[5367, 24614, 6689, 5672, 5680, 9846, 24605, 5511, 5675, 5673, 24596, 5681, 5670, 24591, 5674])).
% 2.62/2.75 tff(24616,plain,
% 2.62/2.75 (((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)) | (~(op(e3, op(e0, e0)) = e3))),
% 2.62/2.75 inference(tautology,[status(thm)],[])).
% 2.62/2.75 tff(24617,plain,
% 2.62/2.75 (~(op(e3, op(e0, e0)) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24616, 24615])).
% 2.62/2.75 tff(24618,plain,
% 2.62/2.75 ($false),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24617, 24586])).
% 2.62/2.75 tff(24619,plain,((~(op(e0, e1) = e0)) | (~(op(e3, e2) = e3)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (op(e0, e2) = e2) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.75 tff(24620,plain,
% 2.62/2.75 (~(op(e0, e1) = e0)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24619, 24579, 24574, 24571, 24569, 24565, 24561, 24559, 24556, 24544, 24529, 24523, 24511, 1219])).
% 2.62/2.75 tff(24621,plain,
% 2.62/2.75 (op(e3, e1) = e0),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23988, 24620, 2639])).
% 2.62/2.75 tff(24622,plain,
% 2.62/2.75 (op(e3, op(e3, e3)) = e0),
% 2.62/2.75 inference(transitivity,[status(thm)],[24606, 24621])).
% 2.62/2.75 tff(24623,plain,
% 2.62/2.75 (op(e3, op(e3, op(e3, e3))) = op(op(e0, e3), e0)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24495, 24622])).
% 2.62/2.75 tff(24624,plain,
% 2.62/2.75 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24623, 24493])).
% 2.62/2.75 tff(24625,plain,
% 2.62/2.75 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24624])).
% 2.62/2.75 tff(24626,plain,
% 2.62/2.75 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24625, 5377])).
% 2.62/2.75 tff(24627,plain,
% 2.62/2.75 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24626])).
% 2.62/2.75 tff(24628,plain,
% 2.62/2.75 (e1 = op(e3, e3)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[24548, 658])).
% 2.62/2.75 tff(24629,plain,
% 2.62/2.75 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.62/2.75 inference(symmetry,[status(thm)],[24608])).
% 2.62/2.75 tff(24630,plain,
% 2.62/2.75 (e0 = op(e3, op(e3, e3))),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[24621, 24629])).
% 2.62/2.75 tff(24631,plain,
% 2.62/2.75 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[5397, 24630, 24628])).
% 2.62/2.75 tff(24632,plain,
% 2.62/2.75 (~(op(e3, e0) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[24631, 24627])).
% 2.62/2.75 tff(24633,plain,
% 2.62/2.75 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24486])).
% 2.62/2.75 tff(24634,plain,
% 2.62/2.75 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24633])).
% 2.62/2.75 tff(24635,plain,
% 2.62/2.75 (~(op(e2, e0) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[989, 24634])).
% 2.62/2.75 tff(24636,plain,
% 2.62/2.75 (op(e0, e0) = e0),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23963, 24620, 2500])).
% 2.62/2.75 tff(24637,plain,
% 2.62/2.75 ((op(e0, e0) = e2) <=> (e0 = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24636])).
% 2.62/2.75 tff(24638,plain,
% 2.62/2.75 ((e0 = e2) <=> (op(e0, e0) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24637])).
% 2.62/2.75 tff(24639,plain,
% 2.62/2.75 ((~(e0 = e2)) <=> (~(op(e0, e0) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24638])).
% 2.62/2.75 tff(24640,plain,
% 2.62/2.75 (~(op(e0, e0) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[14, 24639])).
% 2.62/2.75 tff(24641,plain,
% 2.62/2.75 (op(e3, e0) = e2),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[589, 24640, 24507, 24635])).
% 2.62/2.75 tff(24642,plain,
% 2.62/2.75 ($false),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24641, 24632])).
% 2.62/2.75 tff(24643,plain,((~(op(e1, e1) = e3)) | (~(op(e1, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.75 tff(24644,plain,
% 2.62/2.75 (~(op(e1, e1) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24643, 1219])).
% 2.62/2.75 tff(24645,plain,
% 2.62/2.75 (op(e1, e1) = e1),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[630, 24644, 24119, 2639])).
% 2.62/2.75 tff(24646,plain,
% 2.62/2.75 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24645])).
% 2.62/2.75 tff(24647,plain,
% 2.62/2.75 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24646, 2355])).
% 2.62/2.75 tff(24648,plain,
% 2.62/2.75 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24647])).
% 2.62/2.75 tff(24649,plain,
% 2.62/2.75 (~(op(e2, e1) = e1)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[225, 24648])).
% 2.62/2.75 tff(24650,plain,
% 2.62/2.75 (op(e2, e0) = e1),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23785, 24649, 24491])).
% 2.62/2.75 tff(24651,plain,
% 2.62/2.75 (e1 = op(e2, op(e2, e2))),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[24650, 23619])).
% 2.62/2.75 tff(24652,plain,
% 2.62/2.75 (op(e2, e0) = op(e3, e3)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24650, 24549])).
% 2.62/2.75 tff(24653,plain,
% 2.62/2.75 (op(e2, op(e2, e0)) = op(e2, op(e3, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24652])).
% 2.62/2.75 tff(24654,plain,
% 2.62/2.75 (op(e2, op(e3, e3)) = op(e2, op(e2, e0))),
% 2.62/2.75 inference(symmetry,[status(thm)],[24653])).
% 2.62/2.75 tff(24655,plain,
% 2.62/2.75 (op(e2, op(e3, e3)) = op(e2, e1)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24548])).
% 2.62/2.75 tff(24656,plain,
% 2.62/2.75 (op(e2, e1) = op(e2, op(e3, e3))),
% 2.62/2.75 inference(symmetry,[status(thm)],[24655])).
% 2.62/2.75 tff(24657,plain,
% 2.62/2.75 (op(e2, e1) = e3),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23695, 24649, 24538])).
% 2.62/2.75 tff(24658,plain,
% 2.62/2.75 (e3 = op(e2, e1)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24657])).
% 2.62/2.75 tff(24659,plain,
% 2.62/2.75 (e3 = op(e2, op(e2, op(e2, e2)))),
% 2.62/2.75 inference(transitivity,[status(thm)],[24658, 24656, 24654, 23789])).
% 2.62/2.75 tff(24660,plain,
% 2.62/2.75 ($false),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[23797, 24659, 24651])).
% 2.62/2.75 tff(24661,plain,(~(op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.75 tff(24662,plain,
% 2.62/2.75 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e3, e3) = e0)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[1098, 23804])).
% 2.62/2.75 tff(24663,plain,
% 2.62/2.75 ((op(e0, e3) = e0) | (op(e3, e3) = e0)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24662, 24661])).
% 2.62/2.75 tff(24664,plain,
% 2.62/2.75 (op(e3, e3) = e0),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24663, 15])).
% 2.62/2.75 tff(24665,plain,
% 2.62/2.75 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24664])).
% 2.62/2.75 tff(24666,plain,
% 2.62/2.75 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24665])).
% 2.62/2.75 tff(24667,plain,
% 2.62/2.75 (~(op(e3, e1) = e0)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[437, 24666])).
% 2.62/2.75 tff(24668,plain,
% 2.62/2.75 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e1, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[265])).
% 2.62/2.75 tff(24669,plain,
% 2.62/2.75 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24668])).
% 2.62/2.75 tff(24670,plain,
% 2.62/2.75 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24669])).
% 2.62/2.75 tff(24671,plain,
% 2.62/2.75 (~(op(e0, e3) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[64, 24670])).
% 2.62/2.75 tff(24672,plain,
% 2.62/2.75 ((op(e0, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[19])).
% 2.62/2.75 tff(24673,plain,
% 2.62/2.75 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24672, 5574])).
% 2.62/2.75 tff(24674,plain,
% 2.62/2.75 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24673])).
% 2.62/2.75 tff(24675,plain,
% 2.62/2.75 (~(op(e2, e3) = e1)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[964, 24674])).
% 2.62/2.75 tff(24676,plain,
% 2.62/2.75 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e1, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[265])).
% 2.62/2.75 tff(24677,plain,
% 2.62/2.75 ((op(e2, e3) = e2) <=> (op(e1, e3) = op(e2, e3))),
% 2.62/2.75 inference(transitivity,[status(thm)],[24676, 1687])).
% 2.62/2.75 tff(24678,plain,
% 2.62/2.75 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24677])).
% 2.62/2.75 tff(24679,plain,
% 2.62/2.75 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24678])).
% 2.62/2.75 tff(24680,plain,
% 2.62/2.75 (~(op(e2, e3) = e2)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[118, 24679])).
% 2.62/2.75 tff(24681,plain,
% 2.62/2.75 (op(e2, e3) = e3),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24237, 24680, 24675])).
% 2.62/2.75 tff(24682,plain,
% 2.62/2.75 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24681])).
% 2.62/2.75 tff(24683,plain,
% 2.62/2.75 (e3 = op(e2, e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24681])).
% 2.62/2.75 tff(24684,plain,
% 2.62/2.75 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e2, e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24683])).
% 2.62/2.75 tff(24685,plain,
% 2.62/2.75 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24684])).
% 2.62/2.75 tff(24686,plain,
% 2.62/2.75 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24685])).
% 2.62/2.75 tff(24687,plain,
% 2.62/2.75 (~(op(e2, e1) = e3)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[197, 24686])).
% 2.62/2.75 tff(24688,plain,
% 2.62/2.75 ((e1 = e3) <=> (e1 = op(e1, e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[4971])).
% 2.62/2.75 tff(24689,plain,
% 2.62/2.75 ((e1 = e3) <=> (op(e1, e1) = e1)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24688, 8462])).
% 2.62/2.75 tff(24690,plain,
% 2.62/2.75 ((~(e1 = e3)) <=> (~(op(e1, e1) = e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24689])).
% 2.62/2.75 tff(24691,plain,
% 2.62/2.75 (~(op(e1, e1) = e1)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[303, 24690])).
% 2.62/2.75 tff(24692,plain,
% 2.62/2.75 ((op(e1, e3) = e3) <=> (op(e1, e3) = op(e1, e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[4971])).
% 2.62/2.75 tff(24693,plain,
% 2.62/2.75 ((op(e1, e3) = e3) <=> (op(e1, e1) = op(e1, e3))),
% 2.62/2.75 inference(transitivity,[status(thm)],[24692, 5020])).
% 2.62/2.75 tff(24694,plain,
% 2.62/2.75 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24693])).
% 2.62/2.75 tff(24695,plain,
% 2.62/2.75 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24694])).
% 2.62/2.75 tff(24696,plain,
% 2.62/2.75 (~(op(e1, e3) = e3)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[619, 24695])).
% 2.62/2.75 tff(24697,plain,
% 2.62/2.75 ((op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[104, 24661])).
% 2.62/2.75 tff(24698,plain,
% 2.62/2.75 (op(e1, e3) = e2),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24697, 24696, 65])).
% 2.62/2.75 tff(24699,plain,
% 2.62/2.75 (e2 = op(e1, e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24698])).
% 2.62/2.75 tff(24700,plain,
% 2.62/2.75 (op(e3, e3) = e0),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[24663, 27])).
% 2.62/2.75 tff(24701,plain,
% 2.62/2.75 ((op(e3, e3) = e3) <=> (e0 = e3)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24700])).
% 2.62/2.75 tff(24702,plain,
% 2.62/2.75 ((e0 = e3) <=> (op(e3, e3) = e3)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24701])).
% 2.62/2.75 tff(24703,plain,
% 2.62/2.75 ((~(e0 = e3)) <=> (~(op(e3, e3) = e3))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24702])).
% 2.62/2.75 tff(24704,plain,
% 2.62/2.75 (~(op(e3, e3) = e3)),
% 2.62/2.75 inference(modus_ponens,[status(thm)],[181, 24703])).
% 2.62/2.75 tff(24705,plain,
% 2.62/2.75 (op(e2, e3) = e3),
% 2.62/2.75 inference(unit_resolution,[status(thm)],[480, 24696, 11546, 24704])).
% 2.62/2.75 tff(24706,plain,
% 2.62/2.75 (op(e2, op(e1, e1)) = op(e1, e1)),
% 2.62/2.75 inference(transitivity,[status(thm)],[15725, 24705, 4971])).
% 2.62/2.75 tff(24707,plain,
% 2.62/2.75 ((op(e2, op(e1, e1)) = e2) <=> (op(e1, e1) = e2)),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24706])).
% 2.62/2.75 tff(24708,plain,
% 2.62/2.75 ((op(e1, e1) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.62/2.75 inference(symmetry,[status(thm)],[24707])).
% 2.62/2.75 tff(24709,plain,
% 2.62/2.75 ((op(e1, e1) = e2) <=> (op(e2, e3) = e2)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24708, 15728])).
% 2.62/2.75 tff(24710,plain,
% 2.62/2.75 ((~(op(e1, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[24709])).
% 2.62/2.75 tff(24711,plain,
% 2.62/2.75 ((e2 = e3) <=> (e2 = op(e1, e1))),
% 2.62/2.75 inference(monotonicity,[status(thm)],[4971])).
% 2.62/2.75 tff(24712,plain,
% 2.62/2.75 ((e2 = e3) <=> (op(e1, e1) = e2)),
% 2.62/2.75 inference(transitivity,[status(thm)],[24711, 2166])).
% 2.62/2.76 tff(24713,plain,
% 2.62/2.76 ((~(e2 = e3)) <=> (~(op(e1, e1) = e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24712])).
% 2.62/2.76 tff(24714,plain,
% 2.62/2.76 (~(op(e1, e1) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[1321, 24713])).
% 2.62/2.76 tff(24715,plain,
% 2.62/2.76 (~(op(e2, e3) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[24714, 24710])).
% 2.62/2.76 tff(24716,plain,
% 2.62/2.76 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24700])).
% 2.62/2.76 tff(24717,plain,
% 2.62/2.76 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24716])).
% 2.62/2.76 tff(24718,plain,
% 2.62/2.76 (~(op(e3, e1) = e0)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[437, 24717])).
% 2.62/2.76 tff(24719,plain,
% 2.62/2.76 (op(e0, e1) = e0),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[23988, 4965, 24718])).
% 2.62/2.76 tff(24720,plain,
% 2.62/2.76 (op(e2, op(e0, e1)) = op(e2, e0)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24719])).
% 2.62/2.76 tff(24721,plain,
% 2.62/2.76 ((op(e2, op(e0, e1)) = e2) <=> (op(e2, e0) = e2)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24720])).
% 2.62/2.76 tff(24722,plain,
% 2.62/2.76 ((~(op(e2, op(e0, e1)) = e2)) <=> (~(op(e2, e0) = e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24721])).
% 2.62/2.76 tff(24723,plain,
% 2.62/2.76 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e3) = e0)),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[1830, 23820])).
% 2.62/2.76 tff(24724,plain,
% 2.62/2.76 ((op(e1, e0) = e0) | (op(e1, e1) = e0)),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[24723, 24661])).
% 2.62/2.76 tff(24725,plain,
% 2.62/2.76 (op(e1, e0) = e0),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[24724, 4965])).
% 2.62/2.76 tff(24726,plain,
% 2.62/2.76 ((op(e1, e0) = e1) <=> (e0 = e1)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24725])).
% 2.62/2.76 tff(24727,plain,
% 2.62/2.76 ((e0 = e1) <=> (op(e1, e0) = e1)),
% 2.62/2.76 inference(symmetry,[status(thm)],[24726])).
% 2.62/2.76 tff(24728,plain,
% 2.62/2.76 ((~(e0 = e1)) <=> (~(op(e1, e0) = e1))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24727])).
% 2.62/2.76 tff(24729,plain,
% 2.62/2.76 (~(op(e1, e0) = e1)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[26, 24728])).
% 2.62/2.76 tff(24730,plain,
% 2.62/2.76 ((op(e0, e1) = e2) <=> (e0 = op(e1, e3))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24719, 24699])).
% 2.62/2.76 tff(24731,plain,
% 2.62/2.76 ((op(e0, e1) = e2) <=> (op(e1, e3) = e0)),
% 2.62/2.76 inference(transitivity,[status(thm)],[24730, 6095])).
% 2.62/2.76 tff(24732,plain,
% 2.62/2.76 ((op(e1, e3) = e0) <=> (op(e0, e1) = e2)),
% 2.62/2.76 inference(symmetry,[status(thm)],[24731])).
% 2.62/2.76 tff(24733,plain,
% 2.62/2.76 ((~(op(e1, e3) = e0)) <=> (~(op(e0, e1) = e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24732])).
% 2.62/2.76 tff(24734,plain,
% 2.62/2.76 (~(op(e0, e1) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[24661, 24733])).
% 2.62/2.76 tff(24735,plain,
% 2.62/2.76 (~(op(e0, e0) = e2)),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[23661, 7826, 19])).
% 2.62/2.76 tff(24736,plain,
% 2.62/2.76 (op(e0, e2) = e2),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[3652, 24735, 21344, 24734])).
% 2.62/2.76 tff(24737,plain,
% 2.62/2.76 (op(e1, e1) = op(e1, e3)),
% 2.62/2.76 inference(transitivity,[status(thm)],[4960, 7827, 24736, 24699])).
% 2.62/2.76 tff(24738,plain,
% 2.62/2.76 ($false),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[619, 24737])).
% 2.62/2.76 tff(24739,plain,((~(op(e0, e2) = e3)) | (~(op(e1, e1) = e3)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.76 tff(24740,plain,
% 2.62/2.76 (~(op(e0, e2) = e3)),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[24739, 4960, 19])).
% 2.62/2.76 tff(24741,plain,
% 2.62/2.76 (op(e0, e2) = e2),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[23880, 24740, 11315])).
% 2.62/2.76 tff(24742,plain,
% 2.62/2.76 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24741])).
% 2.62/2.76 tff(24743,plain,
% 2.62/2.76 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 2.62/2.76 inference(transitivity,[status(thm)],[24742, 2234])).
% 2.62/2.76 tff(24744,plain,
% 2.62/2.76 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24743])).
% 2.62/2.76 tff(24745,plain,
% 2.62/2.76 (~(op(e3, e2) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[1467, 24744])).
% 2.62/2.76 tff(24746,assumption,(op(e2, op(e0, e1)) = e2), introduced(assumption)).
% 2.62/2.76 tff(24747,plain,
% 2.62/2.76 (e0 = op(e0, e1)),
% 2.62/2.76 inference(symmetry,[status(thm)],[21471])).
% 2.62/2.76 tff(24748,plain,
% 2.62/2.76 (op(e2, e0) = op(e2, op(e0, e1))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24747])).
% 2.62/2.76 tff(24749,plain,
% 2.62/2.76 (op(e2, e0) = op(e1, e3)),
% 2.62/2.76 inference(transitivity,[status(thm)],[24748, 24746, 265])).
% 2.62/2.76 tff(24750,plain,
% 2.62/2.76 ((op(e2, e0) = e1) <=> (op(e1, e3) = e1)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24749])).
% 2.62/2.76 tff(24751,plain,
% 2.62/2.76 ((op(e1, e3) = e1) <=> (op(e2, e0) = e1)),
% 2.62/2.76 inference(symmetry,[status(thm)],[24750])).
% 2.62/2.76 tff(24752,plain,
% 2.62/2.76 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24751])).
% 2.62/2.76 tff(24753,plain,
% 2.62/2.76 (~(op(e2, e0) = e1)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[87, 24752])).
% 2.62/2.76 tff(24754,plain,
% 2.62/2.76 (op(e3, e0) = e1),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[1480, 24753, 2379, 929])).
% 2.62/2.76 tff(24755,plain,
% 2.62/2.76 (op(e2, e0) = e2),
% 2.62/2.76 inference(transitivity,[status(thm)],[24748, 24746])).
% 2.62/2.76 tff(24756,plain,
% 2.62/2.76 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24755])).
% 2.62/2.76 tff(24757,plain,
% 2.62/2.76 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.62/2.76 inference(transitivity,[status(thm)],[24756, 5377])).
% 2.62/2.76 tff(24758,plain,
% 2.62/2.76 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24757])).
% 2.62/2.76 tff(24759,plain,
% 2.62/2.76 (~(op(e3, e0) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[747, 24758])).
% 2.62/2.76 tff(24760,plain,
% 2.62/2.76 (op(e3, e1) = e2),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[15971, 24759, 2386])).
% 2.62/2.76 tff(24761,plain,
% 2.62/2.76 ($false),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[8647, 24760, 24754, 3066])).
% 2.62/2.76 tff(24762,plain,((~(op(e2, op(e0, e1)) = e2)) | (~(op(e3, e3) = e0)) | (op(e3, e2) = e2) | (op(e0, e0) = e1) | (op(e1, e0) = e1) | (~(op(e0, e1) = e0)) | (op(e1, e3) = e1) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.76 tff(24763,plain,
% 2.62/2.76 (~(op(e2, op(e0, e1)) = e2)),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[24762, 24745, 24700, 11527, 24729, 24719, 65, 24698])).
% 2.62/2.76 tff(24764,plain,
% 2.62/2.76 (~(op(e2, e0) = e2)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[24763, 24722])).
% 2.62/2.76 tff(24765,plain,
% 2.62/2.76 (op(e2, e1) = e2),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[23839, 24764, 24715])).
% 2.62/2.76 tff(24766,plain,
% 2.62/2.76 (op(e2, e1) = op(e1, e3)),
% 2.62/2.76 inference(transitivity,[status(thm)],[24765, 24699])).
% 2.62/2.76 tff(24767,plain,
% 2.62/2.76 ((op(e2, e1) = e1) <=> (op(e1, e3) = e1)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24766])).
% 2.62/2.76 tff(24768,plain,
% 2.62/2.76 ((op(e1, e3) = e1) <=> (op(e2, e1) = e1)),
% 2.62/2.76 inference(symmetry,[status(thm)],[24767])).
% 2.62/2.76 tff(24769,plain,
% 2.62/2.76 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e1) = e1))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24768])).
% 2.62/2.76 tff(24770,plain,
% 2.62/2.76 (~(op(e2, e1) = e1)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[65, 24769])).
% 2.62/2.76 tff(24771,plain,
% 2.62/2.76 (op(e3, e1) = e1),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[1252, 24770, 21369, 24691])).
% 2.62/2.76 tff(24772,plain,
% 2.62/2.76 (op(e3, op(e3, e1)) = op(e3, e1)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24771])).
% 2.62/2.76 tff(24773,plain,
% 2.62/2.76 (op(e3, op(e3, e1)) = e1),
% 2.62/2.76 inference(transitivity,[status(thm)],[24772, 24771])).
% 2.62/2.76 tff(24774,plain,
% 2.62/2.76 (op(op(e0, e1), e1) = op(e0, e1)),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24719])).
% 2.62/2.76 tff(24775,plain,
% 2.62/2.76 (op(op(e0, e1), e1) = e0),
% 2.62/2.76 inference(transitivity,[status(thm)],[24774, 24719])).
% 2.62/2.76 tff(24776,plain,
% 2.62/2.76 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.62/2.76 inference(unit_resolution,[status(thm)],[2650, 24775])).
% 2.62/2.76 tff(24777,plain,
% 2.62/2.76 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e1, e1))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[4971])).
% 2.62/2.76 tff(24778,plain,
% 2.62/2.76 ((op(e1, e2) = e3) <=> (op(e1, e1) = op(e1, e2))),
% 2.62/2.76 inference(transitivity,[status(thm)],[24777, 8420])).
% 2.62/2.76 tff(24779,plain,
% 2.62/2.76 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.62/2.76 inference(symmetry,[status(thm)],[24778])).
% 2.62/2.76 tff(24780,plain,
% 2.62/2.76 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24779])).
% 2.62/2.76 tff(24781,plain,
% 2.62/2.76 (~(op(e1, e2) = e3)),
% 2.62/2.76 inference(modus_ponens,[status(thm)],[1604, 24780])).
% 2.62/2.76 tff(24782,plain,
% 2.62/2.76 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e3))),
% 2.62/2.76 inference(monotonicity,[status(thm)],[24699])).
% 2.62/2.76 tff(24783,plain,
% 2.62/2.76 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24782])).
% 2.66/2.76 tff(24784,plain,
% 2.66/2.76 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24783])).
% 2.66/2.76 tff(24785,plain,
% 2.66/2.76 (~(op(e1, e2) = e2)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[1850, 24784])).
% 2.66/2.76 tff(24786,plain,
% 2.66/2.76 (op(e1, e2) = e1),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[23821, 24785, 24781])).
% 2.66/2.76 tff(24787,plain,
% 2.66/2.76 (op(e1, op(e1, e3)) = op(e1, e2)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24698])).
% 2.66/2.76 tff(24788,plain,
% 2.66/2.76 (op(op(e1, e2), e2) = op(e1, op(e1, e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24786, 24699])).
% 2.66/2.76 tff(24789,plain,
% 2.66/2.76 (op(op(e1, e2), e2) = e1),
% 2.66/2.76 inference(transitivity,[status(thm)],[24788, 24787, 24786])).
% 2.66/2.76 tff(24790,plain,
% 2.66/2.76 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1335, 24789])).
% 2.66/2.76 tff(24791,plain,
% 2.66/2.76 (op(op(e1, e3), e1) = op(e2, e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24698])).
% 2.66/2.76 tff(24792,plain,
% 2.66/2.76 (op(op(e2, e1), e1) = op(op(e1, e3), e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24766])).
% 2.66/2.76 tff(24793,plain,
% 2.66/2.76 (op(op(e2, e1), e1) = e2),
% 2.66/2.76 inference(transitivity,[status(thm)],[24792, 24791, 24765])).
% 2.66/2.76 tff(24794,plain,
% 2.66/2.76 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[2371, 24793])).
% 2.66/2.76 tff(24795,plain,
% 2.66/2.76 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24705])).
% 2.66/2.76 tff(24796,plain,
% 2.66/2.76 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24795])).
% 2.66/2.76 tff(24797,plain,
% 2.66/2.76 (~(op(e2, e0) = e3)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[989, 24796])).
% 2.66/2.76 tff(24798,plain,
% 2.66/2.76 (op(e2, e0) = e1),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[24100, 24764, 24797])).
% 2.66/2.76 tff(24799,plain,
% 2.66/2.76 (op(op(e2, e0), e2) = op(e1, op(e1, e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24798, 24699])).
% 2.66/2.76 tff(24800,plain,
% 2.66/2.76 (op(op(e2, e0), e2) = e1),
% 2.66/2.76 inference(transitivity,[status(thm)],[24799, 24787, 24786])).
% 2.66/2.76 tff(24801,plain,
% 2.66/2.76 ((op(op(e2, e0), e2) = e0) <=> (e1 = e0)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24800])).
% 2.66/2.76 tff(24802,plain,
% 2.66/2.76 ((op(op(e2, e0), e2) = e0) <=> (e0 = e1)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24801, 18])).
% 2.66/2.76 tff(24803,plain,
% 2.66/2.76 ((e0 = e1) <=> (op(op(e2, e0), e2) = e0)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24802])).
% 2.66/2.76 tff(24804,plain,
% 2.66/2.76 ((~(e0 = e1)) <=> (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24803])).
% 2.66/2.76 tff(24805,plain,
% 2.66/2.76 (~(op(op(e2, e0), e2) = e0)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[26, 24804])).
% 2.66/2.76 tff(24806,plain,
% 2.66/2.76 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1379, 24805])).
% 2.66/2.76 tff(24807,plain,
% 2.66/2.76 (op(e3, e2) = e3),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[23653, 24740, 24781])).
% 2.66/2.76 tff(24808,plain,
% 2.66/2.76 (op(op(e3, e2), e2) = e3),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[7919, 24807])).
% 2.66/2.76 tff(24809,plain,
% 2.66/2.76 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1339, 24808])).
% 2.66/2.76 tff(24810,plain,
% 2.66/2.76 (op(e2, e3) = op(e1, e1)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24705, 4971])).
% 2.66/2.76 tff(24811,plain,
% 2.66/2.76 (op(e2, op(e2, e3)) = op(e2, op(e1, e1))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24810])).
% 2.66/2.76 tff(24812,plain,
% 2.66/2.76 (op(e2, op(e2, e3)) = e3),
% 2.66/2.76 inference(transitivity,[status(thm)],[24811, 15725, 24705])).
% 2.66/2.76 tff(24813,plain,
% 2.66/2.76 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[2344, 24812])).
% 2.66/2.76 tff(24814,plain,
% 2.66/2.76 ((op(op(e1, e3), e1) = e3) <=> (op(e2, e1) = op(e1, e1))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24791, 4971])).
% 2.66/2.76 tff(24815,plain,
% 2.66/2.76 ((op(op(e1, e3), e1) = e3) <=> (op(e1, e1) = op(e2, e1))),
% 2.66/2.76 inference(transitivity,[status(thm)],[24814, 8414])).
% 2.66/2.76 tff(24816,plain,
% 2.66/2.76 ((op(e1, e1) = op(e2, e1)) <=> (op(op(e1, e3), e1) = e3)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24815])).
% 2.66/2.76 tff(24817,plain,
% 2.66/2.76 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24816])).
% 2.66/2.76 tff(24818,plain,
% 2.66/2.76 (~(op(op(e1, e3), e1) = e3)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[225, 24817])).
% 2.66/2.76 tff(24819,plain,
% 2.66/2.76 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[160, 24818])).
% 2.66/2.76 tff(24820,plain,
% 2.66/2.76 (op(e0, op(e1, e3)) = op(e0, e2)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24698])).
% 2.66/2.76 tff(24821,plain,
% 2.66/2.76 (op(e0, e2) = op(e1, e3)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24741, 24699])).
% 2.66/2.76 tff(24822,plain,
% 2.66/2.76 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24821])).
% 2.66/2.76 tff(24823,plain,
% 2.66/2.76 (op(e0, op(e0, e2)) = e2),
% 2.66/2.76 inference(transitivity,[status(thm)],[24822, 24820, 24741])).
% 2.66/2.76 tff(24824,plain,
% 2.66/2.76 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1331, 24823])).
% 2.66/2.76 tff(24825,plain,
% 2.66/2.76 (op(e1, op(e1, e0)) = op(e1, e0)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24725])).
% 2.66/2.76 tff(24826,plain,
% 2.66/2.76 (op(e1, op(e1, e0)) = e0),
% 2.66/2.76 inference(transitivity,[status(thm)],[24825, 24725])).
% 2.66/2.76 tff(24827,plain,
% 2.66/2.76 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1836, 24826])).
% 2.66/2.76 tff(24828,plain,
% 2.66/2.76 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e1))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[4971])).
% 2.66/2.76 tff(24829,plain,
% 2.66/2.76 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e3)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24828])).
% 2.66/2.76 tff(24830,plain,
% 2.66/2.76 ((op(e1, e0) = op(e1, e1)) <=> (op(op(e0, e3), e0) = e3)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24829, 11358])).
% 2.66/2.76 tff(24831,plain,
% 2.66/2.76 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24830])).
% 2.66/2.76 tff(24832,plain,
% 2.66/2.76 (~(op(op(e0, e3), e0) = e3)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[737, 24831])).
% 2.66/2.76 tff(24833,plain,
% 2.66/2.76 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[2635, 24832])).
% 2.66/2.76 tff(24834,plain,
% 2.66/2.76 (op(op(e1, e3), e3) = op(e2, op(e1, e1))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24698, 4971])).
% 2.66/2.76 tff(24835,plain,
% 2.66/2.76 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e2)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24741])).
% 2.66/2.76 tff(24836,plain,
% 2.66/2.76 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e2))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24835])).
% 2.66/2.76 tff(24837,plain,
% 2.66/2.76 (~(op(e0, e0) = e2)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[3603, 24836])).
% 2.66/2.76 tff(24838,plain,
% 2.66/2.76 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e1, e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24699])).
% 2.66/2.76 tff(24839,plain,
% 2.66/2.76 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24838])).
% 2.66/2.76 tff(24840,plain,
% 2.66/2.76 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24839])).
% 2.66/2.76 tff(24841,plain,
% 2.66/2.76 (~(op(e1, e0) = e2)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[110, 24840])).
% 2.66/2.76 tff(24842,plain,
% 2.66/2.76 (op(e3, e0) = e2),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[589, 24764, 24841, 24837])).
% 2.66/2.76 tff(24843,plain,
% 2.66/2.76 (op(e3, e0) = op(e1, e3)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24842, 24699])).
% 2.66/2.76 tff(24844,plain,
% 2.66/2.76 (op(op(e3, e0), e3) = op(op(e1, e3), e3)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24843])).
% 2.66/2.76 tff(24845,plain,
% 2.66/2.76 (op(op(e3, e0), e3) = op(e1, e1)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24844, 24834, 15725, 24705, 4971])).
% 2.66/2.76 tff(24846,plain,
% 2.66/2.76 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e1) = e0)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24845])).
% 2.66/2.76 tff(24847,plain,
% 2.66/2.76 ((op(e1, e1) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24846])).
% 2.66/2.76 tff(24848,plain,
% 2.66/2.76 ((~(op(e1, e1) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24847])).
% 2.66/2.76 tff(24849,plain,
% 2.66/2.76 (~(op(op(e3, e0), e3) = e0)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[4965, 24848])).
% 2.66/2.76 tff(24850,plain,
% 2.66/2.76 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1764, 24849])).
% 2.66/2.76 tff(24851,plain,
% 2.66/2.76 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1459, 24850, 24833, 24827, 24824, 24819, 24813, 24809, 24806, 24794, 24790, 24776])).
% 2.66/2.76 tff(24852,plain,
% 2.66/2.76 (~(op(e3, op(e3, e1)) = e1)),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[2594, 24851])).
% 2.66/2.76 tff(24853,plain,
% 2.66/2.76 ($false),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[24852, 24773])).
% 2.66/2.76 tff(24854,plain,((~(op(e1, e1) = e3)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.76 tff(24855,plain,
% 2.66/2.76 (~(op(e1, e1) = e3)),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[24854, 19])).
% 2.66/2.76 tff(24856,plain,
% 2.66/2.76 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[265])).
% 2.66/2.76 tff(24857,plain,
% 2.66/2.76 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24856])).
% 2.66/2.76 tff(24858,plain,
% 2.66/2.76 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24857])).
% 2.66/2.76 tff(24859,plain,
% 2.66/2.76 (~(op(e1, e2) = e2)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[1850, 24858])).
% 2.66/2.76 tff(24860,plain,
% 2.66/2.76 (op(e1, e2) = e1),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[23821, 75, 24859])).
% 2.66/2.76 tff(24861,plain,
% 2.66/2.76 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24860])).
% 2.66/2.76 tff(24862,plain,
% 2.66/2.76 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e2))),
% 2.66/2.76 inference(symmetry,[status(thm)],[24861])).
% 2.66/2.76 tff(24863,plain,
% 2.66/2.76 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[265])).
% 2.66/2.76 tff(24864,plain,
% 2.66/2.76 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24863])).
% 2.66/2.76 tff(24865,plain,
% 2.66/2.76 (~(op(e1, e3) = e3)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[1321, 24864])).
% 2.66/2.76 tff(24866,plain,
% 2.66/2.76 (op(e1, e1) = e1),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[5149, 75, 19, 24855, 264, 24865])).
% 2.66/2.76 tff(24867,plain,
% 2.66/2.76 (op(e1, e1) = op(e1, e2)),
% 2.66/2.76 inference(modus_ponens,[status(thm)],[24866, 24862])).
% 2.66/2.76 tff(24868,plain,
% 2.66/2.76 ($false),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[1604, 24867])).
% 2.66/2.76 tff(24869,plain,((op(e1, e2) = e3) | (~(op(e0, e3) = e1)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.76 tff(24870,plain,
% 2.66/2.76 (op(e1, e2) = e3),
% 2.66/2.76 inference(unit_resolution,[status(thm)],[24869, 264, 19])).
% 2.66/2.76 tff(24871,plain,
% 2.66/2.76 (op(e1, e2) = op(e1, op(e1, e3))),
% 2.66/2.76 inference(symmetry,[status(thm)],[6670])).
% 2.66/2.76 tff(24872,plain,
% 2.66/2.76 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24871])).
% 2.66/2.76 tff(24873,plain,
% 2.66/2.76 ((op(e1, op(e1, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24872])).
% 2.66/2.76 tff(24874,plain,
% 2.66/2.76 (op(e2, e3) = op(op(e1, e3), e3)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[265])).
% 2.66/2.76 tff(24875,plain,
% 2.66/2.76 (op(e1, op(e1, e3)) = op(op(e1, e3), e3)),
% 2.66/2.76 inference(transitivity,[status(thm)],[6670, 24870, 24683, 24874])).
% 2.66/2.76 tff(24876,plain,
% 2.66/2.76 ((op(e1, op(e1, e3)) = e1) <=> (op(op(e1, e3), e3) = e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24875])).
% 2.66/2.76 tff(24877,plain,
% 2.66/2.76 ((op(op(e1, e3), e3) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24876])).
% 2.66/2.76 tff(24878,plain,
% 2.66/2.76 ((op(op(e1, e3), e3) = e1) <=> (op(e1, e2) = e1)),
% 2.66/2.76 inference(transitivity,[status(thm)],[24877, 24873])).
% 2.66/2.76 tff(24879,plain,
% 2.66/2.76 ((~(op(op(e1, e3), e3) = e1)) <=> (~(op(e1, e2) = e1))),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24878])).
% 2.66/2.76 tff(24880,plain,
% 2.66/2.76 (op(op(e1, e3), e3) = op(e2, e3)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24874])).
% 2.66/2.76 tff(24881,plain,
% 2.66/2.76 ((op(op(e1, e3), e3) = e1) <=> (op(e2, e3) = e1)),
% 2.66/2.76 inference(monotonicity,[status(thm)],[24880])).
% 2.66/2.76 tff(24882,plain,
% 2.66/2.76 ((op(e2, e3) = e1) <=> (op(op(e1, e3), e3) = e1)),
% 2.66/2.76 inference(symmetry,[status(thm)],[24881])).
% 2.66/2.76 tff(24883,plain,
% 2.66/2.77 ((~(op(e2, e3) = e1)) <=> (~(op(op(e1, e3), e3) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24882])).
% 2.66/2.77 tff(24884,plain,
% 2.66/2.77 (~(op(op(e1, e3), e3) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[24675, 24883])).
% 2.66/2.77 tff(24885,plain,
% 2.66/2.77 (~(op(e1, e2) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[24884, 24879])).
% 2.66/2.77 tff(24886,plain,
% 2.66/2.77 (op(e3, e2) = e1),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24286, 24885, 11315])).
% 2.66/2.77 tff(24887,plain,
% 2.66/2.77 ((~(op(e3, e3) = e0)) | (~(op(e3, e2) = e1)) | (~(op(e3, e0) = e2)) | (~(op(e1, e2) = e3))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[9342, 23615])).
% 2.66/2.77 tff(24888,plain,
% 2.66/2.77 (~(op(e3, e0) = e2)),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24887, 24886, 24700, 24870])).
% 2.66/2.77 tff(24889,plain,
% 2.66/2.77 ((op(e3, e2) = e2) <=> (e1 = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24886, 265])).
% 2.66/2.77 tff(24890,plain,
% 2.66/2.77 ((op(e3, e2) = e2) <=> (op(e1, e3) = e1)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24889, 28])).
% 2.66/2.77 tff(24891,plain,
% 2.66/2.77 ((op(e1, e3) = e1) <=> (op(e3, e2) = e2)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24890])).
% 2.66/2.77 tff(24892,plain,
% 2.66/2.77 ((~(op(e1, e3) = e1)) <=> (~(op(e3, e2) = e2))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24891])).
% 2.66/2.77 tff(24893,plain,
% 2.66/2.77 (~(op(e3, e2) = e2)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[65, 24892])).
% 2.66/2.77 tff(24894,plain,
% 2.66/2.77 (op(e3, e1) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[15971, 24893, 24888])).
% 2.66/2.77 tff(24895,plain,
% 2.66/2.77 (op(e3, e1) = op(e1, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24894, 265])).
% 2.66/2.77 tff(24896,plain,
% 2.66/2.77 ((op(e3, e1) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24895, 24683])).
% 2.66/2.77 tff(24897,plain,
% 2.66/2.77 ((op(e1, e3) = op(e2, e3)) <=> (op(e3, e1) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24896])).
% 2.66/2.77 tff(24898,plain,
% 2.66/2.77 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24897])).
% 2.66/2.77 tff(24899,plain,
% 2.66/2.77 (~(op(e3, e1) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[118, 24898])).
% 2.66/2.77 tff(24900,plain,
% 2.66/2.77 (op(e0, e1) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1730, 24899, 24855, 24687])).
% 2.66/2.77 tff(24901,plain,
% 2.66/2.77 (op(e0, e1) = op(e2, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24900, 24683])).
% 2.66/2.77 tff(24902,plain,
% 2.66/2.77 (op(e0, op(e0, e1)) = op(e0, op(e2, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24901])).
% 2.66/2.77 tff(24903,plain,
% 2.66/2.77 (op(e0, op(e0, e1)) = e1),
% 2.66/2.77 inference(transitivity,[status(thm)],[24902, 24682, 19])).
% 2.66/2.77 tff(24904,plain,
% 2.66/2.77 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[2449, 24903])).
% 2.66/2.77 tff(24905,plain,
% 2.66/2.77 (op(e1, op(e2, e3)) = op(e1, e3)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24681])).
% 2.66/2.77 tff(24906,plain,
% 2.66/2.77 (op(e1, e2) = op(e2, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24870, 24683])).
% 2.66/2.77 tff(24907,plain,
% 2.66/2.77 (op(e1, op(e1, e2)) = op(e1, op(e2, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24906])).
% 2.66/2.77 tff(24908,plain,
% 2.66/2.77 (op(e1, op(e1, e2)) = e2),
% 2.66/2.77 inference(transitivity,[status(thm)],[24907, 24905, 264])).
% 2.66/2.77 tff(24909,plain,
% 2.66/2.77 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[2377, 24908])).
% 2.66/2.77 tff(24910,plain,
% 2.66/2.77 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24700])).
% 2.66/2.77 tff(24911,plain,
% 2.66/2.77 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24910])).
% 2.66/2.77 tff(24912,plain,
% 2.66/2.77 (~(op(e3, e0) = e0)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[157, 24911])).
% 2.66/2.77 tff(24913,plain,
% 2.66/2.77 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24886])).
% 2.66/2.77 tff(24914,plain,
% 2.66/2.77 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24913])).
% 2.66/2.77 tff(24915,plain,
% 2.66/2.77 (~(op(e3, e0) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[1133, 24914])).
% 2.66/2.77 tff(24916,plain,
% 2.66/2.77 (op(e3, e0) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[5422, 24915, 24912, 24888])).
% 2.66/2.77 tff(24917,plain,
% 2.66/2.77 (op(e3, op(e3, e0)) = op(e3, e3)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24916])).
% 2.66/2.77 tff(24918,plain,
% 2.66/2.77 (op(e3, op(e3, e0)) = e0),
% 2.66/2.77 inference(transitivity,[status(thm)],[24917, 24700])).
% 2.66/2.77 tff(24919,plain,
% 2.66/2.77 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1345, 24918])).
% 2.66/2.77 tff(24920,plain,
% 2.66/2.77 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24870])).
% 2.66/2.77 tff(24921,plain,
% 2.66/2.77 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24920])).
% 2.66/2.77 tff(24922,plain,
% 2.66/2.77 (~(op(e0, e2) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[6205, 24921])).
% 2.66/2.77 tff(24923,plain,
% 2.66/2.77 (op(e0, e2) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23880, 24922, 11315])).
% 2.66/2.77 tff(24924,plain,
% 2.66/2.77 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24923])).
% 2.66/2.77 tff(24925,plain,
% 2.66/2.77 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e2))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24924])).
% 2.66/2.77 tff(24926,plain,
% 2.66/2.77 (~(op(e0, e0) = e2)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[3603, 24925])).
% 2.66/2.77 tff(24927,plain,
% 2.66/2.77 (op(e2, e0) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[589, 24926, 4539, 24888])).
% 2.66/2.77 tff(24928,plain,
% 2.66/2.77 (op(e2, op(e2, e0)) = e0),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23913, 24927])).
% 2.66/2.77 tff(24929,plain,
% 2.66/2.77 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[2653, 24928])).
% 2.66/2.77 tff(24930,plain,
% 2.66/2.77 (op(op(e3, e2), e2) = op(e1, op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24886, 265])).
% 2.66/2.77 tff(24931,plain,
% 2.66/2.77 (op(op(e3, e2), e2) = e3),
% 2.66/2.77 inference(transitivity,[status(thm)],[24930, 6670, 24870])).
% 2.66/2.77 tff(24932,plain,
% 2.66/2.77 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1339, 24931])).
% 2.66/2.77 tff(24933,plain,
% 2.66/2.77 (op(e2, op(e2, e3)) = op(op(e1, e3), e3)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[265, 24681])).
% 2.66/2.77 tff(24934,plain,
% 2.66/2.77 (op(e2, op(e2, e3)) = e3),
% 2.66/2.77 inference(transitivity,[status(thm)],[24933, 24880, 24681])).
% 2.66/2.77 tff(24935,plain,
% 2.66/2.77 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[2344, 24934])).
% 2.66/2.77 tff(24936,plain,
% 2.66/2.77 ((op(e2, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[12131])).
% 2.66/2.77 tff(24937,plain,
% 2.66/2.77 ((op(e2, e1) = op(e2, e3)) <=> (op(op(e1, e3), e1) = e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24685, 24936])).
% 2.66/2.77 tff(24938,plain,
% 2.66/2.77 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24937])).
% 2.66/2.77 tff(24939,plain,
% 2.66/2.77 (~(op(op(e1, e3), e1) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[197, 24938])).
% 2.66/2.77 tff(24940,plain,
% 2.66/2.77 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[160, 24939])).
% 2.66/2.77 tff(24941,plain,
% 2.66/2.77 (op(e0, e2) = op(e1, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24923, 265])).
% 2.66/2.77 tff(24942,plain,
% 2.66/2.77 (op(e0, op(e0, e2)) = op(e0, op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24941])).
% 2.66/2.77 tff(24943,plain,
% 2.66/2.77 (op(e0, op(e0, e2)) = e2),
% 2.66/2.77 inference(transitivity,[status(thm)],[24942, 1927, 24923])).
% 2.66/2.77 tff(24944,plain,
% 2.66/2.77 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1331, 24943])).
% 2.66/2.77 tff(24945,plain,
% 2.66/2.77 (op(op(e2, e3), e2) = op(e3, op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24681, 265])).
% 2.66/2.77 tff(24946,plain,
% 2.66/2.77 (op(e3, op(e3, e1)) = op(op(e2, e3), e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24683, 24894])).
% 2.66/2.77 tff(24947,plain,
% 2.66/2.77 (op(e3, op(e3, e1)) = e1),
% 2.66/2.77 inference(transitivity,[status(thm)],[24946, 24945, 1900, 24886])).
% 2.66/2.77 tff(24948,plain,
% 2.66/2.77 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[2594, 24947])).
% 2.66/2.77 tff(24949,plain,
% 2.66/2.77 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[14938, 24922, 19])).
% 2.66/2.77 tff(24950,plain,
% 2.66/2.77 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24894])).
% 2.66/2.77 tff(24951,plain,
% 2.66/2.77 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24950])).
% 2.66/2.77 tff(24952,plain,
% 2.66/2.77 (~(op(e2, e1) = e2)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[402, 24951])).
% 2.66/2.77 tff(24953,plain,
% 2.66/2.77 (op(e2, e1) = e1),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23695, 24952, 24687])).
% 2.66/2.77 tff(24954,plain,
% 2.66/2.77 (op(e2, op(e2, e1)) = op(op(e1, e3), e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[265, 24953])).
% 2.66/2.77 tff(24955,plain,
% 2.66/2.77 (op(e2, op(e2, e1)) = e1),
% 2.66/2.77 inference(transitivity,[status(thm)],[24954, 12130, 24953])).
% 2.66/2.77 tff(24956,plain,
% 2.66/2.77 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1355, 24955])).
% 2.66/2.77 tff(24957,plain,
% 2.66/2.77 (op(e2, e0) = op(e1, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24927, 265])).
% 2.66/2.77 tff(24958,plain,
% 2.66/2.77 ((op(e2, e0) = e1) <=> (op(e1, e3) = e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24957])).
% 2.66/2.77 tff(24959,plain,
% 2.66/2.77 ((op(e1, e3) = e1) <=> (op(e2, e0) = e1)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24958])).
% 2.66/2.77 tff(24960,plain,
% 2.66/2.77 ((~(op(e1, e3) = e1)) <=> (~(op(e2, e0) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24959])).
% 2.66/2.77 tff(24961,plain,
% 2.66/2.77 (~(op(e2, e0) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[65, 24960])).
% 2.66/2.77 tff(24962,plain,
% 2.66/2.77 (op(e1, e0) = e1),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1480, 24961, 11527, 24915])).
% 2.66/2.77 tff(24963,plain,
% 2.66/2.77 (op(op(e1, e0), e0) = op(e1, e0)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24962])).
% 2.66/2.77 tff(24964,plain,
% 2.66/2.77 (op(op(e1, e0), e0) = e1),
% 2.66/2.77 inference(transitivity,[status(thm)],[24963, 24962])).
% 2.66/2.77 tff(24965,plain,
% 2.66/2.77 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[3015, 24964])).
% 2.66/2.77 tff(24966,plain,
% 2.66/2.77 ($false),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1459, 24965, 24956, 24949, 24948, 24944, 24940, 24935, 24932, 24929, 24919, 24909, 24904])).
% 2.66/2.77 tff(24967,plain,((~(op(e1, e3) = e2)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.77 tff(24968,plain,
% 2.66/2.77 (~(op(e1, e3) = e2)),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24967, 19])).
% 2.66/2.77 tff(24969,plain,
% 2.66/2.77 (op(e2, e3) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[15003, 24968, 21344])).
% 2.66/2.77 tff(24970,plain,
% 2.66/2.77 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24969])).
% 2.66/2.77 tff(24971,plain,
% 2.66/2.77 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24970])).
% 2.66/2.77 tff(24972,plain,
% 2.66/2.77 (~(op(e2, e0) = e2)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[989, 24971])).
% 2.66/2.77 tff(24973,plain,
% 2.66/2.77 (op(e1, e3) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24697, 24968, 65])).
% 2.66/2.77 tff(24974,plain,
% 2.66/2.77 (e3 = op(e1, e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24973])).
% 2.66/2.77 tff(24975,plain,
% 2.66/2.77 ((op(e1, e1) = e0) <=> (e2 = e0)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[2891])).
% 2.66/2.77 tff(24976,plain,
% 2.66/2.77 ((op(e1, e1) = e0) <=> (e0 = e2)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24975, 1])).
% 2.66/2.77 tff(24977,plain,
% 2.66/2.77 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24976])).
% 2.66/2.77 tff(24978,plain,
% 2.66/2.77 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24977])).
% 2.66/2.77 tff(24979,plain,
% 2.66/2.77 (~(op(e1, e1) = e0)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[14, 24978])).
% 2.66/2.77 tff(24980,plain,
% 2.66/2.77 (op(e0, e1) = e0),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23988, 24979, 24718])).
% 2.66/2.77 tff(24981,plain,
% 2.66/2.77 ((op(e0, e1) = e3) <=> (e0 = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24980, 24974])).
% 2.66/2.77 tff(24982,plain,
% 2.66/2.77 ((op(e0, e1) = e3) <=> (op(e1, e3) = e0)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24981, 6095])).
% 2.66/2.77 tff(24983,plain,
% 2.66/2.77 ((op(e1, e3) = e0) <=> (op(e0, e1) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[24982])).
% 2.66/2.77 tff(24984,plain,
% 2.66/2.77 ((~(op(e1, e3) = e0)) <=> (~(op(e0, e1) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24983])).
% 2.66/2.77 tff(24985,plain,
% 2.66/2.77 (~(op(e0, e1) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[24661, 24984])).
% 2.66/2.77 tff(24986,plain,
% 2.66/2.77 (op(e0, e2) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[3652, 24735, 21344, 5828])).
% 2.66/2.77 tff(24987,plain,
% 2.66/2.77 (op(e1, e3) = e2),
% 2.66/2.77 inference(transitivity,[status(thm)],[24973, 7827, 24986])).
% 2.66/2.77 tff(24988,plain,
% 2.66/2.77 ($false),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24968, 24987])).
% 2.66/2.77 tff(24989,plain,((~(op(e0, e2) = e3)) | (op(e0, e1) = e2) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.77 tff(24990,plain,
% 2.66/2.77 (~(op(e0, e2) = e3)),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24989, 5774, 19])).
% 2.66/2.77 tff(24991,plain,
% 2.66/2.77 (op(e0, e0) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1495, 24990, 11546, 24985])).
% 2.66/2.77 tff(24992,plain,
% 2.66/2.77 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24991])).
% 2.66/2.77 tff(24993,plain,
% 2.66/2.77 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[24992, 660])).
% 2.66/2.77 tff(24994,plain,
% 2.66/2.77 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24993])).
% 2.66/2.77 tff(24995,plain,
% 2.66/2.77 (~(op(e2, e0) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[359, 24994])).
% 2.66/2.77 tff(24996,plain,
% 2.66/2.77 (op(e2, e0) = e1),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24100, 24995, 24972])).
% 2.66/2.77 tff(24997,plain,
% 2.66/2.77 (e1 = op(e2, op(e2, e2))),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[24996, 23619])).
% 2.66/2.77 tff(24998,plain,
% 2.66/2.77 (op(e2, op(e2, e0)) = op(e2, e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24996])).
% 2.66/2.77 tff(24999,plain,
% 2.66/2.77 (op(e2, e1) = op(e2, op(e2, e0))),
% 2.66/2.77 inference(symmetry,[status(thm)],[24998])).
% 2.66/2.77 tff(25000,plain,
% 2.66/2.77 ((op(e3, e1) = e3) <=> (op(e3, e1) = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24974])).
% 2.66/2.77 tff(25001,plain,
% 2.66/2.77 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25000])).
% 2.66/2.77 tff(25002,plain,
% 2.66/2.77 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24974])).
% 2.66/2.77 tff(25003,plain,
% 2.66/2.77 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25002])).
% 2.66/2.77 tff(25004,plain,
% 2.66/2.77 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25003])).
% 2.66/2.77 tff(25005,plain,
% 2.66/2.77 (~(op(e1, e2) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[1850, 25004])).
% 2.66/2.77 tff(25006,plain,
% 2.66/2.77 (op(e3, e2) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23653, 24990, 25005])).
% 2.66/2.77 tff(25007,plain,
% 2.66/2.77 (op(e3, e2) = op(e1, e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25006, 24974])).
% 2.66/2.77 tff(25008,plain,
% 2.66/2.77 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25007])).
% 2.66/2.77 tff(25009,plain,
% 2.66/2.77 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e1) = e3)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25008, 25001])).
% 2.66/2.77 tff(25010,plain,
% 2.66/2.77 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25009])).
% 2.66/2.77 tff(25011,plain,
% 2.66/2.77 (~(op(e3, e1) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[3429, 25010])).
% 2.66/2.77 tff(25012,plain,
% 2.66/2.77 (op(e2, e1) = e3),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[1730, 25011, 24855, 24985])).
% 2.66/2.77 tff(25013,plain,
% 2.66/2.77 (e3 = op(e2, e1)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25012])).
% 2.66/2.77 tff(25014,plain,
% 2.66/2.77 (e3 = op(e2, op(e2, op(e2, e2)))),
% 2.66/2.77 inference(transitivity,[status(thm)],[25013, 24999, 23789])).
% 2.66/2.77 tff(25015,plain,
% 2.66/2.77 ($false),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[23797, 25014, 24997])).
% 2.66/2.77 tff(25016,plain,((~(op(e1, e1) = e2)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.77 tff(25017,plain,
% 2.66/2.77 (~(op(e1, e1) = e2)),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[25016, 19])).
% 2.66/2.77 tff(25018,plain,
% 2.66/2.77 (op(e1, op(e0, e3)) = op(e1, e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[19])).
% 2.66/2.77 tff(25019,plain,
% 2.66/2.77 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e1) = e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25018])).
% 2.66/2.77 tff(25020,plain,
% 2.66/2.77 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25019])).
% 2.66/2.77 tff(25021,plain,
% 2.66/2.77 ((op(e2, e3) = e3) <=> (op(e2, e3) = op(e1, e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24974])).
% 2.66/2.77 tff(25022,plain,
% 2.66/2.77 ((op(e2, e3) = e3) <=> (op(e1, e3) = op(e2, e3))),
% 2.66/2.77 inference(transitivity,[status(thm)],[25021, 1687])).
% 2.66/2.77 tff(25023,plain,
% 2.66/2.77 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25022])).
% 2.66/2.77 tff(25024,plain,
% 2.66/2.77 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25023])).
% 2.66/2.77 tff(25025,plain,
% 2.66/2.77 (~(op(e2, e3) = e3)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[118, 25024])).
% 2.66/2.77 tff(25026,plain,
% 2.66/2.77 (op(e0, e1) = e2),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[24989, 7826, 19])).
% 2.66/2.77 tff(25027,plain,
% 2.66/2.77 (op(e1, e1) = e0),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[15044, 25026, 24700, 19, 24969, 25025])).
% 2.66/2.77 tff(25028,plain,
% 2.66/2.77 ((op(e1, e1) = e1) <=> (e0 = e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25027])).
% 2.66/2.77 tff(25029,plain,
% 2.66/2.77 ((e0 = e1) <=> (op(e1, e1) = e1)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25028])).
% 2.66/2.77 tff(25030,plain,
% 2.66/2.77 ((e0 = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25029, 25020])).
% 2.66/2.77 tff(25031,plain,
% 2.66/2.77 ((~(e0 = e1)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25030])).
% 2.66/2.77 tff(25032,plain,
% 2.66/2.77 (~(op(e1, op(e0, e3)) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[26, 25031])).
% 2.66/2.77 tff(25033,plain,
% 2.66/2.77 ((op(e0, op(e0, e3)) = e0) <=> (op(e0, e1) = e0)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[4972])).
% 2.66/2.77 tff(25034,plain,
% 2.66/2.77 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25033])).
% 2.66/2.77 tff(25035,plain,
% 2.66/2.77 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25026])).
% 2.66/2.77 tff(25036,plain,
% 2.66/2.77 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25035, 1])).
% 2.66/2.77 tff(25037,plain,
% 2.66/2.77 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25036])).
% 2.66/2.77 tff(25038,plain,
% 2.66/2.77 ((e0 = e2) <=> (op(e0, op(e0, e3)) = e0)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25037, 25034])).
% 2.66/2.77 tff(25039,plain,
% 2.66/2.77 ((~(e0 = e2)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25038])).
% 2.66/2.77 tff(25040,plain,
% 2.66/2.77 (~(op(e0, op(e0, e3)) = e0)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[14, 25039])).
% 2.66/2.77 tff(25041,plain,
% 2.66/2.77 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e1) = e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[4816])).
% 2.66/2.77 tff(25042,plain,
% 2.66/2.77 ((op(e2, e1) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25041])).
% 2.66/2.77 tff(25043,plain,
% 2.66/2.77 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e2)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[24969])).
% 2.66/2.77 tff(25044,plain,
% 2.66/2.77 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, op(e0, e3)) = e2)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25043, 25042])).
% 2.66/2.77 tff(25045,plain,
% 2.66/2.77 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25044])).
% 2.66/2.77 tff(25046,plain,
% 2.66/2.77 (~(op(e2, op(e0, e3)) = e2)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[197, 25045])).
% 2.66/2.77 tff(25047,plain,
% 2.66/2.77 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 2.66/2.77 inference(monotonicity,[status(thm)],[920])).
% 2.66/2.77 tff(25048,plain,
% 2.66/2.77 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 2.66/2.77 inference(transitivity,[status(thm)],[25047, 69])).
% 2.66/2.77 tff(25049,plain,
% 2.66/2.77 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 2.66/2.77 inference(symmetry,[status(thm)],[25048])).
% 2.66/2.77 tff(25050,plain,
% 2.66/2.77 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25049])).
% 2.66/2.77 tff(25051,plain,
% 2.66/2.77 (~(op(e1, e0) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[708, 25050])).
% 2.66/2.77 tff(25052,plain,
% 2.66/2.77 ((~(e0 = e1)) <=> (~(op(e1, e1) = e1))),
% 2.66/2.77 inference(monotonicity,[status(thm)],[25029])).
% 2.66/2.77 tff(25053,plain,
% 2.66/2.77 (~(op(e1, e1) = e1)),
% 2.66/2.77 inference(modus_ponens,[status(thm)],[26, 25052])).
% 2.66/2.77 tff(25054,plain,
% 2.66/2.77 (op(e1, e2) = e1),
% 2.66/2.77 inference(unit_resolution,[status(thm)],[954, 25051, 65, 25053])).
% 2.66/2.77 tff(25055,plain,
% 2.66/2.77 (op(e2, op(e1, e2)) = op(e2, e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[6683])).
% 2.66/2.78 tff(25056,plain,
% 2.66/2.78 (op(e2, e0) = op(e1, e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[767, 18022])).
% 2.66/2.78 tff(25057,plain,
% 2.66/2.78 (op(e2, op(e2, e0)) = op(e2, op(e1, e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25056])).
% 2.66/2.78 tff(25058,plain,
% 2.66/2.78 (op(e2, op(e2, op(e2, e2))) = op(e2, e1)),
% 2.66/2.78 inference(transitivity,[status(thm)],[23788, 25057, 25055])).
% 2.66/2.78 tff(25059,plain,
% 2.66/2.78 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (e3 = op(e2, e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25058])).
% 2.66/2.78 tff(25060,plain,
% 2.66/2.78 ((e3 = op(e2, op(e2, op(e2, e2)))) <=> (op(e2, e1) = e3)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25059, 1262])).
% 2.66/2.78 tff(25061,plain,
% 2.66/2.78 ((~(e3 = op(e2, op(e2, op(e2, e2))))) <=> (~(op(e2, e1) = e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25060])).
% 2.66/2.78 tff(25062,plain,
% 2.66/2.78 (e1 = op(e2, op(e2, e2))),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[767, 23619])).
% 2.66/2.78 tff(25063,plain,
% 2.66/2.78 (~(e3 = op(e2, op(e2, op(e2, e2))))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[23797, 25062])).
% 2.66/2.78 tff(25064,plain,
% 2.66/2.78 (~(op(e2, e1) = e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[25063, 25061])).
% 2.66/2.78 tff(25065,plain,
% 2.66/2.78 ((op(e2, e0) = e3) <=> (op(e1, e2) = op(e1, e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25056, 11135])).
% 2.66/2.78 tff(25066,plain,
% 2.66/2.78 ((op(e1, e2) = op(e1, e3)) <=> (op(e2, e0) = e3)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25065])).
% 2.66/2.78 tff(25067,plain,
% 2.66/2.78 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25066])).
% 2.66/2.78 tff(25068,plain,
% 2.66/2.78 (~(op(e2, e0) = e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[1850, 25067])).
% 2.66/2.78 tff(25069,plain,
% 2.66/2.78 (op(e2, e1) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[23641, 25068, 11219])).
% 2.66/2.78 tff(25070,plain,
% 2.66/2.78 ($false),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25069, 25064])).
% 2.66/2.78 tff(25071,plain,((~(op(e2, e0) = e1)) | (~(op(e1, e2) = e1)) | (~(op(e1, e3) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.78 tff(25072,plain,
% 2.66/2.78 (~(op(e2, e0) = e1)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25071, 25054, 24973])).
% 2.66/2.78 tff(25073,plain,
% 2.66/2.78 (op(e3, e0) = e1),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1480, 25072, 11527, 25051])).
% 2.66/2.78 tff(25074,plain,
% 2.66/2.78 (op(e3, e0) = op(e0, e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[25073, 11524])).
% 2.66/2.78 tff(25075,plain,
% 2.66/2.78 (op(e3, op(e0, e3)) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[16058, 25074, 25046, 25040, 25032])).
% 2.66/2.78 tff(25076,plain,
% 2.66/2.78 (op(op(e1, e3), e1) = op(e3, e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24973])).
% 2.66/2.78 tff(25077,plain,
% 2.66/2.78 (op(e3, op(e1, e2)) = op(op(e1, e3), e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24974, 25054])).
% 2.66/2.78 tff(25078,plain,
% 2.66/2.78 (e1 = op(e1, e2)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25054])).
% 2.66/2.78 tff(25079,plain,
% 2.66/2.78 (op(e3, e1) = e3),
% 2.66/2.78 inference(transitivity,[status(thm)],[4805, 25075])).
% 2.66/2.78 tff(25080,plain,
% 2.66/2.78 (op(op(e3, e1), e1) = op(e3, op(e1, e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25079, 25078])).
% 2.66/2.78 tff(25081,plain,
% 2.66/2.78 (op(op(e3, e1), e1) = e3),
% 2.66/2.78 inference(transitivity,[status(thm)],[25080, 25077, 25076, 4805, 25075])).
% 2.66/2.78 tff(25082,plain,
% 2.66/2.78 (op(op(e0, e1), e0) = op(e2, e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25026])).
% 2.66/2.78 tff(25083,plain,
% 2.66/2.78 ((op(op(e0, e1), e0) = e1) <=> (op(e2, e0) = e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25082])).
% 2.66/2.78 tff(25084,plain,
% 2.66/2.78 ((op(e2, e0) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25083])).
% 2.66/2.78 tff(25085,plain,
% 2.66/2.78 ((~(op(e2, e0) = e1)) <=> (~(op(op(e0, e1), e0) = e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25084])).
% 2.66/2.78 tff(25086,plain,
% 2.66/2.78 (~(op(op(e0, e1), e0) = e1)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[25072, 25085])).
% 2.66/2.78 tff(25087,plain,
% 2.66/2.78 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1461, 25086])).
% 2.66/2.78 tff(25088,plain,
% 2.66/2.78 (op(op(e1, e2), e2) = op(e1, e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25054])).
% 2.66/2.78 tff(25089,plain,
% 2.66/2.78 (op(op(e1, e2), e2) = e1),
% 2.66/2.78 inference(transitivity,[status(thm)],[25088, 25054])).
% 2.66/2.78 tff(25090,plain,
% 2.66/2.78 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1335, 25089])).
% 2.66/2.78 tff(25091,plain,
% 2.66/2.78 (op(e1, op(e1, e3)) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[169, 24973])).
% 2.66/2.78 tff(25092,plain,
% 2.66/2.78 (op(op(e3, e0), e3) = op(e1, op(e1, e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25073, 24974])).
% 2.66/2.78 tff(25093,plain,
% 2.66/2.78 (op(op(e3, e0), e3) = op(e1, e3)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25092, 25091, 24974])).
% 2.66/2.78 tff(25094,plain,
% 2.66/2.78 ((op(op(e3, e0), e3) = e0) <=> (op(e1, e3) = e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25093])).
% 2.66/2.78 tff(25095,plain,
% 2.66/2.78 ((op(e1, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25094])).
% 2.66/2.78 tff(25096,plain,
% 2.66/2.78 ((~(op(e1, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25095])).
% 2.66/2.78 tff(25097,plain,
% 2.66/2.78 (~(op(op(e3, e0), e3) = e0)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[24661, 25096])).
% 2.66/2.78 tff(25098,plain,
% 2.66/2.78 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1764, 25097])).
% 2.66/2.78 tff(25099,plain,
% 2.66/2.78 ((op(e0, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25026])).
% 2.66/2.78 tff(25100,plain,
% 2.66/2.78 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25099, 637])).
% 2.66/2.78 tff(25101,plain,
% 2.66/2.78 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25100])).
% 2.66/2.78 tff(25102,plain,
% 2.66/2.78 (~(op(e3, e1) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[3046, 25101])).
% 2.66/2.78 tff(25103,plain,
% 2.66/2.78 (op(e3, e2) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[15971, 18562, 25102])).
% 2.66/2.78 tff(25104,plain,
% 2.66/2.78 (op(e2, e0) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[24100, 25072, 24972])).
% 2.66/2.78 tff(25105,plain,
% 2.66/2.78 (op(op(e2, e0), e2) = op(e3, e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25104])).
% 2.66/2.78 tff(25106,plain,
% 2.66/2.78 (op(op(e2, e0), e2) = e2),
% 2.66/2.78 inference(transitivity,[status(thm)],[25105, 25103])).
% 2.66/2.78 tff(25107,plain,
% 2.66/2.78 ((op(op(e2, e0), e2) = e0) <=> (e2 = e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25106])).
% 2.66/2.78 tff(25108,plain,
% 2.66/2.78 ((op(op(e2, e0), e2) = e0) <=> (e0 = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25107, 1])).
% 2.66/2.78 tff(25109,plain,
% 2.66/2.78 ((e0 = e2) <=> (op(op(e2, e0), e2) = e0)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25108])).
% 2.66/2.78 tff(25110,plain,
% 2.66/2.78 ((~(e0 = e2)) <=> (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25109])).
% 2.66/2.78 tff(25111,plain,
% 2.66/2.78 (~(op(op(e2, e0), e2) = e0)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[14, 25110])).
% 2.66/2.78 tff(25112,plain,
% 2.66/2.78 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1379, 25111])).
% 2.66/2.78 tff(25113,plain,
% 2.66/2.78 (op(e3, op(e3, e2)) = op(e3, e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25103])).
% 2.66/2.78 tff(25114,plain,
% 2.66/2.78 (op(e3, op(e3, e2)) = e2),
% 2.66/2.78 inference(transitivity,[status(thm)],[25113, 25103])).
% 2.66/2.78 tff(25115,plain,
% 2.66/2.78 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1904, 25114])).
% 2.66/2.78 tff(25116,plain,
% 2.66/2.78 (op(e2, op(e1, e3)) = op(e2, e3)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24973])).
% 2.66/2.78 tff(25117,plain,
% 2.66/2.78 (op(op(e2, e3), e3) = op(e2, op(e1, e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24969, 24974])).
% 2.66/2.78 tff(25118,plain,
% 2.66/2.78 (op(op(e2, e3), e3) = e2),
% 2.66/2.78 inference(transitivity,[status(thm)],[25117, 25116, 24969])).
% 2.66/2.78 tff(25119,plain,
% 2.66/2.78 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1288, 25118])).
% 2.66/2.78 tff(25120,plain,
% 2.66/2.78 (((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))) | (op(e1, e3) = e2)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[16410, 24661])).
% 2.66/2.78 tff(25121,plain,
% 2.66/2.78 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25120, 24968])).
% 2.66/2.78 tff(25122,plain,
% 2.66/2.78 (op(op(e0, e2), e0) = op(e3, e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[7826])).
% 2.66/2.78 tff(25123,plain,
% 2.66/2.78 ((op(op(e0, e2), e0) = e2) <=> (op(e3, e0) = e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25122])).
% 2.66/2.78 tff(25124,plain,
% 2.66/2.78 ((op(e3, e0) = e2) <=> (op(op(e0, e2), e0) = e2)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25123])).
% 2.66/2.78 tff(25125,plain,
% 2.66/2.78 ((op(e1, e0) = op(e3, e0)) <=> (op(op(e0, e2), e0) = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[18560, 25124])).
% 2.66/2.78 tff(25126,plain,
% 2.66/2.78 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(op(e0, e2), e0) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25125])).
% 2.66/2.78 tff(25127,plain,
% 2.66/2.78 (~(op(op(e0, e2), e0) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[410, 25126])).
% 2.66/2.78 tff(25128,plain,
% 2.66/2.78 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2446, 25127])).
% 2.66/2.78 tff(25129,plain,
% 2.66/2.78 (~(op(op(e1, e0), e1) = e0)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[23694, 18621])).
% 2.66/2.78 tff(25130,plain,
% 2.66/2.78 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1302, 25129])).
% 2.66/2.78 tff(25131,plain,
% 2.66/2.78 ((op(e1, e0) = e3) <=> (op(e1, e0) = op(e1, e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24974])).
% 2.66/2.78 tff(25132,plain,
% 2.66/2.78 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e3)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25131])).
% 2.66/2.78 tff(25133,plain,
% 2.66/2.78 ((op(e1, e0) = op(e1, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25132, 11358])).
% 2.66/2.78 tff(25134,plain,
% 2.66/2.78 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25133])).
% 2.66/2.78 tff(25135,plain,
% 2.66/2.78 (~(op(op(e0, e3), e0) = e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[110, 25134])).
% 2.66/2.78 tff(25136,plain,
% 2.66/2.78 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2635, 25135])).
% 2.66/2.78 tff(25137,plain,
% 2.66/2.78 (op(e2, e1) = e1),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[23785, 25072, 24675])).
% 2.66/2.78 tff(25138,plain,
% 2.66/2.78 (op(e2, op(e1, e2)) = op(e2, e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25054])).
% 2.66/2.78 tff(25139,plain,
% 2.66/2.78 (op(e2, e1) = op(e1, e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25137, 25078])).
% 2.66/2.78 tff(25140,plain,
% 2.66/2.78 (op(e2, op(e2, e1)) = op(e2, op(e1, e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25139])).
% 2.66/2.78 tff(25141,plain,
% 2.66/2.78 (op(e2, op(e2, e1)) = e1),
% 2.66/2.78 inference(transitivity,[status(thm)],[25140, 25138, 25137])).
% 2.66/2.78 tff(25142,plain,
% 2.66/2.78 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1355, 25141])).
% 2.66/2.78 tff(25143,plain,
% 2.66/2.78 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1459, 25142, 25136, 25130, 25128, 25121, 25119, 25115, 25112, 25098, 25090, 25087])).
% 2.66/2.78 tff(25144,plain,
% 2.66/2.78 (~(op(op(e3, e1), e1) = e3)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2416, 25143])).
% 2.66/2.78 tff(25145,plain,
% 2.66/2.78 ($false),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25144, 25081])).
% 2.66/2.78 tff(25146,plain,((~(op(e1, e0) = e2)) | (~(op(e0, e3) = e1)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.78 tff(25147,plain,
% 2.66/2.78 (~(op(e1, e0) = e2)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25146, 7826, 19])).
% 2.66/2.78 tff(25148,plain,
% 2.66/2.78 (op(e3, e0) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[589, 25147, 24972, 24735])).
% 2.66/2.78 tff(25149,plain,
% 2.66/2.78 (op(e3, op(e3, e0)) = op(e3, e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25148])).
% 2.66/2.78 tff(25150,plain,
% 2.66/2.78 (op(e3, op(e3, e3)) = op(e3, e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[24700])).
% 2.66/2.78 tff(25151,plain,
% 2.66/2.78 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25150])).
% 2.66/2.78 tff(25152,plain,
% 2.66/2.78 (op(e3, op(e3, op(e3, e3))) = op(e3, e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25151, 25149])).
% 2.66/2.78 tff(25153,plain,
% 2.66/2.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (e1 = op(e3, e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25152])).
% 2.66/2.78 tff(25154,plain,
% 2.66/2.78 ((e1 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e2) = e1)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25153, 7171])).
% 2.66/2.78 tff(25155,plain,
% 2.66/2.78 ((~(e1 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e2) = e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25154])).
% 2.66/2.78 tff(25156,plain,
% 2.66/2.78 (e0 = op(e3, e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[24700, 3078])).
% 2.66/2.78 tff(25157,plain,
% 2.66/2.78 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25150])).
% 2.66/2.78 tff(25158,plain,
% 2.66/2.78 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25157, 5377])).
% 2.66/2.78 tff(25159,plain,
% 2.66/2.78 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 2.66/2.78 inference(symmetry,[status(thm)],[25158])).
% 2.66/2.78 tff(25160,plain,
% 2.66/2.78 (e2 = op(e3, op(e3, e3))),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[25148, 25159])).
% 2.66/2.78 tff(25161,plain,
% 2.66/2.78 (~(e1 = op(e3, op(e3, op(e3, e3))))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[3093, 25160, 25156])).
% 2.66/2.78 tff(25162,plain,
% 2.66/2.78 (~(op(e3, e2) = e1)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[25161, 25155])).
% 2.66/2.78 tff(25163,plain,
% 2.66/2.78 (op(e1, e2) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2285, 25147, 24968, 25017])).
% 2.66/2.78 tff(25164,plain,
% 2.66/2.78 ((op(e1, e2) = e1) <=> (e2 = e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25163])).
% 2.66/2.78 tff(25165,plain,
% 2.66/2.78 ((op(e1, e2) = e1) <=> (e1 = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25164, 69])).
% 2.66/2.78 tff(25166,plain,
% 2.66/2.78 ((e1 = e2) <=> (op(e1, e2) = e1)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25165])).
% 2.66/2.78 tff(25167,plain,
% 2.66/2.78 ((~(e1 = e2)) <=> (~(op(e1, e2) = e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25166])).
% 2.66/2.78 tff(25168,plain,
% 2.66/2.78 (~(op(e1, e2) = e1)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[708, 25167])).
% 2.66/2.78 tff(25169,plain,
% 2.66/2.78 (op(e3, e2) = e1),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[24286, 25168, 11315])).
% 2.66/2.78 tff(25170,plain,
% 2.66/2.78 ($false),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25169, 25162])).
% 2.66/2.78 tff(25171,plain,((~(op(e0, e2) = e3)) | (~(op(e0, e3) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.78 tff(25172,plain,
% 2.66/2.78 (~(op(e0, e2) = e3)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25171, 19])).
% 2.66/2.78 tff(25173,plain,
% 2.66/2.78 (op(e0, e2) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[23880, 25172, 11315])).
% 2.66/2.78 tff(25174,plain,
% 2.66/2.78 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25173])).
% 2.66/2.78 tff(25175,plain,
% 2.66/2.78 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.66/2.78 inference(transitivity,[status(thm)],[25174, 5762])).
% 2.66/2.78 tff(25176,plain,
% 2.66/2.78 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25175])).
% 2.66/2.78 tff(25177,plain,
% 2.66/2.78 (~(op(e1, e2) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[6205, 25176])).
% 2.66/2.78 tff(25178,plain,
% 2.66/2.78 (op(e1, e0) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2285, 25177, 24968, 25017])).
% 2.66/2.78 tff(25179,plain,
% 2.66/2.78 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25043])).
% 2.66/2.78 tff(25180,plain,
% 2.66/2.78 (~(op(e2, e1) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[197, 25179])).
% 2.66/2.78 tff(25181,plain,
% 2.66/2.78 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25173])).
% 2.66/2.78 tff(25182,plain,
% 2.66/2.78 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25181])).
% 2.66/2.78 tff(25183,plain,
% 2.66/2.78 (~(op(e0, e1) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[2102, 25182])).
% 2.66/2.78 tff(25184,plain,
% 2.66/2.78 (op(e3, e1) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1993, 25183, 25180, 25017])).
% 2.66/2.78 tff(25185,plain,
% 2.66/2.78 (~(op(e3, e0) = e1)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[8647, 25184, 24700])).
% 2.66/2.78 tff(25186,plain,
% 2.66/2.78 (op(e1, e2) = e1),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[23821, 25177, 25005])).
% 2.66/2.78 tff(25187,plain,
% 2.66/2.78 (~(op(e2, e0) = e1)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[25071, 25186, 24973])).
% 2.66/2.78 tff(25188,plain,
% 2.66/2.78 (op(e1, e0) = e1),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[1480, 25187, 11527, 25185])).
% 2.66/2.78 tff(25189,plain,
% 2.66/2.78 (e1 = op(e1, e0)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25188])).
% 2.66/2.78 tff(25190,plain,
% 2.66/2.78 (e1 = e2),
% 2.66/2.78 inference(transitivity,[status(thm)],[25189, 25178])).
% 2.66/2.78 tff(25191,plain,
% 2.66/2.78 ($false),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[708, 25190])).
% 2.66/2.78 tff(25192,plain,(~(op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.78 tff(25193,plain,
% 2.66/2.78 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[7826])).
% 2.66/2.78 tff(25194,plain,
% 2.66/2.78 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25193])).
% 2.66/2.78 tff(25195,plain,
% 2.66/2.78 (~(op(e0, e1) = e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[2102, 25194])).
% 2.66/2.78 tff(25196,plain,
% 2.66/2.78 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[16410, 72, 80])).
% 2.66/2.78 tff(25197,plain,
% 2.66/2.78 (op(e1, e2) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[2285, 72, 68, 6687])).
% 2.66/2.78 tff(25198,plain,
% 2.66/2.78 ((op(e1, e2) = e3) <=> (e2 = e3)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25197])).
% 2.66/2.78 tff(25199,plain,
% 2.66/2.78 ((e2 = e3) <=> (op(e1, e2) = e3)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25198])).
% 2.66/2.78 tff(25200,plain,
% 2.66/2.78 ((~(e2 = e3)) <=> (~(op(e1, e2) = e3))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25199])).
% 2.66/2.78 tff(25201,plain,
% 2.66/2.78 (~(op(e1, e2) = e3)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[1321, 25200])).
% 2.66/2.78 tff(25202,plain,
% 2.66/2.78 ((op(e0, e3) = op(e0, e0)) <=> (op(e0, e0) = op(e0, e3))),
% 2.66/2.78 inference(commutativity,[status(thm)],[])).
% 2.66/2.78 tff(25203,plain,
% 2.66/2.78 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[7109])).
% 2.66/2.78 tff(25204,plain,
% 2.66/2.78 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25203])).
% 2.66/2.78 tff(25205,plain,
% 2.66/2.78 (~(op(e1, e0) = e1)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[110, 25204])).
% 2.66/2.78 tff(25206,plain,
% 2.66/2.78 (op(e1, e0) = e0),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[728, 25205, 2168, 6687])).
% 2.66/2.78 tff(25207,plain,
% 2.66/2.78 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25206])).
% 2.66/2.78 tff(25208,plain,
% 2.66/2.78 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25207])).
% 2.66/2.78 tff(25209,plain,
% 2.66/2.78 (~(op(e0, e0) = e0)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[2471, 25208])).
% 2.66/2.78 tff(25210,plain,
% 2.66/2.78 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e2)),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25197])).
% 2.66/2.78 tff(25211,plain,
% 2.66/2.78 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25210])).
% 2.66/2.78 tff(25212,plain,
% 2.66/2.78 (~(op(e0, e2) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[6205, 25211])).
% 2.66/2.78 tff(25213,plain,
% 2.66/2.78 (op(e1, e1) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[247, 25201, 1080, 2168])).
% 2.66/2.78 tff(25214,plain,
% 2.66/2.78 (~(op(e0, e0) = e3)),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[24278, 25213, 72, 68, 25212])).
% 2.66/2.78 tff(25215,plain,
% 2.66/2.78 (op(e0, e0) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[3612, 25214, 2379, 25209])).
% 2.66/2.78 tff(25216,plain,
% 2.66/2.78 (e2 = op(e0, e0)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25215])).
% 2.66/2.78 tff(25217,plain,
% 2.66/2.78 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e0, e0))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25216])).
% 2.66/2.78 tff(25218,plain,
% 2.66/2.78 ((op(e0, e3) = e2) <=> (op(e0, e0) = op(e0, e3))),
% 2.66/2.78 inference(transitivity,[status(thm)],[25217, 25202])).
% 2.66/2.78 tff(25219,plain,
% 2.66/2.78 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25218])).
% 2.66/2.78 tff(25220,plain,
% 2.66/2.78 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 2.66/2.78 inference(monotonicity,[status(thm)],[25219])).
% 2.66/2.78 tff(25221,plain,
% 2.66/2.78 (~(op(e0, e3) = e2)),
% 2.66/2.78 inference(modus_ponens,[status(thm)],[3414, 25220])).
% 2.66/2.78 tff(25222,plain,
% 2.66/2.78 (op(e2, e3) = e3),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[15235, 25221, 72, 121, 25201, 25196, 80, 1080])).
% 2.66/2.78 tff(25223,plain,
% 2.66/2.78 (op(e2, e3) = e2),
% 2.66/2.78 inference(unit_resolution,[status(thm)],[15003, 25221, 72])).
% 2.66/2.78 tff(25224,plain,
% 2.66/2.78 (e2 = op(e2, e3)),
% 2.66/2.78 inference(symmetry,[status(thm)],[25223])).
% 2.66/2.78 tff(25225,plain,
% 2.66/2.78 (op(e0, e0) = e3),
% 2.66/2.78 inference(transitivity,[status(thm)],[25215, 25224, 25222])).
% 2.66/2.78 tff(25226,plain,
% 2.66/2.79 ($false),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[25214, 25225])).
% 2.66/2.79 tff(25227,plain,((op(e1, e3) = e2) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (op(e1, e3) = e3) | (op(e0, e0) = e1) | (op(e1, e1) = e2) | (op(e1, e0) = e3) | (op(e1, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.79 tff(25228,plain,
% 2.66/2.79 (op(e1, e3) = e2),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[25227, 2379, 80, 1080, 121, 68, 2168, 6687])).
% 2.66/2.79 tff(25229,plain,
% 2.66/2.79 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e2)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.79 tff(25230,plain,
% 2.66/2.79 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25229])).
% 2.66/2.79 tff(25231,plain,
% 2.66/2.79 (~(op(e0, e3) = e2)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[64, 25230])).
% 2.66/2.79 tff(25232,plain,
% 2.66/2.79 (op(e1, e2) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[247, 1291, 1080, 2168])).
% 2.66/2.79 tff(25233,plain,
% 2.66/2.79 (op(e0, op(e1, e2)) = op(e0, e3)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25232])).
% 2.66/2.79 tff(25234,plain,
% 2.66/2.79 (op(e0, e3) = op(e0, op(e1, e2))),
% 2.66/2.79 inference(symmetry,[status(thm)],[25233])).
% 2.66/2.79 tff(25235,plain,
% 2.66/2.79 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25234])).
% 2.66/2.79 tff(25236,plain,
% 2.66/2.79 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e3) = e0)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25235])).
% 2.66/2.79 tff(25237,plain,
% 2.66/2.79 (e3 = op(e1, e2)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25232])).
% 2.66/2.79 tff(25238,plain,
% 2.66/2.79 ((op(e0, e2) = e3) <=> (op(e0, e2) = op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25237])).
% 2.66/2.79 tff(25239,plain,
% 2.66/2.79 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25238])).
% 2.66/2.79 tff(25240,plain,
% 2.66/2.79 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25239])).
% 2.66/2.79 tff(25241,plain,
% 2.66/2.79 (~(op(e0, e2) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[6205, 25240])).
% 2.66/2.79 tff(25242,plain,
% 2.66/2.79 ((e1 = e3) <=> (e1 = op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25237])).
% 2.66/2.79 tff(25243,plain,
% 2.66/2.79 ((e1 = e3) <=> (op(e1, e2) = e1)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25242, 5522])).
% 2.66/2.79 tff(25244,plain,
% 2.66/2.79 ((~(e1 = e3)) <=> (~(op(e1, e2) = e1))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25243])).
% 2.66/2.79 tff(25245,plain,
% 2.66/2.79 (~(op(e1, e2) = e1)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[303, 25244])).
% 2.66/2.79 tff(25246,plain,
% 2.66/2.79 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.79 tff(25247,plain,
% 2.66/2.79 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25246, 69])).
% 2.66/2.79 tff(25248,plain,
% 2.66/2.79 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25247])).
% 2.66/2.79 tff(25249,plain,
% 2.66/2.79 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25248])).
% 2.66/2.79 tff(25250,plain,
% 2.66/2.79 (~(op(e1, e3) = e1)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[708, 25249])).
% 2.66/2.79 tff(25251,plain,
% 2.66/2.79 (op(e0, e3) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[1495, 10447, 2527, 9246])).
% 2.66/2.79 tff(25252,plain,
% 2.66/2.79 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25251])).
% 2.66/2.79 tff(25253,plain,
% 2.66/2.79 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25252])).
% 2.66/2.79 tff(25254,plain,
% 2.66/2.79 (op(e0, e3) = op(e1, e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25251, 2900])).
% 2.66/2.79 tff(25255,plain,
% 2.66/2.79 (op(e1, op(e0, e3)) = op(e1, op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25254])).
% 2.66/2.79 tff(25256,plain,
% 2.66/2.79 (op(e1, op(e0, e3)) = e2),
% 2.66/2.79 inference(transitivity,[status(thm)],[25255, 9273, 264])).
% 2.66/2.79 tff(25257,plain,
% 2.66/2.79 ((op(e1, op(e0, e3)) = e1) <=> (e2 = e1)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25256])).
% 2.66/2.79 tff(25258,plain,
% 2.66/2.79 ((op(e1, op(e0, e3)) = e1) <=> (e1 = e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25257, 69])).
% 2.66/2.79 tff(25259,plain,
% 2.66/2.79 ((e1 = e2) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25258])).
% 2.66/2.79 tff(25260,plain,
% 2.66/2.79 ((~(e1 = e2)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25259])).
% 2.66/2.79 tff(25261,plain,
% 2.66/2.79 (~(op(e1, op(e0, e3)) = e1)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[708, 25260])).
% 2.66/2.79 tff(25262,plain,
% 2.66/2.79 (op(e0, op(e0, e3)) = op(e0, op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25254])).
% 2.66/2.79 tff(25263,plain,
% 2.66/2.79 (op(e0, op(e0, e3)) = op(e1, e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25262, 9345, 25251, 2900])).
% 2.66/2.79 tff(25264,plain,
% 2.66/2.79 ((op(e0, op(e0, e3)) = e0) <=> (op(e1, e2) = e0)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25263])).
% 2.66/2.79 tff(25265,plain,
% 2.66/2.79 ((op(e1, e2) = e0) <=> (op(e0, op(e0, e3)) = e0)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25264])).
% 2.66/2.79 tff(25266,plain,
% 2.66/2.79 ((~(op(e1, e2) = e0)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25265])).
% 2.66/2.79 tff(25267,plain,
% 2.66/2.79 (~(op(e0, op(e0, e3)) = e0)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[23820, 25266])).
% 2.66/2.79 tff(25268,plain,
% 2.66/2.79 (op(e3, op(e0, e3)) = op(e3, e3)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25251])).
% 2.66/2.79 tff(25269,plain,
% 2.66/2.79 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e3) = e3)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25268])).
% 2.66/2.79 tff(25270,plain,
% 2.66/2.79 ((op(e3, e3) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25269])).
% 2.66/2.79 tff(25271,plain,
% 2.66/2.79 ((~(op(e3, e3) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25270])).
% 2.66/2.79 tff(25272,plain,
% 2.66/2.79 ((op(e0, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25251])).
% 2.66/2.79 tff(25273,plain,
% 2.66/2.79 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25272, 666])).
% 2.66/2.79 tff(25274,plain,
% 2.66/2.79 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25273])).
% 2.66/2.79 tff(25275,plain,
% 2.66/2.79 (~(op(e3, e3) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[1077, 25274])).
% 2.66/2.79 tff(25276,plain,
% 2.66/2.79 (~(op(e3, op(e0, e3)) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25275, 25271])).
% 2.66/2.79 tff(25277,plain,
% 2.66/2.79 (op(e2, op(e0, e3)) = op(e2, op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25254])).
% 2.66/2.79 tff(25278,plain,
% 2.66/2.79 (op(e2, op(e0, e3)) = op(e2, e3)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25277, 9377])).
% 2.66/2.79 tff(25279,plain,
% 2.66/2.79 ((op(e2, op(e0, e3)) = e2) <=> (op(e2, e3) = e2)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25278])).
% 2.66/2.79 tff(25280,plain,
% 2.66/2.79 ((op(e2, e3) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25279])).
% 2.66/2.79 tff(25281,plain,
% 2.66/2.79 ((~(op(e2, e3) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25280])).
% 2.66/2.79 tff(25282,plain,
% 2.66/2.79 (~(op(e2, op(e0, e3)) = e2)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[6598, 25281])).
% 2.66/2.79 tff(25283,plain,
% 2.66/2.79 (~(op(e3, e0) = op(e0, e3))),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[4654, 25282, 121, 25276, 25267, 25261])).
% 2.66/2.79 tff(25284,plain,
% 2.66/2.79 (~(op(e3, e0) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25283, 25253])).
% 2.66/2.79 tff(25285,plain,
% 2.66/2.79 (op(e0, e3) = op(e0, op(e1, e2))),
% 2.66/2.79 inference(symmetry,[status(thm)],[9345])).
% 2.66/2.79 tff(25286,plain,
% 2.66/2.79 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25285])).
% 2.66/2.79 tff(25287,plain,
% 2.66/2.79 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e3) = e0)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25286])).
% 2.66/2.79 tff(25288,plain,
% 2.66/2.79 (op(e0, e0) = e0),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[3612, 10447, 2379, 12721])).
% 2.66/2.79 tff(25289,plain,
% 2.66/2.79 ((op(e0, e0) = op(e0, e3)) <=> (e0 = op(e0, op(e1, e2)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25288, 25285])).
% 2.66/2.79 tff(25290,plain,
% 2.66/2.79 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, op(e1, e2)) = e0)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25289, 14863])).
% 2.66/2.79 tff(25291,plain,
% 2.66/2.79 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25290, 25287])).
% 2.66/2.79 tff(25292,plain,
% 2.66/2.79 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25291])).
% 2.66/2.79 tff(25293,plain,
% 2.66/2.79 (~(op(e0, e3) = e0)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[3414, 25292])).
% 2.66/2.79 tff(25294,plain,
% 2.66/2.79 (op(e2, e3) = e1),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[19997, 25293, 80, 121, 677])).
% 2.66/2.79 tff(25295,plain,
% 2.66/2.79 (~(op(e2, e0) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[24207, 25294])).
% 2.66/2.79 tff(25296,plain,
% 2.66/2.79 (op(e3, e0) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[2713, 25295, 2168, 10447])).
% 2.66/2.79 tff(25297,plain,
% 2.66/2.79 ($false),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[25296, 25284])).
% 2.66/2.79 tff(25298,plain,((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e0, e3) = e1) | (op(e1, e3) = e0) | (~(op(e1, e2) = e3)) | (~(op(e1, e3) = e2)) | (op(e0, e1) = e3) | (op(e0, e0) = e1) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.79 tff(25299,plain,
% 2.66/2.79 (op(e0, e0) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[25298, 12721, 121, 80, 25232, 25228, 2527, 2379, 2168])).
% 2.66/2.79 tff(25300,plain,
% 2.66/2.79 ((op(e0, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25299])).
% 2.66/2.79 tff(25301,plain,
% 2.66/2.79 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25300, 404])).
% 2.66/2.79 tff(25302,plain,
% 2.66/2.79 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25301])).
% 2.66/2.79 tff(25303,plain,
% 2.66/2.79 (~(op(e3, e0) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[6384, 25302])).
% 2.66/2.79 tff(25304,plain,
% 2.66/2.79 ((op(e0, e0) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25299])).
% 2.66/2.79 tff(25305,plain,
% 2.66/2.79 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25304, 1364])).
% 2.66/2.79 tff(25306,plain,
% 2.66/2.79 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25305])).
% 2.66/2.79 tff(25307,plain,
% 2.66/2.79 (~(op(e0, e3) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[3414, 25306])).
% 2.66/2.79 tff(25308,plain,
% 2.66/2.79 (op(e0, e3) = e0),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[687, 25307, 121, 25231])).
% 2.66/2.79 tff(25309,plain,
% 2.66/2.79 (op(e0, e0) = op(e1, e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25299, 25237])).
% 2.66/2.79 tff(25310,plain,
% 2.66/2.79 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25309])).
% 2.66/2.79 tff(25311,plain,
% 2.66/2.79 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25310])).
% 2.66/2.79 tff(25312,plain,
% 2.66/2.79 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25311])).
% 2.66/2.79 tff(25313,plain,
% 2.66/2.79 ((op(e0, e3) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25235, 25312])).
% 2.66/2.79 tff(25314,plain,
% 2.66/2.79 (op(e0, op(e0, e0)) = e0),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25308, 25313])).
% 2.66/2.79 tff(25315,plain,
% 2.66/2.79 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[5598, 25314])).
% 2.66/2.79 tff(25316,plain,
% 2.66/2.79 (op(e3, e3) = e1),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[151, 76, 121, 6651])).
% 2.66/2.79 tff(25317,plain,
% 2.66/2.79 ((op(e3, e3) = e3) <=> (e1 = op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25316, 2900])).
% 2.66/2.79 tff(25318,plain,
% 2.66/2.79 ((op(e3, e3) = e3) <=> (op(e1, e2) = e1)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25317, 5522])).
% 2.66/2.79 tff(25319,plain,
% 2.66/2.79 ((op(e1, e2) = e1) <=> (op(e3, e3) = e3)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25318])).
% 2.66/2.79 tff(25320,plain,
% 2.66/2.79 ((~(op(e1, e2) = e1)) <=> (~(op(e3, e3) = e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25319])).
% 2.66/2.79 tff(25321,plain,
% 2.66/2.79 (~(op(e3, e3) = e3)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[9293, 25320])).
% 2.66/2.79 tff(25322,plain,
% 2.66/2.79 (op(e3, e1) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[422, 25321, 9482, 2410])).
% 2.66/2.79 tff(25323,plain,
% 2.66/2.79 (op(e3, op(e3, e3)) = op(op(e1, e2), e1)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[2900, 25316])).
% 2.66/2.79 tff(25324,plain,
% 2.66/2.79 (e1 = op(e3, e3)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25316])).
% 2.66/2.79 tff(25325,plain,
% 2.66/2.79 ((op(e3, e2) = e1) <=> (op(e3, e2) = op(e3, e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25324])).
% 2.66/2.79 tff(25326,plain,
% 2.66/2.79 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25325])).
% 2.66/2.79 tff(25327,plain,
% 2.66/2.79 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25326])).
% 2.66/2.79 tff(25328,plain,
% 2.66/2.79 (~(op(e3, e2) = e1)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[1888, 25327])).
% 2.66/2.79 tff(25329,plain,
% 2.66/2.79 (op(e0, e2) = e1),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[24286, 25328, 9293])).
% 2.66/2.79 tff(25330,plain,
% 2.66/2.79 (op(e0, e2) = op(e3, e3)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25329, 25324])).
% 2.66/2.79 tff(25331,plain,
% 2.66/2.79 (op(e3, op(e0, e2)) = op(e3, op(e3, e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25330])).
% 2.66/2.79 tff(25332,plain,
% 2.66/2.79 (op(e3, op(e0, e2)) = e3),
% 2.66/2.79 inference(transitivity,[status(thm)],[25331, 25323, 9365, 25322])).
% 2.66/2.79 tff(25333,plain,
% 2.66/2.79 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[5635, 25332])).
% 2.66/2.79 tff(25334,plain,
% 2.66/2.79 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25323, 9365])).
% 2.66/2.79 tff(25335,plain,
% 2.66/2.79 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e1) = e3)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25334])).
% 2.66/2.79 tff(25336,plain,
% 2.66/2.79 ((op(e3, e1) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25335])).
% 2.66/2.79 tff(25337,plain,
% 2.66/2.79 (op(e3, op(e3, e3)) = e3),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25322, 25336])).
% 2.66/2.79 tff(25338,plain,
% 2.66/2.79 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[6277, 25337])).
% 2.66/2.79 tff(25339,plain,
% 2.66/2.79 ((op(e2, e3) = e1) | (op(e3, e2) = e3) | (~(op(e3, e1) = e2)) | (op(e2, e3) = e2) | (op(e0, e3) = e1) | (op(e1, e3) = e1)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[18869, 23804])).
% 2.66/2.79 tff(25340,plain,
% 2.66/2.79 (~(op(e3, e1) = e2)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[25339, 76, 6598, 121, 9482, 6651])).
% 2.66/2.79 tff(25341,plain,
% 2.66/2.79 (~(op(e1, e3) = op(e3, e1))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25340, 19315])).
% 2.66/2.79 tff(25342,plain,
% 2.66/2.79 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[6307, 25341])).
% 2.66/2.79 tff(25343,plain,
% 2.66/2.79 (op(e3, e2) = e2),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[24167, 25328, 9482])).
% 2.66/2.79 tff(25344,plain,
% 2.66/2.79 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25343])).
% 2.66/2.79 tff(25345,plain,
% 2.66/2.79 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25344])).
% 2.66/2.79 tff(25346,plain,
% 2.66/2.79 (~(op(e0, e2) = e2)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[1467, 25345])).
% 2.66/2.79 tff(25347,plain,
% 2.66/2.79 (op(e0, e1) = e2),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[3652, 25346, 677, 12721])).
% 2.66/2.79 tff(25348,plain,
% 2.66/2.79 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25347])).
% 2.66/2.79 tff(25349,plain,
% 2.66/2.79 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.66/2.79 inference(symmetry,[status(thm)],[25348])).
% 2.66/2.79 tff(25350,plain,
% 2.66/2.79 ((op(e1, e0) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 2.66/2.79 inference(transitivity,[status(thm)],[25349, 596])).
% 2.66/2.79 tff(25351,plain,
% 2.66/2.79 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25350])).
% 2.66/2.79 tff(25352,plain,
% 2.66/2.79 (~(op(e0, e1) = op(e1, e0))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[6687, 25351])).
% 2.66/2.79 tff(25353,plain,
% 2.66/2.79 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[609, 25352])).
% 2.66/2.79 tff(25354,plain,
% 2.66/2.79 (op(e2, e3) = e3),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[12598, 76, 80, 121, 677])).
% 2.66/2.79 tff(25355,plain,
% 2.66/2.79 (op(e2, e3) = op(e1, e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25354, 2900])).
% 2.66/2.79 tff(25356,plain,
% 2.66/2.79 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25355])).
% 2.66/2.79 tff(25357,plain,
% 2.66/2.79 ((op(e3, e2) = op(e2, e3)) <=> (op(e1, e2) = op(e3, e2))),
% 2.66/2.79 inference(transitivity,[status(thm)],[25356, 3635])).
% 2.66/2.79 tff(25358,plain,
% 2.66/2.79 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.66/2.79 inference(symmetry,[status(thm)],[25357])).
% 2.66/2.79 tff(25359,plain,
% 2.66/2.79 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25358])).
% 2.66/2.79 tff(25360,plain,
% 2.66/2.79 (~(op(e3, e2) = op(e2, e3))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[2292, 25359])).
% 2.66/2.79 tff(25361,plain,
% 2.66/2.79 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[500, 25360])).
% 2.66/2.79 tff(25362,plain,
% 2.66/2.79 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25355])).
% 2.66/2.79 tff(25363,plain,
% 2.66/2.79 ((op(e2, e1) = op(e2, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.66/2.79 inference(transitivity,[status(thm)],[25362, 531])).
% 2.66/2.79 tff(25364,plain,
% 2.66/2.79 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25363])).
% 2.66/2.79 tff(25365,plain,
% 2.66/2.79 (~(op(e1, e2) = op(e2, e1))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[197, 25364])).
% 2.66/2.79 tff(25366,plain,
% 2.66/2.79 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[539, 25365])).
% 2.66/2.79 tff(25367,plain,
% 2.66/2.79 ((~(op(e1, e0) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25349])).
% 2.66/2.79 tff(25368,plain,
% 2.66/2.79 (~(op(e1, e0) = op(e0, e1))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[6687, 25367])).
% 2.66/2.79 tff(25369,plain,
% 2.66/2.79 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[613, 25368])).
% 2.66/2.79 tff(25370,plain,
% 2.66/2.79 (~(op(e3, e1) = op(e1, e3))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[25340, 19311])).
% 2.66/2.79 tff(25371,plain,
% 2.66/2.79 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[6362, 25370])).
% 2.66/2.79 tff(25372,plain,
% 2.66/2.79 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.66/2.79 inference(transitivity,[status(thm)],[25358, 395])).
% 2.66/2.79 tff(25373,plain,
% 2.66/2.79 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25372])).
% 2.66/2.79 tff(25374,plain,
% 2.66/2.79 (~(op(e2, e3) = op(e3, e2))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[2292, 25373])).
% 2.66/2.79 tff(25375,plain,
% 2.66/2.79 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[430, 25374])).
% 2.66/2.79 tff(25376,plain,
% 2.66/2.79 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e1)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25329])).
% 2.66/2.79 tff(25377,plain,
% 2.66/2.79 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e0, e2))),
% 2.66/2.79 inference(symmetry,[status(thm)],[25376])).
% 2.66/2.79 tff(25378,plain,
% 2.66/2.79 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e2)),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25343])).
% 2.66/2.79 tff(25379,plain,
% 2.66/2.79 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e2))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25378])).
% 2.66/2.79 tff(25380,plain,
% 2.66/2.79 (~(op(e3, e0) = e2)),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[1133, 25379])).
% 2.66/2.79 tff(25381,plain,
% 2.66/2.79 (op(e2, e0) = e2),
% 2.66/2.79 inference(unit_resolution,[status(thm)],[589, 25380, 6687, 12721])).
% 2.66/2.79 tff(25382,plain,
% 2.66/2.79 ((op(e2, e0) = e1) <=> (e2 = op(e3, e3))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25381, 25324])).
% 2.66/2.79 tff(25383,plain,
% 2.66/2.79 ((op(e2, e0) = e1) <=> (op(e3, e3) = e2)),
% 2.66/2.79 inference(transitivity,[status(thm)],[25382, 565])).
% 2.66/2.79 tff(25384,plain,
% 2.66/2.79 ((op(e3, e3) = e2) <=> (op(e2, e0) = e1)),
% 2.66/2.79 inference(symmetry,[status(thm)],[25383])).
% 2.66/2.79 tff(25385,plain,
% 2.66/2.79 ((op(e3, e3) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.66/2.79 inference(transitivity,[status(thm)],[25384, 25377, 6337])).
% 2.66/2.79 tff(25386,plain,
% 2.66/2.79 ((~(op(e3, e3) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.66/2.79 inference(monotonicity,[status(thm)],[25385])).
% 2.66/2.79 tff(25387,plain,
% 2.66/2.79 (~(op(e0, e2) = op(e2, e0))),
% 2.66/2.79 inference(modus_ponens,[status(thm)],[15002, 25386])).
% 2.66/2.79 tff(25388,plain,
% 2.66/2.79 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[6347, 25387])).
% 2.66/2.80 tff(25389,plain,
% 2.66/2.80 (op(e0, op(e1, e2)) = e0),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[771, 25286])).
% 2.66/2.80 tff(25390,plain,
% 2.66/2.80 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[6398, 25389])).
% 2.66/2.80 tff(25391,plain,
% 2.66/2.80 (op(e2, op(e2, e2)) = e2),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[25381, 23905])).
% 2.66/2.80 tff(25392,plain,
% 2.66/2.80 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[528, 25391])).
% 2.66/2.80 tff(25393,plain,
% 2.66/2.80 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[771])).
% 2.66/2.80 tff(25394,plain,
% 2.66/2.80 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25393])).
% 2.66/2.80 tff(25395,plain,
% 2.66/2.80 (~(op(e0, e1) = e0)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[818, 25394])).
% 2.66/2.80 tff(25396,plain,
% 2.66/2.80 (op(e3, e1) = op(e1, e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25322, 2900])).
% 2.66/2.80 tff(25397,plain,
% 2.66/2.80 ((op(e3, e1) = e0) <=> (op(e1, e2) = e0)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25396])).
% 2.66/2.80 tff(25398,plain,
% 2.66/2.80 ((op(e1, e2) = e0) <=> (op(e3, e1) = e0)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25397])).
% 2.66/2.80 tff(25399,plain,
% 2.66/2.80 ((~(op(e1, e2) = e0)) <=> (~(op(e3, e1) = e0))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25398])).
% 2.66/2.80 tff(25400,plain,
% 2.66/2.80 (~(op(e3, e1) = e0)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[23820, 25399])).
% 2.66/2.80 tff(25401,plain,
% 2.66/2.80 (op(e1, e1) = e0),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[23988, 25400, 25395])).
% 2.66/2.80 tff(25402,plain,
% 2.66/2.80 (op(e2, op(e1, e1)) = op(e2, e0)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25401])).
% 2.66/2.80 tff(25403,plain,
% 2.66/2.80 (op(e2, op(e1, e1)) = e2),
% 2.66/2.80 inference(transitivity,[status(thm)],[25402, 25381])).
% 2.66/2.80 tff(25404,plain,
% 2.66/2.80 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[16830, 25403])).
% 2.66/2.80 tff(25405,plain,
% 2.66/2.80 ((~(op(e0, e3) = e0)) | (op(e3, e1) = e0) | (op(e3, e0) = op(e0, e3))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[5538, 24134])).
% 2.66/2.80 tff(25406,plain,
% 2.66/2.80 (op(e3, e0) = op(e0, e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[25405, 25400, 771])).
% 2.66/2.80 tff(25407,plain,
% 2.66/2.80 (op(e3, e0) = e0),
% 2.66/2.80 inference(transitivity,[status(thm)],[25406, 771])).
% 2.66/2.80 tff(25408,plain,
% 2.66/2.80 (op(e2, op(e3, e0)) = op(e2, e0)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25407])).
% 2.66/2.80 tff(25409,plain,
% 2.66/2.80 (op(e2, op(e3, e0)) = e2),
% 2.66/2.80 inference(transitivity,[status(thm)],[25408, 25381])).
% 2.66/2.80 tff(25410,plain,
% 2.66/2.80 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[23461, 25409])).
% 2.66/2.80 tff(25411,plain,
% 2.66/2.80 ($false),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[5367, 25410, 25404, 25392, 5667, 25390, 25388, 25375, 25371, 25369, 25366, 25361, 25353, 25342, 25338, 25333])).
% 2.66/2.80 tff(25412,plain,((op(e2, e3) = e1) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (op(e1, e0) = e2) | (~(op(e0, e3) = e0)) | (op(e0, e0) = e2) | (~(op(e1, e2) = e3)) | (op(e3, e0) = e3) | (~(op(e1, e3) = e2)) | (op(e0, e3) = e1) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.80 tff(25413,plain,
% 2.66/2.80 (op(e2, e3) = e1),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[25412, 25315, 6687, 25308, 12721, 25232, 25303, 25228, 121, 80])).
% 2.66/2.80 tff(25414,plain,
% 2.66/2.80 (e1 = op(e2, e3)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25413])).
% 2.66/2.80 tff(25415,plain,
% 2.66/2.80 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25299])).
% 2.66/2.80 tff(25416,plain,
% 2.66/2.80 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25415, 660])).
% 2.66/2.80 tff(25417,plain,
% 2.66/2.80 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25416])).
% 2.66/2.80 tff(25418,plain,
% 2.66/2.80 (~(op(e2, e0) = e3)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[359, 25417])).
% 2.66/2.80 tff(25419,plain,
% 2.66/2.80 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e2, e3))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25414])).
% 2.66/2.80 tff(25420,plain,
% 2.66/2.80 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e1)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25419])).
% 2.66/2.80 tff(25421,plain,
% 2.66/2.80 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e1))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25420])).
% 2.66/2.80 tff(25422,plain,
% 2.66/2.80 (~(op(e2, e0) = e1)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[989, 25421])).
% 2.66/2.80 tff(25423,plain,
% 2.66/2.80 (op(e2, e0) = e2),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[24100, 25422, 25418])).
% 2.66/2.80 tff(25424,plain,
% 2.66/2.80 ((op(e2, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25423])).
% 2.66/2.80 tff(25425,plain,
% 2.66/2.80 ((op(e2, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25424, 3491])).
% 2.66/2.80 tff(25426,plain,
% 2.66/2.80 ((op(e0, e2) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.66/2.80 inference(symmetry,[status(thm)],[25425])).
% 2.66/2.80 tff(25427,plain,
% 2.66/2.80 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.80 tff(25428,plain,
% 2.66/2.80 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25427, 120])).
% 2.66/2.80 tff(25429,plain,
% 2.66/2.80 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25428])).
% 2.66/2.80 tff(25430,plain,
% 2.66/2.80 (~(op(e2, e3) = e2)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[118, 25429])).
% 2.66/2.80 tff(25431,plain,
% 2.66/2.80 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25423])).
% 2.66/2.80 tff(25432,plain,
% 2.66/2.80 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25431, 5377])).
% 2.66/2.80 tff(25433,plain,
% 2.66/2.80 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25432])).
% 2.66/2.80 tff(25434,plain,
% 2.66/2.80 (~(op(e3, e0) = e2)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[747, 25433])).
% 2.66/2.80 tff(25435,plain,
% 2.66/2.80 (op(e1, op(e1, e2)) = op(e1, e3)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25232])).
% 2.66/2.80 tff(25436,plain,
% 2.66/2.80 (op(e1, op(e1, e2)) = e2),
% 2.66/2.80 inference(transitivity,[status(thm)],[25435, 25228])).
% 2.66/2.80 tff(25437,plain,
% 2.66/2.80 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[2377, 25436])).
% 2.66/2.80 tff(25438,plain,
% 2.66/2.80 (op(e2, op(e1, e2)) = op(e2, e3)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25232])).
% 2.66/2.80 tff(25439,plain,
% 2.66/2.80 ((op(e2, e3) = e3) <=> (e1 = op(e1, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25413, 25237])).
% 2.66/2.80 tff(25440,plain,
% 2.66/2.80 ((op(e2, e3) = e3) <=> (op(e1, e2) = e1)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25439, 5522])).
% 2.66/2.80 tff(25441,plain,
% 2.66/2.80 ((op(e1, e2) = e1) <=> (op(e2, e3) = e3)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25440])).
% 2.66/2.80 tff(25442,plain,
% 2.66/2.80 ((~(op(e1, e2) = e1)) <=> (~(op(e2, e3) = e3))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25441])).
% 2.66/2.80 tff(25443,plain,
% 2.66/2.80 (~(op(e2, e3) = e3)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[25245, 25442])).
% 2.66/2.80 tff(25444,plain,
% 2.66/2.80 (op(e2, e1) = e3),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[23641, 25443, 25418])).
% 2.66/2.80 tff(25445,plain,
% 2.66/2.80 (op(e2, e1) = op(e1, e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25444, 25237])).
% 2.66/2.80 tff(25446,plain,
% 2.66/2.80 (op(e2, op(e2, e1)) = op(e2, op(e1, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25445])).
% 2.66/2.80 tff(25447,plain,
% 2.66/2.80 (op(e2, op(e2, e1)) = e1),
% 2.66/2.80 inference(transitivity,[status(thm)],[25446, 25438, 25413])).
% 2.66/2.80 tff(25448,plain,
% 2.66/2.80 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1355, 25447])).
% 2.66/2.80 tff(25449,plain,
% 2.66/2.80 (op(e2, op(e2, e0)) = e0),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[23913, 25423])).
% 2.66/2.80 tff(25450,plain,
% 2.66/2.80 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[2653, 25449])).
% 2.66/2.80 tff(25451,plain,
% 2.66/2.80 (op(e1, op(e1, e3)) = op(e1, e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.80 tff(25452,plain,
% 2.66/2.80 ((op(e1, op(e1, e3)) = e3) <=> (op(e1, e2) = e3)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25451])).
% 2.66/2.80 tff(25453,plain,
% 2.66/2.80 ((op(e1, e2) = e3) <=> (op(e1, op(e1, e3)) = e3)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25452])).
% 2.66/2.80 tff(25454,plain,
% 2.66/2.80 (op(e1, op(e1, e3)) = e3),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[25232, 25453])).
% 2.66/2.80 tff(25455,plain,
% 2.66/2.80 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[162, 25454])).
% 2.66/2.80 tff(25456,plain,
% 2.66/2.80 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[5468, 25231, 121])).
% 2.66/2.80 tff(25457,plain,
% 2.66/2.80 (op(op(e2, e3), e3) = op(e1, op(e1, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25413, 25237])).
% 2.66/2.80 tff(25458,plain,
% 2.66/2.80 (op(op(e2, e3), e3) = e2),
% 2.66/2.80 inference(transitivity,[status(thm)],[25457, 25435, 25228])).
% 2.66/2.80 tff(25459,plain,
% 2.66/2.80 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1288, 25458])).
% 2.66/2.80 tff(25460,plain,
% 2.66/2.80 (op(e3, e2) = e1),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[24286, 4484, 9293])).
% 2.66/2.80 tff(25461,plain,
% 2.66/2.80 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25460])).
% 2.66/2.80 tff(25462,plain,
% 2.66/2.80 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25461])).
% 2.66/2.80 tff(25463,plain,
% 2.66/2.80 (~(op(e3, e0) = e1)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[1133, 25462])).
% 2.66/2.80 tff(25464,plain,
% 2.66/2.80 (op(e3, e0) = e0),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[5422, 25463, 2410, 3786])).
% 2.66/2.80 tff(25465,plain,
% 2.66/2.80 (op(e3, op(e3, e0)) = op(e3, e0)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25464])).
% 2.66/2.80 tff(25466,plain,
% 2.66/2.80 (op(e3, op(e3, e0)) = e0),
% 2.66/2.80 inference(transitivity,[status(thm)],[25465, 25464])).
% 2.66/2.80 tff(25467,plain,
% 2.66/2.80 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1345, 25466])).
% 2.66/2.80 tff(25468,plain,
% 2.66/2.80 (op(e3, e2) = op(e2, e3)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25460, 2685])).
% 2.66/2.80 tff(25469,plain,
% 2.66/2.80 (op(op(e3, e2), e2) = op(op(e2, e3), e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25468])).
% 2.66/2.80 tff(25470,plain,
% 2.66/2.80 (op(op(e3, e2), e2) = e3),
% 2.66/2.80 inference(transitivity,[status(thm)],[25469, 2897, 2899])).
% 2.66/2.80 tff(25471,plain,
% 2.66/2.80 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1339, 25470])).
% 2.66/2.80 tff(25472,plain,
% 2.66/2.80 (op(e0, e2) = e2),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[23880, 4484, 9246])).
% 2.66/2.80 tff(25473,plain,
% 2.66/2.80 (op(e0, op(e0, e2)) = op(e0, e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25472])).
% 2.66/2.80 tff(25474,plain,
% 2.66/2.80 (op(e0, op(e0, e2)) = e2),
% 2.66/2.80 inference(transitivity,[status(thm)],[25473, 25472])).
% 2.66/2.80 tff(25475,plain,
% 2.66/2.80 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1331, 25474])).
% 2.66/2.80 tff(25476,plain,
% 2.66/2.80 (op(e0, e1) = e1),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[384, 4484, 121, 2379])).
% 2.66/2.80 tff(25477,plain,
% 2.66/2.80 (op(e0, e1) = op(e2, e3)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25476, 2685])).
% 2.66/2.80 tff(25478,plain,
% 2.66/2.80 (op(e0, op(e0, e1)) = op(e0, op(e2, e3))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25477])).
% 2.66/2.80 tff(25479,plain,
% 2.66/2.80 (op(e0, op(e0, e1)) = e1),
% 2.66/2.80 inference(transitivity,[status(thm)],[25478, 4447, 25476])).
% 2.66/2.80 tff(25480,plain,
% 2.66/2.80 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[2449, 25479])).
% 2.66/2.80 tff(25481,plain,
% 2.66/2.80 ((op(e3, e2) = e2) <=> (op(e2, e3) = e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25468])).
% 2.66/2.80 tff(25482,plain,
% 2.66/2.80 ((op(e2, e3) = e2) <=> (op(e3, e2) = e2)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25481])).
% 2.66/2.80 tff(25483,plain,
% 2.66/2.80 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e2) = e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25482])).
% 2.66/2.80 tff(25484,plain,
% 2.66/2.80 (~(op(e3, e2) = e2)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[4382, 25483])).
% 2.66/2.80 tff(25485,plain,
% 2.66/2.80 (op(e3, e1) = e2),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[15971, 25484, 3786])).
% 2.66/2.80 tff(25486,plain,
% 2.66/2.80 (op(e3, op(e3, e1)) = op(op(e1, e2), e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[2900, 25485])).
% 2.66/2.80 tff(25487,plain,
% 2.66/2.80 (op(e3, op(e3, e1)) = e1),
% 2.66/2.80 inference(transitivity,[status(thm)],[25486, 9338, 25460])).
% 2.66/2.80 tff(25488,plain,
% 2.66/2.80 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[2594, 25487])).
% 2.66/2.80 tff(25489,plain,
% 2.66/2.80 ((op(e0, e1) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25476])).
% 2.66/2.80 tff(25490,plain,
% 2.66/2.80 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25489, 8462])).
% 2.66/2.80 tff(25491,plain,
% 2.66/2.80 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25490])).
% 2.66/2.80 tff(25492,plain,
% 2.66/2.80 (~(op(e1, e1) = e1)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[792, 25491])).
% 2.66/2.80 tff(25493,plain,
% 2.66/2.80 (op(e1, e1) = e0),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[630, 25492, 68, 1291])).
% 2.66/2.80 tff(25494,plain,
% 2.66/2.80 (op(e1, e0) = e1),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1480, 25463, 2379, 2689])).
% 2.66/2.80 tff(25495,plain,
% 2.66/2.80 (op(e1, op(e1, e0)) = op(e1, e1)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25494])).
% 2.66/2.80 tff(25496,plain,
% 2.66/2.80 (op(e1, op(e1, e0)) = e0),
% 2.66/2.80 inference(transitivity,[status(thm)],[25495, 25493])).
% 2.66/2.80 tff(25497,plain,
% 2.66/2.80 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1836, 25496])).
% 2.66/2.80 tff(25498,plain,
% 2.66/2.80 ($false),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[1459, 25497, 25488, 3342, 1347, 25480, 1304, 25475, 25471, 2421, 1936, 1358, 25467])).
% 2.66/2.80 tff(25499,plain,((op(e0, e2) = e1) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~(op(e1, e2) = e3)) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e3, e0) = e3) | (op(e3, e0) = e2) | (op(e0, e0) = e1) | (~(op(e2, e3) = e1)) | (op(e2, e3) = e2) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.80 tff(25500,plain,
% 2.66/2.80 (op(e0, e2) = e1),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[25499, 25459, 25456, 25455, 25450, 25448, 25437, 25232, 68, 1291, 25303, 25434, 2379, 25413, 25430, 121])).
% 2.66/2.80 tff(25501,plain,
% 2.66/2.80 (op(e0, e2) = op(e2, e3)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25500, 25414])).
% 2.66/2.80 tff(25502,plain,
% 2.66/2.80 ((op(e0, e2) = e2) <=> (op(e2, e3) = e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25501])).
% 2.66/2.80 tff(25503,plain,
% 2.66/2.80 ((op(e2, e3) = e2) <=> (op(e0, e2) = e2)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25502])).
% 2.66/2.80 tff(25504,plain,
% 2.66/2.80 ((op(e2, e3) = e2) <=> (op(e2, e0) = op(e0, e2))),
% 2.66/2.80 inference(transitivity,[status(thm)],[25503, 25426])).
% 2.66/2.80 tff(25505,plain,
% 2.66/2.80 ((~(op(e2, e3) = e2)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25504])).
% 2.66/2.80 tff(25506,plain,
% 2.66/2.80 (~(op(e2, e0) = op(e0, e2))),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[25430, 25505])).
% 2.66/2.80 tff(25507,plain,
% 2.66/2.80 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[6358, 25506])).
% 2.66/2.80 tff(25508,plain,
% 2.66/2.80 (op(e3, e3) = e3),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[480, 25443, 1080, 25307])).
% 2.66/2.80 tff(25509,plain,
% 2.66/2.80 (op(e3, e3) = op(e1, e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25508, 25237])).
% 2.66/2.80 tff(25510,plain,
% 2.66/2.80 (op(e0, op(e3, e3)) = op(e0, op(e1, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25509])).
% 2.66/2.80 tff(25511,plain,
% 2.66/2.80 (op(e0, op(e3, e3)) = e0),
% 2.66/2.80 inference(transitivity,[status(thm)],[25510, 25233, 25308])).
% 2.66/2.80 tff(25512,plain,
% 2.66/2.80 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[392, 25511])).
% 2.66/2.80 tff(25513,plain,
% 2.66/2.80 ((op(e3, e1) = op(e1, e3)) <=> (op(e3, e1) = e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.80 tff(25514,plain,
% 2.66/2.80 ((op(e3, e1) = e2) <=> (op(e3, e1) = op(e1, e3))),
% 2.66/2.80 inference(symmetry,[status(thm)],[25513])).
% 2.66/2.80 tff(25515,plain,
% 2.66/2.80 (op(op(e1, e2), e1) = op(e3, e1)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25232])).
% 2.66/2.80 tff(25516,plain,
% 2.66/2.80 (op(e3, e1) = op(op(e1, e2), e1)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25515])).
% 2.66/2.80 tff(25517,plain,
% 2.66/2.80 ((op(e3, e1) = e2) <=> (op(op(e1, e2), e1) = e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25516])).
% 2.66/2.80 tff(25518,plain,
% 2.66/2.80 ((op(op(e1, e2), e1) = e2) <=> (op(e3, e1) = e2)),
% 2.66/2.80 inference(symmetry,[status(thm)],[25517])).
% 2.66/2.80 tff(25519,plain,
% 2.66/2.80 ((e2 = op(op(e1, e2), e1)) <=> (op(op(e1, e2), e1) = e2)),
% 2.66/2.80 inference(commutativity,[status(thm)],[])).
% 2.66/2.80 tff(25520,plain,
% 2.66/2.80 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e2) = e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25503])).
% 2.66/2.80 tff(25521,plain,
% 2.66/2.80 (~(op(e0, e2) = e2)),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[25430, 25520])).
% 2.66/2.80 tff(25522,plain,
% 2.66/2.80 (op(e0, e1) = e2),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[3652, 25521, 25231, 12721])).
% 2.66/2.80 tff(25523,plain,
% 2.66/2.80 ((op(e0, e1) = op(e3, e1)) <=> (e2 = op(op(e1, e2), e1))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25522, 25516])).
% 2.66/2.80 tff(25524,plain,
% 2.66/2.80 ((op(e0, e1) = op(e3, e1)) <=> (op(op(e1, e2), e1) = e2)),
% 2.66/2.80 inference(transitivity,[status(thm)],[25523, 25519])).
% 2.66/2.80 tff(25525,plain,
% 2.66/2.80 ((op(e0, e1) = op(e3, e1)) <=> (op(e1, e3) = op(e3, e1))),
% 2.66/2.80 inference(transitivity,[status(thm)],[25524, 25518, 25514, 6290])).
% 2.66/2.80 tff(25526,plain,
% 2.66/2.80 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25525])).
% 2.66/2.80 tff(25527,plain,
% 2.66/2.80 (~(op(e1, e3) = op(e3, e1))),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[3046, 25526])).
% 2.66/2.80 tff(25528,plain,
% 2.66/2.80 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[6307, 25527])).
% 2.66/2.80 tff(25529,plain,
% 2.66/2.80 ((op(e1, e0) = op(e0, e1)) <=> (op(e1, e0) = e2)),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25522])).
% 2.66/2.80 tff(25530,plain,
% 2.66/2.80 ((op(e1, e0) = e2) <=> (op(e1, e0) = op(e0, e1))),
% 2.66/2.80 inference(symmetry,[status(thm)],[25529])).
% 2.66/2.80 tff(25531,plain,
% 2.66/2.80 ((op(e1, e0) = e2) <=> (op(e0, e1) = op(e1, e0))),
% 2.66/2.80 inference(transitivity,[status(thm)],[25530, 596])).
% 2.66/2.80 tff(25532,plain,
% 2.66/2.80 ((~(op(e1, e0) = e2)) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25531])).
% 2.66/2.80 tff(25533,plain,
% 2.66/2.80 (~(op(e0, e1) = op(e1, e0))),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[6687, 25532])).
% 2.66/2.80 tff(25534,plain,
% 2.66/2.80 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[609, 25533])).
% 2.66/2.80 tff(25535,plain,
% 2.66/2.80 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25501])).
% 2.66/2.80 tff(25536,plain,
% 2.66/2.80 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.66/2.80 inference(transitivity,[status(thm)],[25535, 394])).
% 2.66/2.80 tff(25537,plain,
% 2.66/2.80 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.66/2.80 inference(monotonicity,[status(thm)],[25536])).
% 2.66/2.80 tff(25538,plain,
% 2.66/2.80 (~(op(e3, e2) = op(e2, e3))),
% 2.66/2.80 inference(modus_ponens,[status(thm)],[1467, 25537])).
% 2.66/2.80 tff(25539,plain,
% 2.66/2.80 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.66/2.80 inference(unit_resolution,[status(thm)],[500, 25538])).
% 2.66/2.80 tff(25540,plain,
% 2.66/2.80 (op(e0, op(e2, e1)) = op(e0, op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25445])).
% 2.66/2.81 tff(25541,plain,
% 2.66/2.81 (op(e0, op(e2, e1)) = e0),
% 2.66/2.81 inference(transitivity,[status(thm)],[25540, 25233, 25308])).
% 2.66/2.81 tff(25542,plain,
% 2.66/2.81 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[13223, 25541])).
% 2.66/2.81 tff(25543,plain,
% 2.66/2.81 ((~(op(e1, e0) = e2)) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25530])).
% 2.66/2.81 tff(25544,plain,
% 2.66/2.81 (~(op(e1, e0) = op(e0, e1))),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[6687, 25543])).
% 2.66/2.81 tff(25545,plain,
% 2.66/2.81 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[613, 25544])).
% 2.66/2.81 tff(25546,plain,
% 2.66/2.81 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 2.66/2.81 inference(transitivity,[status(thm)],[25524, 25518, 25514])).
% 2.66/2.81 tff(25547,plain,
% 2.66/2.81 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25546])).
% 2.66/2.81 tff(25548,plain,
% 2.66/2.81 (~(op(e3, e1) = op(e1, e3))),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[3046, 25547])).
% 2.66/2.81 tff(25549,plain,
% 2.66/2.81 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[6362, 25548])).
% 2.66/2.81 tff(25550,plain,
% 2.66/2.81 ((op(e0, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.66/2.81 inference(transitivity,[status(thm)],[25536, 395])).
% 2.66/2.81 tff(25551,plain,
% 2.66/2.81 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25550])).
% 2.66/2.81 tff(25552,plain,
% 2.66/2.81 (~(op(e2, e3) = op(e3, e2))),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[1467, 25551])).
% 2.66/2.81 tff(25553,plain,
% 2.66/2.81 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[430, 25552])).
% 2.66/2.81 tff(25554,plain,
% 2.66/2.81 ((op(e2, e3) = e2) <=> (op(e0, e2) = op(e2, e0))),
% 2.66/2.81 inference(transitivity,[status(thm)],[25503, 25426, 6337])).
% 2.66/2.81 tff(25555,plain,
% 2.66/2.81 ((~(op(e2, e3) = e2)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25554])).
% 2.66/2.81 tff(25556,plain,
% 2.66/2.81 (~(op(e0, e2) = op(e2, e0))),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[25430, 25555])).
% 2.66/2.81 tff(25557,plain,
% 2.66/2.81 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[6347, 25556])).
% 2.66/2.81 tff(25558,plain,
% 2.66/2.81 (op(e0, op(e1, e2)) = e0),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[25308, 25235])).
% 2.66/2.81 tff(25559,plain,
% 2.66/2.81 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[6398, 25558])).
% 2.66/2.81 tff(25560,plain,
% 2.66/2.81 (op(e2, op(e2, e2)) = e2),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[25423, 23905])).
% 2.66/2.81 tff(25561,plain,
% 2.66/2.81 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[528, 25560])).
% 2.66/2.81 tff(25562,plain,
% 2.66/2.81 (op(e1, e0) = e0),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[24723, 84, 80])).
% 2.66/2.81 tff(25563,plain,
% 2.66/2.81 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25562])).
% 2.66/2.81 tff(25564,plain,
% 2.66/2.81 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25563, 8115])).
% 2.66/2.81 tff(25565,plain,
% 2.66/2.81 ((op(e1, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.66/2.81 inference(transitivity,[status(thm)],[25564, 5533, 453])).
% 2.66/2.81 tff(25566,plain,
% 2.66/2.81 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25565])).
% 2.66/2.81 tff(25567,plain,
% 2.66/2.81 (~(op(e0, e3) = op(e3, e0))),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[410, 25566])).
% 2.66/2.81 tff(25568,plain,
% 2.66/2.81 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[496, 25567])).
% 2.66/2.81 tff(25569,plain,
% 2.66/2.81 ($false),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[5367, 20636, 25568, 5672, 5667, 5680, 9846, 5668, 5511, 5675, 5673, 5671, 5681, 5669, 6688, 5674])).
% 2.66/2.81 tff(25570,plain,((op(e1, e1) = e0) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3))) | (~((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~(op(e0, e3) = e0)) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.81 tff(25571,plain,
% 2.66/2.81 (op(e1, e1) = e0),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[25570, 25561, 25315, 25559, 25557, 25553, 25549, 25545, 25542, 25539, 25534, 25528, 25512, 25507, 25308, 68, 1291, 80])).
% 2.66/2.81 tff(25572,plain,
% 2.66/2.81 ((op(e1, e1) = e1) <=> (e0 = op(e2, e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25571, 25414])).
% 2.66/2.81 tff(25573,plain,
% 2.66/2.81 ((op(e1, e1) = e1) <=> (op(e2, e3) = e0)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25572, 86])).
% 2.66/2.81 tff(25574,plain,
% 2.66/2.81 ((op(e2, e3) = e0) <=> (op(e1, e1) = e1)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25573])).
% 2.66/2.81 tff(25575,plain,
% 2.66/2.81 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e1) = e1))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25574])).
% 2.66/2.81 tff(25576,plain,
% 2.66/2.81 (~(op(e1, e1) = e1)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[23804, 25575])).
% 2.66/2.81 tff(25577,plain,
% 2.66/2.81 (op(e1, e0) = e1),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[954, 25576, 25250, 25245])).
% 2.66/2.81 tff(25578,plain,
% 2.66/2.81 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25571])).
% 2.66/2.81 tff(25579,plain,
% 2.66/2.81 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25578, 5470])).
% 2.66/2.81 tff(25580,plain,
% 2.66/2.81 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25579])).
% 2.66/2.81 tff(25581,plain,
% 2.66/2.81 (~(op(e3, e1) = e0)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[945, 25580])).
% 2.66/2.81 tff(25582,plain,
% 2.66/2.81 (op(e3, e0) = op(e0, e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[25405, 25581, 25308])).
% 2.66/2.81 tff(25583,plain,
% 2.66/2.81 (op(e3, e0) = e0),
% 2.66/2.81 inference(transitivity,[status(thm)],[25582, 25308])).
% 2.66/2.81 tff(25584,plain,
% 2.66/2.81 (op(e1, op(e3, e0)) = op(e1, e0)),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25583])).
% 2.66/2.81 tff(25585,plain,
% 2.66/2.81 (op(e1, op(e3, e0)) = e1),
% 2.66/2.81 inference(transitivity,[status(thm)],[25584, 25577])).
% 2.66/2.81 tff(25586,plain,
% 2.66/2.81 (op(e2, op(e1, e1)) = op(e2, e0)),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25571])).
% 2.66/2.81 tff(25587,plain,
% 2.66/2.81 (op(e2, op(e1, e1)) = e2),
% 2.66/2.81 inference(transitivity,[status(thm)],[25586, 25423])).
% 2.66/2.81 tff(25588,plain,
% 2.66/2.81 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[16830, 25587])).
% 2.66/2.81 tff(25589,plain,
% 2.66/2.81 (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[5367, 25588, 25561, 25315, 25559, 25557, 25553, 25549, 25545, 25542, 25539, 25534, 25528, 25512, 25507])).
% 2.66/2.81 tff(25590,plain,
% 2.66/2.81 (~(op(e1, op(e3, e0)) = e1)),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[8474, 25589])).
% 2.66/2.81 tff(25591,plain,
% 2.66/2.81 ($false),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[25590, 25585])).
% 2.66/2.81 tff(25592,plain,((op(e0, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e1) = e3) | (op(e1, e3) = e0) | (op(e1, e0) = e2) | (op(e0, e0) = e1) | (op(e0, e3) = e1) | (op(e1, e3) = e3) | (op(e0, e1) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.81 tff(25593,plain,
% 2.66/2.81 (op(e0, e0) = e2),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[25592, 1291, 68, 80, 6687, 2379, 121, 1080, 2527, 2168])).
% 2.66/2.81 tff(25594,plain,
% 2.66/2.81 ((op(e0, e0) = e3) <=> (e2 = op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25593, 25237])).
% 2.66/2.81 tff(25595,plain,
% 2.66/2.81 ((op(e0, e0) = e3) <=> (op(e1, e2) = e2)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25594, 5762])).
% 2.66/2.81 tff(25596,plain,
% 2.66/2.81 ((op(e1, e2) = e2) <=> (op(e0, e0) = e3)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25595])).
% 2.66/2.81 tff(25597,plain,
% 2.66/2.81 ((~(op(e1, e2) = e2)) <=> (~(op(e0, e0) = e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25596])).
% 2.66/2.81 tff(25598,plain,
% 2.66/2.81 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25228])).
% 2.66/2.81 tff(25599,plain,
% 2.66/2.81 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25598])).
% 2.66/2.81 tff(25600,plain,
% 2.66/2.81 (~(op(e1, e2) = e2)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[1850, 25599])).
% 2.66/2.81 tff(25601,plain,
% 2.66/2.81 (~(op(e0, e0) = e3)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[25600, 25597])).
% 2.66/2.81 tff(25602,plain,
% 2.66/2.81 (op(e0, e3) = e3),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[1495, 25601, 2527, 25241])).
% 2.66/2.81 tff(25603,plain,
% 2.66/2.81 (op(e0, op(e1, e2)) = op(e1, e2)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25233, 25602, 25237])).
% 2.66/2.81 tff(25604,plain,
% 2.66/2.81 ((op(e0, op(e1, e2)) = e0) <=> (op(e1, e2) = e0)),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25603])).
% 2.66/2.81 tff(25605,plain,
% 2.66/2.81 ((op(e1, e2) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25604])).
% 2.66/2.81 tff(25606,plain,
% 2.66/2.81 ((op(e1, e2) = e0) <=> (op(e0, e3) = e0)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25605, 25236])).
% 2.66/2.81 tff(25607,plain,
% 2.66/2.81 ((~(op(e1, e2) = e0)) <=> (~(op(e0, e3) = e0))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25606])).
% 2.66/2.81 tff(25608,plain,
% 2.66/2.81 (~(op(e0, e3) = e0)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[23820, 25607])).
% 2.66/2.81 tff(25609,plain,
% 2.66/2.81 (op(e2, e3) = e1),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[19997, 25608, 80, 121, 25231])).
% 2.66/2.81 tff(25610,plain,
% 2.66/2.81 ((op(e0, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25602])).
% 2.66/2.81 tff(25611,plain,
% 2.66/2.81 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25610, 112])).
% 2.66/2.81 tff(25612,plain,
% 2.66/2.81 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25611])).
% 2.66/2.81 tff(25613,plain,
% 2.66/2.81 (~(op(e2, e3) = e3)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[964, 25612])).
% 2.66/2.81 tff(25614,plain,
% 2.66/2.81 ((op(e2, e1) = e3) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25237])).
% 2.66/2.81 tff(25615,plain,
% 2.66/2.81 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e3)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25614])).
% 2.66/2.81 tff(25616,plain,
% 2.66/2.81 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25593])).
% 2.66/2.81 tff(25617,plain,
% 2.66/2.81 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25616, 9812])).
% 2.66/2.81 tff(25618,plain,
% 2.66/2.81 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25617])).
% 2.66/2.81 tff(25619,plain,
% 2.66/2.81 (~(op(e2, e0) = e2)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[359, 25618])).
% 2.66/2.81 tff(25620,plain,
% 2.66/2.81 (op(e2, e1) = e2),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[23839, 25619, 25430])).
% 2.66/2.81 tff(25621,plain,
% 2.66/2.81 ((op(e2, e1) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25620])).
% 2.66/2.81 tff(25622,plain,
% 2.66/2.81 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25621, 5762])).
% 2.66/2.81 tff(25623,plain,
% 2.66/2.81 ((op(e1, e2) = e2) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.81 inference(symmetry,[status(thm)],[25622])).
% 2.66/2.81 tff(25624,plain,
% 2.66/2.81 ((op(e1, e2) = e2) <=> (op(e2, e1) = e3)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25623, 25615])).
% 2.66/2.81 tff(25625,plain,
% 2.66/2.81 ((~(op(e1, e2) = e2)) <=> (~(op(e2, e1) = e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25624])).
% 2.66/2.81 tff(25626,plain,
% 2.66/2.81 (~(op(e2, e1) = e3)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[25600, 25625])).
% 2.66/2.81 tff(25627,plain,
% 2.66/2.81 (op(e2, e0) = e3),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[23641, 25626, 25613])).
% 2.66/2.81 tff(25628,plain,
% 2.66/2.81 ($false),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[24207, 25627, 25609])).
% 2.66/2.81 tff(25629,plain,((op(e1, e1) = e3) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e0, e0) = e1) | (op(e1, e3) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.81 tff(25630,plain,
% 2.66/2.81 (op(e1, e1) = e3),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[25629, 2379, 121, 2527, 68, 6687, 80, 1080, 2168])).
% 2.66/2.81 tff(25631,plain,
% 2.66/2.81 ((op(e1, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25630])).
% 2.66/2.81 tff(25632,plain,
% 2.66/2.81 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25631, 1262])).
% 2.66/2.81 tff(25633,plain,
% 2.66/2.81 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25632])).
% 2.66/2.81 tff(25634,plain,
% 2.66/2.81 (~(op(e2, e1) = e3)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[225, 25633])).
% 2.66/2.81 tff(25635,plain,
% 2.66/2.81 ((op(e1, e1) = e0) <=> (e3 = e0)),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25630])).
% 2.66/2.81 tff(25636,plain,
% 2.66/2.81 ((op(e1, e1) = e0) <=> (e0 = e3)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25635, 159])).
% 2.66/2.81 tff(25637,plain,
% 2.66/2.81 ((e0 = e3) <=> (op(e1, e1) = e0)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25636])).
% 2.66/2.81 tff(25638,plain,
% 2.66/2.81 ((~(e0 = e3)) <=> (~(op(e1, e1) = e0))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25637])).
% 2.66/2.81 tff(25639,plain,
% 2.66/2.81 (~(op(e1, e1) = e0)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[181, 25638])).
% 2.66/2.81 tff(25640,plain,
% 2.66/2.81 ((op(e1, e1) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25630])).
% 2.66/2.81 tff(25641,plain,
% 2.66/2.81 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 2.66/2.81 inference(transitivity,[status(thm)],[25640, 532])).
% 2.66/2.81 tff(25642,plain,
% 2.66/2.81 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25641])).
% 2.66/2.81 tff(25643,plain,
% 2.66/2.81 (~(op(e1, e2) = e3)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[1604, 25642])).
% 2.66/2.81 tff(25644,plain,
% 2.66/2.81 (op(e1, e2) = e1),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[23821, 25643, 25600])).
% 2.66/2.81 tff(25645,plain,
% 2.66/2.81 (e1 = op(e1, e2)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25644])).
% 2.66/2.81 tff(25646,plain,
% 2.66/2.81 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25645])).
% 2.66/2.81 tff(25647,plain,
% 2.66/2.81 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 2.66/2.81 inference(symmetry,[status(thm)],[25646])).
% 2.66/2.81 tff(25648,plain,
% 2.66/2.81 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 2.66/2.81 inference(monotonicity,[status(thm)],[25647])).
% 2.66/2.81 tff(25649,plain,
% 2.66/2.81 (~(op(e0, e2) = e1)),
% 2.66/2.81 inference(modus_ponens,[status(thm)],[6205, 25648])).
% 2.66/2.81 tff(25650,plain,
% 2.66/2.81 (op(e0, e1) = e1),
% 2.66/2.81 inference(unit_resolution,[status(thm)],[384, 25649, 121, 2379])).
% 2.66/2.82 tff(25651,plain,
% 2.66/2.82 (op(e0, e1) = op(e1, e2)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25650, 25645])).
% 2.66/2.82 tff(25652,plain,
% 2.66/2.82 ((op(e0, e1) = e0) <=> (op(e1, e2) = e0)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25651])).
% 2.66/2.82 tff(25653,plain,
% 2.66/2.82 ((op(e1, e2) = e0) <=> (op(e0, e1) = e0)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25652])).
% 2.66/2.82 tff(25654,plain,
% 2.66/2.82 ((~(op(e1, e2) = e0)) <=> (~(op(e0, e1) = e0))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25653])).
% 2.66/2.82 tff(25655,plain,
% 2.66/2.82 (~(op(e0, e1) = e0)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[23820, 25654])).
% 2.66/2.82 tff(25656,plain,
% 2.66/2.82 (op(e3, e1) = e0),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[23988, 25655, 25639])).
% 2.66/2.82 tff(25657,plain,
% 2.66/2.82 ((op(e3, e1) = e2) <=> (e0 = e2)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25656])).
% 2.66/2.82 tff(25658,plain,
% 2.66/2.82 ((e0 = e2) <=> (op(e3, e1) = e2)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25657])).
% 2.66/2.82 tff(25659,plain,
% 2.66/2.82 ((e0 = e2) <=> (op(e1, e3) = op(e3, e1))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25658, 25514, 6290])).
% 2.66/2.82 tff(25660,plain,
% 2.66/2.82 ((~(e0 = e2)) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25659])).
% 2.66/2.82 tff(25661,plain,
% 2.66/2.82 (~(op(e1, e3) = op(e3, e1))),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[14, 25660])).
% 2.66/2.82 tff(25662,plain,
% 2.66/2.82 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[6307, 25661])).
% 2.66/2.82 tff(25663,plain,
% 2.66/2.82 (op(e1, e0) = e0),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[24723, 25639, 80])).
% 2.66/2.82 tff(25664,plain,
% 2.66/2.82 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25663])).
% 2.66/2.82 tff(25665,plain,
% 2.66/2.82 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25664])).
% 2.66/2.82 tff(25666,plain,
% 2.66/2.82 (~(op(e0, e0) = e0)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[2471, 25665])).
% 2.66/2.82 tff(25667,plain,
% 2.66/2.82 (op(e0, e3) = e0),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[23963, 25655, 25666])).
% 2.66/2.82 tff(25668,plain,
% 2.66/2.82 ((op(e1, op(e1, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25451])).
% 2.66/2.82 tff(25669,plain,
% 2.66/2.82 ((op(e1, e2) = e1) <=> (op(e1, op(e1, e3)) = e1)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25668])).
% 2.66/2.82 tff(25670,plain,
% 2.66/2.82 (op(e1, op(e1, e3)) = e1),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[25644, 25669])).
% 2.66/2.82 tff(25671,plain,
% 2.66/2.82 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[6674, 25670])).
% 2.66/2.82 tff(25672,plain,
% 2.66/2.82 (e1 = op(e3, e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[5682, 658])).
% 2.66/2.82 tff(25673,plain,
% 2.66/2.82 (op(e3, e3) = op(e1, e2)),
% 2.66/2.82 inference(transitivity,[status(thm)],[5682, 18022])).
% 2.66/2.82 tff(25674,plain,
% 2.66/2.82 (op(e3, op(e3, e3)) = op(e3, op(e1, e2))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25673])).
% 2.66/2.82 tff(25675,plain,
% 2.66/2.82 (op(e3, op(e1, e2)) = op(e3, op(e3, e3))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25674])).
% 2.66/2.82 tff(25676,plain,
% 2.66/2.82 (op(e3, op(e1, e2)) = op(e3, e1)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6683])).
% 2.66/2.82 tff(25677,plain,
% 2.66/2.82 (op(e3, e1) = op(e3, op(e1, e2))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25676])).
% 2.66/2.82 tff(25678,plain,
% 2.66/2.82 (e0 = op(e3, op(e3, e3))),
% 2.66/2.82 inference(transitivity,[status(thm)],[4734, 25677, 25675])).
% 2.66/2.82 tff(25679,plain,
% 2.66/2.82 (op(e3, op(e3, e3)) = e0),
% 2.66/2.82 inference(transitivity,[status(thm)],[25674, 25676, 4731])).
% 2.66/2.82 tff(25680,plain,
% 2.66/2.82 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25679])).
% 2.66/2.82 tff(25681,plain,
% 2.66/2.82 (op(e3, e0) = op(e3, op(e3, op(e3, e3)))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25680])).
% 2.66/2.82 tff(25682,plain,
% 2.66/2.82 ((op(e3, e1) = e2) <=> (e0 = e2)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[4731])).
% 2.66/2.82 tff(25683,plain,
% 2.66/2.82 ((e0 = e2) <=> (op(e3, e1) = e2)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25682])).
% 2.66/2.82 tff(25684,plain,
% 2.66/2.82 ((~(e0 = e2)) <=> (~(op(e3, e1) = e2))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25683])).
% 2.66/2.82 tff(25685,plain,
% 2.66/2.82 (~(op(e3, e1) = e2)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[14, 25684])).
% 2.66/2.82 tff(25686,plain,
% 2.66/2.82 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25564])).
% 2.66/2.82 tff(25687,plain,
% 2.66/2.82 (~(op(e3, e0) = e0)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[410, 25686])).
% 2.66/2.82 tff(25688,plain,
% 2.66/2.82 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 2.66/2.82 inference(symmetry,[status(thm)],[5785])).
% 2.66/2.82 tff(25689,plain,
% 2.66/2.82 ((op(e3, e0) = e0) <=> (op(e0, e3) = op(e3, e0))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25688, 453])).
% 2.66/2.82 tff(25690,plain,
% 2.66/2.82 ((~(op(e3, e0) = e0)) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25689])).
% 2.66/2.82 tff(25691,plain,
% 2.66/2.82 (~(op(e0, e3) = op(e3, e0))),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[25687, 25690])).
% 2.66/2.82 tff(25692,plain,
% 2.66/2.82 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[496, 25691])).
% 2.66/2.82 tff(25693,plain,
% 2.66/2.82 (op(e2, e3) = e3),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[12598, 76, 80, 121, 79])).
% 2.66/2.82 tff(25694,plain,
% 2.66/2.82 ((op(e2, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25695,plain,
% 2.66/2.82 ((op(e2, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25694, 666])).
% 2.66/2.82 tff(25696,plain,
% 2.66/2.82 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25695])).
% 2.66/2.82 tff(25697,plain,
% 2.66/2.82 (~(op(e3, e3) = e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[368, 25696])).
% 2.66/2.82 tff(25698,plain,
% 2.66/2.82 (op(e3, e3) = e1),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[1071, 126, 25697, 5532])).
% 2.66/2.82 tff(25699,plain,
% 2.66/2.82 (e1 = op(e3, e3)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25698])).
% 2.66/2.82 tff(25700,plain,
% 2.66/2.82 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e3, e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25699])).
% 2.66/2.82 tff(25701,plain,
% 2.66/2.82 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e1)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25700])).
% 2.66/2.82 tff(25702,plain,
% 2.66/2.82 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e1))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25701])).
% 2.66/2.82 tff(25703,plain,
% 2.66/2.82 (~(op(e3, e0) = e1)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[157, 25702])).
% 2.66/2.82 tff(25704,plain,
% 2.66/2.82 ((op(e1, e0) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[2180])).
% 2.66/2.82 tff(25705,plain,
% 2.66/2.82 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e0) = e1)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25704])).
% 2.66/2.82 tff(25706,plain,
% 2.66/2.82 ((op(e2, e3) = e2) <=> (e3 = e2)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25707,plain,
% 2.66/2.82 ((op(e2, e3) = e2) <=> (e2 = e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25706, 1314])).
% 2.66/2.82 tff(25708,plain,
% 2.66/2.82 ((e2 = e3) <=> (op(e2, e3) = e2)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25707])).
% 2.66/2.82 tff(25709,plain,
% 2.66/2.82 ((~(e2 = e3)) <=> (~(op(e2, e3) = e2))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25708])).
% 2.66/2.82 tff(25710,plain,
% 2.66/2.82 (~(op(e2, e3) = e2)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[1321, 25709])).
% 2.66/2.82 tff(25711,plain,
% 2.66/2.82 (op(e1, e3) = e2),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[2786, 126, 25710, 79])).
% 2.66/2.82 tff(25712,plain,
% 2.66/2.82 (op(e3, e0) = e3),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[5422, 25703, 1908, 3786])).
% 2.66/2.82 tff(25713,plain,
% 2.66/2.82 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25712])).
% 2.66/2.82 tff(25714,plain,
% 2.66/2.82 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25713])).
% 2.66/2.82 tff(25715,plain,
% 2.66/2.82 (~(op(e1, e0) = e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[410, 25714])).
% 2.66/2.82 tff(25716,plain,
% 2.66/2.82 (op(e1, e1) = e3),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[247, 25715, 10660, 75])).
% 2.66/2.82 tff(25717,plain,
% 2.66/2.82 (~(op(e1, e2) = e0)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[6918, 25716, 6778, 25711])).
% 2.66/2.82 tff(25718,plain,
% 2.66/2.82 (op(e1, e0) = e0),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[1830, 25717, 80, 84])).
% 2.66/2.82 tff(25719,plain,
% 2.66/2.82 (op(e1, op(e0, e3)) = op(e0, e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[2179, 25718, 772])).
% 2.66/2.82 tff(25720,plain,
% 2.66/2.82 ((op(e1, op(e0, e3)) = e1) <=> (op(e0, e3) = op(e3, e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25719, 25699])).
% 2.66/2.82 tff(25721,plain,
% 2.66/2.82 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25720])).
% 2.66/2.82 tff(25722,plain,
% 2.66/2.82 ((op(e0, e3) = op(e3, e3)) <=> (op(e1, e0) = e1)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25721, 25705])).
% 2.66/2.82 tff(25723,plain,
% 2.66/2.82 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e1, e0) = e1))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25722])).
% 2.66/2.82 tff(25724,plain,
% 2.66/2.82 (~(op(e1, e0) = e1)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[1077, 25723])).
% 2.66/2.82 tff(25725,plain,
% 2.66/2.82 (e2 = op(e1, e3)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25711])).
% 2.66/2.82 tff(25726,plain,
% 2.66/2.82 ((op(e1, e0) = op(e2, e0)) <=> (e0 = op(e2, e0))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25718])).
% 2.66/2.82 tff(25727,plain,
% 2.66/2.82 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e0)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25726, 4499])).
% 2.66/2.82 tff(25728,plain,
% 2.66/2.82 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e0))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25727])).
% 2.66/2.82 tff(25729,plain,
% 2.66/2.82 (~(op(e2, e0) = e0)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[756, 25728])).
% 2.66/2.82 tff(25730,plain,
% 2.66/2.82 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25731,plain,
% 2.66/2.82 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25730])).
% 2.66/2.82 tff(25732,plain,
% 2.66/2.82 (~(op(e2, e0) = e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[989, 25731])).
% 2.66/2.82 tff(25733,plain,
% 2.66/2.82 (op(e3, e2) = e2),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[2015, 126, 3786, 82])).
% 2.66/2.82 tff(25734,plain,
% 2.66/2.82 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e2)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25733])).
% 2.66/2.82 tff(25735,plain,
% 2.66/2.82 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e2))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25734])).
% 2.66/2.82 tff(25736,plain,
% 2.66/2.82 (~(op(e2, e2) = e2)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[1546, 25735])).
% 2.66/2.82 tff(25737,plain,
% 2.66/2.82 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25725])).
% 2.66/2.82 tff(25738,plain,
% 2.66/2.82 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25737])).
% 2.66/2.82 tff(25739,plain,
% 2.66/2.82 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25738])).
% 2.66/2.82 tff(25740,plain,
% 2.66/2.82 (~(op(e1, e2) = e2)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[1850, 25739])).
% 2.66/2.82 tff(25741,plain,
% 2.66/2.82 (op(e1, e2) = e1),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[1859, 25717, 75, 25740])).
% 2.66/2.82 tff(25742,plain,
% 2.66/2.82 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25743,plain,
% 2.66/2.82 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25742])).
% 2.66/2.82 tff(25744,plain,
% 2.66/2.82 (~(op(e2, e2) = e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[515, 25743])).
% 2.66/2.82 tff(25745,plain,
% 2.66/2.82 (op(e3, e2) = op(e1, e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25733, 25725])).
% 2.66/2.82 tff(25746,plain,
% 2.66/2.82 ((op(e3, e2) = e3) <=> (op(e1, e3) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25745])).
% 2.66/2.82 tff(25747,plain,
% 2.66/2.82 ((op(e1, e3) = e3) <=> (op(e3, e2) = e3)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25746])).
% 2.66/2.82 tff(25748,plain,
% 2.66/2.82 ((~(op(e1, e3) = e3)) <=> (~(op(e3, e2) = e3))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25747])).
% 2.66/2.82 tff(25749,plain,
% 2.66/2.82 (~(op(e3, e2) = e3)),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[10660, 25748])).
% 2.66/2.82 tff(25750,plain,
% 2.66/2.82 (op(e0, e2) = e3),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[2111, 25749, 25744, 75])).
% 2.66/2.82 tff(25751,plain,
% 2.66/2.82 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25750])).
% 2.66/2.82 tff(25752,plain,
% 2.66/2.82 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25751])).
% 2.66/2.82 tff(25753,plain,
% 2.66/2.82 ((op(e2, e0) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25752, 6337])).
% 2.66/2.82 tff(25754,plain,
% 2.66/2.82 ((~(op(e2, e0) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25753])).
% 2.66/2.82 tff(25755,plain,
% 2.66/2.82 (~(op(e0, e2) = op(e2, e0))),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[25732, 25754])).
% 2.66/2.82 tff(25756,plain,
% 2.66/2.82 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[6347, 25755])).
% 2.66/2.82 tff(25757,plain,
% 2.66/2.82 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25758,plain,
% 2.66/2.82 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25757])).
% 2.66/2.82 tff(25759,plain,
% 2.66/2.82 ((op(e1, e3) = e3) <=> (op(e2, e3) = op(e3, e2))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25747, 25758, 395])).
% 2.66/2.82 tff(25760,plain,
% 2.66/2.82 ((~(op(e1, e3) = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25759])).
% 2.66/2.82 tff(25761,plain,
% 2.66/2.82 (~(op(e2, e3) = op(e3, e2))),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[10660, 25760])).
% 2.66/2.82 tff(25762,plain,
% 2.66/2.82 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[430, 25761])).
% 2.66/2.82 tff(25763,plain,
% 2.66/2.82 (op(e0, op(e0, e2)) = op(op(e0, e3), e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[772, 25750])).
% 2.66/2.82 tff(25764,plain,
% 2.66/2.82 (op(e0, op(e0, e2)) = e0),
% 2.66/2.82 inference(transitivity,[status(thm)],[25763, 8782])).
% 2.66/2.82 tff(25765,plain,
% 2.66/2.82 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[5369, 25764])).
% 2.66/2.82 tff(25766,plain,
% 2.66/2.82 (op(e0, op(e2, e3)) = op(e0, e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[6778])).
% 2.66/2.82 tff(25767,plain,
% 2.66/2.82 ((op(e0, op(e2, e3)) = e0) <=> (op(e0, e3) = e0)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25766])).
% 2.66/2.82 tff(25768,plain,
% 2.66/2.82 ((op(e0, e3) = e0) <=> (op(e0, op(e2, e3)) = e0)),
% 2.66/2.82 inference(symmetry,[status(thm)],[25767])).
% 2.66/2.82 tff(25769,plain,
% 2.66/2.82 (op(e0, op(e2, e3)) = e0),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[771, 25768])).
% 2.66/2.82 tff(25770,plain,
% 2.66/2.82 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[13359, 25769])).
% 2.66/2.82 tff(25771,plain,
% 2.66/2.82 (op(e1, e0) = op(e0, e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25718, 772])).
% 2.66/2.82 tff(25772,plain,
% 2.66/2.82 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e3) = op(e0, e1))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25771])).
% 2.66/2.82 tff(25773,plain,
% 2.66/2.82 ((op(e1, e0) = op(e0, e1)) <=> (op(e0, e1) = op(e0, e3))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25772, 15424])).
% 2.66/2.82 tff(25774,plain,
% 2.66/2.82 ((op(e0, e1) = op(e0, e3)) <=> (op(e1, e0) = op(e0, e1))),
% 2.66/2.82 inference(symmetry,[status(thm)],[25773])).
% 2.66/2.82 tff(25775,plain,
% 2.66/2.82 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = op(e1, e0))),
% 2.66/2.82 inference(transitivity,[status(thm)],[25774, 596])).
% 2.66/2.82 tff(25776,plain,
% 2.66/2.82 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e1, e0)))),
% 2.66/2.82 inference(monotonicity,[status(thm)],[25775])).
% 2.66/2.82 tff(25777,plain,
% 2.66/2.82 (~(op(e0, e1) = op(e1, e0))),
% 2.66/2.82 inference(modus_ponens,[status(thm)],[818, 25776])).
% 2.66/2.82 tff(25778,plain,
% 2.66/2.82 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[609, 25777])).
% 2.66/2.82 tff(25779,plain,
% 2.66/2.82 (op(e0, op(e1, e1)) = op(op(e0, e3), e3)),
% 2.66/2.82 inference(monotonicity,[status(thm)],[772, 25716])).
% 2.66/2.82 tff(25780,plain,
% 2.66/2.82 (op(e0, op(e1, e1)) = e0),
% 2.66/2.82 inference(transitivity,[status(thm)],[25779, 8782])).
% 2.66/2.82 tff(25781,plain,
% 2.66/2.82 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[635, 25780])).
% 2.66/2.82 tff(25782,plain,
% 2.66/2.82 (op(e2, e2) = e0),
% 2.66/2.82 inference(unit_resolution,[status(thm)],[973, 25717, 919, 85])).
% 2.66/2.82 tff(25783,plain,
% 2.66/2.82 (op(e2, e2) = op(e0, e3)),
% 2.66/2.82 inference(transitivity,[status(thm)],[25782, 772])).
% 2.66/2.83 tff(25784,plain,
% 2.66/2.83 (op(e3, op(e2, e2)) = op(e3, op(e0, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25783])).
% 2.66/2.83 tff(25785,plain,
% 2.66/2.83 (op(e3, op(e2, e2)) = e3),
% 2.66/2.83 inference(transitivity,[status(thm)],[25784, 2418, 25712])).
% 2.66/2.83 tff(25786,plain,
% 2.66/2.83 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[12593, 25785])).
% 2.66/2.83 tff(25787,plain,
% 2.66/2.83 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e1, e0) = op(e0, e1)))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25774])).
% 2.66/2.83 tff(25788,plain,
% 2.66/2.83 (~(op(e1, e0) = op(e0, e1))),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[818, 25787])).
% 2.66/2.83 tff(25789,plain,
% 2.66/2.83 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[613, 25788])).
% 2.66/2.83 tff(25790,plain,
% 2.66/2.83 (op(e1, op(e0, e0)) = op(e1, op(e1, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[4541])).
% 2.66/2.83 tff(25791,plain,
% 2.66/2.83 (op(e1, op(e0, e0)) = e1),
% 2.66/2.83 inference(transitivity,[status(thm)],[25790, 6670, 6683])).
% 2.66/2.83 tff(25792,plain,
% 2.66/2.83 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[6717, 25791])).
% 2.66/2.83 tff(25793,plain,
% 2.66/2.83 (op(e2, op(e3, e3)) = op(e2, e1)),
% 2.66/2.83 inference(transitivity,[status(thm)],[311, 12130])).
% 2.66/2.83 tff(25794,plain,
% 2.66/2.83 ((op(e2, op(e3, e3)) = e2) <=> (op(e2, e1) = e2)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25793])).
% 2.66/2.83 tff(25795,plain,
% 2.66/2.83 ((op(e2, e1) = e2) <=> (op(e2, op(e3, e3)) = e2)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25794])).
% 2.66/2.83 tff(25796,plain,
% 2.66/2.83 (op(e2, e1) = e2),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[2088, 982, 4382, 5548])).
% 2.66/2.83 tff(25797,plain,
% 2.66/2.83 (op(e2, op(e3, e3)) = e2),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[25796, 25795])).
% 2.66/2.83 tff(25798,plain,
% 2.66/2.83 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[14770, 25797])).
% 2.66/2.83 tff(25799,plain,
% 2.66/2.83 (op(e1, e2) = op(e3, e3)),
% 2.66/2.83 inference(transitivity,[status(thm)],[6683, 306])).
% 2.66/2.83 tff(25800,plain,
% 2.66/2.83 (op(e2, op(e1, e2)) = op(e2, op(e3, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25799])).
% 2.66/2.83 tff(25801,plain,
% 2.66/2.83 (op(e2, op(e1, e2)) = op(e2, e1)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25800, 311, 12130])).
% 2.66/2.83 tff(25802,plain,
% 2.66/2.83 ((op(e2, op(e1, e2)) = e2) <=> (op(e2, e1) = e2)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25801])).
% 2.66/2.83 tff(25803,plain,
% 2.66/2.83 ((op(e2, e1) = e2) <=> (op(e2, op(e1, e2)) = e2)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25802])).
% 2.66/2.83 tff(25804,plain,
% 2.66/2.83 (op(e2, op(e1, e2)) = e2),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[25796, 25803])).
% 2.66/2.83 tff(25805,plain,
% 2.66/2.83 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[18782, 25804])).
% 2.66/2.83 tff(25806,plain,
% 2.66/2.83 ((op(e2, e1) = op(e1, e2)) <=> (op(e2, e1) = e1)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[6683])).
% 2.66/2.83 tff(25807,plain,
% 2.66/2.83 ((op(e2, e1) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.83 inference(symmetry,[status(thm)],[25806])).
% 2.66/2.83 tff(25808,plain,
% 2.66/2.83 (op(e2, e0) = e1),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[765, 982, 3272, 983])).
% 2.66/2.83 tff(25809,plain,
% 2.66/2.83 ((op(e2, e0) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25808])).
% 2.66/2.83 tff(25810,plain,
% 2.66/2.83 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25809, 2355])).
% 2.66/2.83 tff(25811,plain,
% 2.66/2.83 ((op(e2, e0) = op(e2, e1)) <=> (op(e1, e2) = op(e2, e1))),
% 2.66/2.83 inference(transitivity,[status(thm)],[25810, 25807, 531])).
% 2.66/2.83 tff(25812,plain,
% 2.66/2.83 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25811])).
% 2.66/2.83 tff(25813,plain,
% 2.66/2.83 (~(op(e1, e2) = op(e2, e1))),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[1966, 25812])).
% 2.66/2.83 tff(25814,plain,
% 2.66/2.83 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[539, 25813])).
% 2.66/2.83 tff(25815,plain,
% 2.66/2.83 ($false),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[5367, 25814, 25805, 5675, 5672, 25798, 6689, 5670, 5681, 5669, 25792, 5671, 5511, 5674, 5668, 9846])).
% 2.66/2.83 tff(25816,plain,((op(e2, e0) = e2) | (~((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3))) | (~((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3))) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (~((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3))) | (~((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3))) | (~((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3))) | (~(op(e1, e2) = e1)) | (~(op(e1, e3) = e2)) | (~(op(e3, e3) = e1)) | (op(e2, e3) = e2) | (op(e2, e2) = e2) | (op(e3, e0) = e2) | (op(e2, e0) = e3) | (op(e2, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.83 tff(25817,plain,
% 2.66/2.83 (op(e2, e0) = e2),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25816, 25789, 25786, 25781, 5670, 25778, 5669, 25770, 5511, 25765, 25762, 25756, 25741, 25711, 25698, 25710, 25736, 3786, 25732, 25729])).
% 2.66/2.83 tff(25818,plain,
% 2.66/2.83 (op(e2, e0) = op(e1, e3)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25817, 25725])).
% 2.66/2.83 tff(25819,plain,
% 2.66/2.83 ((op(e2, e0) = e1) <=> (op(e1, e3) = op(e3, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25818, 25699])).
% 2.66/2.83 tff(25820,plain,
% 2.66/2.83 ((op(e1, e3) = op(e3, e3)) <=> (op(e2, e0) = e1)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25819])).
% 2.66/2.83 tff(25821,plain,
% 2.66/2.83 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e2, e0) = e1))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25820])).
% 2.66/2.83 tff(25822,plain,
% 2.66/2.83 (~(op(e2, e0) = e1)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[571, 25821])).
% 2.66/2.83 tff(25823,plain,
% 2.66/2.83 (op(e0, e0) = e1),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[1480, 25822, 25724, 25703])).
% 2.66/2.83 tff(25824,plain,
% 2.66/2.83 (e1 = op(e0, e0)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[25823, 74])).
% 2.66/2.83 tff(25825,plain,
% 2.66/2.83 (op(e0, e0) = op(e3, e3)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25823, 25699])).
% 2.66/2.83 tff(25826,plain,
% 2.66/2.83 (op(e0, op(e0, e0)) = op(e0, op(e3, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25825])).
% 2.66/2.83 tff(25827,plain,
% 2.66/2.83 (op(e0, op(e3, e3)) = op(e0, op(e0, e0))),
% 2.66/2.83 inference(symmetry,[status(thm)],[25826])).
% 2.66/2.83 tff(25828,plain,
% 2.66/2.83 (op(e0, op(e3, e3)) = op(e0, e1)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25698])).
% 2.66/2.83 tff(25829,plain,
% 2.66/2.83 (op(e0, e1) = op(e0, op(e3, e3))),
% 2.66/2.83 inference(symmetry,[status(thm)],[25828])).
% 2.66/2.83 tff(25830,plain,
% 2.66/2.83 ((op(e0, e2) = op(e3, e2)) <=> (op(e0, e2) = e2)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25733])).
% 2.66/2.83 tff(25831,plain,
% 2.66/2.83 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = e2))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25830])).
% 2.66/2.83 tff(25832,plain,
% 2.66/2.83 (~(op(e0, e2) = e2)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[1467, 25831])).
% 2.66/2.83 tff(25833,plain,
% 2.66/2.83 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25817])).
% 2.66/2.83 tff(25834,plain,
% 2.66/2.83 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25833])).
% 2.66/2.83 tff(25835,plain,
% 2.66/2.83 (~(op(e0, e0) = e2)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[359, 25834])).
% 2.66/2.83 tff(25836,plain,
% 2.66/2.83 (op(e0, e1) = e2),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[3652, 25835, 79, 25832])).
% 2.66/2.83 tff(25837,plain,
% 2.66/2.83 (e2 = op(e0, e1)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25836])).
% 2.66/2.83 tff(25838,plain,
% 2.66/2.83 (e2 = op(e0, op(e0, e0))),
% 2.66/2.83 inference(transitivity,[status(thm)],[25837, 25829, 25827])).
% 2.66/2.83 tff(25839,plain,
% 2.66/2.83 (op(e0, op(e0, e0)) = op(e1, e3)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25826, 25828, 25836, 25725])).
% 2.66/2.83 tff(25840,plain,
% 2.66/2.83 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25839])).
% 2.66/2.83 tff(25841,plain,
% 2.66/2.83 (op(e0, op(e1, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.66/2.83 inference(symmetry,[status(thm)],[25840])).
% 2.66/2.83 tff(25842,plain,
% 2.66/2.83 (op(e0, op(e1, e3)) = op(e0, e2)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25711])).
% 2.66/2.83 tff(25843,plain,
% 2.66/2.83 (op(e0, e2) = op(e0, op(e1, e3))),
% 2.66/2.83 inference(symmetry,[status(thm)],[25842])).
% 2.66/2.83 tff(25844,plain,
% 2.66/2.83 (e3 = op(e0, e2)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25750])).
% 2.66/2.83 tff(25845,plain,
% 2.66/2.83 (e3 = op(e0, op(e0, op(e0, e0)))),
% 2.66/2.83 inference(transitivity,[status(thm)],[25844, 25843, 25841])).
% 2.66/2.83 tff(25846,plain,
% 2.66/2.83 ($false),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[3582, 25845, 25838, 25824])).
% 2.66/2.83 tff(25847,plain,((op(e3, e3) = e2) | (op(e0, e3) = e2) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (op(e3, e0) = e2) | (~(op(e0, e3) = e0)) | (op(e1, e2) = e3) | (op(e3, e2) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (~(op(e2, e3) = e3)) | (op(e3, e0) = e0) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.83 tff(25848,plain,
% 2.66/2.83 ((op(e0, e3) = e2) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (op(e3, e0) = e2) | (~(op(e0, e3) = e0)) | (op(e1, e2) = e3) | (op(e3, e2) = e0) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (~(op(e2, e3) = e3)) | (op(e3, e0) = e0) | (op(e3, e1) = e2)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25847, 15002])).
% 2.66/2.83 tff(25849,plain,
% 2.66/2.83 ((op(e0, e3) = e2) | (~((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3))) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (op(e3, e0) = e2) | (~(op(e0, e3) = e0)) | (op(e1, e2) = e3) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (~(op(e2, e3) = e3)) | (op(e3, e0) = e0) | (op(e3, e1) = e2)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25848, 24134])).
% 2.66/2.83 tff(25850,plain,
% 2.66/2.83 (op(e3, e0) = e2),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25849, 25693, 75, 5511, 79, 25692, 771, 5669, 80, 84, 25687, 25685])).
% 2.66/2.83 tff(25851,plain,
% 2.66/2.83 (e2 = op(e3, e0)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25850])).
% 2.66/2.83 tff(25852,plain,
% 2.66/2.83 (e2 = op(e3, op(e3, op(e3, e3)))),
% 2.66/2.83 inference(transitivity,[status(thm)],[25851, 25681])).
% 2.66/2.83 tff(25853,plain,
% 2.66/2.83 ($false),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[5397, 25852, 25678, 25672])).
% 2.66/2.83 tff(25854,plain,((op(e2, e3) = e1) | (~(op(e3, e1) = e0)) | (~(op(e1, e2) = e1)) | (op(e1, e2) = e3) | (~((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3))) | (op(e0, e3) = e2) | (~(op(e0, e3) = e0)) | (~((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3))) | (op(e1, e3) = e0) | (op(e1, e1) = e0) | (op(e0, e3) = e1) | (op(e1, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.83 tff(25855,plain,
% 2.66/2.83 (op(e2, e3) = e1),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25854, 25656, 25644, 25643, 25671, 25231, 25667, 25662, 80, 25639, 121, 25250])).
% 2.66/2.83 tff(25856,plain,
% 2.66/2.83 (~(op(e2, e0) = e3)),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[24207, 25855])).
% 2.66/2.83 tff(25857,plain,
% 2.66/2.83 (op(e2, e3) = e3),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[23641, 25856, 25634])).
% 2.66/2.83 tff(25858,plain,
% 2.66/2.83 (e1 = op(e2, e3)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25855])).
% 2.66/2.83 tff(25859,plain,
% 2.66/2.83 (op(e1, e2) = e3),
% 2.66/2.83 inference(transitivity,[status(thm)],[25644, 25858, 25857])).
% 2.66/2.83 tff(25860,plain,
% 2.66/2.83 ($false),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25643, 25859])).
% 2.66/2.83 tff(25861,plain,((op(e0, e0) = e1) | (op(e1, e3) = e0) | (op(e0, e3) = e1) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e1, e3) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.83 tff(25862,plain,
% 2.66/2.83 (op(e0, e0) = e1),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[25861, 68, 121, 2527, 80, 6687, 1080, 2168])).
% 2.66/2.83 tff(25863,plain,
% 2.66/2.83 (e1 = op(e0, e0)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25862])).
% 2.66/2.83 tff(25864,plain,
% 2.66/2.83 ((e1 = e3) <=> (op(e0, e0) = e3)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25863])).
% 2.66/2.83 tff(25865,plain,
% 2.66/2.83 ((~(e1 = e3)) <=> (~(op(e0, e0) = e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25864])).
% 2.66/2.83 tff(25866,plain,
% 2.66/2.83 (~(op(e0, e0) = e3)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[303, 25865])).
% 2.66/2.83 tff(25867,plain,
% 2.66/2.83 ((op(e1, e0) = e1) <=> (op(e1, e0) = op(e0, e0))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25863])).
% 2.66/2.83 tff(25868,plain,
% 2.66/2.83 ((op(e1, e0) = e1) <=> (op(e0, e0) = op(e1, e0))),
% 2.66/2.83 inference(transitivity,[status(thm)],[25867, 17099])).
% 2.66/2.83 tff(25869,plain,
% 2.66/2.83 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25868])).
% 2.66/2.83 tff(25870,plain,
% 2.66/2.83 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25869])).
% 2.66/2.83 tff(25871,plain,
% 2.66/2.83 (~(op(e1, e0) = e1)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[2471, 25870])).
% 2.66/2.83 tff(25872,plain,
% 2.66/2.83 (op(e1, e0) = e0),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[728, 25871, 2168, 6687])).
% 2.66/2.83 tff(25873,plain,
% 2.66/2.83 (e1 = op(e0, e0)),
% 2.66/2.83 inference(symmetry,[status(thm)],[10406])).
% 2.66/2.83 tff(25874,plain,
% 2.66/2.83 ((op(e1, e1) = e1) <=> (e3 = op(e0, e0))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[4960, 25873])).
% 2.66/2.83 tff(25875,plain,
% 2.66/2.83 ((op(e1, e1) = e1) <=> (op(e0, e0) = e3)),
% 2.66/2.83 inference(transitivity,[status(thm)],[25874, 70])).
% 2.66/2.83 tff(25876,plain,
% 2.66/2.83 ((op(e0, e0) = e3) <=> (op(e1, e1) = e1)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25875])).
% 2.66/2.83 tff(25877,plain,
% 2.66/2.83 ((~(op(e0, e0) = e3)) <=> (~(op(e1, e1) = e1))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25876])).
% 2.66/2.83 tff(25878,plain,
% 2.66/2.83 ((e1 = e3) <=> (op(e0, e0) = e3)),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25873])).
% 2.66/2.83 tff(25879,plain,
% 2.66/2.83 ((~(e1 = e3)) <=> (~(op(e0, e0) = e3))),
% 2.66/2.83 inference(monotonicity,[status(thm)],[25878])).
% 2.66/2.83 tff(25880,plain,
% 2.66/2.83 (~(op(e0, e0) = e3)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[303, 25879])).
% 2.66/2.83 tff(25881,plain,
% 2.66/2.83 (~(op(e1, e1) = e1)),
% 2.66/2.83 inference(modus_ponens,[status(thm)],[25880, 25877])).
% 2.66/2.83 tff(25882,plain,
% 2.66/2.83 (op(e2, e3) = e3),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[23641, 24208, 15670])).
% 2.66/2.83 tff(25883,plain,
% 2.66/2.83 (e3 = op(e2, e3)),
% 2.66/2.83 inference(symmetry,[status(thm)],[25882])).
% 2.66/2.83 tff(25884,plain,
% 2.66/2.83 (op(e1, e1) = e1),
% 2.66/2.83 inference(transitivity,[status(thm)],[4960, 25883, 2684])).
% 2.66/2.83 tff(25885,plain,
% 2.66/2.83 ($false),
% 2.66/2.83 inference(unit_resolution,[status(thm)],[1266, 25884])).
% 2.66/2.84 tff(25886,plain,((~(op(e2, e3) = e1)) | (op(e1, e1) = e1) | (~(op(e1, e1) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.84 tff(25887,plain,
% 2.66/2.84 (~(op(e2, e3) = e1)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[25886, 25881, 4960])).
% 2.66/2.84 tff(25888,plain,
% 2.66/2.84 ((op(e0, op(e0, e0)) = e2) <=> (e2 = op(e0, op(e0, e0)))),
% 2.66/2.84 inference(commutativity,[status(thm)],[])).
% 2.66/2.84 tff(25889,plain,
% 2.66/2.84 ((op(e0, e1) = e2) <=> (op(e0, op(e0, e0)) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[23366])).
% 2.66/2.84 tff(25890,plain,
% 2.66/2.84 ((op(e0, e1) = e2) <=> (e2 = op(e0, op(e0, e0)))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25889, 25888])).
% 2.66/2.84 tff(25891,plain,
% 2.66/2.84 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e0, e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25873])).
% 2.66/2.84 tff(25892,plain,
% 2.66/2.84 ((op(e0, e1) = e1) <=> (op(e0, e0) = op(e0, e1))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25891, 804])).
% 2.66/2.84 tff(25893,plain,
% 2.66/2.84 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e1)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25892])).
% 2.66/2.84 tff(25894,plain,
% 2.66/2.84 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e1))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25893])).
% 2.66/2.84 tff(25895,plain,
% 2.66/2.84 (~(op(e0, e1) = e1)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[811, 25894])).
% 2.66/2.84 tff(25896,plain,
% 2.66/2.84 ((op(e0, e1) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[23366])).
% 2.66/2.84 tff(25897,plain,
% 2.66/2.84 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e1) = e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25896])).
% 2.66/2.84 tff(25898,plain,
% 2.66/2.84 (op(e0, e3) = e0),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[19997, 76, 80, 121, 79])).
% 2.66/2.84 tff(25899,plain,
% 2.66/2.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, op(e0, e0)) = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[23366, 25898])).
% 2.66/2.84 tff(25900,plain,
% 2.66/2.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25899, 25897])).
% 2.66/2.84 tff(25901,plain,
% 2.66/2.84 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25900])).
% 2.66/2.84 tff(25902,plain,
% 2.66/2.84 (~(op(e0, e1) = e0)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[818, 25901])).
% 2.66/2.84 tff(25903,plain,
% 2.66/2.84 (op(e0, e1) = e2),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[829, 25902, 2527, 25895])).
% 2.66/2.84 tff(25904,plain,
% 2.66/2.84 (e2 = op(e0, op(e0, e0))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[25903, 25890])).
% 2.66/2.84 tff(25905,plain,
% 2.66/2.84 (op(e2, op(e1, e1)) = op(e1, e1)),
% 2.66/2.84 inference(transitivity,[status(thm)],[15725, 25693, 4971])).
% 2.66/2.84 tff(25906,plain,
% 2.66/2.84 ((op(e2, op(e1, e1)) = e2) <=> (op(e1, e1) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25905])).
% 2.66/2.84 tff(25907,plain,
% 2.66/2.84 ((op(e1, e1) = e2) <=> (op(e2, op(e1, e1)) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25906])).
% 2.66/2.84 tff(25908,plain,
% 2.66/2.84 ((op(e1, e1) = e2) <=> (op(e2, e3) = e2)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25907, 15728])).
% 2.66/2.84 tff(25909,plain,
% 2.66/2.84 ((~(op(e1, e1) = e2)) <=> (~(op(e2, e3) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25908])).
% 2.66/2.84 tff(25910,plain,
% 2.66/2.84 (~(op(e2, e3) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[68, 25909])).
% 2.66/2.84 tff(25911,plain,
% 2.66/2.84 (op(e1, e3) = e2),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[15003, 25910, 79])).
% 2.66/2.84 tff(25912,plain,
% 2.66/2.84 (e2 = op(e1, e3)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25911])).
% 2.66/2.84 tff(25913,plain,
% 2.66/2.84 (op(e0, op(e0, e0)) = op(e1, e3)),
% 2.66/2.84 inference(transitivity,[status(thm)],[23365, 25903, 25912])).
% 2.66/2.84 tff(25914,plain,
% 2.66/2.84 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25913])).
% 2.66/2.84 tff(25915,plain,
% 2.66/2.84 (op(e0, op(e1, e3)) = op(e0, op(e0, op(e0, e0)))),
% 2.66/2.84 inference(symmetry,[status(thm)],[25914])).
% 2.66/2.84 tff(25916,plain,
% 2.66/2.84 (op(e0, op(e1, e3)) = op(e0, e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25911])).
% 2.66/2.84 tff(25917,plain,
% 2.66/2.84 (op(e0, e2) = op(e0, op(e1, e3))),
% 2.66/2.84 inference(symmetry,[status(thm)],[25916])).
% 2.66/2.84 tff(25918,plain,
% 2.66/2.84 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e3)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25693])).
% 2.66/2.84 tff(25919,plain,
% 2.66/2.84 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25918])).
% 2.66/2.84 tff(25920,plain,
% 2.66/2.84 (~(op(e0, e3) = e3)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[964, 25919])).
% 2.66/2.84 tff(25921,plain,
% 2.66/2.84 (op(e0, e2) = e3),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[1495, 25920, 2527, 25880])).
% 2.66/2.84 tff(25922,plain,
% 2.66/2.84 (e3 = op(e0, e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25921])).
% 2.66/2.84 tff(25923,plain,
% 2.66/2.84 (e3 = op(e0, op(e0, op(e0, e0)))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25922, 25917, 25915])).
% 2.66/2.84 tff(25924,plain,
% 2.66/2.84 ($false),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[3582, 25923, 25904, 23364])).
% 2.66/2.84 tff(25925,plain,((op(e2, e3) = e1) | (~(op(e0, e0) = e1)) | (op(e0, e1) = e3) | (op(e0, e3) = e2) | (op(e1, e1) = e2) | (~(op(e1, e1) = e3)) | (op(e1, e3) = e0) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.84 tff(25926,plain,
% 2.66/2.84 (op(e0, e3) = e2),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[25925, 25887, 2527, 10406, 68, 4960, 80, 121])).
% 2.66/2.84 tff(25927,plain,
% 2.66/2.84 (e2 = op(e0, e3)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25926])).
% 2.66/2.84 tff(25928,plain,
% 2.66/2.84 ((op(e2, op(e1, e1)) = e2) <=> (op(e2, e3) = op(e0, e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[15725, 25927])).
% 2.66/2.84 tff(25929,plain,
% 2.66/2.84 ((op(e2, op(e1, e1)) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25928, 925])).
% 2.66/2.84 tff(25930,plain,
% 2.66/2.84 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, op(e1, e1)) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25929])).
% 2.66/2.84 tff(25931,plain,
% 2.66/2.84 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25930, 15728])).
% 2.66/2.84 tff(25932,plain,
% 2.66/2.84 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25931])).
% 2.66/2.84 tff(25933,plain,
% 2.66/2.84 (~(op(e2, e3) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[964, 25932])).
% 2.66/2.84 tff(25934,plain,
% 2.66/2.84 (op(e2, op(e0, e0)) = op(e2, e1)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[10406])).
% 2.66/2.84 tff(25935,plain,
% 2.66/2.84 (op(e2, e1) = op(e2, op(e0, e0))),
% 2.66/2.84 inference(symmetry,[status(thm)],[25934])).
% 2.66/2.84 tff(25936,plain,
% 2.66/2.84 ((op(e2, e1) = e2) <=> (op(e2, op(e0, e0)) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25935])).
% 2.66/2.84 tff(25937,plain,
% 2.66/2.84 ((op(e2, op(e0, e0)) = e2) <=> (op(e2, e1) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25936])).
% 2.66/2.84 tff(25938,plain,
% 2.66/2.84 ((op(e2, e0) = op(e0, e0)) <=> (op(e0, e0) = op(e2, e0))),
% 2.66/2.84 inference(commutativity,[status(thm)],[])).
% 2.66/2.84 tff(25939,plain,
% 2.66/2.84 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e0, e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25873])).
% 2.66/2.84 tff(25940,plain,
% 2.66/2.84 ((op(e2, e0) = e1) <=> (op(e0, e0) = op(e2, e0))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25939, 25938])).
% 2.66/2.84 tff(25941,plain,
% 2.66/2.84 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25940])).
% 2.66/2.84 tff(25942,plain,
% 2.66/2.84 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25941])).
% 2.66/2.84 tff(25943,plain,
% 2.66/2.84 (~(op(e2, e0) = e1)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[359, 25942])).
% 2.66/2.84 tff(25944,plain,
% 2.66/2.84 (op(e2, e1) = e1),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[23785, 25887, 25943])).
% 2.66/2.84 tff(25945,plain,
% 2.66/2.84 (op(e2, op(e0, e0)) = op(e0, e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25934, 25944, 25873])).
% 2.66/2.84 tff(25946,plain,
% 2.66/2.84 ((op(e2, op(e0, e0)) = e2) <=> (op(e0, e0) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25945])).
% 2.66/2.84 tff(25947,plain,
% 2.66/2.84 ((op(e0, e0) = e2) <=> (op(e2, op(e0, e0)) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25946])).
% 2.66/2.84 tff(25948,plain,
% 2.66/2.84 ((op(e0, e0) = e2) <=> (op(e2, e1) = e2)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25947, 25937])).
% 2.66/2.84 tff(25949,plain,
% 2.66/2.84 ((~(op(e0, e0) = e2)) <=> (~(op(e2, e1) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25948])).
% 2.66/2.84 tff(25950,plain,
% 2.66/2.84 ((e1 = e2) <=> (op(e0, e0) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25873])).
% 2.66/2.84 tff(25951,plain,
% 2.66/2.84 ((~(e1 = e2)) <=> (~(op(e0, e0) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25950])).
% 2.66/2.84 tff(25952,plain,
% 2.66/2.84 (~(op(e0, e0) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[708, 25951])).
% 2.66/2.84 tff(25953,plain,
% 2.66/2.84 (~(op(e2, e1) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[25952, 25949])).
% 2.66/2.84 tff(25954,plain,
% 2.66/2.84 (op(e2, e0) = e2),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[23839, 25953, 25933])).
% 2.66/2.84 tff(25955,plain,
% 2.66/2.84 (e2 = op(e2, e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25954])).
% 2.66/2.84 tff(25956,plain,
% 2.66/2.84 (op(e0, e3) = op(e2, e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25926, 25955])).
% 2.66/2.84 tff(25957,plain,
% 2.66/2.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25956])).
% 2.66/2.84 tff(25958,plain,
% 2.66/2.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e2, e0) = op(e0, e2))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25957, 6336])).
% 2.66/2.84 tff(25959,plain,
% 2.66/2.84 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25958])).
% 2.66/2.84 tff(25960,plain,
% 2.66/2.84 (~(op(e2, e0) = op(e0, e2))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[918, 25959])).
% 2.66/2.84 tff(25961,plain,
% 2.66/2.84 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[6358, 25960])).
% 2.66/2.84 tff(25962,plain,
% 2.66/2.84 (op(op(e0, e3), e0) = op(e2, e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25926])).
% 2.66/2.84 tff(25963,plain,
% 2.66/2.84 (op(e2, e0) = op(e0, e3)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25954, 25927])).
% 2.66/2.84 tff(25964,plain,
% 2.66/2.84 (op(op(e2, e0), e0) = op(op(e0, e3), e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25963])).
% 2.66/2.84 tff(25965,plain,
% 2.66/2.84 (op(e0, e3) = op(e0, op(e1, e1))),
% 2.66/2.84 inference(symmetry,[status(thm)],[15782])).
% 2.66/2.84 tff(25966,plain,
% 2.66/2.84 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e1)) = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25965])).
% 2.66/2.84 tff(25967,plain,
% 2.66/2.84 ((op(e0, op(e1, e1)) = e0) <=> (op(e0, e3) = e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25966])).
% 2.66/2.84 tff(25968,plain,
% 2.66/2.84 (op(e0, op(e1, e1)) = e2),
% 2.66/2.84 inference(transitivity,[status(thm)],[15782, 25926])).
% 2.66/2.84 tff(25969,plain,
% 2.66/2.84 ((op(e0, op(e1, e1)) = e0) <=> (e2 = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25968])).
% 2.66/2.84 tff(25970,plain,
% 2.66/2.84 ((op(e0, op(e1, e1)) = e0) <=> (e0 = e2)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25969, 1])).
% 2.66/2.84 tff(25971,plain,
% 2.66/2.84 ((e0 = e2) <=> (op(e0, op(e1, e1)) = e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25970])).
% 2.66/2.84 tff(25972,plain,
% 2.66/2.84 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25971, 25967])).
% 2.66/2.84 tff(25973,plain,
% 2.66/2.84 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25972])).
% 2.66/2.84 tff(25974,plain,
% 2.66/2.84 (~(op(e0, e3) = e0)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[14, 25973])).
% 2.66/2.84 tff(25975,plain,
% 2.66/2.84 (op(e3, e3) = e0),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[24662, 25974, 80])).
% 2.66/2.84 tff(25976,plain,
% 2.66/2.84 (op(e2, op(e3, e3)) = op(op(e2, e0), e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25955, 25975])).
% 2.66/2.84 tff(25977,plain,
% 2.66/2.84 (op(e2, op(e3, e3)) = e2),
% 2.66/2.84 inference(transitivity,[status(thm)],[25976, 25964, 25962, 25954])).
% 2.66/2.84 tff(25978,plain,
% 2.66/2.84 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[14770, 25977])).
% 2.66/2.84 tff(25979,plain,
% 2.66/2.84 ((e2 = op(e0, op(e0, e0))) <=> (op(e0, e1) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25890])).
% 2.66/2.84 tff(25980,plain,
% 2.66/2.84 ((e2 = op(e0, op(e0, e0))) <=> (op(e0, e3) = op(e0, e1))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25927, 23365])).
% 2.66/2.84 tff(25981,plain,
% 2.66/2.84 ((e2 = op(e0, op(e0, e0))) <=> (op(e0, e1) = op(e0, e3))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25980, 15424])).
% 2.66/2.84 tff(25982,plain,
% 2.66/2.84 ((op(e0, e1) = op(e0, e3)) <=> (e2 = op(e0, op(e0, e0)))),
% 2.66/2.84 inference(symmetry,[status(thm)],[25981])).
% 2.66/2.84 tff(25983,plain,
% 2.66/2.84 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e2)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25982, 25979])).
% 2.66/2.84 tff(25984,plain,
% 2.66/2.84 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25983])).
% 2.66/2.84 tff(25985,plain,
% 2.66/2.84 (~(op(e0, e1) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[818, 25984])).
% 2.66/2.84 tff(25986,plain,
% 2.66/2.84 (op(e3, e1) = e2),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[1993, 25985, 68, 25953])).
% 2.66/2.84 tff(25987,plain,
% 2.66/2.84 (op(e3, e1) = op(e0, e3)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25986, 25927])).
% 2.66/2.84 tff(25988,plain,
% 2.66/2.84 ((op(e3, e1) = op(e1, e3)) <=> (op(e0, e3) = op(e1, e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25987])).
% 2.66/2.84 tff(25989,plain,
% 2.66/2.84 ((op(e0, e3) = op(e1, e3)) <=> (op(e3, e1) = op(e1, e3))),
% 2.66/2.84 inference(symmetry,[status(thm)],[25988])).
% 2.66/2.84 tff(25990,plain,
% 2.66/2.84 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = op(e3, e1))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25989, 6290])).
% 2.66/2.84 tff(25991,plain,
% 2.66/2.84 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = op(e3, e1)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25990])).
% 2.66/2.84 tff(25992,plain,
% 2.66/2.84 (~(op(e1, e3) = op(e3, e1))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[64, 25991])).
% 2.66/2.84 tff(25993,plain,
% 2.66/2.84 ((~(op(e1, e3) = op(e3, e1))) | (op(e0, op(e3, e1)) = e0) | (op(e1, op(e3, e1)) = e1) | (op(e2, op(e3, e1)) = e2) | (op(e3, op(e3, e1)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[6307, 25992])).
% 2.66/2.84 tff(25994,plain,
% 2.66/2.84 (op(e2, op(e1, e0)) = op(e2, e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[6142])).
% 2.66/2.84 tff(25995,plain,
% 2.66/2.84 ((op(e2, op(e1, e0)) = e2) <=> (op(e2, e0) = e2)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25994])).
% 2.66/2.84 tff(25996,plain,
% 2.66/2.84 ((op(e2, e0) = e2) <=> (op(e2, op(e1, e0)) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[25995])).
% 2.66/2.84 tff(25997,plain,
% 2.66/2.84 (op(e2, op(e1, e0)) = e2),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[25954, 25996])).
% 2.66/2.84 tff(25998,plain,
% 2.66/2.84 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[10735, 25997])).
% 2.66/2.84 tff(25999,plain,
% 2.66/2.84 (op(e2, e3) = e3),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[24237, 25933, 25887])).
% 2.66/2.84 tff(26000,plain,
% 2.66/2.84 (op(e3, e2) = op(e3, op(e0, e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25927])).
% 2.66/2.84 tff(26001,plain,
% 2.66/2.84 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26000, 25999])).
% 2.66/2.84 tff(26002,plain,
% 2.66/2.84 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.66/2.84 inference(symmetry,[status(thm)],[26001])).
% 2.66/2.84 tff(26003,plain,
% 2.66/2.84 ((~(op(e3, op(e0, e3)) = e3)) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26002])).
% 2.66/2.84 tff(26004,plain,
% 2.66/2.84 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e0, e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25873])).
% 2.66/2.84 tff(26005,plain,
% 2.66/2.84 ((op(e0, e2) = e1) <=> (op(e0, e0) = op(e0, e2))),
% 2.66/2.84 inference(transitivity,[status(thm)],[26004, 22093])).
% 2.66/2.84 tff(26006,plain,
% 2.66/2.84 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 2.66/2.84 inference(symmetry,[status(thm)],[26005])).
% 2.66/2.84 tff(26007,plain,
% 2.66/2.84 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26006])).
% 2.66/2.84 tff(26008,plain,
% 2.66/2.84 (~(op(e0, e2) = e1)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[3603, 26007])).
% 2.66/2.84 tff(26009,plain,
% 2.66/2.84 ((op(e0, e2) = e2) <=> (op(e0, e2) = op(e0, e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25927])).
% 2.66/2.84 tff(26010,plain,
% 2.66/2.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 2.66/2.84 inference(symmetry,[status(thm)],[26009])).
% 2.66/2.84 tff(26011,plain,
% 2.66/2.84 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26010])).
% 2.66/2.84 tff(26012,plain,
% 2.66/2.84 (~(op(e0, e2) = e2)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[918, 26011])).
% 2.66/2.84 tff(26013,plain,
% 2.66/2.84 (op(e0, e2) = e3),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[23880, 26012, 26008])).
% 2.66/2.84 tff(26014,plain,
% 2.66/2.84 ((op(e0, e2) = op(e3, e2)) <=> (e3 = op(e3, op(e0, e3)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26013, 26000])).
% 2.66/2.84 tff(26015,plain,
% 2.66/2.84 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, op(e0, e3)) = e3)),
% 2.66/2.84 inference(transitivity,[status(thm)],[26014, 10461])).
% 2.66/2.84 tff(26016,plain,
% 2.66/2.84 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26015])).
% 2.66/2.84 tff(26017,plain,
% 2.66/2.84 (~(op(e3, op(e0, e3)) = e3)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[1467, 26016])).
% 2.66/2.84 tff(26018,plain,
% 2.66/2.84 (~(op(e3, e2) = op(e2, e3))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[26017, 26003])).
% 2.66/2.84 tff(26019,plain,
% 2.66/2.84 ((~(op(e3, e2) = op(e2, e3))) | (op(e0, op(e2, e3)) = e0) | (op(e1, op(e2, e3)) = e1) | (op(e2, op(e2, e3)) = e2) | (op(e3, op(e2, e3)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[500, 26018])).
% 2.66/2.84 tff(26020,plain,
% 2.66/2.84 (op(e2, e1) = op(e0, e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25944, 25873])).
% 2.66/2.84 tff(26021,plain,
% 2.66/2.84 (op(e0, op(e2, e1)) = op(e0, op(e0, e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26020])).
% 2.66/2.84 tff(26022,plain,
% 2.66/2.84 ((op(e0, op(e2, e1)) = e0) <=> (op(e0, op(e0, e0)) = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26021])).
% 2.66/2.84 tff(26023,plain,
% 2.66/2.84 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, op(e2, e1)) = e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[26022])).
% 2.66/2.84 tff(26024,plain,
% 2.66/2.84 ((op(e0, e1) = e0) <=> (op(e0, op(e2, e1)) = e0)),
% 2.66/2.84 inference(transitivity,[status(thm)],[25896, 26023])).
% 2.66/2.84 tff(26025,plain,
% 2.66/2.84 ((op(e0, e0) = e0) <=> (e1 = e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[10406])).
% 2.66/2.84 tff(26026,plain,
% 2.66/2.84 ((op(e0, e0) = e0) <=> (e0 = e1)),
% 2.66/2.84 inference(transitivity,[status(thm)],[26025, 18])).
% 2.66/2.84 tff(26027,plain,
% 2.66/2.84 ((e0 = e1) <=> (op(e0, e0) = e0)),
% 2.66/2.84 inference(symmetry,[status(thm)],[26026])).
% 2.66/2.84 tff(26028,plain,
% 2.66/2.84 ((~(e0 = e1)) <=> (~(op(e0, e0) = e0))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26027])).
% 2.66/2.84 tff(26029,plain,
% 2.66/2.84 (~(op(e0, e0) = e0)),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[26, 26028])).
% 2.66/2.84 tff(26030,plain,
% 2.66/2.84 (op(e0, e1) = e0),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[23963, 25974, 26029])).
% 2.66/2.84 tff(26031,plain,
% 2.66/2.84 (op(e0, op(e2, e1)) = e0),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[26030, 26024])).
% 2.66/2.84 tff(26032,plain,
% 2.66/2.84 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[13223, 26031])).
% 2.66/2.84 tff(26033,plain,
% 2.66/2.84 (op(e2, op(e0, e1)) = op(op(e2, e0), e0)),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25955, 26030])).
% 2.66/2.84 tff(26034,plain,
% 2.66/2.84 (op(e2, op(e0, e1)) = e2),
% 2.66/2.84 inference(transitivity,[status(thm)],[26033, 25964, 25962, 25954])).
% 2.66/2.84 tff(26035,plain,
% 2.66/2.84 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[9902, 26034])).
% 2.66/2.84 tff(26036,plain,
% 2.66/2.84 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25989])).
% 2.66/2.84 tff(26037,plain,
% 2.66/2.84 (~(op(e3, e1) = op(e1, e3))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[64, 26036])).
% 2.66/2.84 tff(26038,plain,
% 2.66/2.84 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[6362, 26037])).
% 2.66/2.84 tff(26039,plain,
% 2.66/2.84 ((op(e3, op(e0, e3)) = e3) <=> (op(e2, e3) = op(e3, e2))),
% 2.66/2.84 inference(transitivity,[status(thm)],[26002, 395])).
% 2.66/2.84 tff(26040,plain,
% 2.66/2.84 ((~(op(e3, op(e0, e3)) = e3)) <=> (~(op(e2, e3) = op(e3, e2)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26039])).
% 2.66/2.84 tff(26041,plain,
% 2.66/2.84 (~(op(e2, e3) = op(e3, e2))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[26017, 26040])).
% 2.66/2.84 tff(26042,plain,
% 2.66/2.84 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[430, 26041])).
% 2.66/2.84 tff(26043,plain,
% 2.66/2.84 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = op(e2, e0))),
% 2.66/2.84 inference(transitivity,[status(thm)],[25958, 6337])).
% 2.66/2.84 tff(26044,plain,
% 2.66/2.84 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[26043])).
% 2.66/2.84 tff(26045,plain,
% 2.66/2.84 (~(op(e0, e2) = op(e2, e0))),
% 2.66/2.84 inference(modus_ponens,[status(thm)],[918, 26044])).
% 2.66/2.84 tff(26046,plain,
% 2.66/2.84 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.66/2.84 inference(unit_resolution,[status(thm)],[6347, 26045])).
% 2.66/2.84 tff(26047,plain,
% 2.66/2.84 ((op(e2, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 2.66/2.84 inference(monotonicity,[status(thm)],[25944])).
% 2.66/2.84 tff(26048,plain,
% 2.66/2.84 ((op(e2, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26047, 5522])).
% 2.66/2.85 tff(26049,plain,
% 2.66/2.85 ((op(e1, e2) = e1) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.85 inference(symmetry,[status(thm)],[26048])).
% 2.66/2.85 tff(26050,plain,
% 2.66/2.85 ((op(e1, op(e1, e1)) = e2) <=> (e2 = op(e1, op(e1, e1)))),
% 2.66/2.85 inference(commutativity,[status(thm)],[])).
% 2.66/2.85 tff(26051,plain,
% 2.66/2.85 (op(e1, e3) = op(e1, op(e1, e1))),
% 2.66/2.85 inference(symmetry,[status(thm)],[12670])).
% 2.66/2.85 tff(26052,plain,
% 2.66/2.85 ((op(e1, e3) = e2) <=> (op(e1, op(e1, e1)) = e2)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26051])).
% 2.66/2.85 tff(26053,plain,
% 2.66/2.85 ((op(e1, e3) = e2) <=> (e2 = op(e1, op(e1, e1)))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26052, 26050])).
% 2.66/2.85 tff(26054,plain,
% 2.66/2.85 ((e2 = op(e1, op(e1, e1))) <=> (op(e1, e3) = e2)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26053])).
% 2.66/2.85 tff(26055,plain,
% 2.66/2.85 ((e2 = op(e1, op(e1, e1))) <=> (op(e0, e3) = op(e1, e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[25927, 12670])).
% 2.66/2.85 tff(26056,plain,
% 2.66/2.85 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, op(e1, e1)))),
% 2.66/2.85 inference(symmetry,[status(thm)],[26055])).
% 2.66/2.85 tff(26057,plain,
% 2.66/2.85 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26056, 26054])).
% 2.66/2.85 tff(26058,plain,
% 2.66/2.85 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26057])).
% 2.66/2.85 tff(26059,plain,
% 2.66/2.85 (~(op(e1, e3) = e2)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[64, 26058])).
% 2.66/2.85 tff(26060,plain,
% 2.66/2.85 (op(e1, e2) = e2),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[2285, 26059, 68, 6687])).
% 2.66/2.85 tff(26061,plain,
% 2.66/2.85 (op(e1, e2) = op(e2, e0)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26060, 25955])).
% 2.66/2.85 tff(26062,plain,
% 2.66/2.85 ((op(e1, e2) = e1) <=> (op(e2, e0) = op(e0, e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26061, 25873])).
% 2.66/2.85 tff(26063,plain,
% 2.66/2.85 ((op(e1, e2) = e1) <=> (op(e0, e0) = op(e2, e0))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26062, 25938])).
% 2.66/2.85 tff(26064,plain,
% 2.66/2.85 ((op(e0, e0) = op(e2, e0)) <=> (op(e1, e2) = e1)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26063])).
% 2.66/2.85 tff(26065,plain,
% 2.66/2.85 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e1) = op(e1, e2))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26064, 26049])).
% 2.66/2.85 tff(26066,plain,
% 2.66/2.85 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e1) = op(e1, e2)))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26065])).
% 2.66/2.85 tff(26067,plain,
% 2.66/2.85 (~(op(e2, e1) = op(e1, e2))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[359, 26066])).
% 2.66/2.85 tff(26068,plain,
% 2.66/2.85 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[557, 26067])).
% 2.66/2.85 tff(26069,plain,
% 2.66/2.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[25963])).
% 2.66/2.85 tff(26070,plain,
% 2.66/2.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26069, 452])).
% 2.66/2.85 tff(26071,plain,
% 2.66/2.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e0, e3) = op(e3, e0))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26070, 453])).
% 2.66/2.85 tff(26072,plain,
% 2.66/2.85 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26071])).
% 2.66/2.85 tff(26073,plain,
% 2.66/2.85 (~(op(e0, e3) = op(e3, e0))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[747, 26072])).
% 2.66/2.85 tff(26074,plain,
% 2.66/2.85 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[496, 26073])).
% 2.66/2.85 tff(26075,plain,
% 2.66/2.85 ((op(e1, e3) = e1) <=> (op(e1, op(e1, e1)) = e1)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26051])).
% 2.66/2.85 tff(26076,plain,
% 2.66/2.85 (op(e1, e3) = e1),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[104, 26059, 80, 1080])).
% 2.66/2.85 tff(26077,plain,
% 2.66/2.85 (op(e1, op(e1, e1)) = e1),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26076, 26075])).
% 2.66/2.85 tff(26078,plain,
% 2.66/2.85 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[5678, 26077])).
% 2.66/2.85 tff(26079,plain,
% 2.66/2.85 (op(e2, op(e2, e2)) = e2),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[25954, 23905])).
% 2.66/2.85 tff(26080,plain,
% 2.66/2.85 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[528, 26079])).
% 2.66/2.85 tff(26081,plain,
% 2.66/2.85 (op(e0, op(e0, e0)) = e0),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26030, 25896])).
% 2.66/2.85 tff(26082,plain,
% 2.66/2.85 ((op(e0, op(e0, e0)) = e0) | (op(e1, op(e0, e0)) = e1) | (op(e2, op(e0, e0)) = e2) | (op(e3, op(e0, e0)) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[5598, 26081])).
% 2.66/2.85 tff(26083,plain,
% 2.66/2.85 ($false),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[5367, 26082, 26080, 26078, 26074, 26068, 26046, 26042, 26038, 26035, 26032, 26019, 25998, 25993, 25978, 25961])).
% 2.66/2.85 tff(26084,plain,((~(op(e1, e1) = e3)) | (~(op(e0, e0) = e1)) | (~(op(e1, e0) = e0)) | (op(e1, e3) = e0) | (op(e1, e3) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e0, e1) = e3) | (op(e0, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.85 tff(26085,plain,
% 2.66/2.85 (~(op(e1, e1) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[26084, 25862, 25872, 80, 1080, 68, 6687, 2527, 121])).
% 2.66/2.85 tff(26086,plain,
% 2.66/2.85 (op(e1, e2) = e3),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[247, 26085, 1080, 2168])).
% 2.66/2.85 tff(26087,plain,
% 2.66/2.85 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26086])).
% 2.66/2.85 tff(26088,plain,
% 2.66/2.85 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26087])).
% 2.66/2.85 tff(26089,plain,
% 2.66/2.85 (~(op(e0, e2) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[6205, 26088])).
% 2.66/2.85 tff(26090,plain,
% 2.66/2.85 (op(e0, e3) = e3),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[1495, 26089, 2527, 25866])).
% 2.66/2.85 tff(26091,plain,
% 2.66/2.85 (op(e1, op(e0, e3)) = op(e1, e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26090])).
% 2.66/2.85 tff(26092,plain,
% 2.66/2.85 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e1)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26091])).
% 2.66/2.85 tff(26093,plain,
% 2.66/2.85 ((op(e1, e3) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26092])).
% 2.66/2.85 tff(26094,plain,
% 2.66/2.85 ((~(op(e1, e3) = e1)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26093])).
% 2.66/2.85 tff(26095,plain,
% 2.66/2.85 ((op(e1, e0) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[25872])).
% 2.66/2.85 tff(26096,plain,
% 2.66/2.85 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26095, 122])).
% 2.66/2.85 tff(26097,plain,
% 2.66/2.85 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26096])).
% 2.66/2.85 tff(26098,plain,
% 2.66/2.85 (~(op(e1, e1) = e0)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[737, 26097])).
% 2.66/2.85 tff(26099,plain,
% 2.66/2.85 (op(e1, e1) = e1),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[630, 26085, 68, 26098])).
% 2.66/2.85 tff(26100,plain,
% 2.66/2.85 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26099])).
% 2.66/2.85 tff(26101,plain,
% 2.66/2.85 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26100, 28])).
% 2.66/2.85 tff(26102,plain,
% 2.66/2.85 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26101])).
% 2.66/2.85 tff(26103,plain,
% 2.66/2.85 (~(op(e1, e3) = e1)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[619, 26102])).
% 2.66/2.85 tff(26104,plain,
% 2.66/2.85 (~(op(e1, op(e0, e3)) = e1)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26103, 26094])).
% 2.66/2.85 tff(26105,plain,
% 2.66/2.85 (op(e0, op(e0, e3)) = op(e0, e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26090])).
% 2.66/2.85 tff(26106,plain,
% 2.66/2.85 (op(e0, op(e0, e3)) = e3),
% 2.66/2.85 inference(transitivity,[status(thm)],[26105, 26090])).
% 2.66/2.85 tff(26107,plain,
% 2.66/2.85 ((op(e0, op(e0, e3)) = e0) <=> (e3 = e0)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26106])).
% 2.66/2.85 tff(26108,plain,
% 2.66/2.85 ((op(e0, op(e0, e3)) = e0) <=> (e0 = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26107, 159])).
% 2.66/2.85 tff(26109,plain,
% 2.66/2.85 ((e0 = e3) <=> (op(e0, op(e0, e3)) = e0)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26108])).
% 2.66/2.85 tff(26110,plain,
% 2.66/2.85 ((~(e0 = e3)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26109])).
% 2.66/2.85 tff(26111,plain,
% 2.66/2.85 (~(op(e0, op(e0, e3)) = e0)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[181, 26110])).
% 2.66/2.85 tff(26112,plain,
% 2.66/2.85 ((op(e1, e2) = e2) <=> (e3 = e2)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26086])).
% 2.66/2.85 tff(26113,plain,
% 2.66/2.85 ((op(e1, e2) = e2) <=> (e2 = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26112, 1314])).
% 2.66/2.85 tff(26114,plain,
% 2.66/2.85 ((e2 = e3) <=> (op(e1, e2) = e2)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26113])).
% 2.66/2.85 tff(26115,plain,
% 2.66/2.85 ((~(e2 = e3)) <=> (~(op(e1, e2) = e2))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26114])).
% 2.66/2.85 tff(26116,plain,
% 2.66/2.85 (~(op(e1, e2) = e2)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[1321, 26115])).
% 2.66/2.85 tff(26117,plain,
% 2.66/2.85 (op(e1, e3) = e2),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[2285, 26116, 68, 6687])).
% 2.66/2.85 tff(26118,plain,
% 2.66/2.85 (e2 = op(e1, e3)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26117])).
% 2.66/2.85 tff(26119,plain,
% 2.66/2.85 ((op(e2, e0) = e1) <=> (op(e2, e0) = op(e0, e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[25863])).
% 2.66/2.85 tff(26120,plain,
% 2.66/2.85 ((op(e2, e0) = e1) <=> (op(e0, e0) = op(e2, e0))),
% 2.66/2.85 inference(transitivity,[status(thm)],[26119, 25938])).
% 2.66/2.85 tff(26121,plain,
% 2.66/2.85 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26120])).
% 2.66/2.85 tff(26122,plain,
% 2.66/2.85 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26121])).
% 2.66/2.85 tff(26123,plain,
% 2.66/2.85 (~(op(e2, e0) = e1)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[359, 26122])).
% 2.66/2.85 tff(26124,plain,
% 2.66/2.85 ((op(e1, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26099])).
% 2.66/2.85 tff(26125,plain,
% 2.66/2.85 ((op(e1, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26124, 2355])).
% 2.66/2.85 tff(26126,plain,
% 2.66/2.85 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26125])).
% 2.66/2.85 tff(26127,plain,
% 2.66/2.85 (~(op(e2, e1) = e1)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[225, 26126])).
% 2.66/2.85 tff(26128,plain,
% 2.66/2.85 (op(e2, e3) = e1),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[23785, 26127, 26123])).
% 2.66/2.85 tff(26129,plain,
% 2.66/2.85 (op(op(e1, e3), e3) = op(e2, e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26117])).
% 2.66/2.85 tff(26130,plain,
% 2.66/2.85 (op(e2, op(e0, e3)) = op(op(e1, e3), e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26118, 26090])).
% 2.66/2.85 tff(26131,plain,
% 2.66/2.85 (op(e2, op(e0, e3)) = e1),
% 2.66/2.85 inference(transitivity,[status(thm)],[26130, 26129, 26128])).
% 2.66/2.85 tff(26132,plain,
% 2.66/2.85 ((op(e2, op(e0, e3)) = e2) <=> (e1 = op(e1, e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26131, 26118])).
% 2.66/2.85 tff(26133,plain,
% 2.66/2.85 ((op(e2, op(e0, e3)) = e2) <=> (op(e1, e3) = e1)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26132, 28])).
% 2.66/2.85 tff(26134,plain,
% 2.66/2.85 ((op(e1, e3) = e1) <=> (op(e2, op(e0, e3)) = e2)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26133])).
% 2.66/2.85 tff(26135,plain,
% 2.66/2.85 ((~(op(e1, e3) = e1)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26134])).
% 2.66/2.85 tff(26136,plain,
% 2.66/2.85 (~(op(e2, op(e0, e3)) = e2)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26103, 26135])).
% 2.66/2.85 tff(26137,plain,
% 2.66/2.85 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26090])).
% 2.66/2.85 tff(26138,plain,
% 2.66/2.85 ((op(e3, e0) = e3) <=> (op(e3, e0) = op(e0, e3))),
% 2.66/2.85 inference(symmetry,[status(thm)],[26137])).
% 2.66/2.85 tff(26139,plain,
% 2.66/2.85 (~(op(e2, e0) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[24207, 26128])).
% 2.66/2.85 tff(26140,plain,
% 2.66/2.85 (op(e3, e0) = e3),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[2713, 26139, 2168, 25866])).
% 2.66/2.85 tff(26141,plain,
% 2.66/2.85 (op(e3, e0) = op(e0, e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26140, 26138])).
% 2.66/2.85 tff(26142,plain,
% 2.66/2.85 (op(e3, op(e0, e3)) = op(e3, e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26090])).
% 2.66/2.85 tff(26143,plain,
% 2.66/2.85 ((op(e3, op(e0, e3)) = e3) <=> (op(e3, e3) = e3)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26142])).
% 2.66/2.85 tff(26144,plain,
% 2.66/2.85 ((op(e3, e3) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26143])).
% 2.66/2.85 tff(26145,plain,
% 2.66/2.85 ((~(op(e3, e3) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26144])).
% 2.66/2.85 tff(26146,plain,
% 2.66/2.85 ((op(e0, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26090])).
% 2.66/2.85 tff(26147,plain,
% 2.66/2.85 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26146, 666])).
% 2.66/2.85 tff(26148,plain,
% 2.66/2.85 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26147])).
% 2.66/2.85 tff(26149,plain,
% 2.66/2.85 (~(op(e3, e3) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[1077, 26148])).
% 2.66/2.85 tff(26150,plain,
% 2.66/2.85 (~(op(e3, op(e0, e3)) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[26149, 26145])).
% 2.66/2.85 tff(26151,plain,
% 2.66/2.85 ($false),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[4654, 26150, 26141, 121, 26136, 26111, 26104])).
% 2.66/2.85 tff(26152,plain,((op(e1, e1) = e2) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e0, e1) = e3) | (op(e1, e0) = e2) | (op(e1, e3) = e3) | (op(e1, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 2.66/2.85 tff(26153,plain,
% 2.66/2.85 ((op(e1, e1) = e2) | (op(e0, e3) = e1) | (op(e1, e0) = e3) | (op(e0, e1) = e3) | (op(e1, e0) = e2) | (op(e1, e3) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[26152, 24661])).
% 2.66/2.85 tff(26154,plain,
% 2.66/2.85 (op(e1, e0) = e3),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[26153, 4539, 25192, 741, 6613, 25195])).
% 2.66/2.85 tff(26155,plain,
% 2.66/2.85 ((op(e1, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26154])).
% 2.66/2.85 tff(26156,plain,
% 2.66/2.85 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26155, 660])).
% 2.66/2.85 tff(26157,plain,
% 2.66/2.85 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26156])).
% 2.66/2.85 tff(26158,plain,
% 2.66/2.85 (~(op(e2, e0) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[756, 26157])).
% 2.66/2.85 tff(26159,plain,
% 2.66/2.85 ((op(e1, e0) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26154])).
% 2.66/2.85 tff(26160,plain,
% 2.66/2.85 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26159, 1112])).
% 2.66/2.85 tff(26161,plain,
% 2.66/2.85 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26160])).
% 2.66/2.85 tff(26162,plain,
% 2.66/2.85 (~(op(e1, e1) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[737, 26161])).
% 2.66/2.85 tff(26163,plain,
% 2.66/2.85 (~(op(e2, e3) = e1)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[20764, 26162, 7826, 264, 741, 26158])).
% 2.66/2.85 tff(26164,plain,
% 2.66/2.85 ((op(e0, e2) = op(e0, e3)) <=> (e3 = op(e0, e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[7826])).
% 2.66/2.85 tff(26165,plain,
% 2.66/2.85 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26164, 1364])).
% 2.66/2.85 tff(26166,plain,
% 2.66/2.85 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e3))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26165])).
% 2.66/2.85 tff(26167,plain,
% 2.66/2.85 (~(op(e0, e3) = e3)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[918, 26166])).
% 2.66/2.85 tff(26168,plain,
% 2.66/2.85 (op(e0, e3) = e0),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[687, 24671, 25192, 26167])).
% 2.66/2.85 tff(26169,plain,
% 2.66/2.85 ((op(e1, e0) = e0) <=> (e3 = e0)),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26154])).
% 2.66/2.85 tff(26170,plain,
% 2.66/2.85 ((op(e1, e0) = e0) <=> (e0 = e3)),
% 2.66/2.85 inference(transitivity,[status(thm)],[26169, 159])).
% 2.66/2.85 tff(26171,plain,
% 2.66/2.85 ((e0 = e3) <=> (op(e1, e0) = e0)),
% 2.66/2.85 inference(symmetry,[status(thm)],[26170])).
% 2.66/2.85 tff(26172,plain,
% 2.66/2.85 ((~(e0 = e3)) <=> (~(op(e1, e0) = e0))),
% 2.66/2.85 inference(monotonicity,[status(thm)],[26171])).
% 2.66/2.85 tff(26173,plain,
% 2.66/2.85 (~(op(e1, e0) = e0)),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[181, 26172])).
% 2.66/2.85 tff(26174,plain,
% 2.66/2.85 (op(e1, e1) = e0),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[24724, 26173])).
% 2.66/2.85 tff(26175,plain,
% 2.66/2.85 (~(op(e2, e3) = e3)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[19078, 26174, 26168, 19400, 264])).
% 2.66/2.85 tff(26176,plain,
% 2.66/2.85 ((op(e2, e3) = e3) | (op(e0, e3) = e1) | (op(e2, e3) = e1) | (op(e0, e3) = e2)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[12598, 24661])).
% 2.66/2.85 tff(26177,plain,
% 2.66/2.85 ($false),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[26176, 26175, 26163, 25192, 24671])).
% 2.66/2.85 tff(26178,plain,((~(op(e1, e3) = e2)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.66/2.85 tff(26179,plain,
% 2.66/2.85 (~(op(e1, e3) = e2)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[26178, 7826])).
% 2.76/2.85 tff(26180,plain,
% 2.76/2.85 ((op(e1, e3) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[164])).
% 2.76/2.85 tff(26181,plain,
% 2.76/2.85 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 2.76/2.85 inference(transitivity,[status(thm)],[26180, 112])).
% 2.76/2.85 tff(26182,plain,
% 2.76/2.85 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26181])).
% 2.76/2.85 tff(26183,plain,
% 2.76/2.85 (~(op(e2, e3) = e3)),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[118, 26182])).
% 2.76/2.85 tff(26184,plain,
% 2.76/2.85 ((op(e1, e3) = e1) <=> (e3 = e1)),
% 2.76/2.85 inference(monotonicity,[status(thm)],[164])).
% 2.76/2.85 tff(26185,plain,
% 2.76/2.85 ((op(e1, e3) = e1) <=> (e1 = e3)),
% 2.76/2.85 inference(transitivity,[status(thm)],[26184, 128])).
% 2.76/2.85 tff(26186,plain,
% 2.76/2.85 ((e1 = e3) <=> (op(e1, e3) = e1)),
% 2.76/2.85 inference(symmetry,[status(thm)],[26185])).
% 2.76/2.85 tff(26187,plain,
% 2.76/2.85 ((~(e1 = e3)) <=> (~(op(e1, e3) = e1))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26186])).
% 2.76/2.85 tff(26188,plain,
% 2.76/2.85 (~(op(e1, e3) = e1)),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[303, 26187])).
% 2.76/2.85 tff(26189,plain,
% 2.76/2.85 (op(e3, e2) = e2),
% 2.76/2.85 inference(unit_resolution,[status(thm)],[23856, 5766, 19326])).
% 2.76/2.85 tff(26190,plain,
% 2.76/2.85 (e2 = op(e3, e2)),
% 2.76/2.85 inference(symmetry,[status(thm)],[26189])).
% 2.76/2.85 tff(26191,plain,
% 2.76/2.85 (op(e1, e0) = e0),
% 2.76/2.85 inference(unit_resolution,[status(thm)],[24724, 24979])).
% 2.76/2.85 tff(26192,plain,
% 2.76/2.85 (op(e1, e2) = e1),
% 2.76/2.85 inference(unit_resolution,[status(thm)],[23821, 5766, 19400])).
% 2.76/2.85 tff(26193,plain,
% 2.76/2.85 (op(e1, op(e1, e1)) = e1),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[26192, 23824])).
% 2.76/2.85 tff(26194,plain,
% 2.76/2.85 ((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3)),
% 2.76/2.85 inference(unit_resolution,[status(thm)],[5678, 26193])).
% 2.76/2.85 tff(26195,plain,
% 2.76/2.85 (e2 = op(e3, e2)),
% 2.76/2.85 inference(symmetry,[status(thm)],[8955])).
% 2.76/2.85 tff(26196,plain,
% 2.76/2.85 (op(e0, e3) = op(e3, e2)),
% 2.76/2.85 inference(transitivity,[status(thm)],[2, 26195])).
% 2.76/2.85 tff(26197,plain,
% 2.76/2.85 ((op(e0, e3) = e0) <=> (op(e3, e2) = e0)),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26196])).
% 2.76/2.85 tff(26198,plain,
% 2.76/2.85 ((op(e3, e2) = e0) <=> (op(e0, e3) = e0)),
% 2.76/2.85 inference(symmetry,[status(thm)],[26197])).
% 2.76/2.85 tff(26199,plain,
% 2.76/2.85 ((~(op(e3, e2) = e0)) <=> (~(op(e0, e3) = e0))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26198])).
% 2.76/2.85 tff(26200,plain,
% 2.76/2.85 (~(op(e0, e3) = e0)),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[24134, 26199])).
% 2.76/2.85 tff(26201,plain,
% 2.76/2.85 ((op(e2, e3) = e2) <=> (op(e2, e3) = op(e3, e2))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26195])).
% 2.76/2.85 tff(26202,plain,
% 2.76/2.85 ((op(e2, e3) = e2) <=> (op(e3, e2) = op(e2, e3))),
% 2.76/2.85 inference(transitivity,[status(thm)],[26201, 394])).
% 2.76/2.85 tff(26203,plain,
% 2.76/2.85 ((op(e3, e2) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.76/2.85 inference(symmetry,[status(thm)],[26202])).
% 2.76/2.85 tff(26204,plain,
% 2.76/2.85 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e2) = op(e2, e3))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26196])).
% 2.76/2.85 tff(26205,plain,
% 2.76/2.85 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.76/2.85 inference(transitivity,[status(thm)],[26204, 26203])).
% 2.76/2.85 tff(26206,plain,
% 2.76/2.85 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26205])).
% 2.76/2.85 tff(26207,plain,
% 2.76/2.85 (~(op(e2, e3) = e2)),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[964, 26206])).
% 2.76/2.85 tff(26208,plain,
% 2.76/2.85 (op(e2, e3) = e1),
% 2.76/2.85 inference(unit_resolution,[status(thm)],[24237, 26207, 26183])).
% 2.76/2.85 tff(26209,plain,
% 2.76/2.85 (op(e2, e3) = op(e1, e2)),
% 2.76/2.85 inference(transitivity,[status(thm)],[26208, 18022])).
% 2.76/2.85 tff(26210,plain,
% 2.76/2.85 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = op(e1, e2))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26209])).
% 2.76/2.85 tff(26211,plain,
% 2.76/2.85 ((op(e2, e1) = op(e2, e3)) <=> (op(e1, e2) = op(e2, e1))),
% 2.76/2.85 inference(transitivity,[status(thm)],[26210, 531])).
% 2.76/2.85 tff(26212,plain,
% 2.76/2.85 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e1, e2) = op(e2, e1)))),
% 2.76/2.85 inference(monotonicity,[status(thm)],[26211])).
% 2.76/2.85 tff(26213,plain,
% 2.76/2.85 (~(op(e1, e2) = op(e2, e1))),
% 2.76/2.85 inference(modus_ponens,[status(thm)],[197, 26212])).
% 2.76/2.85 tff(26214,plain,
% 2.76/2.85 ((~(op(e1, e2) = op(e2, e1))) | (op(e0, op(e2, e1)) = e0) | (op(e1, op(e2, e1)) = e1) | (op(e2, op(e2, e1)) = e2) | (op(e3, op(e2, e1)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[539, 26213])).
% 2.76/2.86 tff(26215,plain,
% 2.76/2.86 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e2) = op(e2, e3)))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26204])).
% 2.76/2.86 tff(26216,plain,
% 2.76/2.86 (~(op(e3, e2) = op(e2, e3))),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[964, 26215])).
% 2.76/2.86 tff(26217,plain,
% 2.76/2.86 ((op(e2, e0) = op(e0, e2)) <=> (op(e2, e0) = e3)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[7826])).
% 2.76/2.86 tff(26218,plain,
% 2.76/2.86 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e0, e2))),
% 2.76/2.86 inference(symmetry,[status(thm)],[26217])).
% 2.76/2.86 tff(26219,plain,
% 2.76/2.86 ((~(op(e2, e0) = e3)) <=> (~(op(e2, e0) = op(e0, e2)))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26218])).
% 2.76/2.86 tff(26220,plain,
% 2.76/2.86 (~(op(e2, e0) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[24207, 26208])).
% 2.76/2.86 tff(26221,plain,
% 2.76/2.86 (~(op(e2, e0) = op(e0, e2))),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[26220, 26219])).
% 2.76/2.86 tff(26222,plain,
% 2.76/2.86 ((~(op(e2, e0) = op(e0, e2))) | (op(e0, op(e0, e2)) = e0) | (op(e1, op(e0, e2)) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e3, op(e0, e2)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[6358, 26221])).
% 2.76/2.86 tff(26223,plain,
% 2.76/2.86 (op(e2, e0) = e2),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23839, 26207, 3540])).
% 2.76/2.86 tff(26224,plain,
% 2.76/2.86 (op(e3, e3) = e0),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[24663, 26200])).
% 2.76/2.86 tff(26225,plain,
% 2.76/2.86 (op(e2, op(e3, e3)) = op(e2, e0)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26224])).
% 2.76/2.86 tff(26226,plain,
% 2.76/2.86 (op(e2, op(e3, e3)) = e2),
% 2.76/2.86 inference(transitivity,[status(thm)],[26225, 26223])).
% 2.76/2.86 tff(26227,plain,
% 2.76/2.86 ((op(e0, op(e3, e3)) = e0) | (op(e1, op(e3, e3)) = e1) | (op(e2, op(e3, e3)) = e2) | (op(e3, op(e3, e3)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[14770, 26226])).
% 2.76/2.86 tff(26228,plain,
% 2.76/2.86 ((op(e3, e0) = op(e0, e3)) <=> (op(e3, e0) = op(e3, e2))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26196])).
% 2.76/2.86 tff(26229,plain,
% 2.76/2.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = op(e0, e3))),
% 2.76/2.86 inference(symmetry,[status(thm)],[26228])).
% 2.76/2.86 tff(26230,plain,
% 2.76/2.86 ((op(e3, e0) = op(e3, e2)) <=> (op(e0, e3) = op(e3, e0))),
% 2.76/2.86 inference(transitivity,[status(thm)],[26229, 453])).
% 2.76/2.86 tff(26231,plain,
% 2.76/2.86 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e0, e3) = op(e3, e0)))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26230])).
% 2.76/2.86 tff(26232,plain,
% 2.76/2.86 (~(op(e0, e3) = op(e3, e0))),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[1133, 26231])).
% 2.76/2.86 tff(26233,plain,
% 2.76/2.86 ((~(op(e0, e3) = op(e3, e0))) | (op(e0, op(e3, e0)) = e0) | (op(e1, op(e3, e0)) = e1) | (op(e2, op(e3, e0)) = e2) | (op(e3, op(e3, e0)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[496, 26232])).
% 2.76/2.86 tff(26234,plain,
% 2.76/2.86 (op(e2, op(e1, e0)) = e2),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[26223, 25996])).
% 2.76/2.86 tff(26235,plain,
% 2.76/2.86 ((~(op(e0, e1) = op(e1, e0))) | (op(e0, op(e1, e0)) = e0) | (op(e1, op(e1, e0)) = e1) | (op(e2, op(e1, e0)) = e2) | (op(e3, op(e1, e0)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[10735, 26234])).
% 2.76/2.86 tff(26236,plain,
% 2.76/2.86 ((op(e2, e0) = e3) <=> (op(e0, e2) = op(e2, e0))),
% 2.76/2.86 inference(transitivity,[status(thm)],[26218, 6337])).
% 2.76/2.86 tff(26237,plain,
% 2.76/2.86 ((~(op(e2, e0) = e3)) <=> (~(op(e0, e2) = op(e2, e0)))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26236])).
% 2.76/2.86 tff(26238,plain,
% 2.76/2.86 (~(op(e0, e2) = op(e2, e0))),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[26220, 26237])).
% 2.76/2.86 tff(26239,plain,
% 2.76/2.86 ((~(op(e0, e2) = op(e2, e0))) | (op(e0, op(e2, e0)) = e0) | (op(e1, op(e2, e0)) = e1) | (op(e2, op(e2, e0)) = e2) | (op(e3, op(e2, e0)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[6347, 26238])).
% 2.76/2.86 tff(26240,plain,
% 2.76/2.86 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[6142])).
% 2.76/2.86 tff(26241,plain,
% 2.76/2.86 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26240])).
% 2.76/2.86 tff(26242,plain,
% 2.76/2.86 (~(op(e0, e0) = e0)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[2471, 26241])).
% 2.76/2.86 tff(26243,plain,
% 2.76/2.86 (op(e0, e1) = e0),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23963, 26200, 26242])).
% 2.76/2.86 tff(26244,plain,
% 2.76/2.86 (op(e2, op(e0, e1)) = op(e2, e0)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26243])).
% 2.76/2.86 tff(26245,plain,
% 2.76/2.86 (op(e2, op(e0, e1)) = e2),
% 2.76/2.86 inference(transitivity,[status(thm)],[26244, 26223])).
% 2.76/2.86 tff(26246,plain,
% 2.76/2.86 ((~(op(e1, e0) = op(e0, e1))) | (op(e0, op(e0, e1)) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e2, op(e0, e1)) = e2) | (op(e3, op(e0, e1)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[9902, 26245])).
% 2.76/2.86 tff(26247,plain,
% 2.76/2.86 ((op(e3, e3) = e1) <=> (e0 = op(e1, e2))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26224, 18022])).
% 2.76/2.86 tff(26248,plain,
% 2.76/2.86 ((op(e3, e3) = e1) <=> (op(e1, e2) = e0)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26247, 67])).
% 2.76/2.86 tff(26249,plain,
% 2.76/2.86 ((op(e1, e2) = e0) <=> (op(e3, e3) = e1)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26248])).
% 2.76/2.86 tff(26250,plain,
% 2.76/2.86 ((~(op(e1, e2) = e0)) <=> (~(op(e3, e3) = e1))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26249])).
% 2.76/2.86 tff(26251,plain,
% 2.76/2.86 (~(op(e3, e3) = e1)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[23820, 26250])).
% 2.76/2.86 tff(26252,plain,
% 2.76/2.86 (op(e1, op(e3, e2)) = op(op(e1, e2), e2)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[18022, 8955])).
% 2.76/2.86 tff(26253,plain,
% 2.76/2.86 (op(e1, op(e3, e2)) = e1),
% 2.76/2.86 inference(transitivity,[status(thm)],[26252, 18017, 6683])).
% 2.76/2.86 tff(26254,plain,
% 2.76/2.86 ((~(op(e2, e3) = op(e3, e2))) | (op(e0, op(e3, e2)) = e0) | (op(e1, op(e3, e2)) = e1) | (op(e2, op(e3, e2)) = e2) | (op(e3, op(e3, e2)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[12544, 26253])).
% 2.76/2.86 tff(26255,plain,
% 2.76/2.86 (op(e2, op(e2, e2)) = e2),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[26223, 23905])).
% 2.76/2.86 tff(26256,plain,
% 2.76/2.86 ((op(e0, op(e2, e2)) = e0) | (op(e1, op(e2, e2)) = e1) | (op(e2, op(e2, e2)) = e2) | (op(e3, op(e2, e2)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[528, 26255])).
% 2.76/2.86 tff(26257,plain,
% 2.76/2.86 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e3)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[7826])).
% 2.76/2.86 tff(26258,plain,
% 2.76/2.86 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26257])).
% 2.76/2.86 tff(26259,plain,
% 2.76/2.86 (~(op(e0, e0) = e3)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[3603, 26258])).
% 2.76/2.86 tff(26260,plain,
% 2.76/2.86 (op(e0, e0) = e1),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[3612, 16923, 26259, 26242])).
% 2.76/2.86 tff(26261,plain,
% 2.76/2.86 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e1) = e0)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[18021])).
% 2.76/2.86 tff(26262,plain,
% 2.76/2.86 ((op(e0, e1) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26261])).
% 2.76/2.86 tff(26263,plain,
% 2.76/2.86 (op(e0, op(e1, e2)) = e0),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[26243, 26262])).
% 2.76/2.86 tff(26264,plain,
% 2.76/2.86 ((~(op(e2, e1) = op(e1, e2))) | (op(e0, op(e1, e2)) = e0) | (op(e1, op(e1, e2)) = e1) | (op(e2, op(e1, e2)) = e2) | (op(e3, op(e1, e2)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[6398, 26263])).
% 2.76/2.86 tff(26265,plain,
% 2.76/2.86 (op(e3, e0) = e3),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2713, 26220, 26259, 13176])).
% 2.76/2.86 tff(26266,plain,
% 2.76/2.86 ((op(e3, e0) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26265])).
% 2.76/2.86 tff(26267,plain,
% 2.76/2.86 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26266, 396])).
% 2.76/2.86 tff(26268,plain,
% 2.76/2.86 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = op(e1, e3))),
% 2.76/2.86 inference(transitivity,[status(thm)],[26267, 11299])).
% 2.76/2.86 tff(26269,plain,
% 2.76/2.86 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = op(e1, e3)))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26268])).
% 2.76/2.86 tff(26270,plain,
% 2.76/2.86 (~(op(e3, e1) = op(e1, e3))),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[580, 26269])).
% 2.76/2.86 tff(26271,plain,
% 2.76/2.86 ((~(op(e3, e1) = op(e1, e3))) | (op(e0, op(e1, e3)) = e0) | (op(e1, op(e1, e3)) = e1) | (op(e2, op(e1, e3)) = e2) | (op(e3, op(e1, e3)) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[6362, 26270])).
% 2.76/2.86 tff(26272,plain,
% 2.76/2.86 ($false),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23979, 26271, 26264, 26260, 26256, 6683, 6689, 26254, 26251, 26246, 26239, 26235, 26233, 26227, 26222, 25192, 26216, 26188, 26214, 26200])).
% 2.76/2.86 tff(26273,plain,((~(op(e0, e3) = e2)) | (~(op(e1, e2) = e1)) | (~((op(e0, op(e1, e1)) = e0) | (op(e1, op(e1, e1)) = e1) | (op(e2, op(e1, e1)) = e2) | (op(e3, op(e1, e1)) = e3))) | (~(op(e1, e3) = e3)) | (~(op(e0, e2) = e3)) | (~(op(e1, e0) = e0)) | (op(e2, e1) = e2) | (~(op(e3, e2) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.86 tff(26274,plain,
% 2.76/2.86 (~(op(e0, e3) = e2)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[26273, 26192, 26194, 164, 7826, 26191, 21868, 26189])).
% 2.76/2.86 tff(26275,plain,
% 2.76/2.86 (op(e2, e3) = e2),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[15003, 26274, 26179])).
% 2.76/2.86 tff(26276,plain,
% 2.76/2.86 ((op(e1, e3) = e2) | (op(e0, e3) = e2) | (op(e2, e3) = e1) | (op(e2, e3) = e3) | (op(e0, e3) = e1)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[16098, 24661])).
% 2.76/2.86 tff(26277,plain,
% 2.76/2.86 (op(e2, e3) = e1),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[26276, 26274, 25192, 26179, 26183])).
% 2.76/2.86 tff(26278,plain,
% 2.76/2.86 (e1 = op(e2, e3)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26277])).
% 2.76/2.86 tff(26279,plain,
% 2.76/2.86 (op(e1, e2) = op(e3, e2)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26192, 26278, 26275, 26190])).
% 2.76/2.86 tff(26280,plain,
% 2.76/2.86 ($false),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2292, 26279])).
% 2.76/2.86 tff(26281,plain,((~(op(e1, e1) = e2)) | (~(op(e1, e3) = e3)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.86 tff(26282,plain,
% 2.76/2.86 (~(op(e1, e1) = e2)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[26281, 164, 7826])).
% 2.76/2.86 tff(26283,plain,
% 2.76/2.86 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[2])).
% 2.76/2.86 tff(26284,plain,
% 2.76/2.86 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26283, 120])).
% 2.76/2.86 tff(26285,plain,
% 2.76/2.86 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26284])).
% 2.76/2.86 tff(26286,plain,
% 2.76/2.86 (~(op(e2, e3) = e2)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[964, 26285])).
% 2.76/2.86 tff(26287,plain,
% 2.76/2.86 (op(e2, e3) = e1),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[24237, 26286, 124])).
% 2.76/2.86 tff(26288,plain,
% 2.76/2.86 (op(e2, e0) = e2),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23808, 26287, 2])).
% 2.76/2.86 tff(26289,plain,
% 2.76/2.86 ((op(e2, e0) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26288])).
% 2.76/2.86 tff(26290,plain,
% 2.76/2.86 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26289, 1960])).
% 2.76/2.86 tff(26291,plain,
% 2.76/2.86 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26290])).
% 2.76/2.86 tff(26292,plain,
% 2.76/2.86 (~(op(e2, e1) = e2)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[1966, 26291])).
% 2.76/2.86 tff(26293,plain,
% 2.76/2.86 (op(e3, e1) = e2),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[1993, 26292, 68, 10380])).
% 2.76/2.86 tff(26294,plain,
% 2.76/2.86 (op(e3, op(e2, e3)) = op(e3, e1)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26287])).
% 2.76/2.86 tff(26295,plain,
% 2.76/2.86 (e1 = op(e2, e3)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26287])).
% 2.76/2.86 tff(26296,plain,
% 2.76/2.86 ((op(e0, e2) = e1) <=> (e3 = e1)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[7826])).
% 2.76/2.86 tff(26297,plain,
% 2.76/2.86 ((op(e0, e2) = e1) <=> (e1 = e3)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26296, 128])).
% 2.76/2.86 tff(26298,plain,
% 2.76/2.86 ((e1 = e3) <=> (op(e0, e2) = e1)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26297])).
% 2.76/2.86 tff(26299,plain,
% 2.76/2.86 ((~(e1 = e3)) <=> (~(op(e0, e2) = e1))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26298])).
% 2.76/2.86 tff(26300,plain,
% 2.76/2.86 (~(op(e0, e2) = e1)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[303, 26299])).
% 2.76/2.86 tff(26301,plain,
% 2.76/2.86 (op(e1, e2) = op(e1, op(e0, e3))),
% 2.76/2.86 inference(symmetry,[status(thm)],[10421])).
% 2.76/2.86 tff(26302,plain,
% 2.76/2.86 ((op(e1, e2) = e1) <=> (op(e1, op(e0, e3)) = e1)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26301])).
% 2.76/2.86 tff(26303,plain,
% 2.76/2.86 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e2) = e1)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26302])).
% 2.76/2.86 tff(26304,plain,
% 2.76/2.86 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26288])).
% 2.76/2.86 tff(26305,plain,
% 2.76/2.86 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26304])).
% 2.76/2.86 tff(26306,plain,
% 2.76/2.86 (~(op(e1, e0) = e2)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[756, 26305])).
% 2.76/2.86 tff(26307,plain,
% 2.76/2.86 (op(e1, e2) = e2),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2285, 26306, 26179, 68])).
% 2.76/2.86 tff(26308,plain,
% 2.76/2.86 (op(e1, op(e0, e3)) = op(e0, e3)),
% 2.76/2.86 inference(transitivity,[status(thm)],[10421, 26307, 2560])).
% 2.76/2.86 tff(26309,plain,
% 2.76/2.86 ((op(e1, op(e0, e3)) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26308, 26295])).
% 2.76/2.86 tff(26310,plain,
% 2.76/2.86 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, op(e0, e3)) = e1)),
% 2.76/2.86 inference(symmetry,[status(thm)],[26309])).
% 2.76/2.86 tff(26311,plain,
% 2.76/2.86 ((op(e0, e3) = op(e2, e3)) <=> (op(e1, e2) = e1)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26310, 26303])).
% 2.76/2.86 tff(26312,plain,
% 2.76/2.86 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e1, e2) = e1))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26311])).
% 2.76/2.86 tff(26313,plain,
% 2.76/2.86 (~(op(e1, e2) = e1)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[964, 26312])).
% 2.76/2.86 tff(26314,plain,
% 2.76/2.86 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e3, e2) = e1)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[1613, 24048])).
% 2.76/2.86 tff(26315,plain,
% 2.76/2.86 (op(e3, e2) = e1),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[26314, 26313, 26300])).
% 2.76/2.86 tff(26316,plain,
% 2.76/2.86 (op(e3, e2) = op(e2, e3)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26315, 26295])).
% 2.76/2.86 tff(26317,plain,
% 2.76/2.86 (op(e3, op(e3, e2)) = op(e3, op(e2, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26316])).
% 2.76/2.86 tff(26318,plain,
% 2.76/2.86 (op(e3, op(e3, e2)) = e2),
% 2.76/2.86 inference(transitivity,[status(thm)],[26317, 26294, 26293])).
% 2.76/2.86 tff(26319,plain,
% 2.76/2.86 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[1904, 26318])).
% 2.76/2.86 tff(26320,plain,
% 2.76/2.86 (op(op(e2, e3), e2) = op(e1, op(e0, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26287, 2560])).
% 2.76/2.86 tff(26321,plain,
% 2.76/2.86 (op(e1, op(e1, e2)) = op(op(e2, e3), e2)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26295, 26307])).
% 2.76/2.86 tff(26322,plain,
% 2.76/2.86 (op(e1, op(e1, e2)) = e2),
% 2.76/2.86 inference(transitivity,[status(thm)],[26321, 26320, 10421, 26307])).
% 2.76/2.86 tff(26323,plain,
% 2.76/2.86 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2377, 26322])).
% 2.76/2.86 tff(26324,plain,
% 2.76/2.86 ((e0 = e2) <=> (e0 = op(e0, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[2560])).
% 2.76/2.86 tff(26325,plain,
% 2.76/2.86 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 2.76/2.86 inference(transitivity,[status(thm)],[26324, 1079])).
% 2.76/2.86 tff(26326,plain,
% 2.76/2.86 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26325])).
% 2.76/2.86 tff(26327,plain,
% 2.76/2.86 (~(op(e0, e3) = e0)),
% 2.76/2.86 inference(modus_ponens,[status(thm)],[14, 26326])).
% 2.76/2.86 tff(26328,plain,
% 2.76/2.86 (op(e3, e3) = e0),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[24663, 26327])).
% 2.76/2.86 tff(26329,plain,
% 2.76/2.86 (~(op(e2, e0) = e3)),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[24207, 26287])).
% 2.76/2.86 tff(26330,plain,
% 2.76/2.86 (op(e3, e0) = e3),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2713, 26329, 26259, 2168])).
% 2.76/2.86 tff(26331,plain,
% 2.76/2.86 (op(e3, op(e3, e0)) = op(e3, e3)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26330])).
% 2.76/2.86 tff(26332,plain,
% 2.76/2.86 (op(e3, op(e3, e0)) = e0),
% 2.76/2.86 inference(transitivity,[status(thm)],[26331, 26328])).
% 2.76/2.86 tff(26333,plain,
% 2.76/2.86 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[1345, 26332])).
% 2.76/2.86 tff(26334,plain,
% 2.76/2.86 (op(e2, op(e2, e0)) = e0),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23913, 26288])).
% 2.76/2.86 tff(26335,plain,
% 2.76/2.86 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2653, 26334])).
% 2.76/2.86 tff(26336,plain,
% 2.76/2.86 (op(e2, e1) = e3),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[23641, 26329, 124])).
% 2.76/2.86 tff(26337,plain,
% 2.76/2.86 (op(e2, op(e2, e3)) = op(e2, e1)),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26287])).
% 2.76/2.86 tff(26338,plain,
% 2.76/2.86 (op(op(e3, e1), e1) = op(e2, op(e2, e3))),
% 2.76/2.86 inference(monotonicity,[status(thm)],[26293, 26295])).
% 2.76/2.86 tff(26339,plain,
% 2.76/2.86 (op(op(e3, e1), e1) = e3),
% 2.76/2.86 inference(transitivity,[status(thm)],[26338, 26337, 26336])).
% 2.76/2.86 tff(26340,plain,
% 2.76/2.86 ((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1))),
% 2.76/2.86 inference(unit_resolution,[status(thm)],[2416, 26339])).
% 2.76/2.87 tff(26341,plain,
% 2.76/2.87 (op(e2, op(e2, e3)) = e3),
% 2.76/2.87 inference(transitivity,[status(thm)],[26337, 26336])).
% 2.76/2.87 tff(26342,plain,
% 2.76/2.87 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[2344, 26341])).
% 2.76/2.87 tff(26343,plain,
% 2.76/2.87 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[25120, 26179])).
% 2.76/2.87 tff(26344,plain,
% 2.76/2.87 (op(e0, op(e0, e2)) = op(e0, e3)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[7826])).
% 2.76/2.87 tff(26345,plain,
% 2.76/2.87 ((op(e0, op(e0, e2)) = e2) <=> (op(e0, e3) = e2)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26344])).
% 2.76/2.87 tff(26346,plain,
% 2.76/2.87 ((op(e0, e3) = e2) <=> (op(e0, op(e0, e2)) = e2)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26345])).
% 2.76/2.87 tff(26347,plain,
% 2.76/2.87 (op(e0, op(e0, e2)) = e2),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[2, 26346])).
% 2.76/2.87 tff(26348,plain,
% 2.76/2.87 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1331, 26347])).
% 2.76/2.87 tff(26349,plain,
% 2.76/2.87 (op(e2, op(e2, e1)) = op(op(e0, e3), e3)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[2560, 26336])).
% 2.76/2.87 tff(26350,plain,
% 2.76/2.87 (op(e2, op(e2, e1)) = e1),
% 2.76/2.87 inference(transitivity,[status(thm)],[26349, 3277, 26287])).
% 2.76/2.87 tff(26351,plain,
% 2.76/2.87 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1355, 26350])).
% 2.76/2.87 tff(26352,plain,
% 2.76/2.87 (op(e0, op(e0, e3)) = e3),
% 2.76/2.87 inference(transitivity,[status(thm)],[17663, 7826])).
% 2.76/2.87 tff(26353,plain,
% 2.76/2.87 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1938, 26352])).
% 2.76/2.87 tff(26354,plain,
% 2.76/2.87 (op(e3, e1) = op(e0, e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26293, 2560])).
% 2.76/2.87 tff(26355,plain,
% 2.76/2.87 ((op(e3, e1) = e1) <=> (op(e0, e3) = op(e2, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26354, 26295])).
% 2.76/2.87 tff(26356,plain,
% 2.76/2.87 ((op(e0, e3) = op(e2, e3)) <=> (op(e3, e1) = e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26355])).
% 2.76/2.87 tff(26357,plain,
% 2.76/2.87 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e3, e1) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26356])).
% 2.76/2.87 tff(26358,plain,
% 2.76/2.87 (~(op(e3, e1) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[964, 26357])).
% 2.76/2.87 tff(26359,plain,
% 2.76/2.87 ((op(e1, e1) = e1) <=> (op(e3, e3) = op(e2, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[20798, 2685])).
% 2.76/2.87 tff(26360,plain,
% 2.76/2.87 ((op(e1, e1) = e1) <=> (op(e2, e3) = op(e3, e3))),
% 2.76/2.87 inference(transitivity,[status(thm)],[26359, 2820])).
% 2.76/2.87 tff(26361,plain,
% 2.76/2.87 ((op(e2, e3) = op(e3, e3)) <=> (op(e1, e1) = e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26360])).
% 2.76/2.87 tff(26362,plain,
% 2.76/2.87 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e1, e1) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26361])).
% 2.76/2.87 tff(26363,plain,
% 2.76/2.87 (~(op(e1, e1) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[368, 26362])).
% 2.76/2.87 tff(26364,plain,
% 2.76/2.87 (op(e1, e0) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[954, 26363, 87, 4515])).
% 2.76/2.87 tff(26365,plain,
% 2.76/2.87 (op(e1, op(e1, e0)) = op(e1, e1)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26364])).
% 2.76/2.87 tff(26366,plain,
% 2.76/2.87 (op(e1, op(e1, e0)) = e0),
% 2.76/2.87 inference(transitivity,[status(thm)],[26365, 249])).
% 2.76/2.87 tff(26367,plain,
% 2.76/2.87 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1836, 26366])).
% 2.76/2.87 tff(26368,plain,
% 2.76/2.87 (op(e0, e1) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1252, 26363, 21187, 2826])).
% 2.76/2.87 tff(26369,plain,
% 2.76/2.87 (op(e0, e1) = op(e2, e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26368, 2685])).
% 2.76/2.87 tff(26370,plain,
% 2.76/2.87 (op(e0, op(e0, e1)) = op(e0, op(e2, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26369])).
% 2.76/2.87 tff(26371,plain,
% 2.76/2.87 (op(e0, op(e0, e1)) = e1),
% 2.76/2.87 inference(transitivity,[status(thm)],[26370, 4447, 26368])).
% 2.76/2.87 tff(26372,plain,
% 2.76/2.87 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[2449, 26371])).
% 2.76/2.87 tff(26373,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1459, 26372, 26367, 3342, 1936, 1363, 1304, 1347, 1275, 2421, 1926, 1358, 3341])).
% 2.76/2.87 tff(26374,plain,((~(op(e1, e1) = e0)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2)))) | (~(op(e2, e3) = e1)) | (op(e3, e1) = e1) | (op(e1, e3) = e1) | (op(e1, e2) = e1) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26375,plain,
% 2.76/2.87 (~(op(e1, e1) = e0)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26374, 26353, 26351, 26348, 26343, 26342, 26340, 26335, 26333, 26323, 26319, 26287, 26358, 87, 26313, 26328])).
% 2.76/2.87 tff(26376,plain,
% 2.76/2.87 (op(e1, e0) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24724, 26375])).
% 2.76/2.87 tff(26377,plain,
% 2.76/2.87 (op(e1, op(e3, e3)) = op(e1, e0)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26328])).
% 2.76/2.87 tff(26378,plain,
% 2.76/2.87 (e0 = op(e3, e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26328])).
% 2.76/2.87 tff(26379,plain,
% 2.76/2.87 (op(e1, e0) = op(e3, e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26376, 26378])).
% 2.76/2.87 tff(26380,plain,
% 2.76/2.87 (op(e1, op(e1, e0)) = op(e1, op(e3, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26379])).
% 2.76/2.87 tff(26381,plain,
% 2.76/2.87 (op(e1, op(e1, e0)) = e0),
% 2.76/2.87 inference(transitivity,[status(thm)],[26380, 26377, 26376])).
% 2.76/2.87 tff(26382,plain,
% 2.76/2.87 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1836, 26381])).
% 2.76/2.87 tff(26383,plain,
% 2.76/2.87 (op(e1, e0) = e2),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26153, 12623, 25192, 23704, 12023, 2527])).
% 2.76/2.87 tff(26384,plain,
% 2.76/2.87 (e0 = op(e1, e0)),
% 2.76/2.87 inference(symmetry,[status(thm)],[24725])).
% 2.76/2.87 tff(26385,plain,
% 2.76/2.87 (e0 = e2),
% 2.76/2.87 inference(transitivity,[status(thm)],[26384, 26383])).
% 2.76/2.87 tff(26386,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[14, 26385])).
% 2.76/2.87 tff(26387,plain,((~(op(e1, e1) = e3)) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26388,plain,
% 2.76/2.87 (~(op(e1, e1) = e3)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26387, 25195])).
% 2.76/2.87 tff(26389,plain,
% 2.76/2.87 ((op(e1, e1) = e0) | (~(op(e0, e2) = e3)) | (~(op(e2, e3) = e1)) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e1, e1) = e3) | (op(e0, e1) = e0)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[20749, 23694])).
% 2.76/2.87 tff(26390,plain,
% 2.76/2.87 (op(e0, e1) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26389, 26375, 68, 7826, 26287, 26292, 26388])).
% 2.76/2.87 tff(26391,plain,
% 2.76/2.87 (op(e0, op(e2, e3)) = op(e0, e1)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26287])).
% 2.76/2.87 tff(26392,plain,
% 2.76/2.87 (op(op(e0, e1), e1) = op(e0, op(e2, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26390, 26295])).
% 2.76/2.87 tff(26393,plain,
% 2.76/2.87 (op(op(e0, e1), e1) = e0),
% 2.76/2.87 inference(transitivity,[status(thm)],[26392, 26391, 26390])).
% 2.76/2.87 tff(26394,plain,
% 2.76/2.87 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[2650, 26393])).
% 2.76/2.87 tff(26395,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1459, 26394, 26382, 26353, 26351, 26348, 26343, 26342, 26340, 26335, 26333, 26323, 26319])).
% 2.76/2.87 tff(26396,plain,((~(op(e0, e3) = e2)) | (op(e1, e1) = e2) | (~(op(e0, e2) = e3)) | (op(e1, e3) = e1) | (op(e2, e3) = e3) | (op(e1, e0) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26397,plain,
% 2.76/2.87 (~(op(e0, e3) = e2)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26396, 26282, 7826, 26188, 26183, 13176])).
% 2.76/2.87 tff(26398,plain,
% 2.76/2.87 (op(e2, e3) = e2),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[15003, 26397, 26179])).
% 2.76/2.87 tff(26399,plain,
% 2.76/2.87 (e2 = op(e2, e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26398])).
% 2.76/2.87 tff(26400,plain,
% 2.76/2.87 ((e1 = e2) <=> (e1 = op(e2, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26399])).
% 2.76/2.87 tff(26401,plain,
% 2.76/2.87 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26400, 5574])).
% 2.76/2.87 tff(26402,plain,
% 2.76/2.87 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26401])).
% 2.76/2.87 tff(26403,plain,
% 2.76/2.87 (op(e2, e3) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26276, 26397, 25192, 26179, 26183])).
% 2.76/2.87 tff(26404,plain,
% 2.76/2.87 (e1 = e2),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26403, 26402])).
% 2.76/2.87 tff(26405,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[708, 26404])).
% 2.76/2.87 tff(26406,plain,((~(op(e1, e3) = e3)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26407,plain,
% 2.76/2.87 (~(op(e1, e3) = e3)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26406, 7826])).
% 2.76/2.87 tff(26408,plain,
% 2.76/2.87 (op(e1, e3) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24697, 26407, 26179])).
% 2.76/2.87 tff(26409,plain,
% 2.76/2.87 (e1 = op(e1, e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26408])).
% 2.76/2.87 tff(26410,plain,
% 2.76/2.87 ((op(e2, e3) = e1) <=> (op(e2, e3) = op(e1, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26409])).
% 2.76/2.87 tff(26411,plain,
% 2.76/2.87 ((op(e2, e3) = e1) <=> (op(e1, e3) = op(e2, e3))),
% 2.76/2.87 inference(transitivity,[status(thm)],[26410, 1687])).
% 2.76/2.87 tff(26412,plain,
% 2.76/2.87 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26411])).
% 2.76/2.87 tff(26413,plain,
% 2.76/2.87 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26412])).
% 2.76/2.87 tff(26414,plain,
% 2.76/2.87 (~(op(e2, e3) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[118, 26413])).
% 2.76/2.87 tff(26415,plain,
% 2.76/2.87 ((op(e1, e2) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26409])).
% 2.76/2.87 tff(26416,plain,
% 2.76/2.87 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26415])).
% 2.76/2.87 tff(26417,plain,
% 2.76/2.87 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26416])).
% 2.76/2.87 tff(26418,plain,
% 2.76/2.87 (~(op(e1, e2) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[1850, 26417])).
% 2.76/2.87 tff(26419,plain,
% 2.76/2.87 (op(e3, e2) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24286, 26418, 26300])).
% 2.76/2.87 tff(26420,plain,
% 2.76/2.87 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e1)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26419])).
% 2.76/2.87 tff(26421,plain,
% 2.76/2.87 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26420])).
% 2.76/2.87 tff(26422,plain,
% 2.76/2.87 (~(op(e3, e0) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[1133, 26421])).
% 2.76/2.87 tff(26423,plain,
% 2.76/2.87 (op(e1, e0) = e3),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[247, 26407, 19400, 26388])).
% 2.76/2.87 tff(26424,plain,
% 2.76/2.87 ((op(e1, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26423])).
% 2.76/2.87 tff(26425,plain,
% 2.76/2.87 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26424, 404])).
% 2.76/2.87 tff(26426,plain,
% 2.76/2.87 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26425])).
% 2.76/2.87 tff(26427,plain,
% 2.76/2.87 (~(op(e3, e0) = e3)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[410, 26426])).
% 2.76/2.87 tff(26428,plain,
% 2.76/2.87 ((~(op(e3, e0) = op(e0, e3))) <=> (~(op(e3, e0) = e2))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[23865])).
% 2.76/2.87 tff(26429,plain,
% 2.76/2.87 (op(op(e1, e3), e1) = op(e1, e1)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26408])).
% 2.76/2.87 tff(26430,plain,
% 2.76/2.87 ((op(op(e1, e3), e1) = e3) <=> (op(e1, e1) = e3)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26429])).
% 2.76/2.87 tff(26431,plain,
% 2.76/2.87 ((op(e1, e1) = e3) <=> (op(op(e1, e3), e1) = e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26430])).
% 2.76/2.87 tff(26432,plain,
% 2.76/2.87 ((~(op(e1, e1) = e3)) <=> (~(op(op(e1, e3), e1) = e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26431])).
% 2.76/2.87 tff(26433,plain,
% 2.76/2.87 (~(op(op(e1, e3), e1) = e3)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26388, 26432])).
% 2.76/2.87 tff(26434,plain,
% 2.76/2.87 ((op(e1, e0) = e0) <=> (e3 = e0)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26423])).
% 2.76/2.87 tff(26435,plain,
% 2.76/2.87 ((op(e1, e0) = e0) <=> (e0 = e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26434, 159])).
% 2.76/2.87 tff(26436,plain,
% 2.76/2.87 ((e0 = e3) <=> (op(e1, e0) = e0)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26435])).
% 2.76/2.87 tff(26437,plain,
% 2.76/2.87 ((~(e0 = e3)) <=> (~(op(e1, e0) = e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26436])).
% 2.76/2.87 tff(26438,plain,
% 2.76/2.87 (~(op(e1, e0) = e0)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[181, 26437])).
% 2.76/2.87 tff(26439,plain,
% 2.76/2.87 (op(e1, e1) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24724, 26438])).
% 2.76/2.87 tff(26440,plain,
% 2.76/2.87 (e0 = op(e1, e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26439])).
% 2.76/2.87 tff(26441,plain,
% 2.76/2.87 (op(e2, op(e0, e3)) = op(e1, e1)),
% 2.76/2.87 inference(transitivity,[status(thm)],[18346, 23615, 26440])).
% 2.76/2.87 tff(26442,plain,
% 2.76/2.87 ((op(e2, op(e0, e3)) = e2) <=> (op(e1, e1) = e2)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26441])).
% 2.76/2.87 tff(26443,plain,
% 2.76/2.87 ((op(e1, e1) = e2) <=> (op(e2, op(e0, e3)) = e2)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26442])).
% 2.76/2.87 tff(26444,plain,
% 2.76/2.87 ((~(op(e1, e1) = e2)) <=> (~(op(e2, op(e0, e3)) = e2))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26443])).
% 2.76/2.87 tff(26445,plain,
% 2.76/2.87 (op(e1, e2) = e2),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[23821, 26418, 19400])).
% 2.76/2.87 tff(26446,plain,
% 2.76/2.87 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e2)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26445])).
% 2.76/2.87 tff(26447,plain,
% 2.76/2.87 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e2))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26446])).
% 2.76/2.87 tff(26448,plain,
% 2.76/2.87 (~(op(e1, e1) = e2)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[1604, 26447])).
% 2.76/2.87 tff(26449,plain,
% 2.76/2.87 (~(op(e2, op(e0, e3)) = e2)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26448, 26444])).
% 2.76/2.87 tff(26450,plain,
% 2.76/2.87 ((op(e0, op(e0, e3)) = e0) <=> (e3 = op(e1, e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26352, 26440])).
% 2.76/2.87 tff(26451,plain,
% 2.76/2.87 ((op(e0, op(e0, e3)) = e0) <=> (op(e1, e1) = e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26450, 1112])).
% 2.76/2.87 tff(26452,plain,
% 2.76/2.87 ((op(e1, e1) = e3) <=> (op(e0, op(e0, e3)) = e0)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26451])).
% 2.76/2.87 tff(26453,plain,
% 2.76/2.87 ((~(op(e1, e1) = e3)) <=> (~(op(e0, op(e0, e3)) = e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26452])).
% 2.76/2.87 tff(26454,plain,
% 2.76/2.87 (~(op(e0, op(e0, e3)) = e0)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26388, 26453])).
% 2.76/2.87 tff(26455,plain,
% 2.76/2.87 (op(e3, op(e0, e3)) = op(e1, e3)),
% 2.76/2.87 inference(transitivity,[status(thm)],[857, 26419, 26409])).
% 2.76/2.87 tff(26456,plain,
% 2.76/2.87 ((op(e3, op(e0, e3)) = e3) <=> (op(e1, e3) = e3)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26455])).
% 2.76/2.87 tff(26457,plain,
% 2.76/2.87 ((op(e1, e3) = e3) <=> (op(e3, op(e0, e3)) = e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26456])).
% 2.76/2.87 tff(26458,plain,
% 2.76/2.87 ((~(op(e1, e3) = e3)) <=> (~(op(e3, op(e0, e3)) = e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26457])).
% 2.76/2.87 tff(26459,plain,
% 2.76/2.87 (~(op(e3, op(e0, e3)) = e3)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26407, 26458])).
% 2.76/2.87 tff(26460,plain,
% 2.76/2.87 (op(e1, op(e0, e3)) = e2),
% 2.76/2.87 inference(transitivity,[status(thm)],[10421, 26445])).
% 2.76/2.87 tff(26461,plain,
% 2.76/2.87 ((op(e1, op(e0, e3)) = e1) <=> (e2 = op(e1, e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26460, 26409])).
% 2.76/2.87 tff(26462,plain,
% 2.76/2.87 ((op(e1, op(e0, e3)) = e1) <=> (op(e1, e3) = e2)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26461, 66])).
% 2.76/2.87 tff(26463,plain,
% 2.76/2.87 ((op(e1, e3) = e2) <=> (op(e1, op(e0, e3)) = e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26462])).
% 2.76/2.87 tff(26464,plain,
% 2.76/2.87 ((~(op(e1, e3) = e2)) <=> (~(op(e1, op(e0, e3)) = e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26463])).
% 2.76/2.87 tff(26465,plain,
% 2.76/2.87 (~(op(e1, op(e0, e3)) = e1)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26179, 26464])).
% 2.76/2.87 tff(26466,plain,
% 2.76/2.87 (~(op(e3, e0) = op(e0, e3))),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[3220, 26465, 25192, 26459, 26454, 26449, 26433])).
% 2.76/2.87 tff(26467,plain,
% 2.76/2.87 (~(op(e3, e0) = e2)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26466, 26428])).
% 2.76/2.87 tff(26468,plain,
% 2.76/2.87 ((op(e0, e3) = e0) <=> (e2 = op(e1, e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[2, 26440])).
% 2.76/2.87 tff(26469,plain,
% 2.76/2.87 ((op(e0, e3) = e0) <=> (op(e1, e1) = e2)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26468, 2166])).
% 2.76/2.87 tff(26470,plain,
% 2.76/2.87 ((op(e1, e1) = e2) <=> (op(e0, e3) = e0)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26469])).
% 2.76/2.87 tff(26471,plain,
% 2.76/2.87 ((~(op(e1, e1) = e2)) <=> (~(op(e0, e3) = e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26470])).
% 2.76/2.87 tff(26472,plain,
% 2.76/2.87 (~(op(e0, e3) = e0)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[26448, 26471])).
% 2.76/2.87 tff(26473,plain,
% 2.76/2.87 (op(e3, e3) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24663, 26472])).
% 2.76/2.87 tff(26474,plain,
% 2.76/2.87 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26473])).
% 2.76/2.87 tff(26475,plain,
% 2.76/2.87 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26474])).
% 2.76/2.87 tff(26476,plain,
% 2.76/2.87 (~(op(e3, e0) = e0)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[157, 26475])).
% 2.76/2.87 tff(26477,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[5422, 26476, 26467, 26427, 26422])).
% 2.76/2.87 tff(26478,plain,((~(op(e0, e3) = e2)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26479,plain,
% 2.76/2.87 (~(op(e0, e3) = e2)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26478, 7826])).
% 2.76/2.87 tff(26480,plain,
% 2.76/2.87 (op(e2, e3) = e3),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26276, 26479, 25192, 26179, 26414])).
% 2.76/2.87 tff(26481,plain,
% 2.76/2.87 (op(e2, e3) = e2),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[15003, 26479, 26179])).
% 2.76/2.87 tff(26482,plain,
% 2.76/2.87 (e2 = op(e2, e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26481])).
% 2.76/2.87 tff(26483,plain,
% 2.76/2.87 (e2 = e3),
% 2.76/2.87 inference(transitivity,[status(thm)],[26482, 26480])).
% 2.76/2.87 tff(26484,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1321, 26483])).
% 2.76/2.87 tff(26485,plain,(~(op(e0, e2) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26486,plain,
% 2.76/2.87 ((op(e0, e2) = e1) | (op(e0, e2) = e2)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[23880, 26485])).
% 2.76/2.87 tff(26487,plain,
% 2.76/2.87 (op(e0, e2) = e1),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26486, 23847])).
% 2.76/2.87 tff(26488,plain,
% 2.76/2.87 (op(e2, e1) = e3),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[23641, 20711, 24208])).
% 2.76/2.87 tff(26489,plain,
% 2.76/2.87 (e3 = op(e2, e1)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26488])).
% 2.76/2.87 tff(26490,plain,
% 2.76/2.87 ((op(e0, e1) = e3) <=> (op(e0, e1) = op(e2, e1))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26489])).
% 2.76/2.87 tff(26491,plain,
% 2.76/2.87 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26490])).
% 2.76/2.87 tff(26492,plain,
% 2.76/2.87 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26491])).
% 2.76/2.87 tff(26493,plain,
% 2.76/2.87 (~(op(e0, e1) = e3)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[606, 26492])).
% 2.76/2.87 tff(26494,plain,
% 2.76/2.87 (op(e1, e0) = e3),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26153, 26493, 25192, 6613, 741, 675])).
% 2.76/2.87 tff(26495,plain,
% 2.76/2.87 (op(e1, e0) = op(e2, e1)),
% 2.76/2.87 inference(transitivity,[status(thm)],[26494, 26489])).
% 2.76/2.87 tff(26496,plain,
% 2.76/2.87 ((op(e1, e0) = e0) <=> (op(e2, e1) = e0)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26495])).
% 2.76/2.87 tff(26497,plain,
% 2.76/2.87 ((op(e2, e1) = e0) <=> (op(e1, e0) = e0)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26496])).
% 2.76/2.87 tff(26498,plain,
% 2.76/2.87 ((~(op(e2, e1) = e0)) <=> (~(op(e1, e0) = e0))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26497])).
% 2.76/2.87 tff(26499,plain,
% 2.76/2.87 (~(op(e1, e0) = e0)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[23694, 26498])).
% 2.76/2.87 tff(26500,plain,
% 2.76/2.87 (op(e1, e1) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24724, 26499])).
% 2.76/2.87 tff(26501,plain,
% 2.76/2.87 (~(op(e3, e3) = e0)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[20809, 26500, 2684, 264, 26494])).
% 2.76/2.87 tff(26502,plain,
% 2.76/2.87 (op(e0, e3) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[24663, 26501])).
% 2.76/2.87 tff(26503,plain,
% 2.76/2.87 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e3)),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26494])).
% 2.76/2.87 tff(26504,plain,
% 2.76/2.87 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e3))),
% 2.76/2.87 inference(monotonicity,[status(thm)],[26503])).
% 2.76/2.87 tff(26505,plain,
% 2.76/2.87 (~(op(e0, e0) = e3)),
% 2.76/2.87 inference(modus_ponens,[status(thm)],[2471, 26504])).
% 2.76/2.87 tff(26506,plain,
% 2.76/2.87 (op(e0, e3) = e3),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[1495, 26505, 26485, 26493])).
% 2.76/2.87 tff(26507,plain,
% 2.76/2.87 (e3 = op(e0, e3)),
% 2.76/2.87 inference(symmetry,[status(thm)],[26506])).
% 2.76/2.87 tff(26508,plain,
% 2.76/2.87 (op(e2, e1) = e0),
% 2.76/2.87 inference(transitivity,[status(thm)],[26488, 26507, 26502])).
% 2.76/2.87 tff(26509,plain,
% 2.76/2.87 ($false),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[23694, 26508])).
% 2.76/2.87 tff(26510,plain,((~(op(e2, e3) = e1)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.87 tff(26511,plain,
% 2.76/2.87 (~(op(e2, e3) = e1)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26510, 264])).
% 2.76/2.87 tff(26512,plain,
% 2.76/2.87 ((op(e0, e3) = e1) | (op(e0, e3) = e2) | (op(e0, e3) = e0) | (op(e2, e3) = e1)),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[19997, 24661])).
% 2.76/2.87 tff(26513,plain,
% 2.76/2.87 (op(e0, e3) = e0),
% 2.76/2.87 inference(unit_resolution,[status(thm)],[26512, 26511, 25192, 677])).
% 2.76/2.88 tff(26514,plain,
% 2.76/2.88 (e0 = op(e0, e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26513])).
% 2.76/2.88 tff(26515,plain,
% 2.76/2.88 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e0, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26514])).
% 2.76/2.88 tff(26516,plain,
% 2.76/2.88 (op(e2, e3) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26176, 26511, 25192, 677])).
% 2.76/2.88 tff(26517,plain,
% 2.76/2.88 (op(e1, e2) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[19078, 249, 264, 26516, 26513])).
% 2.76/2.88 tff(26518,plain,
% 2.76/2.88 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26517])).
% 2.76/2.88 tff(26519,plain,
% 2.76/2.88 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26518])).
% 2.76/2.88 tff(26520,plain,
% 2.76/2.88 (~(op(e1, e0) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1312, 26519])).
% 2.76/2.88 tff(26521,plain,
% 2.76/2.88 (op(e0, e1) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26153, 26520, 25192, 6613, 741, 675])).
% 2.76/2.88 tff(26522,plain,
% 2.76/2.88 ((op(e0, e1) = op(e3, e1)) <=> (e3 = op(e3, e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26521])).
% 2.76/2.88 tff(26523,plain,
% 2.76/2.88 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26522, 396])).
% 2.76/2.88 tff(26524,plain,
% 2.76/2.88 ((op(e3, e1) = e3) <=> (op(e0, e1) = op(e3, e1))),
% 2.76/2.88 inference(symmetry,[status(thm)],[26523])).
% 2.76/2.88 tff(26525,plain,
% 2.76/2.88 (op(e3, e3) = e1),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[151, 26511, 25192, 6651])).
% 2.76/2.88 tff(26526,plain,
% 2.76/2.88 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26525])).
% 2.76/2.88 tff(26527,plain,
% 2.76/2.88 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26526])).
% 2.76/2.88 tff(26528,plain,
% 2.76/2.88 (~(op(e3, e1) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[437, 26527])).
% 2.76/2.88 tff(26529,plain,
% 2.76/2.88 (e3 = op(e2, e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26516])).
% 2.76/2.88 tff(26530,plain,
% 2.76/2.88 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e2, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26529])).
% 2.76/2.88 tff(26531,plain,
% 2.76/2.88 ((op(e3, e2) = op(e2, e3)) <=> (op(e3, e2) = e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26530])).
% 2.76/2.88 tff(26532,plain,
% 2.76/2.88 (op(e1, e2) = op(e2, e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26517, 26529])).
% 2.76/2.88 tff(26533,plain,
% 2.76/2.88 ((op(e1, e2) = op(e3, e2)) <=> (op(e2, e3) = op(e3, e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26532])).
% 2.76/2.88 tff(26534,plain,
% 2.76/2.88 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = op(e2, e3))),
% 2.76/2.88 inference(transitivity,[status(thm)],[26533, 394])).
% 2.76/2.88 tff(26535,plain,
% 2.76/2.88 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26534, 26531])).
% 2.76/2.88 tff(26536,plain,
% 2.76/2.88 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26535])).
% 2.76/2.88 tff(26537,plain,
% 2.76/2.88 (~(op(e3, e2) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[2292, 26536])).
% 2.76/2.88 tff(26538,plain,
% 2.76/2.88 (~(op(e3, e1) = e2)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[25339, 26537, 25192, 6651, 26511, 6598])).
% 2.76/2.88 tff(26539,plain,
% 2.76/2.88 (op(e3, e1) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[446, 26538, 13208, 26528])).
% 2.76/2.88 tff(26540,plain,
% 2.76/2.88 (op(e0, e1) = op(e3, e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[26539, 26524])).
% 2.76/2.88 tff(26541,plain,
% 2.76/2.88 ($false),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[3046, 26540])).
% 2.76/2.88 tff(26542,plain,((~(op(e1, e1) = e0)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.88 tff(26543,plain,
% 2.76/2.88 (~(op(e1, e1) = e0)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26542, 264])).
% 2.76/2.88 tff(26544,plain,
% 2.76/2.88 (op(e1, e0) = e0),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[24724, 26543])).
% 2.76/2.88 tff(26545,plain,
% 2.76/2.88 ((op(e1, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26544])).
% 2.76/2.88 tff(26546,plain,
% 2.76/2.88 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26545, 8115])).
% 2.76/2.88 tff(26547,plain,
% 2.76/2.88 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = op(e0, e3))),
% 2.76/2.88 inference(transitivity,[status(thm)],[26546, 26515])).
% 2.76/2.88 tff(26548,plain,
% 2.76/2.88 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = op(e0, e3)))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26547])).
% 2.76/2.88 tff(26549,plain,
% 2.76/2.88 (~(op(e3, e0) = op(e0, e3))),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[410, 26548])).
% 2.76/2.88 tff(26550,plain,
% 2.76/2.88 ((op(e0, e3) = e3) <=> (e0 = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26513])).
% 2.76/2.88 tff(26551,plain,
% 2.76/2.88 ((e0 = e3) <=> (op(e0, e3) = e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26550])).
% 2.76/2.88 tff(26552,plain,
% 2.76/2.88 ((~(e0 = e3)) <=> (~(op(e0, e3) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26551])).
% 2.76/2.88 tff(26553,plain,
% 2.76/2.88 (~(op(e0, e3) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[181, 26552])).
% 2.76/2.88 tff(26554,plain,
% 2.76/2.88 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26546])).
% 2.76/2.88 tff(26555,plain,
% 2.76/2.88 (~(op(e3, e0) = e0)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[410, 26554])).
% 2.76/2.88 tff(26556,plain,
% 2.76/2.88 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e1) = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26516])).
% 2.76/2.88 tff(26557,plain,
% 2.76/2.88 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26556])).
% 2.76/2.88 tff(26558,plain,
% 2.76/2.88 (~(op(e2, e1) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[197, 26557])).
% 2.76/2.88 tff(26559,plain,
% 2.76/2.88 ((op(e1, e0) = e3) <=> (e0 = op(e2, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26544, 26529])).
% 2.76/2.88 tff(26560,plain,
% 2.76/2.88 ((op(e1, e0) = e3) <=> (op(e2, e3) = e0)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26559, 86])).
% 2.76/2.88 tff(26561,plain,
% 2.76/2.88 ((op(e2, e3) = e0) <=> (op(e1, e0) = e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26560])).
% 2.76/2.88 tff(26562,plain,
% 2.76/2.88 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e0) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26561])).
% 2.76/2.88 tff(26563,plain,
% 2.76/2.88 (~(op(e1, e0) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[23804, 26562])).
% 2.76/2.88 tff(26564,plain,
% 2.76/2.88 (op(e0, e1) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26153, 26563, 25192, 6613, 741, 675])).
% 2.76/2.88 tff(26565,plain,
% 2.76/2.88 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26564])).
% 2.76/2.88 tff(26566,plain,
% 2.76/2.88 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26565, 1112])).
% 2.76/2.88 tff(26567,plain,
% 2.76/2.88 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26566])).
% 2.76/2.88 tff(26568,plain,
% 2.76/2.88 (~(op(e1, e1) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[792, 26567])).
% 2.76/2.88 tff(26569,plain,
% 2.76/2.88 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e1) = e0)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26513])).
% 2.76/2.88 tff(26570,plain,
% 2.76/2.88 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26569])).
% 2.76/2.88 tff(26571,plain,
% 2.76/2.88 (~(op(e0, e1) = e0)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[818, 26570])).
% 2.76/2.88 tff(26572,plain,
% 2.76/2.88 (op(e3, e1) = e0),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[23988, 26543, 26571])).
% 2.76/2.88 tff(26573,plain,
% 2.76/2.88 ((op(e3, e1) = e2) <=> (e0 = e2)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26572])).
% 2.76/2.88 tff(26574,plain,
% 2.76/2.88 ((e0 = e2) <=> (op(e3, e1) = e2)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26573])).
% 2.76/2.88 tff(26575,plain,
% 2.76/2.88 ((~(e0 = e2)) <=> (~(op(e3, e1) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26574])).
% 2.76/2.88 tff(26576,plain,
% 2.76/2.88 (~(op(e3, e1) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[14, 26575])).
% 2.76/2.88 tff(26577,plain,
% 2.76/2.88 (op(e3, op(e3, e1)) = op(e3, e0)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26572])).
% 2.76/2.88 tff(26578,plain,
% 2.76/2.88 (op(e3, op(e3, e3)) = op(e3, e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26525])).
% 2.76/2.88 tff(26579,plain,
% 2.76/2.88 (op(e3, op(e3, op(e3, e3))) = op(e3, op(e3, e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26578])).
% 2.76/2.88 tff(26580,plain,
% 2.76/2.88 (op(e3, op(e3, op(e3, e3))) = op(e3, e0)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26579, 26577])).
% 2.76/2.88 tff(26581,plain,
% 2.76/2.88 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (e2 = op(e3, e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26580])).
% 2.76/2.88 tff(26582,plain,
% 2.76/2.88 ((e2 = op(e3, op(e3, op(e3, e3)))) <=> (op(e3, e0) = e2)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26581, 5377])).
% 2.76/2.88 tff(26583,plain,
% 2.76/2.88 ((~(e2 = op(e3, op(e3, op(e3, e3))))) <=> (~(op(e3, e0) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26582])).
% 2.76/2.88 tff(26584,plain,
% 2.76/2.88 (e1 = op(e3, e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[26525, 658])).
% 2.76/2.88 tff(26585,plain,
% 2.76/2.88 ((e0 = op(e3, op(e3, e3))) <=> (e0 = op(e3, e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26578])).
% 2.76/2.88 tff(26586,plain,
% 2.76/2.88 ((e0 = op(e3, op(e3, e3))) <=> (op(e3, e1) = e0)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26585, 5470])).
% 2.76/2.88 tff(26587,plain,
% 2.76/2.88 ((op(e3, e1) = e0) <=> (e0 = op(e3, op(e3, e3)))),
% 2.76/2.88 inference(symmetry,[status(thm)],[26586])).
% 2.76/2.88 tff(26588,plain,
% 2.76/2.88 (e0 = op(e3, op(e3, e3))),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[26572, 26587])).
% 2.76/2.88 tff(26589,plain,
% 2.76/2.88 (~(e2 = op(e3, op(e3, op(e3, e3))))),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[5397, 26588, 26584])).
% 2.76/2.88 tff(26590,plain,
% 2.76/2.88 (~(op(e3, e0) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[26589, 26583])).
% 2.76/2.88 tff(26591,plain,
% 2.76/2.88 (op(e3, e2) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[15971, 26590, 26576])).
% 2.76/2.88 tff(26592,plain,
% 2.76/2.88 ($false),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[8994, 26591, 26568, 26513, 26558, 26555, 26553, 26525, 26485, 26549, 677])).
% 2.76/2.88 tff(26593,plain,(~(op(e1, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.88 tff(26594,plain,
% 2.76/2.88 ((op(e1, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[164])).
% 2.76/2.88 tff(26595,plain,
% 2.76/2.88 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26594, 666])).
% 2.76/2.88 tff(26596,plain,
% 2.76/2.88 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26595])).
% 2.76/2.88 tff(26597,plain,
% 2.76/2.88 (~(op(e3, e3) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[571, 26596])).
% 2.76/2.88 tff(26598,plain,
% 2.76/2.88 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[164])).
% 2.76/2.88 tff(26599,plain,
% 2.76/2.88 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26598])).
% 2.76/2.88 tff(26600,plain,
% 2.76/2.88 (~(op(e1, e2) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1850, 26599])).
% 2.76/2.88 tff(26601,plain,
% 2.76/2.88 (op(e3, e2) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[23653, 26600, 26485])).
% 2.76/2.88 tff(26602,plain,
% 2.76/2.88 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26601])).
% 2.76/2.88 tff(26603,plain,
% 2.76/2.88 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26602])).
% 2.76/2.88 tff(26604,plain,
% 2.76/2.88 (~(op(e3, e0) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1133, 26603])).
% 2.76/2.88 tff(26605,plain,
% 2.76/2.88 ((op(e3, e2) = e2) <=> (e3 = e2)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26601])).
% 2.76/2.88 tff(26606,plain,
% 2.76/2.88 ((op(e3, e2) = e2) <=> (e2 = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26605, 1314])).
% 2.76/2.88 tff(26607,plain,
% 2.76/2.88 ((e2 = e3) <=> (op(e3, e2) = e2)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26606])).
% 2.76/2.88 tff(26608,plain,
% 2.76/2.88 ((~(e2 = e3)) <=> (~(op(e3, e2) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26607])).
% 2.76/2.88 tff(26609,plain,
% 2.76/2.88 (~(op(e3, e2) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1321, 26608])).
% 2.76/2.88 tff(26610,plain,
% 2.76/2.88 (op(e3, e3) = e0),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[15018, 2825, 468])).
% 2.76/2.88 tff(26611,plain,
% 2.76/2.88 (e0 = op(e3, e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26610])).
% 2.76/2.88 tff(26612,plain,
% 2.76/2.88 ((op(e3, e0) = e0) <=> (op(e3, e0) = op(e3, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26611])).
% 2.76/2.88 tff(26613,plain,
% 2.76/2.88 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e0)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26612])).
% 2.76/2.88 tff(26614,plain,
% 2.76/2.88 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26613])).
% 2.76/2.88 tff(26615,plain,
% 2.76/2.88 (~(op(e3, e0) = e0)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[157, 26614])).
% 2.76/2.88 tff(26616,plain,
% 2.76/2.88 (op(e2, e0) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[24100, 2689, 24208])).
% 2.76/2.88 tff(26617,plain,
% 2.76/2.88 (e2 = op(e2, e0)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26616])).
% 2.76/2.88 tff(26618,plain,
% 2.76/2.88 ((op(e3, e0) = e2) <=> (op(e3, e0) = op(e2, e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26617])).
% 2.76/2.88 tff(26619,plain,
% 2.76/2.88 ((op(e3, e0) = e2) <=> (op(e2, e0) = op(e3, e0))),
% 2.76/2.88 inference(transitivity,[status(thm)],[26618, 6131])).
% 2.76/2.88 tff(26620,plain,
% 2.76/2.88 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26619])).
% 2.76/2.88 tff(26621,plain,
% 2.76/2.88 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26620])).
% 2.76/2.88 tff(26622,plain,
% 2.76/2.88 (~(op(e3, e0) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[747, 26621])).
% 2.76/2.88 tff(26623,plain,
% 2.76/2.88 (op(e3, e0) = e1),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[5422, 26622, 2410, 26615])).
% 2.76/2.88 tff(26624,plain,
% 2.76/2.88 (op(e3, e1) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[15971, 26622, 2386])).
% 2.76/2.88 tff(26625,plain,
% 2.76/2.88 ($false),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[8647, 26624, 26623, 26610])).
% 2.76/2.88 tff(26626,plain,((~(op(e2, e3) = e1)) | (op(e3, e2) = e2) | (op(e3, e0) = e3) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.88 tff(26627,plain,
% 2.76/2.88 (~(op(e2, e3) = e1)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26626, 26609, 26604, 26597])).
% 2.76/2.88 tff(26628,plain,
% 2.76/2.88 (op(e2, e3) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[24237, 26627, 26183])).
% 2.76/2.88 tff(26629,plain,
% 2.76/2.88 (e2 = op(e2, e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26628])).
% 2.76/2.88 tff(26630,plain,
% 2.76/2.88 (op(e0, e3) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26176, 26627, 25192, 26183])).
% 2.76/2.88 tff(26631,plain,
% 2.76/2.88 (op(e0, e3) = op(e2, e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26630, 26629])).
% 2.76/2.88 tff(26632,plain,
% 2.76/2.88 ($false),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[964, 26631])).
% 2.76/2.88 tff(26633,plain,(~(op(e1, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.88 tff(26634,plain,
% 2.76/2.88 (op(e1, e3) = e1),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[24697, 26633, 26593])).
% 2.76/2.88 tff(26635,plain,
% 2.76/2.88 ((op(e1, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26634])).
% 2.76/2.88 tff(26636,plain,
% 2.76/2.88 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26635, 5574])).
% 2.76/2.88 tff(26637,plain,
% 2.76/2.88 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26636])).
% 2.76/2.88 tff(26638,plain,
% 2.76/2.88 (~(op(e2, e3) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[118, 26637])).
% 2.76/2.88 tff(26639,plain,
% 2.76/2.88 ((op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[24237, 26638])).
% 2.76/2.88 tff(26640,plain,
% 2.76/2.88 (op(e2, e3) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26639, 26286])).
% 2.76/2.88 tff(26641,plain,
% 2.76/2.88 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26640])).
% 2.76/2.88 tff(26642,plain,
% 2.76/2.88 ((op(e2, e0) = op(e2, e3)) <=> (op(op(e0, e3), e0) = e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26641, 17696])).
% 2.76/2.88 tff(26643,plain,
% 2.76/2.88 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(op(e0, e3), e0) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26642])).
% 2.76/2.88 tff(26644,plain,
% 2.76/2.88 (~(op(op(e0, e3), e0) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[989, 26643])).
% 2.76/2.88 tff(26645,plain,
% 2.76/2.88 ((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3))),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[2635, 26644])).
% 2.76/2.88 tff(26646,plain,
% 2.76/2.88 ((op(e0, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[8026])).
% 2.76/2.88 tff(26647,plain,
% 2.76/2.88 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26646, 7171])).
% 2.76/2.88 tff(26648,plain,
% 2.76/2.88 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26647])).
% 2.76/2.88 tff(26649,plain,
% 2.76/2.88 (~(op(e3, e2) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1467, 26648])).
% 2.76/2.88 tff(26650,plain,
% 2.76/2.88 ((~(op(e1, e1) = e0)) | (~(op(e1, e2) = e3))),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[14511, 26593])).
% 2.76/2.88 tff(26651,plain,
% 2.76/2.88 (~(op(e1, e2) = e3)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26650, 249])).
% 2.76/2.88 tff(26652,plain,
% 2.76/2.88 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26634])).
% 2.76/2.88 tff(26653,plain,
% 2.76/2.88 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26652])).
% 2.76/2.88 tff(26654,plain,
% 2.76/2.88 (~(op(e1, e2) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1850, 26653])).
% 2.76/2.88 tff(26655,plain,
% 2.76/2.88 ((op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[23821, 26654])).
% 2.76/2.88 tff(26656,plain,
% 2.76/2.88 (op(e1, e2) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26655, 26651])).
% 2.76/2.88 tff(26657,plain,
% 2.76/2.88 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e2)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26656])).
% 2.76/2.88 tff(26658,plain,
% 2.76/2.88 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26657])).
% 2.76/2.88 tff(26659,plain,
% 2.76/2.88 (~(op(e1, e0) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[1312, 26658])).
% 2.76/2.88 tff(26660,plain,
% 2.76/2.88 (op(e2, e3) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26639, 4382])).
% 2.76/2.88 tff(26661,plain,
% 2.76/2.88 (e3 = op(e2, e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26660])).
% 2.76/2.88 tff(26662,plain,
% 2.76/2.88 ((op(e2, e2) = e3) <=> (e0 = e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[23615])).
% 2.76/2.88 tff(26663,plain,
% 2.76/2.88 ((e0 = e3) <=> (op(e2, e2) = e3)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26662])).
% 2.76/2.88 tff(26664,plain,
% 2.76/2.88 ((~(e0 = e3)) <=> (~(op(e2, e2) = e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26663])).
% 2.76/2.88 tff(26665,plain,
% 2.76/2.88 (~(op(e2, e2) = e3)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[181, 26664])).
% 2.76/2.88 tff(26666,plain,
% 2.76/2.88 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e3, e2) = e3)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[2111, 26665])).
% 2.76/2.88 tff(26667,plain,
% 2.76/2.88 ((op(e1, e2) = e3) | (op(e3, e2) = e3)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26666, 26485])).
% 2.76/2.88 tff(26668,plain,
% 2.76/2.88 (op(e3, e2) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26667, 26651])).
% 2.76/2.88 tff(26669,plain,
% 2.76/2.88 (op(e3, e2) = op(e2, e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26668, 26661])).
% 2.76/2.88 tff(26670,plain,
% 2.76/2.88 ((op(e3, e2) = e2) <=> (op(e2, e3) = e2)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26669])).
% 2.76/2.88 tff(26671,plain,
% 2.76/2.88 ((op(e2, e3) = e2) <=> (op(e3, e2) = e2)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26670])).
% 2.76/2.88 tff(26672,plain,
% 2.76/2.88 ((~(op(e2, e3) = e2)) <=> (~(op(e3, e2) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26671])).
% 2.76/2.88 tff(26673,plain,
% 2.76/2.88 (~(op(e3, e2) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[4382, 26672])).
% 2.76/2.88 tff(26674,plain,
% 2.76/2.88 ((op(e2, e0) = e1) <=> (e2 = e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[1940])).
% 2.76/2.88 tff(26675,plain,
% 2.76/2.88 ((op(e2, e0) = e1) <=> (e1 = e2)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26674, 69])).
% 2.76/2.88 tff(26676,plain,
% 2.76/2.88 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26675])).
% 2.76/2.88 tff(26677,plain,
% 2.76/2.88 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26676])).
% 2.76/2.88 tff(26678,plain,
% 2.76/2.88 (~(op(e2, e0) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[708, 26677])).
% 2.76/2.88 tff(26679,plain,
% 2.76/2.88 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26634])).
% 2.76/2.88 tff(26680,plain,
% 2.76/2.88 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26679])).
% 2.76/2.88 tff(26681,plain,
% 2.76/2.88 (~(op(e1, e0) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[110, 26680])).
% 2.76/2.88 tff(26682,plain,
% 2.76/2.88 ((op(e0, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[1480, 26681])).
% 2.76/2.88 tff(26683,plain,
% 2.76/2.88 (op(e3, e0) = e1),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26682, 26678, 2379])).
% 2.76/2.88 tff(26684,plain,
% 2.76/2.88 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[1940])).
% 2.76/2.88 tff(26685,plain,
% 2.76/2.88 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26684, 5377])).
% 2.76/2.88 tff(26686,plain,
% 2.76/2.88 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26685])).
% 2.76/2.88 tff(26687,plain,
% 2.76/2.88 (~(op(e3, e0) = e2)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[747, 26686])).
% 2.76/2.88 tff(26688,plain,
% 2.76/2.88 (op(e3, e1) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[15971, 26687, 2386])).
% 2.76/2.88 tff(26689,plain,
% 2.76/2.88 ($false),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[8647, 26688, 26683, 3066])).
% 2.76/2.88 tff(26690,plain,((~(op(e2, e0) = e2)) | (~(op(e3, e3) = e0)) | (op(e3, e2) = e2) | (op(e0, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 2.76/2.88 tff(26691,plain,
% 2.76/2.88 (~(op(e2, e0) = e2)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26690, 26673, 3066, 13900])).
% 2.76/2.88 tff(26692,plain,
% 2.76/2.88 (op(e3, e0) = e2),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[589, 26691, 12721, 26659])).
% 2.76/2.88 tff(26693,plain,
% 2.76/2.88 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26692])).
% 2.76/2.88 tff(26694,plain,
% 2.76/2.88 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26693, 69])).
% 2.76/2.88 tff(26695,plain,
% 2.76/2.88 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26694])).
% 2.76/2.88 tff(26696,plain,
% 2.76/2.88 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26695])).
% 2.76/2.88 tff(26697,plain,
% 2.76/2.88 (~(op(e3, e0) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[708, 26696])).
% 2.76/2.88 tff(26698,plain,
% 2.76/2.88 ((op(e1, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26634])).
% 2.76/2.88 tff(26699,plain,
% 2.76/2.88 ((op(e1, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26698, 657])).
% 2.76/2.88 tff(26700,plain,
% 2.76/2.88 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26699])).
% 2.76/2.88 tff(26701,plain,
% 2.76/2.88 (~(op(e3, e3) = e1)),
% 2.76/2.88 inference(modus_ponens,[status(thm)],[571, 26700])).
% 2.76/2.88 tff(26702,plain,
% 2.76/2.88 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1)),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[939, 26701])).
% 2.76/2.88 tff(26703,plain,
% 2.76/2.88 (op(e3, e1) = e1),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[26702, 26697, 26649])).
% 2.76/2.88 tff(26704,plain,
% 2.76/2.88 (op(e3, op(e3, e1)) = op(e3, e1)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26703])).
% 2.76/2.88 tff(26705,plain,
% 2.76/2.88 (op(e3, op(e3, e1)) = e1),
% 2.76/2.88 inference(transitivity,[status(thm)],[26704, 26703])).
% 2.76/2.88 tff(26706,plain,
% 2.76/2.88 (op(op(e3, e2), e2) = e3),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[7919, 26668])).
% 2.76/2.88 tff(26707,plain,
% 2.76/2.88 ((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[1339, 26706])).
% 2.76/2.88 tff(26708,plain,
% 2.76/2.88 (op(e1, op(e1, e2)) = op(e1, e2)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26656])).
% 2.76/2.88 tff(26709,plain,
% 2.76/2.88 (op(e1, op(e1, e2)) = e2),
% 2.76/2.88 inference(transitivity,[status(thm)],[26708, 26656])).
% 2.76/2.88 tff(26710,plain,
% 2.76/2.88 ((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2))),
% 2.76/2.88 inference(unit_resolution,[status(thm)],[2377, 26709])).
% 2.76/2.88 tff(26711,plain,
% 2.76/2.88 (op(e2, op(e2, e3)) = op(e2, e3)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26660])).
% 2.76/2.88 tff(26712,plain,
% 2.76/2.88 (op(op(e3, e0), e3) = op(e2, op(e2, e3))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26692, 26661])).
% 2.76/2.88 tff(26713,plain,
% 2.76/2.88 (op(op(e3, e0), e3) = op(e2, e3)),
% 2.76/2.88 inference(transitivity,[status(thm)],[26712, 26711])).
% 2.76/2.88 tff(26714,plain,
% 2.76/2.88 ((op(op(e3, e0), e3) = e0) <=> (op(e2, e3) = e0)),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26713])).
% 2.76/2.88 tff(26715,plain,
% 2.76/2.88 ((op(e2, e3) = e0) <=> (op(op(e3, e0), e3) = e0)),
% 2.76/2.88 inference(symmetry,[status(thm)],[26714])).
% 2.76/2.88 tff(26716,plain,
% 2.76/2.88 ((~(op(e2, e3) = e0)) <=> (~(op(op(e3, e0), e3) = e0))),
% 2.76/2.88 inference(monotonicity,[status(thm)],[26715])).
% 2.76/2.89 tff(26717,plain,
% 2.76/2.89 (~(op(op(e3, e0), e3) = e0)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[23804, 26716])).
% 2.76/2.89 tff(26718,plain,
% 2.76/2.89 ((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[1764, 26717])).
% 2.76/2.89 tff(26719,plain,
% 2.76/2.89 ((op(e2, e0) = e3) <=> (op(e2, e0) = op(e2, e3))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26661])).
% 2.76/2.89 tff(26720,plain,
% 2.76/2.89 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e3)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26719])).
% 2.76/2.89 tff(26721,plain,
% 2.76/2.89 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e3))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26720])).
% 2.76/2.89 tff(26722,plain,
% 2.76/2.89 (~(op(e2, e0) = e3)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[989, 26721])).
% 2.76/2.89 tff(26723,plain,
% 2.76/2.89 (op(e2, e0) = e1),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[24100, 26691, 26722])).
% 2.76/2.89 tff(26724,plain,
% 2.76/2.89 (op(op(e2, e0), e2) = op(e1, e2)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26723])).
% 2.76/2.89 tff(26725,plain,
% 2.76/2.89 (op(op(e2, e0), e2) = e2),
% 2.76/2.89 inference(transitivity,[status(thm)],[26724, 26656])).
% 2.76/2.89 tff(26726,plain,
% 2.76/2.89 ((op(op(e2, e0), e2) = e0) <=> (e2 = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26725])).
% 2.76/2.89 tff(26727,plain,
% 2.76/2.89 ((op(op(e2, e0), e2) = e0) <=> (e0 = e2)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26726, 1])).
% 2.76/2.89 tff(26728,plain,
% 2.76/2.89 ((e0 = e2) <=> (op(op(e2, e0), e2) = e0)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26727])).
% 2.76/2.89 tff(26729,plain,
% 2.76/2.89 ((~(e0 = e2)) <=> (~(op(op(e2, e0), e2) = e0))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26728])).
% 2.76/2.89 tff(26730,plain,
% 2.76/2.89 (~(op(op(e2, e0), e2) = e0)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[14, 26729])).
% 2.76/2.89 tff(26731,plain,
% 2.76/2.89 ((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[1379, 26730])).
% 2.76/2.89 tff(26732,plain,
% 2.76/2.89 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[8026])).
% 2.76/2.89 tff(26733,plain,
% 2.76/2.89 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e1))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26732])).
% 2.76/2.89 tff(26734,plain,
% 2.76/2.89 (~(op(e0, e1) = e1)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[2102, 26733])).
% 2.76/2.89 tff(26735,plain,
% 2.76/2.89 (op(e0, e1) = e3),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[829, 13158, 26734, 5828])).
% 2.76/2.89 tff(26736,plain,
% 2.76/2.89 (op(op(e0, e1), e0) = op(e3, e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26735])).
% 2.76/2.89 tff(26737,plain,
% 2.76/2.89 ((op(op(e0, e1), e0) = e1) <=> (op(e3, e0) = e1)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26736])).
% 2.76/2.89 tff(26738,plain,
% 2.76/2.89 ((op(e3, e0) = e1) <=> (op(op(e0, e1), e0) = e1)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26737])).
% 2.76/2.89 tff(26739,plain,
% 2.76/2.89 ((e1 = e2) <=> (op(op(e0, e1), e0) = e1)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26695, 26738])).
% 2.76/2.89 tff(26740,plain,
% 2.76/2.89 ((~(e1 = e2)) <=> (~(op(op(e0, e1), e0) = e1))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26739])).
% 2.76/2.89 tff(26741,plain,
% 2.76/2.89 (~(op(op(e0, e1), e0) = e1)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[708, 26740])).
% 2.76/2.89 tff(26742,plain,
% 2.76/2.89 ((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[1461, 26741])).
% 2.76/2.89 tff(26743,plain,
% 2.76/2.89 (op(e2, op(e2, e3)) = e3),
% 2.76/2.89 inference(transitivity,[status(thm)],[26711, 26660])).
% 2.76/2.89 tff(26744,plain,
% 2.76/2.89 ((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[2344, 26743])).
% 2.76/2.89 tff(26745,plain,
% 2.76/2.89 ((op(op(e0, e2), e0) = e2) <=> (op(e1, e0) = e2)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[10297])).
% 2.76/2.89 tff(26746,plain,
% 2.76/2.89 ((op(e1, e0) = e2) <=> (op(op(e0, e2), e0) = e2)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26745])).
% 2.76/2.89 tff(26747,plain,
% 2.76/2.89 ((op(e1, e0) = op(e1, e2)) <=> (op(op(e0, e2), e0) = e2)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26657, 26746])).
% 2.76/2.89 tff(26748,plain,
% 2.76/2.89 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(op(e0, e2), e0) = e2))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26747])).
% 2.76/2.89 tff(26749,plain,
% 2.76/2.89 (~(op(op(e0, e2), e0) = e2)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[1312, 26748])).
% 2.76/2.89 tff(26750,plain,
% 2.76/2.89 ((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[2446, 26749])).
% 2.76/2.89 tff(26751,plain,
% 2.76/2.89 ((op(e1, e1) = e3) <=> (e0 = op(e2, e3))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[249, 26661])).
% 2.76/2.89 tff(26752,plain,
% 2.76/2.89 ((op(e1, e1) = e3) <=> (op(e2, e3) = e0)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26751, 86])).
% 2.76/2.89 tff(26753,plain,
% 2.76/2.89 ((op(e2, e3) = e0) <=> (op(e1, e1) = e3)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26752])).
% 2.76/2.89 tff(26754,plain,
% 2.76/2.89 ((~(op(e2, e3) = e0)) <=> (~(op(e1, e1) = e3))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26753])).
% 2.76/2.89 tff(26755,plain,
% 2.76/2.89 (~(op(e1, e1) = e3)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[23804, 26754])).
% 2.76/2.89 tff(26756,plain,
% 2.76/2.89 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3)),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[247, 26633])).
% 2.76/2.89 tff(26757,plain,
% 2.76/2.89 (op(e1, e0) = e3),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[26756, 26755, 26651])).
% 2.76/2.89 tff(26758,plain,
% 2.76/2.89 (op(op(e1, e0), e1) = op(e3, e1)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26757])).
% 2.76/2.89 tff(26759,plain,
% 2.76/2.89 ((op(op(e1, e0), e1) = e0) <=> (op(e3, e1) = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26758])).
% 2.76/2.89 tff(26760,plain,
% 2.76/2.89 ((op(e3, e1) = e0) <=> (op(op(e1, e0), e1) = e0)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26759])).
% 2.76/2.89 tff(26761,plain,
% 2.76/2.89 ((~(op(e3, e1) = e0)) <=> (~(op(op(e1, e0), e1) = e0))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26760])).
% 2.76/2.89 tff(26762,plain,
% 2.76/2.89 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[3066])).
% 2.76/2.89 tff(26763,plain,
% 2.76/2.89 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26762])).
% 2.76/2.89 tff(26764,plain,
% 2.76/2.89 (~(op(e3, e1) = e0)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[437, 26763])).
% 2.76/2.89 tff(26765,plain,
% 2.76/2.89 (~(op(op(e1, e0), e1) = e0)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[26764, 26761])).
% 2.76/2.89 tff(26766,plain,
% 2.76/2.89 ((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[1302, 26765])).
% 2.76/2.89 tff(26767,plain,
% 2.76/2.89 (op(e2, e1) = e2),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[23839, 26691, 4382])).
% 2.76/2.89 tff(26768,plain,
% 2.76/2.89 (op(op(e2, e1), e1) = op(e2, e1)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26767])).
% 2.76/2.89 tff(26769,plain,
% 2.76/2.89 (op(op(e2, e1), e1) = e2),
% 2.76/2.89 inference(transitivity,[status(thm)],[26768, 26767])).
% 2.76/2.89 tff(26770,plain,
% 2.76/2.89 ((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[2371, 26769])).
% 2.76/2.89 tff(26771,plain,
% 2.76/2.89 ((op(e1, op(e1, e3)) = e3) | (op(op(e1, e3), e3) = e1) | (~(op(op(e1, e3), e1) = e3))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[25120, 26593])).
% 2.76/2.89 tff(26772,plain,
% 2.76/2.89 ((~((op(e0, op(e0, e1)) = e1) | (op(op(e0, e1), e1) = e0) | (~(op(op(e0, e1), e0) = e1)))) | (~((op(e1, op(e1, e0)) = e0) | (op(op(e1, e0), e0) = e1) | (~(op(op(e1, e0), e1) = e0)))) | (~((op(e0, op(e0, e2)) = e2) | (op(op(e0, e2), e2) = e0) | (~(op(op(e0, e2), e0) = e2)))) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (~((op(e1, op(e1, e2)) = e2) | (op(op(e1, e2), e2) = e1) | (~(op(op(e1, e2), e1) = e2)))) | (~((op(e2, op(e2, e0)) = e0) | (op(op(e2, e0), e0) = e2) | (~(op(op(e2, e0), e2) = e0)))) | (~((op(e2, op(e2, e1)) = e1) | (op(op(e2, e1), e1) = e2) | (~(op(op(e2, e1), e2) = e1)))) | (~((op(e2, op(e2, e3)) = e3) | (op(op(e2, e3), e3) = e2) | (~(op(op(e2, e3), e2) = e3)))) | (~((op(e3, op(e3, e0)) = e0) | (op(op(e3, e0), e0) = e3) | (~(op(op(e3, e0), e3) = e0)))) | (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))) | (~((op(e3, op(e3, e2)) = e2) | (op(op(e3, e2), e2) = e3) | (~(op(op(e3, e2), e3) = e2))))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[1459, 26771])).
% 2.76/2.89 tff(26773,plain,
% 2.76/2.89 (~((op(e3, op(e3, e1)) = e1) | (op(op(e3, e1), e1) = e3) | (~(op(op(e3, e1), e3) = e1)))),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[26772, 26770, 26766, 3342, 26750, 26744, 26742, 26731, 26718, 26710, 26707])).
% 2.76/2.89 tff(26774,plain,
% 2.76/2.89 (~(op(e3, op(e3, e1)) = e1)),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[2594, 26773])).
% 2.76/2.89 tff(26775,plain,
% 2.76/2.89 ($false),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[26774, 26705])).
% 2.76/2.89 tff(26776,plain,((~(op(e1, e1) = e0)) | (~((op(e0, op(e0, e3)) = e3) | (op(op(e0, e3), e3) = e0) | (~(op(op(e0, e3), e0) = e3)))) | (op(e2, e3) = e2) | (op(e0, e0) = e2) | (~(op(e3, e3) = e0)) | (op(e0, e1) = e2) | (~(op(e0, e2) = e1))), inference(lemma,lemma(discharge,[]))).
% 2.76/2.89 tff(26777,plain,
% 2.76/2.89 (~(op(e1, e1) = e0)),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[26776, 26645, 26286, 16923, 24664, 18332, 26487])).
% 2.76/2.89 tff(26778,plain,
% 2.76/2.89 (op(e0, e1) = e0),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[23988, 26777, 24667])).
% 2.76/2.89 tff(26779,plain,
% 2.76/2.89 (op(e1, e2) = op(e1, op(e1, e1))),
% 2.76/2.89 inference(symmetry,[status(thm)],[21621])).
% 2.76/2.89 tff(26780,plain,
% 2.76/2.89 ((op(e1, e2) = e2) <=> (op(e1, e2) = op(e1, e1))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[4872])).
% 2.76/2.89 tff(26781,plain,
% 2.76/2.89 ((op(e1, e2) = e2) <=> (op(e1, e1) = op(e1, e2))),
% 2.76/2.89 inference(transitivity,[status(thm)],[26780, 8420])).
% 2.76/2.89 tff(26782,plain,
% 2.76/2.89 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26781])).
% 2.76/2.89 tff(26783,plain,
% 2.76/2.89 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26782])).
% 2.76/2.89 tff(26784,plain,
% 2.76/2.89 (~(op(e1, e2) = e2)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[1604, 26783])).
% 2.76/2.89 tff(26785,plain,
% 2.76/2.89 (op(e1, e2) = e3),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[23821, 26784, 26654])).
% 2.76/2.89 tff(26786,plain,
% 2.76/2.89 (e3 = op(e1, e2)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26785])).
% 2.76/2.89 tff(26787,plain,
% 2.76/2.89 (op(e1, e2) = op(e1, op(e1, e1))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[4872])).
% 2.76/2.89 tff(26788,plain,
% 2.76/2.89 (e3 = op(e1, op(e1, e1))),
% 2.76/2.89 inference(transitivity,[status(thm)],[26786, 26787])).
% 2.76/2.89 tff(26789,plain,
% 2.76/2.89 ((op(e0, e3) = e3) <=> (e2 = op(e1, op(e1, e1)))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[2, 26788])).
% 2.76/2.89 tff(26790,plain,
% 2.76/2.89 ((e2 = op(e1, op(e1, e1))) <=> (op(e0, e3) = e3)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26789])).
% 2.76/2.89 tff(26791,plain,
% 2.76/2.89 ((~(e2 = op(e1, op(e1, e1)))) <=> (~(op(e0, e3) = e3))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26790])).
% 2.76/2.89 tff(26792,plain,
% 2.76/2.89 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, op(e1, e1)))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[2891, 26787])).
% 2.76/2.89 tff(26793,plain,
% 2.76/2.89 ((~(op(e1, e1) = op(e1, e2))) <=> (~(e2 = op(e1, op(e1, e1))))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26792])).
% 2.76/2.89 tff(26794,plain,
% 2.76/2.89 (~(e2 = op(e1, op(e1, e1)))),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[1604, 26793])).
% 2.76/2.89 tff(26795,plain,
% 2.76/2.89 (~(op(e0, e3) = e3)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[26794, 26791])).
% 2.76/2.89 tff(26796,plain,
% 2.76/2.89 (op(e1, e0) = e0),
% 2.76/2.89 inference(unit_resolution,[status(thm)],[24724, 21894])).
% 2.76/2.89 tff(26797,plain,
% 2.76/2.89 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26796])).
% 2.76/2.89 tff(26798,plain,
% 2.76/2.89 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e0))),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26797])).
% 2.76/2.89 tff(26799,plain,
% 2.76/2.89 (~(op(e0, e0) = e0)),
% 2.76/2.89 inference(modus_ponens,[status(thm)],[2471, 26798])).
% 2.76/2.89 tff(26800,plain,
% 2.76/2.89 (op(e0, op(e1, e2)) = op(e0, e3)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26785])).
% 2.76/2.89 tff(26801,plain,
% 2.76/2.89 (op(e0, e3) = op(e0, op(e1, e2))),
% 2.76/2.89 inference(symmetry,[status(thm)],[26800])).
% 2.76/2.89 tff(26802,plain,
% 2.76/2.89 ((op(e0, e3) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26801])).
% 2.76/2.89 tff(26803,plain,
% 2.76/2.89 ((op(e0, op(e1, e2)) = e0) <=> (op(e0, e3) = e0)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26802])).
% 2.76/2.89 tff(26804,plain,
% 2.76/2.89 (op(e0, op(e1, e2)) = op(e1, e1)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26800, 2, 4872])).
% 2.76/2.89 tff(26805,plain,
% 2.76/2.89 ((op(e0, op(e1, e2)) = e0) <=> (op(e1, e1) = e0)),
% 2.76/2.89 inference(monotonicity,[status(thm)],[26804])).
% 2.76/2.89 tff(26806,plain,
% 2.76/2.89 ((op(e1, e1) = e0) <=> (op(e0, op(e1, e2)) = e0)),
% 2.76/2.89 inference(symmetry,[status(thm)],[26805])).
% 2.76/2.89 tff(26807,plain,
% 2.76/2.89 ((op(e1, e1) = e0) <=> (op(e0, e3) = e0)),
% 2.76/2.89 inference(transitivity,[status(thm)],[26806, 26803])).
% 2.79/2.89 tff(26808,plain,
% 2.79/2.89 ((~(op(e1, e1) = e0)) <=> (~(op(e0, e3) = e0))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26807])).
% 2.79/2.89 tff(26809,plain,
% 2.79/2.89 (~(op(e0, e3) = e0)),
% 2.79/2.89 inference(modus_ponens,[status(thm)],[21894, 26808])).
% 2.79/2.89 tff(26810,plain,
% 2.79/2.89 (op(e0, e1) = e0),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[23963, 26809, 26799])).
% 2.79/2.89 tff(26811,plain,
% 2.79/2.89 ((op(e0, e1) = e3) <=> (e0 = op(e1, op(e1, e1)))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26810, 26788])).
% 2.79/2.89 tff(26812,plain,
% 2.79/2.89 ((e0 = op(e1, op(e1, e1))) <=> (op(e0, e1) = e3)),
% 2.79/2.89 inference(symmetry,[status(thm)],[26811])).
% 2.79/2.89 tff(26813,plain,
% 2.79/2.89 ((~(e0 = op(e1, op(e1, e1)))) <=> (~(op(e0, e1) = e3))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26812])).
% 2.79/2.89 tff(26814,plain,
% 2.79/2.89 (op(e1, op(e1, e1)) = op(e1, e2)),
% 2.79/2.89 inference(symmetry,[status(thm)],[26787])).
% 2.79/2.89 tff(26815,plain,
% 2.79/2.89 ((e0 = op(e1, op(e1, e1))) <=> (e0 = op(e1, e2))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26814])).
% 2.79/2.89 tff(26816,plain,
% 2.79/2.89 ((e0 = op(e1, op(e1, e1))) <=> (op(e1, e2) = e0)),
% 2.79/2.89 inference(transitivity,[status(thm)],[26815, 67])).
% 2.79/2.89 tff(26817,plain,
% 2.79/2.89 ((op(e1, e2) = e0) <=> (e0 = op(e1, op(e1, e1)))),
% 2.79/2.89 inference(symmetry,[status(thm)],[26816])).
% 2.79/2.89 tff(26818,plain,
% 2.79/2.89 ((~(op(e1, e2) = e0)) <=> (~(e0 = op(e1, op(e1, e1))))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26817])).
% 2.79/2.89 tff(26819,plain,
% 2.79/2.89 (~(e0 = op(e1, op(e1, e1)))),
% 2.79/2.89 inference(modus_ponens,[status(thm)],[23820, 26818])).
% 2.79/2.89 tff(26820,plain,
% 2.79/2.89 (~(op(e0, e1) = e3)),
% 2.79/2.89 inference(modus_ponens,[status(thm)],[26819, 26813])).
% 2.79/2.89 tff(26821,plain,
% 2.79/2.89 (op(e0, e0) = e3),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[1495, 26820, 26485, 26795])).
% 2.79/2.89 tff(26822,plain,
% 2.79/2.89 (e3 = op(e0, e0)),
% 2.79/2.89 inference(modus_ponens,[status(thm)],[26821, 71])).
% 2.79/2.89 tff(26823,plain,
% 2.79/2.89 (op(e0, e0) = op(e1, e2)),
% 2.79/2.89 inference(transitivity,[status(thm)],[26821, 26786])).
% 2.79/2.89 tff(26824,plain,
% 2.79/2.89 (op(e0, op(e0, e0)) = op(e0, op(e1, e2))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26823])).
% 2.79/2.89 tff(26825,plain,
% 2.79/2.89 (op(e0, op(e1, e2)) = op(e0, op(e0, e0))),
% 2.79/2.89 inference(symmetry,[status(thm)],[26824])).
% 2.79/2.89 tff(26826,plain,
% 2.79/2.89 (e2 = op(e0, op(e0, e0))),
% 2.79/2.89 inference(transitivity,[status(thm)],[2560, 26801, 26825])).
% 2.79/2.89 tff(26827,plain,
% 2.79/2.89 (op(e0, op(e0, e0)) = op(e1, e1)),
% 2.79/2.89 inference(transitivity,[status(thm)],[26824, 26800, 2, 4872])).
% 2.79/2.89 tff(26828,plain,
% 2.79/2.89 (op(e0, op(e0, op(e0, e0))) = op(e0, op(e1, e1))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26827])).
% 2.79/2.89 tff(26829,plain,
% 2.79/2.89 (op(e0, op(e1, e1)) = op(e0, op(e0, op(e0, e0)))),
% 2.79/2.89 inference(symmetry,[status(thm)],[26828])).
% 2.79/2.89 tff(26830,plain,
% 2.79/2.89 (op(e0, e2) = op(e0, op(e1, e1))),
% 2.79/2.89 inference(symmetry,[status(thm)],[4939])).
% 2.79/2.89 tff(26831,plain,
% 2.79/2.89 (op(e0, e2) = e1),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[23880, 23847, 26485])).
% 2.79/2.89 tff(26832,plain,
% 2.79/2.89 (e1 = op(e0, e2)),
% 2.79/2.89 inference(symmetry,[status(thm)],[26831])).
% 2.79/2.89 tff(26833,plain,
% 2.79/2.89 (e1 = op(e0, op(e0, op(e0, e0)))),
% 2.79/2.89 inference(transitivity,[status(thm)],[26832, 26830, 26829])).
% 2.79/2.89 tff(26834,plain,
% 2.79/2.89 ($false),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[2760, 26833, 26826, 26822])).
% 2.79/2.89 tff(26835,plain,((~(op(e0, e3) = e2)) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 2.79/2.89 tff(26836,plain,
% 2.79/2.89 (~(op(e0, e3) = e2)),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[26835, 2891])).
% 2.79/2.89 tff(26837,plain,
% 2.79/2.89 (op(e2, e3) = e3),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[26276, 26836, 25192, 26593, 26638])).
% 2.79/2.89 tff(26838,plain,
% 2.79/2.89 (op(e2, e3) = e2),
% 2.79/2.89 inference(unit_resolution,[status(thm)],[15003, 26836, 26593])).
% 2.79/2.89 tff(26839,plain,
% 2.79/2.89 (e2 = op(e2, e3)),
% 2.79/2.89 inference(symmetry,[status(thm)],[26838])).
% 2.79/2.89 tff(26840,plain,
% 2.79/2.89 (e2 = op(e1, op(e1, e1))),
% 2.79/2.89 inference(transitivity,[status(thm)],[26839, 26837, 26786, 26779])).
% 2.79/2.89 tff(26841,plain,
% 2.79/2.89 ((op(e1, e1) = op(e1, e2)) <=> (e2 = op(e1, op(e1, e1)))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[2891, 26779])).
% 2.79/2.89 tff(26842,plain,
% 2.79/2.89 ((~(op(e1, e1) = op(e1, e2))) <=> (~(e2 = op(e1, op(e1, e1))))),
% 2.79/2.89 inference(monotonicity,[status(thm)],[26841])).
% 2.79/2.89 tff(26843,plain,
% 2.79/2.89 (~(e2 = op(e1, op(e1, e1)))),
% 2.79/2.91 inference(modus_ponens,[status(thm)],[1604, 26842])).
% 2.79/2.91 tff(26844,plain,
% 2.79/2.91 ($false),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26843, 26840])).
% 2.79/2.91 tff(26845,plain,(~(op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.79/2.91 tff(26846,plain,
% 2.79/2.91 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e1)),
% 2.79/2.91 inference(monotonicity,[status(thm)],[26634])).
% 2.79/2.91 tff(26847,plain,
% 2.79/2.91 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e1))),
% 2.79/2.91 inference(monotonicity,[status(thm)],[26846])).
% 2.79/2.91 tff(26848,plain,
% 2.79/2.91 (~(op(e1, e1) = e1)),
% 2.79/2.91 inference(modus_ponens,[status(thm)],[619, 26847])).
% 2.79/2.91 tff(26849,plain,
% 2.79/2.91 ((op(e1, e1) = e0) | (op(e1, e1) = e3)),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[630, 26848, 26845])).
% 2.79/2.91 tff(26850,plain,
% 2.79/2.91 (op(e1, e1) = e3),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26849, 26777])).
% 2.79/2.91 tff(26851,plain,
% 2.79/2.91 (op(e0, e1) = e3),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26387, 26850])).
% 2.79/2.91 tff(26852,plain,
% 2.79/2.91 (e3 = op(e0, e1)),
% 2.79/2.91 inference(symmetry,[status(thm)],[26851])).
% 2.79/2.91 tff(26853,plain,
% 2.79/2.91 (op(e2, e3) = e0),
% 2.79/2.91 inference(transitivity,[status(thm)],[26640, 26852, 26778])).
% 2.79/2.91 tff(26854,plain,
% 2.79/2.91 ($false),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[23804, 26853])).
% 2.79/2.91 tff(26855,plain,(~(op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 2.79/2.91 tff(26856,plain,
% 2.79/2.91 ((op(e0, e3) = e2) | (op(e2, e3) = e3)),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26276, 25192, 26593, 26638])).
% 2.79/2.91 tff(26857,plain,
% 2.79/2.91 (op(e2, e3) = e3),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26856, 26855])).
% 2.79/2.91 tff(26858,plain,
% 2.79/2.91 ((op(e0, e3) = e2) | (op(e2, e3) = e2)),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[15003, 26593])).
% 2.79/2.91 tff(26859,plain,
% 2.79/2.91 (op(e2, e3) = e2),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[26858, 26855])).
% 2.79/2.91 tff(26860,plain,
% 2.79/2.91 (e2 = op(e2, e3)),
% 2.79/2.91 inference(symmetry,[status(thm)],[26859])).
% 2.79/2.91 tff(26861,plain,
% 2.79/2.91 (e2 = e3),
% 2.79/2.91 inference(transitivity,[status(thm)],[26860, 26857])).
% 2.79/2.91 tff(26862,plain,
% 2.79/2.91 ($false),
% 2.79/2.91 inference(unit_resolution,[status(thm)],[1321, 26861])).
% 2.79/2.91 % SZS output end Proof
%------------------------------------------------------------------------------